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Beam under bending: with held ends: left end fixed: right end fixed: temperature gradient: across depth: linearly varying

Small deflections of rectangular plates: 2 facing sides clamped, 2 supported: uniform load

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: combined loads

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge free: applied angular displacement

Thin-walled cylindrical shell: Fixed-free: applied moment

Circular arch: uniform section: end A: pinned: end B: horiz.slide: uniform load: per unit length of arch: horizontal

Circular arch: uniform section: end A: pinned: end B: horiz.guide: uniform temperature change

Annular flat plate: with uniform thickness: simple bending: outer edge free: inner edge clamped: uniform load

Continuous beam: over 5 spans: in simple bending: concentrated moment

Tapered fixed beam under simple bending: main inertia symmetrically varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: concentrated moment

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: linearly decreasing load

Circular pipes: supported at bottom: loaded by self weight: directed downwards

Beam under simple bending: left end supported: right end guided: concentrated load

Beam under bending: with axial tension: left end fixed: right end free: distributed load

Beam under bending: with axial tension: left end fixed: right end supported: temperature gradient: across depth: linearly varying

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end fixed: distributed partial load: linearly varying: on girder

Circular arch: uniform section: end A: fixed: end B: fixed: uniform load: per unit vertical projection: horizontal

Tapered simply supported beam under simple bending: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: distributed load

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge clamped: uniform load

Thin-walled cylindrical shell: Supported-free: uniform radial pressure: from 'a' to 'b'

Beam under bending: with axial tension: left end supported: right end supported: uniform load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: uniform load: horizontal: on girder right half

Beam under bending: with axial compression: left end fixed: right end fixed: applied vertical displacement

Solid circular flat plate with uniform thickness: simple bending: on (mono)elastic foundation: free edge: center load + uniform load

Circular arch: uniform section: end A: pinned: end B: horiz.guide: combined loads

Circular arch: uniform section: end A: fixed: end B: vertical guide: combined loads

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: distributed partial load: linearly varying: horizontal: on right post

Disc springs: stack in series and in parallel: with or without bearing flats

Circular arch: uniform section: end A: fixed: end B: inclined guide: uniform load: radial

Beam under bending: with axial tension: left end fixed: right end free: combined loads

Elastic stability of a beam-column: with two stepped sections: under two axial compressive loads: base fixed: top guided

Junction between the large end of a cone and a cylinder: without a knuckle: cone and cylinder with constant thicknesses: under internal pressure

Beam under simple bending: large deflections: left end fixed: right end fixed: concentrated load

Beam under bending: with held ends: left end fixed: right end guided: distributed load

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: concentrated load

Large deflections of rectangular plates: 4 supported & held sides: uniform load

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: distributed partial load: linearly varying: vertical: on girder

Solid circular flat plate with uniform thickness: simple bending: on (mono)elastic foundation: fixed edge: distributed + uniform load

Beam under simple bending: large deflections: left end supported: right end guided: distributed load

Circular arch: uniform section: end A: pinned: end B: horiz.guide: distributed load: vertical: partial

Tapered cantilever under simple bending: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: concentrated load

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge supported: temperature differential across thickness

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: uniform load: horizontal: on girder

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 4th power of x (n=4): under a single axial compressive load: base supported: top supported

Circular arch: uniform section: end A: pinned: end B: inclined guide: concentrated load: horizontal

Tapered fixed beam under simple bending: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: linearly decreasing load

Circular arch: uniform section: end A: pinned: end B: pinned: concentrated load: tangential

Annular flat plate: with uniform thickness: simple bending: outer edge simply guided: inner edge fixed: temperature differential across thickness

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: point load: horizontal: on left post

Circular arch: uniform section: end A: pinned: end B: horiz.slide: concentrated load: horizontal

Circular arch: uniform section: end A: fixed: end B: inclined guide: uniform load: per unit length of arch: horizontal

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: supported: distributed + uniform load

Thin-walled cylindrical shell: Supported-guided: radial load

Circular arch: uniform section: end A: pinned: end B: horiz.slide: concentrated load: vertical

Thin-walled cylindrical shell: Fixed-supported: uniform radial pressure: from 'a' to B

Circular arch: uniform section: end A: pinned: end B: inclined guide: uniform load: per unit length of arch: vertical

Circular arch: uniform section: end A: pinned: end B: pinned: uniform load: tangential

Tapered simply supported beam under simple bending: main inertia symmetrically varying with the 1st power of x: resistance modulus varying with the 1st power of x: uniform load

Elastic stability of a beam-column: prismatic: under a single axial compressive load: base fixed: top supported

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: uniform load: vertical: on girder

Beam under bending: with held ends: left end supported: right end guided: concentrated load

Beam under bending: with axial compression: left end fixed: right end free: uniform load

Circular arch: uniform section: end A: fixed: end B: inclined slide: uniform temperature change

Beam under bending: with axial tension: left end fixed: right end guided: distributed load

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end pinned: uniform load: on post

Tapered cantilever under simple bending: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: combined loads

Circular arch: uniform section: end A: fixed: end B: pinned: distributed load: tangential

Tapered simply supported beam under simple bending: main inertia symmetrically varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: combined loads

Circular arch: uniform section: end A: fixed: end B: horiz.slide: combined loads

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end fixed: uniform temperature change

Beam under simple bending: left end fixed: right end free: concentrated load

Small deflections of rectangular plates: 2 adjacent supported sides, 2 free: uniform load

Circular arch: uniform section: end A: fixed: end B: vertical guide: concentrated load: vertical

Small deflections of rectangular plates: 4 clamped sides: distributed load: linearly varying: along side a

Small deflections of rectangular plates: 3 supported sides, 1 free: distributed load: linearly varying: along side a

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: uniform load: vertical: on girder

Beam under bending: with held ends: left end fixed: right end free: uniform load

Tapered simply supported beam under simple bending: main inertia symmetrically varying with the 2nd power of x: resistance modulus varying with the 1st power of x: concentrated moment

Tapered cantilever under simple bending: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: distributed load

Solid circular flat plate: simple bending: simply supported: with linearly decreasing thickness: center load

Beam under simple bending: left end fixed: right end supported: uniform load

Flat face flanges with metal-to-metal contact outside the bolt circle: analysis of an identical (Class 1) flange pair: same material: integral (Cat.1) flanges: hub of constant thickness: with spacer: self-sealing gasket with negligible loads

Circular arch: uniform section: end A: fixed: end B: free: uniform temperature change

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: distributed partial load: linearly varying: horizontal: on right post

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end pinned: uniform load: on girder

Beam under simple bending: left end fixed: right end free: distributed load

Beam under simple bending: left end fixed: right end guided: concentrated load

Annular flat plate: with uniform thickness: simple bending: outer edge guided: inner edge supported: parabolically increasing load

Circular arch: uniform section: end A: fixed: end B: pinned: uniform load: radial

Thin-walled cylindrical shell: Free-guided: uniform radial pressure: from 'a' to 'b'

Circular ring beam: supported at bottom: combined loads

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: uniform pressure: on girder right half

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: point load: on right post

Circular arch: uniform section: end A: fixed: end B: vertical slide: uniform temperature change

Tapered fixed beam under simple bending: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: concentrated load

Small deflections of rectangular plates: 2 opposite sides clamped, 2 free: distributed load: over a partial rectangular area

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: uniform temperature gradient: across depth

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: uniform load: horizontal: on left post

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end pinned: point load: on girder

Beam under bending+shear: left end fixed: right end free: uniform load

Solid circular flat plate with uniform thickness: large deflections behaviour: supported & held: uniform distributed load

Thin-walled cylindrical shell: Guided-free: uniform radial pressure: from 'a' to 'b'

Thin-walled cylindrical shell: Supported-fixed: linearly varying radial pressure

Circular arch: uniform section: end A: pinned: end B: inclined slide: uniform load: per unit vertical projection: horizontal

Supported-fixed beam: on elastic foundation: distributed load: linearly varying: from 'a' to 'b'

Thin-walled cylindrical shell: Fixed-fixed: uniform radial pressure: from 'a' to 'b'

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge free: uniform annular line load

Circular arch: uniform section: end A: fixed: end B: inclined slide: concentrated load: vertical

Tapered simply supported beam under simple bending: main inertia symmetrically varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: concentrated load

Circular arch: uniform section: end A: fixed: end B: vertical slide: concentrated load: vertical

Free-free beam: on elastic foundation: concentrated moment

Semiinfinite beam: on elastic foundation: distributed load: linearly varying: from 'a' to 'b'

W.R.C. Bulletin 297-Aug.84,Supplement to WRC Bulletin No. 107: Local Stresses in Cylindrical Shells Due to External Loadings on a Radial Flush Nozzle: Pressure stresses per BS5500 G.2.3.5.2(a): (radial load should not include pressure end load)

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end sliding: uniform load: on girder

Circular arch: uniform section: end A: pinned: end B: horiz.slide: uniform load: per unit horizontal projection: vertical

Tapered fixed beam under simple bending: main inertia varying symmetrically with the 1st power of x: resistance modulus varying with the 1st power of x: combined loads

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: fixed edge: uniform load

Small deflections of rectangular plates: 1 clamped side, 2 supported(adjacent) and 1 free: uniform load

Thin-walled cylindrical shell: Supported-fixed: applied moment

Beam under simple bending: left end supported: right end supported: applied vertical displacement

Circular arch: uniform section: end A: fixed: end B: inclined slide: combined loads

Circular arch: uniform section: end A: fixed: end B: fixed: distributed load: radial

Small deflections of rectangular plates: bending + shear: 4 simply supported sides: distributed load: over a partial rectangular area

Continuous beam: over 3 spans: in simple bending: distributed load

Annular flat plate: with uniform thickness: simple bending: outer edge free: inner edge supported: applied angular displacement

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: combined loads

Thin-walled cylindrical shell: Fixed-fixed: uniform radial pressure: from 'a' to B

Small deflections of rectangular plates: 2 simply supported opposite sides and 2 free: combined loads

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: point load: vertical: on girder left half

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: distributed partial load: linearly varying: horizontal: on right post

Circular arch: uniform section: end A: fixed: end B: fixed: uniform temperature gradient: across depth

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: fixed edge: center load + uniform load

Circular arch: uniform section: end A: fixed: end B: horiz.slide: uniform load: per unit length of arch: vertical

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: uniform load: on right post

Tapered fixed beam under simple bending: main inertia symmetrically varying with the 2nd power of x: resistance modulus varying with the 1st power of x: concentrated load

Sphere in contact with a flat plate under load: Hertz's theory

Circular arch: uniform section: end A: fixed: end B: horiz.guide: uniform load: per unit vertical projection: horizontal: on left half arch

Small deflections of rectangular plates: 3 supported sides, 1 clamped: uniform load

Beam under bending: with held ends: left end fixed: right end free: concentrated moment

Circular arch: uniform section: end A: fixed: end B: free: uniform load: per unit length of arch: horizontal

Beam under bending: with axial compression: left end fixed: right end fixed: concentrated moment

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: distributed load: vertical: partial

Small deflections of rectangular plates: 2 adjacent clamped sides, 2 supported: uniform load

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end fixed: distributed partial load: linearly varying: on girder

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge free: uniform annular line moment

Thin-walled cylindrical shell: Free-free: applied moment

Tapered fixed beam under simple bending: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: distributed load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: uniform temperature change

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge fixed: applied vertical displacement

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: uniform load: horizontal: on right post

Beam under bending: with axial compression: left end fixed: right end free: temperature gradient: across depth: linearly varying

Tapered fixed beam under simple bending: main inertia symmetrically varying with the 4th power of x: resistance modulus varying with the 3rd power of x: concentrated moment

Small deflections of rectangular plates: 4 simply supported sides: distributed load: linearly varying: along side a: starting at x0

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: free edge: distributed load

Circular arch: uniform section: end A: fixed: end B: horiz.guide: uniform load: per unit length of arch: vertical

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: fixed edge: annular line load + uniform load

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge guided: uniform annular line moment

Beam under bending: with axial compression: left end fixed: right end guided: uniform load

Small deflections of rectangular plates: 2 simply supported opposite sides and 2 free: distributed load linearly varying along side a

Small deflections of rectangular plates: 4 free sides: supported at 4 corners: distributed load: over a partial rectangular area

Circular arch: uniform section: end A: fixed: end B: inclined guide: concentrated moment

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: point load: vertical: on girder

Beam under bending: with held ends: left end supported: right end supported: temperature gradient: across depth: linearly varying

Fixed-fixed beam: on elastic foundation: point load

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: uniform load: horizontal: on left post

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: point load: horizontal: on left post

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: point load: on left post

Tapered simply supported beam under simple bending: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: linearly decreasing load

Large deflections of rectangular plates: 4 free sides: supported at 4 (sliding) corners: uniform load

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge guided: applied angular displacement

Small deflections of rectangular plates: 4 clamped sides: concentrated load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: distributed partial load: linearly varying: on left post

Solid circular flat plate with uniform thickness: pure membrane behaviour: simply supported: uniform annular line load

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: distributed partial load: linearly varying: horizontal: on right post

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: guided edge: annular line load + uniform load

Tapered cantilever under simple bending: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: uniform load

Circular arch: uniform section: end A: pinned: end B: inclined slide: concentrated load: tangential

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: uniform load

Circular arch: uniform section: end A: fixed: end B: pinned: concentrated moment

Beam under bending+shear: left end supported: right end supported: point load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: distributed partial load: linearly varying: on girder

Circular arch: uniform section: end A: fixed: end B: horiz.guide: distributed load: tangential

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge fixed: applied angular displacement

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: uniform load: vertical: on girder right half

Thin-walled cylindrical shell: Fixed-guided: uniform radial pressure: from 'a' to B

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge fixed: distributed load

Circular arch: uniform section: end A: fixed: end B: inclined slide: uniform load: tangential

Tapered simply supported beam under simple bending: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: concentrated load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: point load: on left post

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge supported: applied angular displacement

Beam under bending: with axial compression: left end fixed: right end free: concentrated load

Thin-walled cylindrical shell: Free-free: linearly varying radial pressure

Tapered fixed beam under simple bending: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: concentrated load

Beam under bending: with held ends: left end fixed: right end guided: applied angular displacement

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge supported: uniform annular line load

Supported-free beam: on elastic foundation: concentrated load

Fixed-guided beam: on elastic foundation: distributed load: linearly varying: from 'a' to 'b'

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: uniform temperature change

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end fixed: point load: on girder

Beam under simple bending: left end fixed: right end guided: uniform load

Beam under simple bending: left end fixed: right end supported: concentrated moment

Tapered fixed beam under simple bending: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: concentrated moment

Circular arch: uniform section: end A: fixed: end B: horiz.guide: uniform temperature change

Thin-walled cylindrical shell: Guided-supported: linearly varying radial pressure

Beam under bending: with held ends: left end fixed: right end supported: temperature gradient: across depth: linearly varying

Small deflections of rectangular plates: 3 clamped sides, 1 free: combined loads

Tapered cantilever under simple bending: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: concentrated moment

Small deflections of rectangular plates: 3 supported sides, 1 clamped: distributed load: linearly varying: along side a: starting at x0

Circular arch: uniform section: end A: fixed: end B: fixed: uniform load: per unit horizontal projection: vertical

Beam under bending: with axial tension: left end fixed: right end guided: concentrated moment

Circular arch: uniform section: end A: fixed: end B: vertical slide: uniform load: per unit horizontal projection: vertical

Circular arch: uniform section: end A: fixed: end B: inclined guide: hydrostatic load

Circular arch: uniform section: end A: fixed: end B: vertical guide: uniform load: per unit vertical projection: horizontal: on left half arch

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: uniform pressure: on girder right half

Tapered simply supported beam under simple bending: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: concentrated moment

Solid circular flat plate with uniform thickness: pure membrane behaviour: supported & held: uniform annular line load

Circular arch: uniform section: end A: pinned: end B: inclined guide: uniform load: tangential

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: distributed partial load: linearly varying: vertical: on girder

Beam under bending: with axial tension: left end fixed: right end supported: concentrated load

Tapered cantilever under simple bending: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: combined loads

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: combined loads

Annular flat plate: with uniform thickness: simple bending: outer edge clamped: inner edge free: combined loads

Beam under bending: with axial tension: left end supported: right end supported: concentrated load

Beam under bending: with held ends: left end supported: right end guided: uniform load

Annular flat plate: with uniform thickness: simple bending: outer edge free: inner edge fixed: uniform annular line load

Thin-walled cylindrical shell: Supported-supported: radial load

Circular flat flanges without hubs: lap joint: to internal pressure: gasket laying inside inner edge of bolt holes: split ring: along a diameter

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: uniform temperature change

Circular arch: uniform section: end A: fixed: end B: horiz.slide: uniform temperature change

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: uniform load: radial

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 2nd power of x (n=2): under a single axial compressive load: base fixed: top free

Continuous beam: over 3 spans: in simple bending: combined loads

Tapered fixed beam under simple bending: main inertia symmetrically varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: linearly decreasing load

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 4th power of x (n=4): under a single axial compressive load: base fixed: top fixed

Annular flat plate: with uniform thickness: simple bending: outer edge guided: inner edge fixed: parabolically increasing load

Circular arch: uniform section: end A: fixed: end B: pinned: uniform temperature gradient: across depth

Thin-walled cylindrical shell: Supported-fixed: uniform radial pressure: from 'a' to 'b'

Tapered simply supported beam under simple bending: main inertia symmetrically varying with the 1st power of x: resistance modulus varying with the 1st power of x: concentrated load

Guided-free beam: on elastic foundation: distributed load: linearly varying: from 'a' to 'b'

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: point load: horizontal: on left post

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: uniform load: vertical: on girder

Tapered fixed beam under simple bending: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: uniform load

Circular arch: uniform section: end A: fixed: end B: vertical guide: uniform temperature change

Beam under bending: with axial tension: left end fixed: right end fixed: applied angular displacement

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: distributed partial load: linearly varying: on right post

Beam under bending: with held ends: left end fixed: right end supported: distributed load

W.R.C. Bulletin 297-Aug.84,Supplement to WRC Bulletin No. 107: Local Stresses in Cylindrical Shells Due to External Loadings on a Radial Flush Nozzle: Loads specified at nozzle/wall intersection

Small deflections of rectangular plates: 2 opposite sides clamped, 2 free: concentrated load at center

Continuous beam: over 4 spans: in simple bending: combined loads

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end pinned: point load: on post

Beam under bending: with axial compression: left end supported: right end supported: temperature gradient: across depth: linearly varying

Circular expansion joints: single: unreinforced bellows: without collar: to internal pressure: zero corrosion allowance: cyclic movement due to thermal expansion

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: distributed partial load: linearly varying: horizontal: on right post

Continuous beam: over 5 spans: in simple bending: point load

Solid circular flat plate: simple bending: clamped: with uniform thickness: center load

Circular arch: uniform section: end A: fixed: end B: vertical slide: concentrated load: radial

Tapered cantilever under simple bending: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: uniform load

Tapered cantilever under simple bending: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: concentrated moment

Annular flat plate: with uniform thickness: simple bending: outer edge clamped: inner edge supported: combined loads

Solid circular flat plate: simple bending: simply supported: with linearly decreasing thickness: combined loads

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: concentrated load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: uniform load: horizontal: on left post

Disc springs: single: with or without bearing flats

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge supported: applied angular displacement

Thin-walled cylindrical shell: Supported-free: linearly varying radial pressure

Circular arch: uniform section: end A: pinned: end B: horiz.slide: hydrostatic load

Annular flat plate: with uniform thickness: simple bending: outer edge free: inner edge fixed: applied angular displacement

Circular arch: uniform section: end A: pinned: end B: horiz.slide: combined loads

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: fixed: distributed + uniform load

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge free: parabolically increasing load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: uniform load: on right post

Beam under bending: with axial tension: left end supported: right end supported: applied angular displacement

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: uniform load: on right post

Tapered simply supported beam under simple bending: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: combined loads

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: concentrated load: vertical

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: distributed partial load: linearly varying: vertical: on girder right half

Spheres in contact with a cylindrical socket under load: Hertz's theory

Small deflections of rectangular plates: bending + shear: 4 simply supported sides: distributed load linearly varying along side a

Beam under bending: with axial compression: left end fixed: right end free: combined loads

Beam under bending: with axial compression: left end fixed: right end fixed: distributed load

Beam under bending+shear: left end supported: right end guided: point load

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: point load: horizontal: on girder

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: uniform load: on girder

Guided-guided beam: on elastic foundation: concentrated load

Small deflections of rectangular plates: 1 clamped side, 2 supported(adjacent) and 1 free: distributed load linearly varying along side a: starting at x0

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: point load: horizontal: on girder

Large deflections of rectangular plates: 4 supported & held sides: distributed load linearly varying along side a

Beam under bending: with held ends: left end fixed: right end fixed: applied vertical displacement

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: uniform temperature change

Guided-infinite beam: on elastic foundation: point load

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: uniform load: vertical: on girder

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: point load: horizontal: on girder left half

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: free edge: annular line load + uniform load

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge guided: uniform annular line moment

Small deflections of rectangular plates: 3 supported sides, 1 free: distributed load: over a partial rectangular area

Beam under bending+shear: left end fixed: right end guided: combined loads

Large deflections of rectangular plates: 4 simply supported sides: distributed load linearly varying along side a: starting at x0

Circular arch: uniform section: end A: fixed: end B: horiz.guide: hydrostatic load

Annular flat plate: with uniform thickness: simple bending: outer edge simply guided: inner edge supported: temperature differential across thickness

Elastic stability of a beam-column: prismatic: under a single axial compressive load: base fixed: top free

Solid circular flat plate: simple bending: simply supported: with linearly increasing thickness: uniform load

Thin-walled cylindrical shell: Guided-guided: applied moment

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: point load: vertical: on girder left half

Fixed-free beam: on elastic foundation: distributed load: linearly varying: from 'a' to 'b'

Minimum thickness of: torispherical ends: under internal pressure

Beam under bending: with axial compression: left end fixed: right end supported: applied vertical displacement

Beam under bending: with held ends: left end fixed: right end free: distributed load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: point load: horizontal: on left post

Solid circular flat plate with uniform thickness: large deflections behaviour: clamped edge: uniform annular line load

Circular arch: uniform section: end A: pinned: end B: inclined slide: uniform load: tangential

Solid circular flat plate: simple bending: simply supported: with uniform thickness: distributed load

Beam under bending: with held ends: left end supported: right end supported: concentrated moment

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge fixed: uniform annular line moment

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge free: distributed load

Beam under bending: with axial compression: left end fixed: right end fixed: uniform load

Beam under bending: with axial compression: left end fixed: right end guided: applied angular displacement

Circular arch: uniform section: end A: fixed: end B: inclined guide: concentrated load: radial

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: uniform load: horizontal: on girder

Circular arch: uniform section: end A: fixed: end B: horiz.slide: uniform load: per unit vertical projection: horizontal: on left half arch

Small deflections of rectangular plates: 4 simply supported sides: concentrated load

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: free edge: center load

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: supported edge: center load + uniform load

Tapered fixed beam under simple bending: main inertia varying symmetrically with the 2nd power of x: resistance modulus varying with the 1st power of x: combined loads

Circular arch: uniform section: end A: pinned: end B: horiz.guide: uniform load: radial

Beam under simple bending: left end fixed: right end fixed: applied vertical displacement

Continuous beam: over 2 spans: in simple bending: combined loads

Small deflections of rectangular plates: 2 adjacent supported sides, 2 free: combined loads

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge guided: applied angular displacement

Continuous beam: over 5 spans: in simple bending: combined loads

Circular arch: uniform section: end A: fixed: end B: horiz.guide: distributed load: vertical: partial

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: uniform load: horizontal: on girder right half

Large deflections of rectangular plates: 4 supported & fully held sides: uniform load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: uniform load: horizontal: on girder right half

Semiinfinite beam: on elastic foundation: point load

Beam under bending+shear: left end supported: right end supported: uniform load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: distributed partial load: linearly varying: on right post

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end sliding: point load: on girder

Small deflections of rectangular plates: 2 simply supported opposite sides and 2 free: concentrated load

Circular arch: uniform section: end A: fixed: end B: pinned: distributed load: vertical: partial

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: guided edge: center load

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end sliding: right end fixed: point load: on girder

Beam under bending+shear: left end fixed: right end free: point load

Tapered simply supported beam under simple bending: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: linearly decreasing load

Circular arch: uniform section: end A: pinned: end B: inclined slide: uniform temperature change

Circular arch: uniform section: end A: fixed: end B: horiz.slide: distributed load: vertical: partial

Circular arch: uniform section: end A: fixed: end B: horiz.slide: distributed load: radial

Small deflections of rectangular plates: 2 adjacent supported sides, 2 free: distributed load: over a partial rectangular area

Circular arch: uniform section: end A: fixed: end B: vertical slide: combined loads

Beam under bending: with axial tension: left end fixed: right end supported: combined loads

Solid circular flat plate with uniform thickness: simple bending: on (mono)elastic foundation: supported edge: distributed + uniform load

Beam under bending+shear: left end fixed: right end supported: uniform load

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge supported: combined loads

Small deflections of triangular plates: equilateral: 2 supported sides, 1 free: distributed load: linearly varying: along height a

Solid circular flat plate: simple bending: simply supported: with uniform thickness: uniform annular line load

Circular arch: uniform section: end A: fixed: end B: pinned: concentrated load: horizontal

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: point load: horizontal: on girder

Small deflections of rectangular plates: bending + shear: 4 simply supported sides: uniform load

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 3rd power of x (n=3): under a single axial compressive load: base fixed: top fixed

Small deflections of rectangular plates: 4 free sides: supported at 4 corners: combined loads

Circular arch: uniform section: end A: pinned: end B: horiz.slide: concentrated moment

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge supported: uniform annular line moment

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: distributed partial load: linearly varying: vertical: on girder left half

Design rules for clamp connections: clamping faces parallel

Circular arch: uniform section: end A: fixed: end B: pinned: uniform load: per unit vertical projection: horizontal: on left half arch

Circular arch: uniform section: end A: pinned: end B: horiz.guide: uniform load: tangential

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end pinned: combined loads

Circular arch: uniform section: end A: pinned: end B: horiz.slide: uniform temperature change

Beam under bending: with axial tension: left end fixed: right end supported: applied vertical displacement

Thickness of shells and tubes: under external pressure

Small deflections of triangular plates: equilateral: 3 clamped sides: combined loads

Circular arch: uniform section: end A: fixed: end B: inclined guide: combined loads

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end sliding: right end fixed: uniform load: on post

Tapered simply supported beam under simple bending: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: concentrated moment

Thin-walled cylindrical shell: Guided-guided: radial load

Beam under bending: with axial compression: left end supported: right end guided: uniform load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: point load: vertical: on girder right half

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: distributed partial load: linearly varying: vertical: on girder right half

Simply supported beam: on elastic foundation: distributed load: linearly varying: from 'a' to 'b'

Two spheres in contact under load: Hertz's theory

Circular arch: uniform section: end A: pinned: end B: pinned: uniform load: per unit length of arch: horizontal

Beam under simple bending: large deflections: left end supported: right end supported: uniform load

Large deflections of rectangular plates: 4 clamped & held sides: uniform load

Beam under bending: with axial compression: left end supported: right end supported: combined loads

Beam under bending: with axial compression: left end fixed: right end supported: distributed load

Small deflections of triangular plates: equilateral: 2 clamped sides, 1 free: uniform load

Circular arch: uniform section: end A: fixed: end B: pinned: concentrated load: tangential

Circular arch: uniform section: end A: fixed: end B: free: uniform load: per unit vertical projection: horizontal: on left half arch

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: distributed partial load: linearly varying: vertical: on girder

Annular flat plate: with uniform thickness: simple bending: outer edge free: inner edge supported: distributed load

Beam under simple bending: left end supported: right end guided: applied angular displacement

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end pinned: distributed partial load: linearly varying: on girder

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: uniform load: horizontal: on girder left half

Beam under bending: with axial tension: left end supported: right end supported: combined loads

Small deflections of triangular plates: equilateral: 2 supported sides, 1 free: uniform load

Circular arch: uniform section: end A: fixed: end B: horiz.slide: concentrated moment

Circular arch: uniform section: end A: fixed: end B: vertical slide: concentrated moment

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: free edge: distributed + uniform load

Annular flat plate: with uniform thickness: simple bending: outer edge guided: inner edge fixed: uniform annular line moment

Circular arch: uniform section: end A: fixed: end B: horiz.guide: concentrated load: tangential

Circular arch: uniform section: end A: fixed: end B: horiz.slide: concentrated load: tangential

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: distributed partial load: linearly varying: horizontal: on right post

Full face flanges: with soft ring type gaskets: to internal pressure

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: concentrated load: horizontal

Thin-walled cylindrical shell: Free-guided: applied moment

Tapered simply supported beam under simple bending: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: concentrated load

Beam under simple bending: left end fixed: right end fixed: applied angular displacement

Beam under simple bending: left end fixed: right end fixed: uniform load

Tapered simply supported beam under simple bending: main inertia symmetrically varying with the 4th power of x: resistance modulus varying with the 3rd power of x: linearly decreasing load

Tapered simply supported beam under simple bending: main inertia symmetrically varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: uniform load

Supported-guided beam: on elastic foundation: concentrated moment

Circular arch: uniform section: end A: pinned: end B: inclined slide: hydrostatic load

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: uniform temperature change

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end sliding: distributed partial load: linearly varying: on post

Circular arch: uniform section: end A: fixed: end B: horiz.slide: uniform load: per unit vertical projection: horizontal

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end fixed: combined loads

Cylinder in contact on a flat plate under load: Hertz's theory

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: uniform load

Circular arch: uniform section: end A: pinned: end B: pinned: concentrated load: vertical

Continuous beam: over 2 spans: in simple bending: distributed load

Small deflections of rectangular plates: 2 opposite sides clamped, 2 free: distributed load linearly varying along side a

Beam under bending: with axial compression: left end supported: right end guided: concentrated load

Thin-walled cylindrical shell: Guided-guided: uniform radial pressure: from 'a' to B

Rectangular membranes: 4 fully held sides: uniform load

Small deflections of rectangular plates: 4 free sides: supported at 4 corners: uniform load

Tapered fixed beam under simple bending: main inertia varying symmetrically with the 3rd power of x: resistance modulus varying with the 2nd power of x: combined loads

Beam under simple bending: large deflections: left end supported: right end supported: concentrated load

Circular arch: uniform section: end A: pinned: end B: inclined guide: concentrated load: vertical

Small deflections of rectangular plates: 3 clamped sides, 1 supported: uniform load

Circular arch: uniform section: end A: fixed: end B: vertical guide: concentrated load: tangential

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge guided: combined loads

Beam under bending+shear: left end fixed: right end fixed: combined loads

Thin-walled cylindrical shell: Free-free: uniform radial pressure: from 'a' to 'b'

Circular arch: uniform section: end A: pinned: end B: pinned: uniform temperature gradient: across depth

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge supported: uniform annular line moment

Beam under simple bending: large deflections: left end fixed: right end free: concentrated load

Annular flat plate: with uniform thickness: simple bending: outer edge free: inner edge supported: parabolically increasing load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: uniform temperature change

Beam under bending: with axial tension: left end supported: right end guided: distributed load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: uniform load: horizontal: on left post

Annular flat plate: with uniform thickness: simple bending: outer edge guided: inner edge supported: distributed load

Supported-infinite beam: on elastic foundation: concentrated load

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge free: applied angular displacement

Circular arch: uniform section: end A: fixed: end B: fixed: concentrated moment

Thin-walled cylindrical shell: Guided-supported: uniform radial pressure: from 'a' to B

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge fixed: parabolically increasing load

Thin-walled cylindrical shell: Fixed-supported: linearly varying radial pressure

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge guided: uniform load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: distributed partial load: linearly varying: vertical: on girder left half

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: uniform load: horizontal: on right post

Small deflections of rectangular plates: 3 supported sides, 1 free: combined loads

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: combined loads

Circular arch: uniform section: end A: fixed: end B: fixed: distributed load: tangential

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: uniform pressure: on girder left half

Thin-walled cylindrical shell: Supported-guided: uniform radial pressure: from 'a' to B

Thin-walled cylindrical shell: Guided-fixed: radial load

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: guided edge: distributed load

Circular arch: uniform section: end A: pinned: end B: inclined slide: uniform load: per unit length of arch: horizontal

Beam under bending: with axial tension: left end fixed: right end fixed: uniform load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: distributed partial load: linearly varying: on left post

Small deflections of rectangular plates: 2 facing sides clamped, 2 supported: distributed load: over a partial rectangular area

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: point load: on girder

Fixed-free beam: on elastic foundation: point load

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end fixed: uniform load: on post

Beam under bending: with axial tension: left end fixed: right end free: concentrated moment

Tapered fixed beam under simple bending: main inertia varying symmetrically with the 1st power of x: resistance modulus varying with the 1st power of x: uniform load

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: concentrated load

Flat face flanges with metal-to-metal contact outside the bolt circle: analysis of an identical (Class 1) flange pair: same material: integral (Cat.1) flanges: hub of constant thickness: no spacer: self-sealing gasket with negligible loads

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge guided: distributed load

Small deflections of rectangular plates: 1 clamped side, 3 free: distributed load linearly varying along side a

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge supported: distributed load

Beam under bending: with held ends: left end fixed: right end fixed: uniform load

Circular arch: uniform section: end A: fixed: end B: vertical slide: uniform load: radial

Beam under bending: with axial compression: left end fixed: right end guided: concentrated moment

Beam under bending: with axial tension: left end fixed: right end supported: distributed load

Infinite beam: on elastic foundation: concentrated moment

Small deflections of rectangular plates: 2 adjacent supported sides, 2 free: point load

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: point load: vertical: on girder

Thin-walled cylindrical shell: Free-fixed: uniform radial pressure: from 'a' to 'b'

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: uniform load: vertical: on girder

Fixed-infinite beam: on elastic foundation: concentrated moment

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge guided: temperature differential across thickness

Beam: simple bending: with held ends: left end supported: right end supported: uniform load

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 3rd power of x (n=3): under a single axial compressive load: base fixed: top free

Beam under simple bending: left end fixed: right end supported: applied vertical displacement

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end fixed: point load: on post

Small deflections of rectangular plates: 1 clamped side, 2 supported and 1 free: distributed load: over a partial rectangular area

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: distributed load

Tapered simply supported beam under simple bending: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: uniform load

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end fixed: uniform load: on girder

Circular pipes: supported at bottom: filled with liquid

Annular flat plate: with uniform thickness: simple bending: outer edge simply fixed: inner edge fixed: uniform annular line load

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: concentrated moment

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: uniform load: horizontal: on girder left half

Circular arch: uniform section: end A: fixed: end B: horiz.guide: distributed load: radial

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: uniform load: vertical: on girder left half

Simply supported beam: on elastic foundation: point load

Beam under bending: with axial tension: left end fixed: right end guided: combined loads

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: point load: on girder

Minimum thickness of cylindrical shells under internal pressure: e/De<=0.16: Calculation based on inner diameter

Circular arch: uniform section: end A: fixed: end B: inclined slide: concentrated load: horizontal

Beam under bending: with axial tension: left end fixed: right end fixed: concentrated load

Tapered cantilever under simple bending: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: distributed load

Beam under bending: with axial compression: left end supported: right end supported: uniform load

Elastic stability of a beam-column: with two stepped sections: under two axial compressive loads: base fixed: top free

Beam under simple bending: left end fixed: right end supported: temperature gradient: across depth: linearly varying

Circular flat flanges without hubs: loose, welded: to internal pressure: gasket laying inside inner edge of bolt holes

Solid circular flat plate with uniform thickness: large deflections behaviour: simply supported: distributed load

Annular flat plate: with uniform thickness: simple bending: outer edge free: inner edge fixed: parabolically increasing load

Circular arch: uniform section: end A: fixed: end B: inclined guide: uniform temperature change

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: uniform load: vertical: on girder

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: distributed partial load: linearly varying: on girder

Small deflections of rectangular plates: 3 clamped sides, 1 supported: distributed load linearly varying along side a: starting at x0

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge fixed: uniform annular line load

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: distributed partial load: linearly varying: horizontal: on left post

Thin-walled cylindrical shell: Free-supported: linearly varying radial pressure

Thin-walled cylindrical shell: Free-supported: uniform radial pressure: from 'a' to 'b'

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: point load: vertical: on girder left half

Tapered simply supported beam under simple bending: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: uniform load

Circular arch: uniform section: end A: pinned: end B: horiz.guide: concentrated load: tangential

Large deflections of rectangular plates: 4 supported & held sides: distributed load linearly varying along side a: starting at x0

Thin-walled cylindrical shell: Guided-free: uniform radial pressure: from 'a' to B

Circular ring beam: supported at bottom: load at top

Large deflections of rectangular plates: 4 clamped & held sides: distributed load linearly varying along side a: starting at x0

Supported-free beam: on elastic foundation: distributed load: linearly varying: from 'a' to 'b'

Circular flanges with hub: hub with constant thickness: loose, welded: fig.2-4(3): to internal pressure: gasket laying inside inner edge of bolt holes: with bolt spacing correction

Circular arch: uniform section: end A: fixed: end B: vertical slide: hydrostatic load

Circular arch: uniform section: end A: fixed: end B: free: concentrated load: tangential

Circular arch: uniform section: end A: fixed: end B: fixed: hydrostatic load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: uniform temperature change

Tapered simply supported beam under simple bending: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: combined loads

Solid circular flat plate: simple bending: clamped: with uniform thickness: distributed load

Tapered cantilever under simple bending: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: linearly decreasing load

Beam under bending: with axial compression: left end fixed: right end supported: concentrated moment

Circular arch: uniform section: end A: fixed: end B: inclined guide: distributed load: tangential

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: free edge: center load + uniform load

Circular ring beam: supported at bottom: 2 tangential loads

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: uniform load: horizontal: on girder left half

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: point load: horizontal: on left post

Circular arch: uniform section: end A: fixed: end B: free: distributed load: tangential

Solid circular flat plate with uniform thickness: large deflections behaviour: clamped & held: uniform distributed load

Elastic stability of a beam-column: with two stepped sections: under two axial compressive loads: base fixed: top supported

Circular arch: uniform section: end A: fixed: end B: inclined guide: uniform load: per unit vertical projection: horizontal: on left half arch

Circular arch: uniform section: end A: pinned: end B: inclined slide: concentrated load: vertical

Beam under simple bending: left end fixed: right end fixed: concentrated moment

Supported-infinite beam: on elastic foundation: distributed load: linearly varying: from 'a' to 'b'

Beam under bending: with held ends: left end supported: right end guided: applied angular displacement

Guided-free beam: on elastic foundation: concentrated moment

Circular arch: uniform section: end A: pinned: end B: horiz.guide: uniform load: per unit length of arch: vertical

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: uniform load: per unit length of arch: vertical

Small deflections of rectangular plates: 3 clamped sides, 1 supported: combined loads

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end pinned: distributed partial load: linearly varying: on post

Small deflections of rectangular plates: 2 adjacent clamped sides, 2 free: distributed load linearly varying along side a: starting at x0

Thin-walled cylindrical shell: Guided-free: radial load

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: point load: horizontal: on right post

Beam under bending+shear: left end fixed: right end fixed: distributed load

Continuous beam: over 2 spans: in simple bending: uniform load

Circular arch: uniform section: end A: pinned: end B: inclined guide: distributed load: vertical: partial

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: point load: horizontal: on girder left half

Circular ring beam: supported at bottom: 2 radial loads

Beam under simple bending: large deflections: left end fixed: right end free: uniform load

Circular arch: uniform section: end A: fixed: end B: vertical slide: uniform load: per unit length of arch: horizontal

Circular arch: uniform section: end A: fixed: end B: vertical guide: uniform load: per unit length of arch: horizontal

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end sliding: combined loads

Continuous beam: over 3 spans: in simple bending: uniform load

Circular arch: uniform section: end A: fixed: end B: pinned: uniform load: per unit length of arch: vertical

Solid circular flat plate with uniform thickness: simple bending: on (mono)elastic foundation: free edge: annular line load + uniform load

Solid circular flat plate with uniform thickness: simple bending: on (mono)elastic foundation: guided edge: distributed + uniform load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: uniform load: on girder

Circular arch: uniform section: end A: fixed: end B: pinned: hydrostatic load

Beam under bending: with axial tension: left end fixed: right end fixed: applied vertical displacement

Small deflections of rectangular plates: 2 adjacent clamped sides, 2 free: uniform load

Continuous beam: over 4 spans: in simple bending: uniform load

Small deflections of triangular plates: equilateral: 2 clamped sides, 1 free: combined loads

Circular arch: uniform section: end A: fixed: end B: fixed: concentrated load: radial

Small deflections of rectangular plates: 1 clamped side, 2 supported and 1 free: distributed load linearly varying along side a

Circular arch: uniform section: end A: fixed: end B: vertical slide: uniform temperature gradient: across depth

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: uniform load

Thin-walled cylindrical shell: Supported-supported: applied moment

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end pinned: uniform temperature change

Circular arch: uniform section: end A: pinned: end B: horiz.slide: uniform load: tangential

Circular arch: uniform section: end A: pinned: end B: inclined slide: distributed load: radial

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 1st power of x (n=1): under a single axial compressive load: base fixed: top fixed

Circular arch: uniform section: end A: pinned: end B: pinned: hydrostatic load

Small deflections of rectangular plates: 1 clamped side, 3 free: combined loads

Small deflections of rectangular plates: 2 adjacent clamped sides, 2 supported: distributed load linearly varying along side a: starting at x0

Annular flat plate: with uniform thickness: simple bending: outer edge free: inner edge supported: temperature differential across thickness

Circular arch: uniform section: end A: pinned: end B: pinned: concentrated load: radial

Small deflections of triangular plates: equilateral: 3 clamped sides: uniform load

Beam under bending: with held ends: left end supported: right end supported: applied vertical displacement

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge free: combined loads

Circular arch: uniform section: end A: fixed: end B: free: hydrostatic load

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: supported edge: annular line load + uniform load

Tapered cantilever under simple bending: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: concentrated load

Beam under bending+shear: left end fixed: right end supported: point load

Thin-walled cylindrical shell: Supported-supported: uniform radial pressure: from 'a' to 'b'

Circular arch: uniform section: end A: pinned: end B: inclined guide: concentrated load: tangential

Beam under bending: with axial tension: left end supported: right end guided: temperature gradient: across depth: linearly varying

Circular arch: uniform section: end A: pinned: end B: inclined slide: combined loads

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: uniform temperature change

Elastic stability of a beam-column: prismatic: under a single axial compressive load: base fixed: top fixed

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: distributed partial load: linearly varying: horizontal: on left post

Required thickness of conical shells: under internal pressure: Calculation based on inside diameter

Annular flat plate: with uniform thickness: simple bending: outer edge guided: inner edge fixed: distributed load

Beam under bending: with axial tension: left end supported: right end supported: distributed load

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end fixed: distributed partial load: linearly varying: on post

Thin-walled cylindrical shell: Free-guided: uniform radial pressure: from 'a' to B

Thin-walled cylindrical shell: Guided-fixed: uniform radial pressure: from 'a' to B

Beam under simple bending: left end supported: right end supported: uniform load

Tapered simply supported beam under simple bending: main inertia symmetrically varying with the 1st power of x: resistance modulus varying with the 1st power of x: concentrated moment

Rectangular membranes: 4 held sides: uniform load

Circular arch: uniform section: end A: fixed: end B: pinned: uniform temperature change

Beam under bending: with axial compression: left end fixed: right end guided: distributed load

Small deflections of rectangular plates: 2 facing sides clamped, 2 supported: distributed load linearly varying along side a

Thin-walled cylindrical shell: Guided-supported: radial load

Guided-infinite beam: on elastic foundation: distributed load: linearly varying: from 'a' to 'b'

Beam under simple bending: large deflections: left end fixed: right end guided: uniform load

Tapered fixed beam under simple bending: main inertia varying symmetrically with the 4th power of x: resistance modulus varying with the 3rd power of x: uniform load

Circular arch: uniform section: end A: fixed: end B: horiz.slide: concentrated load: horizontal

Tapered cantilever under simple bending: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: concentrated load

Beam under simple bending: left end supported: right end guided: temperature gradient: across depth: linearly varying

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: concentrated load

Beam under simple bending: left end fixed: right end supported: concentrated load

Circular arch: uniform section: end A: fixed: end B: vertical guide: uniform load: radial

Beam under bending: with axial compression: left end fixed: right end fixed: temperature gradient: across depth: linearly varying

Solid circular flat plate with uniform thickness: large deflections behaviour: clamped & held: distributed load

Solid circular flat plate with uniform thickness: large deflections behaviour: clamped: distributed load

Circular arch: uniform section: end A: fixed: end B: vertical guide: concentrated load: horizontal

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: distributed partial load: linearly varying: vertical: on girder left half

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: point load: on right post

Tapered simply supported beam under simple bending: main inertia symmetrically varying with the 4th power of x: resistance modulus varying with the 3rd power of x: concentrated moment

Circular pipes: supported at bottom: load at top

Thin-walled cylindrical shell: Fixed-fixed: applied moment

Annular flat plate: with uniform thickness: simple bending: outer edge guided: inner edge supported: uniform annular line moment

Circular pipes: supported at bottom: uniform radial pressure: over an arc

Circular arch: uniform section: end A: pinned: end B: inclined slide: uniform load: per unit horizontal projection: vertical

Circular arch: uniform section: end A: pinned: end B: horiz.slide: uniform load: per unit vertical projection: horizontal

Circular arch: uniform section: end A: fixed: end B: inclined guide: distributed load: vertical: partial

Solid circular flat plate: simple bending: clamped: with uniform thickness: combined loads

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: point load: horizontal: on girder

Continuous beam: over 4 spans: in simple bending: distributed load

Supported-guided beam: on elastic foundation: concentrated load

Circular arch: uniform section: end A: pinned: end B: horiz.guide: distributed load: tangential

Beam under simple bending: left end fixed: right end guided: applied angular displacement

Elastic stability of a beam-column: prismatic: under a single axial compressive load: base fixed: top guided

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge guided: parabolically increasing load

Beam under bending: with axial tension: left end fixed: right end free: applied angular displacement

Guided-guided beam: on elastic foundation: distributed load: linearly varying: from 'a' to 'b'

Small deflections of rectangular plates: 3 clamped sides, 1 free: distributed load linearly varying along side a: starting at x0

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge fixed: temperature differential across thickness

Annular flat plate: with uniform thickness: simple bending: outer edge free: inner edge fixed: temperature differential across thickness

Beam under simple bending: left end fixed: right end guided: concentrated moment

Thin-walled cylindrical shell: Fixed-free: uniform radial pressure: from 'a' to 'b'

Tapered fixed beam under simple bending: main inertia symmetrically varying with the 2nd power of x: resistance modulus varying with the 1st power of x: concentrated moment

Thin-walled cylindrical shell: Free-fixed: linearly varying radial pressure

Circular arch: uniform section: end A: pinned: end B: inclined guide: uniform load: radial

Tapered fixed beam under simple bending: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: combined loads

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: distributed load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: combined loads

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: concentrated moment

Supported-fixed beam: on elastic foundation: concentrated load

Beam under bending: with axial compression: left end supported: right end guided: temperature gradient: across depth: linearly varying

Beam under bending: with held ends: left end fixed: right end supported: applied vertical displacement

Circular arch: uniform section: end A: pinned: end B: horiz.guide: concentrated load: horizontal

Solid circular flat plate: simple bending: clamped: with uniform thickness: uniform annular line load

Solid circular flat plate with uniform thickness: large deflections behaviour: supported & held: distributed load

Tapered fixed beam under simple bending: main inertia varying symmetrically with the 2nd power of x: resistance modulus varying with the 1st power of x: uniform load

Solid circular flat plate with uniform thickness: large deflections behaviour: simply supported: uniform annular line load

Thin-walled cylindrical shell: Supported-guided: linearly varying radial pressure

Circular pipes: supported at bottom: 2 facing horizontal line loads

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: combined loads

Beam under bending: with axial compression: left end fixed: right end fixed: combined loads

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: uniform load: on left post

Circular arch: uniform section: end A: fixed: end B: horiz.guide: concentrated load: radial

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: point load: horizontal: on right post

Tapered fixed beam under simple bending: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: concentrated moment

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 2nd power of x (n=2): under a single axial compressive load: base fixed: top supported

Small deflections of rectangular plates: 1 clamped side, 2 supported(adjacent) and 1 free: distributed load: over a partial rectangular area

Tapered cantilever under simple bending: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: uniform load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: uniform load: vertical: on girder right half

Small deflections of rectangular plates: 4 simply supported sides: uniform load

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: uniform load: horizontal: on girder

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 1st power of x (n=1): under a single axial compressive load: base supported: top supported

Beam under bending: with held ends: left end fixed: right end guided: concentrated moment

Annular flat plate: with uniform thickness: simple bending: outer edge clamped: inner edge clamped: combined loads

Tapered fixed beam under simple bending: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: linearly decreasing load

Beam under bending: with held ends: left end fixed: right end fixed: distributed load

Tapered fixed beam under simple bending: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: distributed load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: uniform load: on left post

Tapered fixed beam under simple bending: main inertia symmetrically varying with the 1st power of x: resistance modulus varying with the 1st power of x: concentrated load

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: uniform load: horizontal: on left post

Circular arch: uniform section: end A: fixed: end B: free: concentrated load: horizontal

Circular arch: uniform section: end A: fixed: end B: vertical slide: uniform load: per unit vertical projection: horizontal: on left half arch

Circular arch: uniform section: end A: fixed: end B: inclined slide: concentrated load: tangential

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: combined loads

Circular arch: uniform section: end A: fixed: end B: fixed: uniform load: per unit length of arch: horizontal

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: uniform load: vertical: on girder left half

Tapered fixed beam under simple bending: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: linearly decreasing load

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge fixed: parabolically increasing load

Circular arch: uniform section: end A: fixed: end B: vertical guide: distributed load: radial

Circular arch: uniform section: end A: pinned: end B: inclined guide: uniform temperature change

Circular arch: uniform section: end A: fixed: end B: inclined slide: uniform load: per unit length of arch: vertical

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: uniform load: on left post

Annular flat plate: with uniform thickness: simple bending: outer edge simply fixed: inner edge supported: uniform annular line load

Tapered simply supported beam under simple bending: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: uniform load

Continuous beam: over 3 spans: in simple bending: point load

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: point load: vertical: on girder

Small deflections of rectangular plates: on elastic foundation: free: concentrated load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: point load: on left post

Beam under bending: with axial compression: left end fixed: right end free: concentrated moment

Circular arch: uniform section: end A: pinned: end B: horiz.slide: uniform load: radial

Thin-walled cylindrical shell: Fixed-fixed: linearly varying radial pressure

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: point load: on left post

Circular arch: uniform section: end A: fixed: end B: horiz.guide: uniform load: per unit horizontal projection: vertical

Beam under bending: with held ends: left end supported: right end supported: applied angular displacement

Beam under bending: with axial compression: left end supported: right end guided: concentrated moment

Solid circular flat plate: simple bending: clamped: with uniform thickness: distributed parabolically increasing load

Beam under bending: with axial compression: left end fixed: right end fixed: concentrated load

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: point load: horizontal: on left post

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: combined loads

Circular arch: uniform section: end A: pinned: end B: inclined slide: concentrated load: radial

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: uniform load: horizontal: on right post

Thin-walled cylindrical shell: Fixed-guided: uniform radial pressure: from 'a' to 'b'

Thin-walled cylindrical shell: Supported-fixed: uniform radial pressure: from 'a' to B

Tapered fixed beam under simple bending: main inertia symmetrically varying with the 4th power of x: resistance modulus varying with the 3rd power of x: concentrated load

Beam under bending+shear: left end supported: right end supported: combined loads

Supported-fixed beam: on elastic foundation: concentrated moment

Annular flat plate: with uniform thickness: simple bending: outer edge free: inner edge supported: combined loads

Tapered fixed beam under simple bending: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: distributed load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: combined loads

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge free: uniform annular line load

Tapered simply supported beam under simple bending: main inertia symmetrically varying with the 4th power of x: resistance modulus varying with the 3rd power of x: concentrated load

Circular arch: uniform section: end A: fixed: end B: fixed: combined loads

Circular arch: uniform section: end A: pinned: end B: pinned: uniform load: per unit horizontal projection: vertical

Beam under bending: with axial compression: left end fixed: right end supported: applied angular displacement

Annular flat plate: with uniform thickness: simple bending: outer edge simply fixed: inner edge guided: uniform annular line load

Circular arch: uniform section: end A: pinned: end B: horiz.guide: uniform load: per unit horizontal projection: vertical

Spheres in contact with a spherical socket under load: Hertz's theory

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 4th power of x (n=4): under a single axial compressive load: base fixed: top guided

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: concentrated load: tangential

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: point load: horizontal: on right post

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: point load: vertical: on girder right half

Circular arch: uniform section: end A: fixed: end B: fixed: uniform load: per unit length of arch: vertical

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: distributed load: radial

Beam under simple bending: left end supported: right end supported: applied angular displacement

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: uniform load: per unit vertical projection: horizontal

Elastic stability of a beam-column: prismatic: under a single axial compressive load: base supported: top supported

Tapered fixed beam under simple bending: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: linearly decreasing load

Circular arch: uniform section: end A: fixed: end B: pinned: combined loads

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge guided: parabolically increasing load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: uniform temperature change

Circular arch: uniform section: end A: pinned: end B: inclined guide: concentrated moment

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: uniform pressure: on girder left half

Circular arch: uniform section: end A: fixed: end B: horiz.guide: uniform load: tangential

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end sliding: right end fixed: point load: on post

Circular arch: uniform section: end A: fixed: end B: fixed: concentrated load: horizontal

Circular arch: uniform section: end A: fixed: end B: horiz.guide: combined loads

Beam under simple bending: left end supported: right end guided: uniform load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: uniform load: on girder

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: point load: horizontal: on right post

Thin-walled cylindrical shell: Free-guided: radial load

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end sliding: uniform load: on post

Small deflections of rectangular plates: 2 simply supported opposite sides and 2 free: uniform load

Junction between the large end of a cone and a cylinder: with knuckle: cone and cylinder with constant thicknesses: under internal pressure

Beam under bending: with held ends: left end fixed: right end guided: temperature gradient: across depth: linearly varying

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge fixed: temperature differential across thickness

Circular flanges with hub: integral with hub slope 1/3 max: WN or LWN type: to internal pressure: gasket laying inside inner edge of bolt holes

Small deflections of rectangular plates: 4 simply supported sides: distributed load: over a partial rectangular area

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: uniform load: horizontal: on right post

Beam under bending: with axial tension: left end supported: right end guided: combined loads

Beam under bending: with held ends: left end fixed: right end guided: uniform load

Small deflections of rectangular plates: 2 adjacent clamped sides, 2 supported: distributed load linearly varying along side a

Circular arch: uniform section: end A: pinned: end B: inclined guide: uniform load: per unit length of arch: horizontal

Beam under bending+shear: left end fixed: right end free: combined loads

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: uniform load: on right post

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge clamped: combined loads

Small deflections of rectangular plates: 3 supported sides, 1 clamped: combined loads

Beam under simple bending: left end supported: right end supported: point load

Solid circular flat plate with uniform thickness: pure membrane behaviour: simply supported: distributed load

Beam under bending: with held ends: left end fixed: right end free: concentrated load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: distributed partial load: linearly varying: on left post

Tapered cantilever under simple bending: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: linearly decreasing load

Beam: simple bending: with held ends: left end supported: right end supported: uniform load

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: guided edge: uniform annular line load

Solid circular flat plate with uniform thickness: simple bending: on (mono)elastic foundation: supported edge: center load + uniform load

Circular arch: uniform section: end A: fixed: end B: horiz.guide: uniform load: per unit length of arch: horizontal

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: uniform load: horizontal: on left post

Small deflections of rectangular plates: 4 free sides: supported at 4 corners: concentrated load

Small deflections of rectangular plates: 4 clamped sides: combined loads

Tapered simply supported beam under simple bending: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: linearly decreasing load

Thin-walled cylindrical shell: Free-fixed: radial load

Circular arch: uniform section: end A: fixed: end B: inclined slide: uniform load: per unit vertical projection: horizontal

Circular arch: uniform section: end A: pinned: end B: horiz.guide: uniform temperature gradient: across depth

Disc springs: stack in series: with or without bearing flats

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: uniform load: horizontal: on left post

Circular arch: uniform section: end A: fixed: end B: pinned: uniform load: per unit horizontal projection: vertical

Tapered cantilever under simple bending: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: combined loads

Circular arch: uniform section: end A: fixed: end B: vertical slide: distributed load: vertical: partial

Circular arch: uniform section: end A: fixed: end B: free: uniform load: radial

Beam under bending: with held ends: left end fixed: right end supported: applied angular displacement

Circular arch: uniform section: end A: pinned: end B: horiz.slide: distributed load: vertical: partial

Thin-walled cylindrical shell: Supported-free: uniform radial pressure: from 'a' to B

Circular arch: uniform section: end A: pinned: end B: pinned: concentrated moment

Beam under bending: with axial compression: left end fixed: right end fixed: applied angular displacement

Beam under simple bending: left end fixed: right end free(cantilever): combined loads

Elastic stability of a beam-column: with two stepped sections: under two axial compressive loads: base fixed: top fixed

Small deflections of rectangular plates: on elastic foundation: free: distributed load: over a partial rectangular area

Annular flat plate: with uniform thickness: simple bending: outer edge free: inner edge fixed: distributed load

Disc springs: stack in parallel: with or without bearing flats

Beam under bending: with held ends: left end fixed: right end fixed: concentrated moment

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: uniform load: horizontal: on right post

Fixed-fixed beam: on elastic foundation: distributed load: linearly varying: from 'a' to 'b'

Tapered simply supported beam under simple bending: main inertia symmetrically varying with the 4th power of x: resistance modulus varying with the 3rd power of x: combined loads

Circular arch: uniform section: end A: pinned: end B: horiz.guide: uniform load: per unit length of arch: horizontal

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: uniform load: vertical: on girder

Tapered fixed beam under simple bending: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: uniform load

Circular arch: uniform section: end A: pinned: end B: inclined guide: hydrostatic load

Beam under bending: with axial tension: left end supported: right end supported: concentrated moment

Tapered simply supported beam under simple bending: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: distributed load

Beam under simple bending: large deflections: left end fixed: right end guided: concentrated load

Circular arch: uniform section: end A: fixed: end B: pinned: uniform load: per unit length of arch: horizontal

Thin-walled cylindrical shell: Fixed-free: linearly varying radial pressure

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: concentrated moment

Circular arch: uniform section: end A: fixed: end B: vertical guide: uniform temperature gradient: across depth

Circular arch: uniform section: end A: fixed: end B: free: concentrated moment

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: linearly decreasing load

Circular arch: uniform section: end A: fixed: end B: inclined slide: uniform load: per unit horizontal projection: vertical

Tapered fixed beam under simple bending: main inertia symmetrically varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: concentrated load

Annular flat plate: with uniform thickness: simple bending: outer edge guided: inner edge fixed: applied angular displacement

Solid circular flat plate with uniform thickness: pure membrane behaviour: supported & held: distributed load

Circular arch: uniform section: end A: pinned: end B: horiz.guide: concentrated moment

Tapered cantilever under simple bending: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: distributed load

Small deflections of rectangular plates: 2 opposite sides clamped, 2 free: combined loads

Small deflections of triangular plates: equilateral: 3 supported sides: distributed load: linearly varying: along height a

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: concentrated moment

Beam under simple bending: large deflections: left end supported: right end guided: concentrated load

Circular arch: uniform section: end A: fixed: end B: inclined slide: uniform load: per unit length of arch: horizontal

Tapered simply supported beam under simple bending: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: distributed load

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 2nd power of x (n=2): under a single axial compressive load: base supported: top supported

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 4th power of x (n=4): under a single axial compressive load: base fixed: top free

Small deflections of rectangular plates: 1 clamped side, 3 free: distributed load: over a partial rectangular area

Tapered simply supported beam under simple bending: main inertia symmetrically varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: concentrated moment

Circular arch: uniform section: end A: fixed: end B: horiz.slide: concentrated load: vertical

Circular arch: uniform section: end A: fixed: end B: inclined guide: uniform load: per unit length of arch: vertical

Solid circular flat plate: simple bending: simply supported: with uniform thickness: distributed parabolically increasing load

Circular arch: uniform section: end A: pinned: end B: inclined slide: uniform load: radial

Tapered cantilever under simple bending: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: concentrated load

Continuous beam: over 5 spans: in simple bending: distributed load

Circular arch: uniform section: end A: pinned: end B: inclined guide: combined loads

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: point load: horizontal: on girder left half

Solid circular flat plate with uniform thickness: simple bending: on (mono)elastic foundation: fixed edge: center load + uniform load

Beam under simple bending: left end fixed: right end free(cantilever): uniform load

Guided-infinite beam: on elastic foundation: concentrated moment

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge supported: parabolically increasing load

Beam under bending: with held ends: left end fixed: right end fixed: applied angular displacement

Circular arch: uniform section: end A: pinned: end B: horiz.slide: concentrated load: radial

Beam under bending: with held ends: left end fixed: right end supported: uniform load

Circular flat flanges without hubs: loose, welded: to internal pressure: gasket laying inside inner edge of bolt holes: with bolt spacing correction

Small deflections of rectangular plates: 3 supported sides, 1 free: uniform load

Small deflections of rectangular plates: 4 clamped sides: distributed load: linearly varying: along side a: starting at x0

Tapered simply supported beam under simple bending: main inertia symmetrically varying with the 2nd power of x: resistance modulus varying with the 1st power of x: combined loads

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end fixed: combined loads

Beam under bending: with axial compression: left end supported: right end supported: concentrated moment

Thin-walled cylindrical shell: Fixed-fixed: radial load

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge supported: temperature differential across thickness

Beam under bending: with held ends: left end supported: right end guided: concentrated moment

Circular arch: uniform section: end A: fixed: end B: inclined guide: distributed load: radial

Annular flat plate: with uniform thickness: simple bending: outer edge guided: inner edge supported: combined loads

Circular arch: uniform section: end A: pinned: end B: horiz.slide: distributed load: tangential

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: supported: distributed load

Beam under bending: with axial tension: left end fixed: right end fixed: temperature gradient: across depth: linearly varying

Full face flanges with soft ring type gaskets: external pressure

Beam under simple bending: large deflections: left end fixed: right end fixed: distributed load

Circular arch: uniform section: end A: fixed: end B: free: uniform temperature gradient: across depth

Circular arch: uniform section: end A: pinned: end B: pinned: uniform load: per unit length of arch: vertical

Circular arch: uniform section: end A: fixed: end B: inclined guide: uniform load: per unit horizontal projection: vertical

Annular flat plate: with uniform thickness: simple bending: outer edge guided: inner edge supported: applied angular displacement

Circular ring beam: supported at bottom: 2 vertical loads

Solid circular flat plate with uniform thickness: simple bending: on (mono)elastic foundation: guided edge: annular line load + uniform load

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end pinned: point load: on girder

Circular arch: uniform section: end A: fixed: end B: vertical guide: distributed load: tangential

Fixed-infinite beam: on elastic foundation: point load

Fixed-guided beam: on elastic foundation: concentrated moment

Solid circular flat plate: simple bending: simply supported: with linearly increasing thickness: center load

Circular arch: uniform section: end A: fixed: end B: horiz.slide: distributed load: tangential

Circular arch: uniform section: end A: fixed: end B: inclined slide: uniform temperature gradient: across depth

Beam under simple bending: left end supported: right end guided: distributed load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: uniform pressure: on girder left half

Beam under bending+shear: left end supported: right end guided: distributed load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: distributed partial load: linearly varying: horizontal: on left post

Infinite beam: on elastic foundation: concentrated load

Circular arch: uniform section: end A: pinned: end B: pinned: uniform load: per unit vertical projection: horizontal: on left half arch

Circular arch: uniform section: end A: fixed: end B: horiz.slide: uniform load: per unit horizontal projection: vertical

Beam under simple bending: left end fixed: right end supported: distributed load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: uniform pressure: on girder right half

Circular arch: uniform section: end A: fixed: end B: horiz.slide: uniform load: radial

Beam under bending+shear: left end supported: right end guided: combined loads

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end pinned: uniform load: on post

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: point load: horizontal: on girder right half

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 2nd power of x (n=2): under a single axial compressive load: base fixed: top guided

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 3rd power of x (n=3): under a single axial compressive load: base fixed: top guided

Tapered simply supported beam under simple bending: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: concentrated moment

Semi-infinite beam: on elastic foundation: concentrated moment

Thin-walled cylindrical shell: Supported-guided: uniform radial pressure: from 'a' to 'b'

Thin-walled cylindrical shell: Fixed-guided: applied moment

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: uniform load: horizontal: on left post

Beam under bending+shear: left end fixed: right end supported: distributed load

Tapered fixed beam under simple bending: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: concentrated moment

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge free: uniform annular line moment

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: distributed load: tangential

Thin-walled cylindrical shell: Fixed-supported: applied moment

Minimum thickness of: ellipsoidal ends: under internal pressure

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: linearly decreasing load

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end sliding: right end fixed: uniform load: on girder

Tapered simply supported beam under simple bending: main inertia symmetrically varying with the 2nd power of x: resistance modulus varying with the 1st power of x: concentrated load

Beam under bending+shear: left end fixed: right end guided: point load

Beam under bending: with axial tension: left end fixed: right end guided: concentrated load

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: point load: horizontal: on left post

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: distributed partial load: linearly varying: horizontal: on right post

Fixed-free beam: on elastic foundation: concentrated moment

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: distributed load

Circular arch: uniform section: end A: fixed: end B: fixed: uniform temperature change

Small deflections of rectangular plates: 2 simply supported opposite sides and 2 free: distributed load: over a partial rectangular area

Annular flat plate: with uniform thickness: simple bending: outer edge clamped: inner edge supported: uniform load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: distributed partial load: linearly varying: on girder

Annular flat plate: with uniform thickness: simple bending: outer edge clamped: inner edge guided: uniform load

Continuous beam: over 3 spans: in simple bending: concentrated moment

Circular flat flanges without hubs: lap joint: to internal pressure: gasket laying inside inner edge of bolt holes: split ring: along a diameter: with bolt spacing correction

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: concentrated moment

Circular arch: uniform section: end A: fixed: end B: horiz.slide: uniform load: tangential

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: uniform load: tangential

Circular arch: uniform section: end A: pinned: end B: horiz.guide: distributed load: radial

Spheres in contact: with a grooved outer ring: under load: Hertz's theory

Allowable external pressure: of cylindrical shells: circularity within tolerance

Beam under bending+shear: left end supported: right end supported: distributed load

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: supported edge: center load

Circular arch: uniform section: end A: fixed: end B: horiz.slide: uniform load: per unit length of arch: horizontal

Two cylinders in contact under load: axes at right angles: Hertz's theory

Circular arch: uniform section: end A: fixed: end B: fixed: distributed load: vertical: partial

Spheres in contact: with a grooved inner ring: under load: Hertz's theory

Beam under bending: with axial compression: left end fixed: right end free: applied angular displacement

Beam under bending: with axial tension: left end supported: right end supported: temperature gradient: across depth: linearly varying

Circular arch: uniform section: end A: pinned: end B: horiz.guide: uniform load: per unit vertical projection: horizontal

Solid circular flat plate with uniform thickness: large deflections behaviour: supported & held: uniform annular line load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: distributed partial load: linearly varying: horizontal: on right post

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: uniform load: on left post

Small deflections of rectangular plates: 2 simply supported opposite sides and 2 free: concentrated load at center

Rectangular membranes: 3 held sides, 1 free: uniform load

Solid circular flat plate with uniform thickness: simple bending: on (mono)elastic foundation: supported edge: annular line load + uniform load

Beam under simple bending: left end fixed: right end fixed: combined loads

Beam under bending: with axial compression: left end supported: right end guided: applied angular displacement

Solid circular flat plate: simple bending: simply supported: with uniform thickness: combined loads

Large deflections of rectangular plates: 4 simply supported sides: distributed load linearly varying along side a

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: point load: horizontal: on girder left half

Circular arch: uniform section: end A: pinned: end B: horiz.guide: concentrated load: radial

Large deflections of rectangular plates: 4 clamped & held sides: distributed load linearly varying along side a

Circular arch: uniform section: end A: fixed: end B: pinned: distributed load: radial

Beam under bending: with axial compression: left end fixed: right end guided: temperature gradient: across depth: linearly varying

Small deflections of rectangular plates: bending + shear: 4 simply supported sides: distributed load linearly varying along side a: starting at x0

Circular arch: uniform section: end A: pinned: end B: inclined slide: uniform load: per unit vertical projection: horizontal: on left half arch

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end fixed: uniform load: on post

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end sliding: point load: on post

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge free: uniform load

Circular arch: uniform section: end A: pinned: end B: inclined guide: uniform load: per unit horizontal projection: vertical

Beam under simple bending: large deflections: left end fixed: right end supported: distributed load

Small deflections of rectangular plates: 1 clamped side, 2 supported and 1 free: uniform load

Solid circular flat plate: simple bending: simply supported: with linearly increasing thickness: combined loads

Circular arch: uniform section: end A: pinned: end B: pinned: uniform load: radial

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: uniform load: on left post

Small deflections of triangular plates: equilateral: 2 supported sides, 1 free: combined loads

Circular arch: uniform section: end A: pinned: end B: inclined guide: distributed load: radial

Tapered fixed beam under simple bending: main inertia varying symmetrically with the 4th power of x: resistance modulus varying with the 3rd power of x: combined loads

Circular arch: uniform section: end A: fixed: end B: horiz.guide: concentrated load: vertical

Supported-free beam: on elastic foundation: concentrated moment

Beam under simple bending: left end supported: right end supported: combined loads

Solid circular flat plate: simple bending: simply supported: with uniform thickness: uniform line moment

Circular arch: uniform section: end A: fixed: end B: inclined guide: concentrated load: tangential

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge fixed: applied vertical displacement

Circular arch: uniform section: end A: fixed: end B: inclined guide: uniform load: tangential

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: fixed edge: uniform annular line load

Thin-walled cylindrical shell: Fixed-guided: linearly varying radial pressure

Beam under bending: with axial compression: left end fixed: right end guided: combined loads

Beam under bending: with held ends: left end supported: right end guided: distributed load

Circular pipes: supported at bottom: loaded by self weight: directed upwards

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end fixed: point load: on post

Thin-walled cylindrical shell: Supported-free: applied moment

Thin-walled cylindrical shell: Guided-guided: linearly varying radial pressure

Circular arch: uniform section: end A: pinned: end B: pinned: distributed load: tangential

Beam under simple bending: left end fixed: right end guided: distributed load

Beam under bending: with axial tension: left end fixed: right end supported: concentrated moment

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: uniform load: horizontal: on right post

Small deflections of rectangular plates: 2 adjacent supported sides, 2 free: distributed load linearly varying along side a

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: distributed load

Circular arch: uniform section: end A: fixed: end B: free: concentrated load: radial

Small deflections of rectangular plates: 1 clamped side, 3 free: point load: over a partial rectangular area

Annular flat plate: with uniform thickness: simple bending: outer edge free: inner edge fixed: uniform annular line moment

Small deflections of rectangular plates: 4 simply supported sides: concentrated load at center

Solid circular flat plate with uniform thickness: simple bending: on (mono)elastic foundation: fixed edge: annular line load + uniform load

Small deflections of rectangular plates: 3 supported sides, 1 clamped: distributed load: over a partial rectangular area

Circular arch: uniform section: end A: pinned: end B: inclined slide: concentrated moment

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: uniform load: horizontal: on right post

Annular flat plate: with uniform thickness: simple bending: outer edge clamped: inner edge clamped: uniform load

Annular flat plate: with uniform thickness: simple bending: outer edge free: inner edge supported: uniform load

Thin-walled cylindrical shell: Fixed-supported: uniform radial pressure: from 'a' to 'b'

Circular arch: uniform section: end A: fixed: end B: fixed: uniform load: per unit vertical projection: horizontal: on left half arch

Tapered fixed beam under simple bending: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: combined loads

Beam under bending: with axial compression: left end supported: right end supported: applied vertical displacement

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: combined loads

Beam under bending: with held ends: left end fixed: right end supported: concentrated load

Circular arch: uniform section: end A: pinned: end B: inclined guide: concentrated load: radial

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: clamped edge: center load

Circular arch: uniform section: end A: fixed: end B: inclined slide: distributed load: radial

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge free: temperature differential across thickness

Beam under simple bending: left end fixed: right end free: concentrated moment

Beam under bending: with axial tension: left end fixed: right end guided: temperature gradient: across depth: linearly varying

Beam under bending: with held ends: left end fixed: right end supported: concentrated moment

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: combined loads

Circular arch: uniform section: end A: pinned: end B: inclined guide: uniform load: per unit vertical projection: horizontal: on left half arch

Circular arch: uniform section: end A: fixed: end B: horiz.guide: uniform temperature gradient: across depth

Beam under bending+shear: left end supported: right end guided: uniform load

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge fixed: uniform annular line moment

Tapered simply supported beam under simple bending: main inertia symmetrically varying with the 1st power of x: resistance modulus varying with the 1st power of x: linearly decreasing load

Beam under bending+shear: left end fixed: right end guided: distributed load

Circular arch: uniform section: end A: fixed: end B: vertical guide: uniform load: per unit vertical projection: horizontal

Small deflections of rectangular plates: 4 clamped sides: uniform load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: point load: on right post

Circular arch: uniform section: end A: fixed: end B: pinned: concentrated load: vertical

Circular arch: uniform section: end A: fixed: end B: horiz.slide: uniform temperature gradient: across depth

Circular arch: uniform section: end A: fixed: end B: vertical guide: concentrated moment

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: point load: vertical: on girder left half

Thin-walled cylindrical shell: Guided-supported: applied moment

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end fixed: distributed partial load: linearly varying: on post

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 4th power of x (n=4): under a single axial compressive load: base fixed: top supported

Tapered fixed beam under simple bending: main inertia varying symmetrically with the 3rd power of x: resistance modulus varying with the 2nd power of x: uniform load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: point load: on girder

Flat face flanges with metal-to-metal contact outside the bolt circle: analysis of a flange cover assembly (Class 3): integral (Cat.1) flange: hub of constant thickness: no spacer: self-sealing gasket with negligible loads

Circular arch: uniform section: end A: fixed: end B: vertical guide: hydrostatic load

Tapered cantilever under simple bending: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: combined loads

Circular arch: uniform section: end A: fixed: end B: fixed: uniform load: radial

Small deflections of rectangular plates: 2 opposite sides clamped, 2 free: concentrated load

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: distributed partial load: linearly varying: horizontal: on left post

Beam under bending: with axial tension: left end fixed: right end free: uniform load

Beam under bending: with axial compression: left end fixed: right end supported: uniform load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: point load: on right post

Supported-infinite beam: on elastic foundation: concentrated moment

Circular arch: uniform section: end A: fixed: end B: inclined slide: distributed load: tangential

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: combined loads

Circular arch: uniform section: end A: fixed: end B: vertical slide: distributed load: radial

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: distributed partial load: linearly varying: horizontal: on left post

Beam under bending: with axial tension: left end supported: right end guided: uniform load

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge supported: applied vertical displacement

Beam under bending: with axial compression: left end supported: right end supported: applied angular displacement

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: uniform temperature change

Thin-walled cylindrical shell: Guided-fixed: applied moment

Circular arch: uniform section: end A: pinned: end B: horiz.slide: uniform load: per unit length of arch: vertical

Solid circular flat plate: simple bending: clamped: with uniform thickness: uniform line moment

Circular arch: uniform section: end A: fixed: end B: vertical slide: distributed load: tangential

Beam under bending: with axial compression: left end fixed: right end free: distributed load

Circular arch: uniform section: end A: fixed: end B: free: distributed load: vertical: partial

Tapered simply supported beam under simple bending: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: distributed load

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end pinned: distributed partial load: linearly varying: on girder

Small deflections of rectangular plates: 2 adjacent clamped sides, 2 free: combined loads

Continuous beam: over 5 spans: in simple bending: uniform load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: uniform load: vertical: on girder left half

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: guided edge: center load + uniform load

Infinite beam: on elastic foundation: distributed load: linearly varying over 'a'

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end fixed: uniform load: on girder

Beam under bending: with axial compression: left end supported: right end guided: combined loads

Small deflections of rectangular plates: 3 supported sides, 1 free: distributed load linearly varying along side a: starting at x0

Beam under simple bending: large deflections: left end fixed: right end guided: distributed load

Beam under simple bending: left end fixed: right end fixed: distributed load

Thin-walled cylindrical shell: Fixed-free: radial load

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end fixed: point load: on girder

Circular arch: uniform section: end A: fixed: end B: vertical slide: concentrated load: tangential

Fixed-infinite beam: on elastic foundation: distributed load: linearly varying: from 'a' to 'b'

Small deflections of rectangular plates: 1 clamped side, 3 free: distributed load linearly varying along side a: starting at x0

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: distributed partial load: linearly varying: on right post

Beam: simple bending: with held ends: left end supported: right end supported: distributed load

Small deflections of rectangular plates: 2 adjacent clamped sides, 2 supported: combined loads

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 1st power of x (n=1): under a single axial compressive load: base fixed: top guided

Circular arch: uniform section: end A: fixed: end B: vertical slide: concentrated load: horizontal

Beam under bending: with axial tension: left end fixed: right end free: concentrated load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: distributed partial load: linearly varying: on girder

Circular arch: uniform section: end A: fixed: end B: vertical guide: distributed load: vertical: partial

Circular arch: uniform section: end A: pinned: end B: pinned: combined loads

Thin-walled cylindrical shell: Free-fixed: uniform radial pressure: from 'a' to B

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge supported: uniform load

Thin-walled cylindrical shell: Guided-free: applied moment

Circular flat flanges without hubs: lap joint: to internal pressure: gasket laying inside inner edge of bolt holes

Tapered fixed beam under simple bending: main inertia symmetrically varying with the 1st power of x: resistance modulus varying with the 1st power of x: linearly decreasing load

Annular flat plate: with uniform thickness: simple bending: outer edge clamped: inner edge guided: combined loads

Beam under bending: with axial tension: left end fixed: right end guided: applied angular displacement

Tapered fixed beam under simple bending: main inertia symmetrically varying with the 2nd power of x: resistance modulus varying with the 1st power of x: linearly decreasing load

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: fixed: distributed load

Fixed-guided beam: on elastic foundation: point load

Continuous beam: over 4 spans: in simple bending: concentrated moment

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: combined loads

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 3rd power of x (n=3): under a single axial compressive load: base supported: top supported

Beam under simple bending: left end fixed: right end supported: combined loads

Beam under simple bending: large deflections: left end fixed: right end free: distributed load

Large deflections of rectangular plates: 4 simply supported sides: uniform load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: uniform temperature change

Beam under bending: with axial tension: left end fixed: right end fixed: concentrated moment

Circular arch: uniform section: end A: pinned: end B: horiz.guide: concentrated load: vertical

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: distributed partial load: linearly varying: horizontal: on left post

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: uniform load: vertical: on girder right half

Circular pipes: supported at bottom: partially filled with liquid

Circular arch: uniform section: end A: fixed: end B: vertical slide: uniform load: per unit length of arch: vertical

Solid circular flat plate with uniform thickness: large deflections behaviour: simply supported: uniform distributed load

Tapered fixed beam under simple bending: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: combined loads

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: free edge: uniform annular line load

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: distributed partial load: linearly varying: vertical: on girder

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: distributed partial load: linearly varying: on left post

Small deflections of triangular plates: equilateral: 3 supported sides: combined loads

Circular arch: uniform section: end A: pinned: end B: pinned: distributed load: radial

Solid circular flat plate: simple bending: clamped: with uniform thickness: uniform load

Circular arch: uniform section: end A: fixed: end B: vertical slide: uniform load: per unit vertical projection: horizontal

Circular flanges with hub: integral with hub slope 1/3 max: WN or LWN type: to internal pressure: gasket laying inside inner edge of bolt holes: with bolt spacing correction

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: uniform load: vertical: on girder left half

Circular arch: uniform section: end A: fixed: end B: inclined slide: concentrated load: radial

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: uniform load: on girder

Circular ring beam: supported at bottom: loaded by uniform vertical load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: point load: vertical: on girder right half

Circular arch: uniform section: end A: fixed: end B: vertical guide: uniform load: tangential

Small deflections of triangular plates: equilateral: 3 clamped sides: distributed load: linearly varying: along height a

Elastic stability of a beam-column: with two stepped sections: under two axial compressive loads: base supported: top supported

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: uniform load: per unit vertical projection: horizontal: on left half arch

Tapered simply supported beam under simple bending: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: concentrated load

Beam under simple bending: left end fixed: right end supported: applied angular displacement

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 3rd power of x (n=3): under a single axial compressive load: base fixed: top supported

Thin-walled cylindrical shell: Guided-fixed: linearly varying radial pressure

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 1st power of x (n=1): under a single axial compressive load: base fixed: top free

Free-free beam: on elastic foundation: distributed load: linearly varying: from 'a' to 'b'

Beam under bending: with axial compression: left end fixed: right end supported: temperature gradient: across depth: linearly varying

Annular flat plate: with uniform thickness: simple bending: outer edge free: inner edge clamped: combined loads

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: uniform pressure: on girder right half

Minimum thickness of: spherical shells: spherical parts of shells: hemispherical ends: central zone of torispherical ends: spherical knuckles of cones to cylinders: under internal pressure: e/De<=0.16: Calculation based on outer radius

Circular arch: uniform section: end A: pinned: end B: pinned: uniform temperature change

Beam under bending: with held ends: left end supported: right end guided: temperature gradient: across depth: linearly varying

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: point load: horizontal: on right post

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge supported: parabolically increasing load

Circular arch: uniform section: end A: fixed: end B: inclined guide: uniform temperature gradient: across depth

Tapered fixed beam under simple bending: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: combined loads

Beam under simple bending: left end supported: right end supported: concentrated moment

Circular arch: uniform section: end A: pinned: end B: inclined slide: uniform temperature gradient: across depth

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: combined loads

Thin-walled cylindrical shell: Free-free: uniform radial pressure: from 'a' to B

Beam under simple bending: left end fixed: right end fixed: concentrated load

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: uniform load: vertical: on girder

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: point load: horizontal: on left post

Tapered simply supported beam under simple bending: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: concentrated load

Circular arch: uniform section: end A: fixed: end B: inclined guide: concentrated load: horizontal

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: uniform load: horizontal: on right post

Annular flat plate: with uniform thickness: simple bending: outer edge free: inner edge supported: uniform annular line load

Beam under simple bending: left end fixed: right end fixed: temperature gradient: across depth: linearly varying

Circular arch: uniform section: end A: fixed: end B: pinned: uniform load: per unit vertical projection: horizontal

Circular arch: uniform section: end A: pinned: end B: horiz.slide: uniform temperature gradient: across depth

Full faced flanges with soft ring type gaskets: non metallic gaskets not less than 1.5 mm thick

Small deflections of rectangular plates: 2 adjacent clamped sides, 2 free: distributed load: over a partial rectangular area

Circular arch: uniform section: end A: pinned: end B: pinned: uniform load: per unit vertical projection: horizontal

Tapered simply supported beam under simple bending: main inertia symmetrically varying with the 2nd power of x: resistance modulus varying with the 1st power of x: linearly decreasing load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: uniform load: on right post

Circular arch: uniform section: end A: pinned: end B: inclined guide: uniform load: per unit vertical projection: horizontal

Circular arch: uniform section: end A: fixed: end B: inclined slide: hydrostatic load

Small deflections of rectangular plates: 4 simply supported sides: distributed load: linearly varying: along side a

Circular arch: uniform section: end A: fixed: end B: free: concentrated load: vertical

Annular flat plate: with uniform thickness: simple bending: outer edge simply guided: inner edge fixed: uniform annular line load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: point load: horizontal: on right post

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge fixed: applied angular displacement

Small deflections of rectangular plates: 3 clamped sides, 1 free: distributed load: over a partial rectangular area

Small deflections of rectangular plates: 2 adjacent clamped sides, 2 free: distributed load linearly varying along side a

Circular arch: uniform section: end A: pinned: end B: inclined slide: uniform load: per unit length of arch: vertical

Tapered simply supported beam under simple bending: main inertia symmetrically varying with the 2nd power of x: resistance modulus varying with the 1st power of x: uniform load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: uniform pressure: on girder left half

Tapered cantilever under simple bending: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: concentrated moment

Circular arch: uniform section: end A: pinned: end B: inclined slide: distributed load: vertical: partial

Thin-walled cylindrical shell: Free-supported: applied moment

Small deflections of triangular plates: equilateral: 2 clamped sides, 1 free: distributed load: linearly varying: along height a

Tapered fixed beam under simple bending: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: distributed load

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: point load: horizontal: on right post

Beam under bending: with axial tension: left end supported: right end supported: applied vertical displacement

Solid circular flat plate with uniform thickness: large deflections behaviour: clamped & held: uniform annular line load

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end fixed: uniform temperature change

Beam under bending: with axial compression: left end fixed: right end supported: concentrated load

Circular arch: uniform section: end A: pinned: end B: horiz.slide: uniform load: per unit vertical projection: horizontal: on left half arch

Small deflections of rectangular plates: 1 clamped side, 2 supported(adjacent) and 1 free: combined loads

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end pinned: point load: on post

Small deflections of rectangular plates: 2 opposite sides clamped, 2 free: distributed load linearly varying along side a: starting at x0

Continuous beam: over 2 spans: in simple bending: concentrated moment

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: uniform load: per unit length of arch: horizontal

Thin-walled cylindrical shell: Guided-fixed: uniform radial pressure: from 'a' to 'b'

Cylinder in contact in a cylindrical socket under load: Hertz's theory

Circular arch: uniform section: end A: fixed: end B: fixed: concentrated load: tangential

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge guided: temperature differential across thickness

Supported-guided beam: on elastic foundation: distributed load: linearly varying: from 'a' to 'b'

Circular pipes: supported at bottom: combined loads

Beam under bending: with axial tension: left end supported: right end guided: concentrated load

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: supported edge: uniform load

Rectangular membranes: 4 fully held sides: distributed load linearly varying along side a

Beam under bending+shear: left end fixed: right end free: distributed load

Tapered cantilever under simple bending: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: linearly decreasing load

Circular arch: uniform section: end A: pinned: end B: horiz.guide: uniform load: per unit vertical projection: horizontal: on left half arch

Beam under bending+shear: left end fixed: right end fixed: point load

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: point load: vertical: on girder

Beam under simple bending: large deflections: left end fixed: right end supported: concentrated load

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end sliding: distributed partial load: linearly varying: on girder

Minimum thickness of: spherical shells: spherical parts of shells: hemispherical ends: central zone of torispherical ends: spherical knuckles of cones to cylinders: under internal pressure: e/De<=0.16: Calculation based on inner radius

Tapered simply supported beam under simple bending: main inertia symmetrically varying with the 1st power of x: resistance modulus varying with the 1st power of x: combined loads

Solid circular flat plate: simple bending: simply supported: with uniform thickness: center load

Thin-walled cylindrical shell: Supported-fixed: radial load

Small deflections of rectangular plates: 1 clamped side, 2 supported(adjacent) and 1 free: distributed load linearly varying along side a

Circular arch: uniform section: end A: pinned: end B: inclined guide: distributed load: tangential

Circular arch: uniform section: end A: fixed: end B: free: uniform load: tangential

Beam under bending: with axial tension: left end supported: right end guided: concentrated moment

Simply supported beam: on elastic foundation: concentrated moment

Tapered simply supported beam under simple bending: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: concentrated moment

Small deflections of rectangular plates: 2 facing sides clamped, 2 supported: distributed load linearly varying along side a: starting at x0

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: distributed partial load: linearly varying: horizontal: on left post

Circular arch: uniform section: end A: pinned: end B: pinned: concentrated load: horizontal

Circular arch: uniform section: end A: pinned: end B: horiz.slide: distributed load: radial

Small deflections of rectangular plates: 4 simply supported sides: combined loads

Tapered simply supported beam under simple bending: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: uniform load

Beam under bending: with axial tension: left end fixed: right end supported: uniform load

Thin-walled cylindrical shell: Free-fixed: applied moment

Annular flat plate: with uniform thickness: simple bending: outer edge guided: inner edge supported: uniform load

Thin-walled cylindrical shell: Guided-guided: uniform radial pressure: from 'a' to 'b'

Circular arch: uniform section: end A: fixed: end B: free: uniform load: per unit horizontal projection: vertical

Circular arch: uniform section: end A: fixed: end B: inclined guide: concentrated load: vertical

Thin-walled cylindrical shell: Guided-supported: uniform radial pressure: from 'a' to 'b'

Design rules for clamp connections: clamping faces parallel: hub calculated as loose flange

Small deflections of rectangular plates: 2 simply supported opposite sides and 2 free: distributed load linearly varying along side a: starting at x0

Small deflections of rectangular plates: 3 clamped sides, 1 supported: distributed load linearly varying along side a

Guided-guided beam: on elastic foundation: concentrated moment

Circular pipes: supported at bottom: 2 vertical line loads: symmetric

Circular arch: uniform section: end A: fixed: end B: inclined slide: uniform load: radial

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: uniform load: horizontal: on girder

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: concentrated load: radial

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: uniform load: horizontal: on girder left half

Beam under bending: with axial compression: left end supported: right end guided: distributed load

Thin-walled cylindrical shell: Supported-supported: linearly varying radial pressure

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: distributed partial load: linearly varying: on right post

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: uniform load: per unit horizontal projection: vertical

Small deflections of rectangular plates: 3 clamped sides, 1 free: uniform load

Beam under simple bending: left end fixed: right end guided: combined loads

Beam under bending+shear: left end fixed: right end guided: uniform load

Circular arch: uniform section: end A: fixed: end B: fixed: uniform load: tangential

Circular pipes: supported at bottom: 2 radial line loads: symmetric

Thin-walled cylindrical shell: Fixed-supported: radial load

Circular arch: uniform section: end A: fixed: end B: vertical guide: concentrated load: radial

Beam under bending: with axial tension: left end fixed: right end free: temperature gradient: across depth: linearly varying

Tapered fixed beam under simple bending: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: concentrated load

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: guided edge: distributed + uniform load

Circular arch: uniform section: end A: fixed: end B: horiz.guide: uniform load: radial

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: distributed partial load: linearly varying: on girder

Circular arch: uniform section: end A: fixed: end B: free: distributed load: radial

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: point load: horizontal: on right post

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: uniform temperature change

Small deflections of rectangular plates: 4 clamped sides: distributed load: over a partial rectangular area

Circular arch: uniform section: end A: fixed: end B: horiz.guide: uniform load: per unit vertical projection: horizontal

Circular arch: uniform section: end A: fixed: end B: inclined slide: distributed load: vertical: partial

Beam under simple bending: large deflections: left end supported: right end supported: distributed load

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge free: parabolically increasing load

Free-free beam: on elastic foundation: point load

Tapered simply supported beam under simple bending: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: linearly decreasing load

Tapered fixed beam under simple bending: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: uniform load

Small deflections of rectangular plates: 3 clamped sides, 1 free: distributed load linearly varying along side a

Tapered simply supported beam under simple bending: main inertia symmetrically varying with the 4th power of x: resistance modulus varying with the 3rd power of x: uniform load

Annular flat plate: with uniform thickness: simple bending: outer edge simply guided: inner edge supported: uniform annular line load

Thin-walled cylindrical shell: Fixed-free: uniform radial pressure: from 'a' to B

Thin-walled cylindrical shell: Supported-guided: applied moment

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: distributed partial load: linearly varying: horizontal: on left post

Minimum thickness of cylindrical shells under internal pressure: e/De<=0.16: Calculation based on outer diameter

Beam under simple bending: left end fixed: right end guided: temperature gradient: across depth: linearly varying

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: point load: horizontal: on girder right half

Beam under bending: with held ends: left end fixed: right end free: temperature gradient: across depth: linearly varying

Small deflections of rectangular plates: 3 supported sides, 1 clamped: distributed load: linearly varying: along side a

Solid circular flat plate: simple bending: simply supported: with uniform thickness: uniform load

Circular arch: uniform section: end A: fixed: end B: horiz.guide: concentrated moment

Beam under simple bending: large deflections: left end fixed: right end fixed: uniform load

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 2nd power of x (n=2): under a single axial compressive load: base fixed: top fixed

Small deflections of rectangular plates: 3 clamped sides, 1 supported: distributed load: over a partial rectangular area

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: uniform load: on girder

Beam under bending: with held ends: left end fixed: right end guided: concentrated load

Thin-walled cylindrical shell: Free-supported: radial load

Allowable external pressure: of cylindrical shells: circularity outside tolerance

Circular arch: uniform section: end A: fixed: end B: inclined slide: concentrated moment

Beam under simple bending: large deflections: left end fixed: right end supported: uniform load

Annular flat plate: with uniform thickness: simple bending: outer edge guided: inner edge clamped: combined loads

Continuous beam: over 4 spans: in simple bending: point load

Small deflections of rectangular plates: 1 clamped side, 3 free: uniform load

Tapered fixed beam under simple bending: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: uniform load

Beam under bending: with held ends: left end fixed: right end free: applied angular displacement

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 1st power of x (n=1): under a single axial compressive load: base fixed: top supported

Solid circular flat plate with uniform thickness: simple bending: on (mono)elastic foundation: free edge: distributed + uniform load

Circular arch: uniform section: end A: fixed: end B: inclined slide: uniform load: per unit vertical projection: horizontal: on left half arch

Tapered fixed beam under simple bending: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: concentrated load

Tapered cantilever under simple bending: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: uniform load

Circular arch: uniform section: end A: fixed: end B: free: combined loads

Beam under simple bending: left end fixed: right end free: temperature gradient: across depth: linearly varying

Circular ring beam: supported at bottom: 2 horizontal loads

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge fixed: distributed load

Tapered fixed beam under simple bending: main inertia symmetrically varying with the 1st power of x: resistance modulus varying with the 1st power of x: concentrated moment

Small deflections of triangular plates: equilateral: 3 supported sides: uniform load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: distributed partial load: linearly varying: vertical: on girder right half

Circular arch: uniform section: end A: fixed: end B: vertical slide: uniform load: tangential

Beam under bending: with axial tension: left end fixed: right end supported: applied angular displacement

Beam under bending: with axial compression: left end fixed: right end supported: combined loads

Small deflections of rectangular plates: 4 free sides: supported at 4 corners: distributed load linearly varying along side a: starting at x0

Beam under bending: with held ends: left end fixed: right end fixed: concentrated load

Circular flat flanges without hubs: lap joint: to internal pressure: gasket laying inside inner edge of bolt holes: with bolt spacing correction

Circular arch: uniform section: end A: pinned: end B: inclined guide: uniform temperature gradient: across depth

Beam under simple bending: left end supported: right end supported: temperature gradient: across depth: linearly varying

Fixed-fixed beam: on elastic foundation: concentrated moment

Guided-free beam: on elastic foundation: point load

Tapered simply supported beam under simple bending: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: combined loads

Beam under bending: with axial tension: left end fixed: right end fixed: distributed load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: point load: on girder

Circular arch: uniform section: end A: pinned: end B: horiz.slide: concentrated load: tangential

Beam under bending+shear: left end fixed: right end fixed: uniform load

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: uniform temperature change

Circular arch: uniform section: end A: fixed: end B: pinned: concentrated load: radial

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge supported: applied vertical displacement

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: combined loads

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end pinned: uniform temperature change

Tapered fixed beam under simple bending: main inertia symmetrically varying with the 4th power of x: resistance modulus varying with the 3rd power of x: linearly decreasing load

Thin-walled cylindrical shell: Guided-free: linearly varying radial pressure

Thin-walled cylindrical shell: Free-free: radial load

Required thickness of conical shells: under internal pressure: Calculation based on outside diameter

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge guided: uniform annular line load

Beam under simple bending: left end supported: right end guided: combined loads

Beam under simple bending: large deflections: left end supported: right end guided: uniform load

Circular arch: uniform section: end A: fixed: end B: inclined guide: uniform load: per unit vertical projection: horizontal

Thin-walled cylindrical shell: Free-guided: linearly varying radial pressure

Small deflections of rectangular plates: 2 opposite sides clamped, 2 free: uniform load

Small deflections of rectangular plates: 1 clamped side, 2 supported and 1 free: distributed load linearly varying along side a: starting at x0

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: uniform load: horizontal: on girder right half

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: combined loads

Solid circular flat plate with uniform thickness: simple bending: on (mono)elastic foundation: guided edge: center load + uniform load

Circular arch: uniform section: end A: fixed: end B: pinned: uniform load: tangential

Tapered cantilever under simple bending: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: linearly decreasing load

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge supported: distributed load

Beam under bending: with axial tension: left end fixed: right end guided: uniform load

Annular flat plate: with uniform thickness: simple bending: outer edge guided: inner edge clamped: uniform load

Beam under bending: with axial tension: left end fixed: right end fixed: combined loads

Beam under bending: with axial compression: left end supported: right end supported: distributed load

Thin-walled cylindrical shell: Supported-free: radial load

Circular flanges with hub: hub with constant thickness: loose, welded: fig.2-4(3): to internal pressure: gasket laying inside inner edge of bolt holes

Tapered fixed beam under simple bending: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: concentrated moment

Thin-walled cylindrical shell: Free-supported: uniform radial pressure: from 'a' to B

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end pinned: distributed partial load: linearly varying: on post

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: combined loads

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: distributed partial load: linearly varying: vertical: on girder left half

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: hydrostatic load

Small deflections of rectangular plates: 1 clamped side, 2 supported and 1 free: combined loads

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: point load: horizontal: on girder right half

Circular arch: uniform section: end A: pinned: end B: inclined slide: distributed load: tangential

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge free: temperature differential across thickness

Circular arch: uniform section: end A: pinned: end B: horiz.guide: hydrostatic load

Circular arch: uniform section: end A: fixed: end B: vertical guide: uniform load: per unit length of arch: vertical

Circular arch: uniform section: end A: pinned: end B: inclined slide: concentrated load: horizontal

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: linearly decreasing load

Two cylinders in contact under load: parallel axes: Hertz's theory

Beam under bending: with axial compression: left end supported: right end supported: concentrated load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: uniform load: vertical: on girder right half

Annular flat plate: with uniform thickness: simple bending: outer edge free: inner edge supported: uniform annular line moment

Circular arch: uniform section: end A: fixed: end B: free: uniform load: per unit length of arch: vertical

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end sliding: uniform temperature change

Narrow face gasketed flanges: integral method: with hub: WN or LWN type: to internal pressure

Solid circular flat plate with uniform thickness: large deflections behaviour: clamped: uniform distributed load

Small deflections of rectangular plates: bending + shear: 4 simply supported sides: concentrated load

Circular arch: uniform section: end A: fixed: end B: horiz.slide: hydrostatic load

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: supported edge: uniform annular line load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: point load: vertical: on girder right half

Solid circular flat plate: simple bending: simply supported: with linearly decreasing thickness: uniform load

Thin-walled cylindrical shell: Supported-supported: uniform radial pressure: from 'a' to B

Circular arch: uniform section: end A: pinned: end B: pinned: distributed load: vertical: partial

Tapered cantilever under simple bending: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: concentrated moment

Beam under simple bending: left end supported: right end guided: concentrated moment

Tapered simply supported beam under simple bending: main inertia symmetrically varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: linearly decreasing load

Beam under bending: with axial tension: left end supported: right end guided: applied angular displacement

Tapered cantilever under simple bending: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: distributed load

Circular arch: uniform section: end A: fixed: end B: horiz.guide: concentrated load: horizontal

Tapered simply supported beam under simple bending: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: combined loads

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge free: distributed load

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end pinned: uniform load: on girder

Thin-walled cylindrical shell: Fixed-guided: radial load

Small deflections of rectangular plates: 2 adjacent clamped sides, 2 supported: distributed load: over a partial rectangular area

Rectangular membranes: 4 held sides: liquid filled+self weight

Small deflections of rectangular plates: 4 free sides: supported at 4 corners: distributed load linearly varying along side a

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end pinned: combined loads

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: uniform load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: point load: horizontal: on girder right half

Beam under simple bending: left end supported: right end supported: distributed load

Continuous beam: over 2 spans: in simple bending: point load

Annular flat plate: with uniform thickness: simple bending: outer edge clamped: inner edge free: uniform load

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge guided: distributed load

Beam under bending: with axial compression: left end fixed: right end guided: concentrated load

Beam under bending+shear: left end fixed: right end supported: combined loads

Circular arch: uniform section: end A: fixed: end B: free: uniform load: per unit vertical projection: horizontal

Circular arch: uniform section: end A: fixed: end B: horiz.slide: concentrated load: radial

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: distributed partial load: linearly varying: vertical: on girder right half

Circular arch: uniform section: end A: fixed: end B: vertical guide: uniform load: per unit horizontal projection: vertical

Circular arch: uniform section: end A: fixed: end B: fixed: concentrated load: vertical

Small deflections of rectangular plates: 2 facing sides clamped, 2 supported: uniform load

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: combined loads

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge free: applied angular displacement

Thin-walled cylindrical shell: Fixed-free: applied moment

Circular arch: uniform section: end A: pinned: end B: horiz.slide: uniform load: per unit length of arch: horizontal

Circular arch: uniform section: end A: pinned: end B: horiz.guide: uniform temperature change

Annular flat plate: with uniform thickness: simple bending: outer edge free: inner edge clamped: uniform load

Continuous beam: over 5 spans: in simple bending: concentrated moment

Tapered fixed beam under simple bending: main inertia symmetrically varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: concentrated moment

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: linearly decreasing load

Circular pipes: supported at bottom: loaded by self weight: directed downwards

Beam under simple bending: left end supported: right end guided: concentrated load

Beam under bending: with axial tension: left end fixed: right end free: distributed load

Beam under bending: with axial tension: left end fixed: right end supported: temperature gradient: across depth: linearly varying

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end fixed: distributed partial load: linearly varying: on girder

Circular arch: uniform section: end A: fixed: end B: fixed: uniform load: per unit vertical projection: horizontal

Tapered simply supported beam under simple bending: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: distributed load

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge clamped: uniform load

Thin-walled cylindrical shell: Supported-free: uniform radial pressure: from 'a' to 'b'

Beam under bending: with axial tension: left end supported: right end supported: uniform load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: uniform load: horizontal: on girder right half

Beam under bending: with axial compression: left end fixed: right end fixed: applied vertical displacement

Solid circular flat plate with uniform thickness: simple bending: on (mono)elastic foundation: free edge: center load + uniform load

Circular arch: uniform section: end A: pinned: end B: horiz.guide: combined loads

Circular arch: uniform section: end A: fixed: end B: vertical guide: combined loads

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: distributed partial load: linearly varying: horizontal: on right post

Disc springs: stack in series and in parallel: with or without bearing flats

Circular arch: uniform section: end A: fixed: end B: inclined guide: uniform load: radial

Beam under bending: with axial tension: left end fixed: right end free: combined loads

Elastic stability of a beam-column: with two stepped sections: under two axial compressive loads: base fixed: top guided

Junction between the large end of a cone and a cylinder: without a knuckle: cone and cylinder with constant thicknesses: under internal pressure

Beam under simple bending: large deflections: left end fixed: right end fixed: concentrated load

Beam under bending: with held ends: left end fixed: right end guided: distributed load

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: concentrated load

Large deflections of rectangular plates: 4 supported & held sides: uniform load

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: distributed partial load: linearly varying: vertical: on girder

Solid circular flat plate with uniform thickness: simple bending: on (mono)elastic foundation: fixed edge: distributed + uniform load

Beam under simple bending: large deflections: left end supported: right end guided: distributed load

Circular arch: uniform section: end A: pinned: end B: horiz.guide: distributed load: vertical: partial

Tapered cantilever under simple bending: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: concentrated load

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge supported: temperature differential across thickness

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: uniform load: horizontal: on girder

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 4th power of x (n=4): under a single axial compressive load: base supported: top supported

Circular arch: uniform section: end A: pinned: end B: inclined guide: concentrated load: horizontal

Tapered fixed beam under simple bending: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: linearly decreasing load

Circular arch: uniform section: end A: pinned: end B: pinned: concentrated load: tangential

Annular flat plate: with uniform thickness: simple bending: outer edge simply guided: inner edge fixed: temperature differential across thickness

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: point load: horizontal: on left post

Circular arch: uniform section: end A: pinned: end B: horiz.slide: concentrated load: horizontal

Circular arch: uniform section: end A: fixed: end B: inclined guide: uniform load: per unit length of arch: horizontal

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: supported: distributed + uniform load

Thin-walled cylindrical shell: Supported-guided: radial load

Circular arch: uniform section: end A: pinned: end B: horiz.slide: concentrated load: vertical

Thin-walled cylindrical shell: Fixed-supported: uniform radial pressure: from 'a' to B

Circular arch: uniform section: end A: pinned: end B: inclined guide: uniform load: per unit length of arch: vertical

Circular arch: uniform section: end A: pinned: end B: pinned: uniform load: tangential

Tapered simply supported beam under simple bending: main inertia symmetrically varying with the 1st power of x: resistance modulus varying with the 1st power of x: uniform load

Elastic stability of a beam-column: prismatic: under a single axial compressive load: base fixed: top supported

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: uniform load: vertical: on girder

Beam under bending: with held ends: left end supported: right end guided: concentrated load

Beam under bending: with axial compression: left end fixed: right end free: uniform load

Circular arch: uniform section: end A: fixed: end B: inclined slide: uniform temperature change

Beam under bending: with axial tension: left end fixed: right end guided: distributed load

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end pinned: uniform load: on post

Tapered cantilever under simple bending: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: combined loads

Circular arch: uniform section: end A: fixed: end B: pinned: distributed load: tangential

Tapered simply supported beam under simple bending: main inertia symmetrically varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: combined loads

Circular arch: uniform section: end A: fixed: end B: horiz.slide: combined loads

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end fixed: uniform temperature change

Beam under simple bending: left end fixed: right end free: concentrated load

Small deflections of rectangular plates: 2 adjacent supported sides, 2 free: uniform load

Circular arch: uniform section: end A: fixed: end B: vertical guide: concentrated load: vertical

Small deflections of rectangular plates: 4 clamped sides: distributed load: linearly varying: along side a

Small deflections of rectangular plates: 3 supported sides, 1 free: distributed load: linearly varying: along side a

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: uniform load: vertical: on girder

Beam under bending: with held ends: left end fixed: right end free: uniform load

Tapered simply supported beam under simple bending: main inertia symmetrically varying with the 2nd power of x: resistance modulus varying with the 1st power of x: concentrated moment

Tapered cantilever under simple bending: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: distributed load

Solid circular flat plate: simple bending: simply supported: with linearly decreasing thickness: center load

Beam under simple bending: left end fixed: right end supported: uniform load

Flat face flanges with metal-to-metal contact outside the bolt circle: analysis of an identical (Class 1) flange pair: same material: integral (Cat.1) flanges: hub of constant thickness: with spacer: self-sealing gasket with negligible loads

Circular arch: uniform section: end A: fixed: end B: free: uniform temperature change

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: distributed partial load: linearly varying: horizontal: on right post

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end pinned: uniform load: on girder

Beam under simple bending: left end fixed: right end free: distributed load

Beam under simple bending: left end fixed: right end guided: concentrated load

Annular flat plate: with uniform thickness: simple bending: outer edge guided: inner edge supported: parabolically increasing load

Circular arch: uniform section: end A: fixed: end B: pinned: uniform load: radial

Thin-walled cylindrical shell: Free-guided: uniform radial pressure: from 'a' to 'b'

Circular ring beam: supported at bottom: combined loads

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: uniform pressure: on girder right half

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: point load: on right post

Circular arch: uniform section: end A: fixed: end B: vertical slide: uniform temperature change

Tapered fixed beam under simple bending: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: concentrated load

Small deflections of rectangular plates: 2 opposite sides clamped, 2 free: distributed load: over a partial rectangular area

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: uniform temperature gradient: across depth

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: uniform load: horizontal: on left post

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end pinned: point load: on girder

Beam under bending+shear: left end fixed: right end free: uniform load

Solid circular flat plate with uniform thickness: large deflections behaviour: supported & held: uniform distributed load

Thin-walled cylindrical shell: Guided-free: uniform radial pressure: from 'a' to 'b'

Thin-walled cylindrical shell: Supported-fixed: linearly varying radial pressure

Circular arch: uniform section: end A: pinned: end B: inclined slide: uniform load: per unit vertical projection: horizontal

Supported-fixed beam: on elastic foundation: distributed load: linearly varying: from 'a' to 'b'

Thin-walled cylindrical shell: Fixed-fixed: uniform radial pressure: from 'a' to 'b'

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge free: uniform annular line load

Circular arch: uniform section: end A: fixed: end B: inclined slide: concentrated load: vertical

Tapered simply supported beam under simple bending: main inertia symmetrically varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: concentrated load

Circular arch: uniform section: end A: fixed: end B: vertical slide: concentrated load: vertical

Free-free beam: on elastic foundation: concentrated moment

Semiinfinite beam: on elastic foundation: distributed load: linearly varying: from 'a' to 'b'

W.R.C. Bulletin 297-Aug.84,Supplement to WRC Bulletin No. 107: Local Stresses in Cylindrical Shells Due to External Loadings on a Radial Flush Nozzle: Pressure stresses per BS5500 G.2.3.5.2(a): (radial load should not include pressure end load)

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end sliding: uniform load: on girder

Circular arch: uniform section: end A: pinned: end B: horiz.slide: uniform load: per unit horizontal projection: vertical

Tapered fixed beam under simple bending: main inertia varying symmetrically with the 1st power of x: resistance modulus varying with the 1st power of x: combined loads

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: fixed edge: uniform load

Small deflections of rectangular plates: 1 clamped side, 2 supported(adjacent) and 1 free: uniform load

Thin-walled cylindrical shell: Supported-fixed: applied moment

Beam under simple bending: left end supported: right end supported: applied vertical displacement

Circular arch: uniform section: end A: fixed: end B: inclined slide: combined loads

Circular arch: uniform section: end A: fixed: end B: fixed: distributed load: radial

Small deflections of rectangular plates: bending + shear: 4 simply supported sides: distributed load: over a partial rectangular area

Continuous beam: over 3 spans: in simple bending: distributed load

Annular flat plate: with uniform thickness: simple bending: outer edge free: inner edge supported: applied angular displacement

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: combined loads

Thin-walled cylindrical shell: Fixed-fixed: uniform radial pressure: from 'a' to B

Small deflections of rectangular plates: 2 simply supported opposite sides and 2 free: combined loads

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: point load: vertical: on girder left half

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: distributed partial load: linearly varying: horizontal: on right post

Circular arch: uniform section: end A: fixed: end B: fixed: uniform temperature gradient: across depth

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: fixed edge: center load + uniform load

Circular arch: uniform section: end A: fixed: end B: horiz.slide: uniform load: per unit length of arch: vertical

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: uniform load: on right post

Tapered fixed beam under simple bending: main inertia symmetrically varying with the 2nd power of x: resistance modulus varying with the 1st power of x: concentrated load

Sphere in contact with a flat plate under load: Hertz's theory

Circular arch: uniform section: end A: fixed: end B: horiz.guide: uniform load: per unit vertical projection: horizontal: on left half arch

Small deflections of rectangular plates: 3 supported sides, 1 clamped: uniform load

Beam under bending: with held ends: left end fixed: right end free: concentrated moment

Circular arch: uniform section: end A: fixed: end B: free: uniform load: per unit length of arch: horizontal

Beam under bending: with axial compression: left end fixed: right end fixed: concentrated moment

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: distributed load: vertical: partial

Small deflections of rectangular plates: 2 adjacent clamped sides, 2 supported: uniform load

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end fixed: distributed partial load: linearly varying: on girder

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge free: uniform annular line moment

Thin-walled cylindrical shell: Free-free: applied moment

Tapered fixed beam under simple bending: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: distributed load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: uniform temperature change

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge fixed: applied vertical displacement

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: uniform load: horizontal: on right post

Beam under bending: with axial compression: left end fixed: right end free: temperature gradient: across depth: linearly varying

Tapered fixed beam under simple bending: main inertia symmetrically varying with the 4th power of x: resistance modulus varying with the 3rd power of x: concentrated moment

Small deflections of rectangular plates: 4 simply supported sides: distributed load: linearly varying: along side a: starting at x0

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: free edge: distributed load

Circular arch: uniform section: end A: fixed: end B: horiz.guide: uniform load: per unit length of arch: vertical

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: fixed edge: annular line load + uniform load

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge guided: uniform annular line moment

Beam under bending: with axial compression: left end fixed: right end guided: uniform load

Small deflections of rectangular plates: 2 simply supported opposite sides and 2 free: distributed load linearly varying along side a

Small deflections of rectangular plates: 4 free sides: supported at 4 corners: distributed load: over a partial rectangular area

Circular arch: uniform section: end A: fixed: end B: inclined guide: concentrated moment

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: point load: vertical: on girder

Beam under bending: with held ends: left end supported: right end supported: temperature gradient: across depth: linearly varying

Fixed-fixed beam: on elastic foundation: point load

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: uniform load: horizontal: on left post

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: point load: horizontal: on left post

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: point load: on left post

Tapered simply supported beam under simple bending: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: linearly decreasing load

Large deflections of rectangular plates: 4 free sides: supported at 4 (sliding) corners: uniform load

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge guided: applied angular displacement

Small deflections of rectangular plates: 4 clamped sides: concentrated load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: distributed partial load: linearly varying: on left post

Solid circular flat plate with uniform thickness: pure membrane behaviour: simply supported: uniform annular line load

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: distributed partial load: linearly varying: horizontal: on right post

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: guided edge: annular line load + uniform load

Tapered cantilever under simple bending: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: uniform load

Circular arch: uniform section: end A: pinned: end B: inclined slide: concentrated load: tangential

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: uniform load

Circular arch: uniform section: end A: fixed: end B: pinned: concentrated moment

Beam under bending+shear: left end supported: right end supported: point load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: distributed partial load: linearly varying: on girder

Circular arch: uniform section: end A: fixed: end B: horiz.guide: distributed load: tangential

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge fixed: applied angular displacement

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: uniform load: vertical: on girder right half

Thin-walled cylindrical shell: Fixed-guided: uniform radial pressure: from 'a' to B

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge fixed: distributed load

Circular arch: uniform section: end A: fixed: end B: inclined slide: uniform load: tangential

Tapered simply supported beam under simple bending: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: concentrated load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: point load: on left post

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge supported: applied angular displacement

Beam under bending: with axial compression: left end fixed: right end free: concentrated load

Thin-walled cylindrical shell: Free-free: linearly varying radial pressure

Tapered fixed beam under simple bending: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: concentrated load

Beam under bending: with held ends: left end fixed: right end guided: applied angular displacement

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge supported: uniform annular line load

Supported-free beam: on elastic foundation: concentrated load

Fixed-guided beam: on elastic foundation: distributed load: linearly varying: from 'a' to 'b'

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: uniform temperature change

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end fixed: point load: on girder

Beam under simple bending: left end fixed: right end guided: uniform load

Beam under simple bending: left end fixed: right end supported: concentrated moment

Tapered fixed beam under simple bending: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: concentrated moment

Circular arch: uniform section: end A: fixed: end B: horiz.guide: uniform temperature change

Thin-walled cylindrical shell: Guided-supported: linearly varying radial pressure

Beam under bending: with held ends: left end fixed: right end supported: temperature gradient: across depth: linearly varying

Small deflections of rectangular plates: 3 clamped sides, 1 free: combined loads

Tapered cantilever under simple bending: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: concentrated moment

Small deflections of rectangular plates: 3 supported sides, 1 clamped: distributed load: linearly varying: along side a: starting at x0

Circular arch: uniform section: end A: fixed: end B: fixed: uniform load: per unit horizontal projection: vertical

Beam under bending: with axial tension: left end fixed: right end guided: concentrated moment

Circular arch: uniform section: end A: fixed: end B: vertical slide: uniform load: per unit horizontal projection: vertical

Circular arch: uniform section: end A: fixed: end B: inclined guide: hydrostatic load

Circular arch: uniform section: end A: fixed: end B: vertical guide: uniform load: per unit vertical projection: horizontal: on left half arch

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: uniform pressure: on girder right half

Tapered simply supported beam under simple bending: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: concentrated moment

Solid circular flat plate with uniform thickness: pure membrane behaviour: supported & held: uniform annular line load

Circular arch: uniform section: end A: pinned: end B: inclined guide: uniform load: tangential

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: distributed partial load: linearly varying: vertical: on girder

Beam under bending: with axial tension: left end fixed: right end supported: concentrated load

Tapered cantilever under simple bending: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: combined loads

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: combined loads

Annular flat plate: with uniform thickness: simple bending: outer edge clamped: inner edge free: combined loads

Beam under bending: with axial tension: left end supported: right end supported: concentrated load

Beam under bending: with held ends: left end supported: right end guided: uniform load

Annular flat plate: with uniform thickness: simple bending: outer edge free: inner edge fixed: uniform annular line load

Thin-walled cylindrical shell: Supported-supported: radial load

Circular flat flanges without hubs: lap joint: to internal pressure: gasket laying inside inner edge of bolt holes: split ring: along a diameter

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: uniform temperature change

Circular arch: uniform section: end A: fixed: end B: horiz.slide: uniform temperature change

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: uniform load: radial

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 2nd power of x (n=2): under a single axial compressive load: base fixed: top free

Continuous beam: over 3 spans: in simple bending: combined loads

Tapered fixed beam under simple bending: main inertia symmetrically varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: linearly decreasing load

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 4th power of x (n=4): under a single axial compressive load: base fixed: top fixed

Annular flat plate: with uniform thickness: simple bending: outer edge guided: inner edge fixed: parabolically increasing load

Circular arch: uniform section: end A: fixed: end B: pinned: uniform temperature gradient: across depth

Thin-walled cylindrical shell: Supported-fixed: uniform radial pressure: from 'a' to 'b'

Tapered simply supported beam under simple bending: main inertia symmetrically varying with the 1st power of x: resistance modulus varying with the 1st power of x: concentrated load

Guided-free beam: on elastic foundation: distributed load: linearly varying: from 'a' to 'b'

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: point load: horizontal: on left post

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: uniform load: vertical: on girder

Tapered fixed beam under simple bending: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: uniform load

Circular arch: uniform section: end A: fixed: end B: vertical guide: uniform temperature change

Beam under bending: with axial tension: left end fixed: right end fixed: applied angular displacement

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: distributed partial load: linearly varying: on right post

Beam under bending: with held ends: left end fixed: right end supported: distributed load

W.R.C. Bulletin 297-Aug.84,Supplement to WRC Bulletin No. 107: Local Stresses in Cylindrical Shells Due to External Loadings on a Radial Flush Nozzle: Loads specified at nozzle/wall intersection

Small deflections of rectangular plates: 2 opposite sides clamped, 2 free: concentrated load at center

Continuous beam: over 4 spans: in simple bending: combined loads

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end pinned: point load: on post

Beam under bending: with axial compression: left end supported: right end supported: temperature gradient: across depth: linearly varying

Circular expansion joints: single: unreinforced bellows: without collar: to internal pressure: zero corrosion allowance: cyclic movement due to thermal expansion

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: distributed partial load: linearly varying: horizontal: on right post

Continuous beam: over 5 spans: in simple bending: point load

Solid circular flat plate: simple bending: clamped: with uniform thickness: center load

Circular arch: uniform section: end A: fixed: end B: vertical slide: concentrated load: radial

Tapered cantilever under simple bending: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: uniform load

Tapered cantilever under simple bending: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: concentrated moment

Annular flat plate: with uniform thickness: simple bending: outer edge clamped: inner edge supported: combined loads

Solid circular flat plate: simple bending: simply supported: with linearly decreasing thickness: combined loads

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: concentrated load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: uniform load: horizontal: on left post

Disc springs: single: with or without bearing flats

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge supported: applied angular displacement

Thin-walled cylindrical shell: Supported-free: linearly varying radial pressure

Circular arch: uniform section: end A: pinned: end B: horiz.slide: hydrostatic load

Annular flat plate: with uniform thickness: simple bending: outer edge free: inner edge fixed: applied angular displacement

Circular arch: uniform section: end A: pinned: end B: horiz.slide: combined loads

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: fixed: distributed + uniform load

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge free: parabolically increasing load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: uniform load: on right post

Beam under bending: with axial tension: left end supported: right end supported: applied angular displacement

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: uniform load: on right post

Tapered simply supported beam under simple bending: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: combined loads

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: concentrated load: vertical

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: distributed partial load: linearly varying: vertical: on girder right half

Spheres in contact with a cylindrical socket under load: Hertz's theory

Small deflections of rectangular plates: bending + shear: 4 simply supported sides: distributed load linearly varying along side a

Beam under bending: with axial compression: left end fixed: right end free: combined loads

Beam under bending: with axial compression: left end fixed: right end fixed: distributed load

Beam under bending+shear: left end supported: right end guided: point load

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: point load: horizontal: on girder

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: uniform load: on girder

Guided-guided beam: on elastic foundation: concentrated load

Small deflections of rectangular plates: 1 clamped side, 2 supported(adjacent) and 1 free: distributed load linearly varying along side a: starting at x0

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: point load: horizontal: on girder

Large deflections of rectangular plates: 4 supported & held sides: distributed load linearly varying along side a

Beam under bending: with held ends: left end fixed: right end fixed: applied vertical displacement

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: uniform temperature change

Guided-infinite beam: on elastic foundation: point load

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: uniform load: vertical: on girder

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: point load: horizontal: on girder left half

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: free edge: annular line load + uniform load

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge guided: uniform annular line moment

Small deflections of rectangular plates: 3 supported sides, 1 free: distributed load: over a partial rectangular area

Beam under bending+shear: left end fixed: right end guided: combined loads

Large deflections of rectangular plates: 4 simply supported sides: distributed load linearly varying along side a: starting at x0

Circular arch: uniform section: end A: fixed: end B: horiz.guide: hydrostatic load

Annular flat plate: with uniform thickness: simple bending: outer edge simply guided: inner edge supported: temperature differential across thickness

Elastic stability of a beam-column: prismatic: under a single axial compressive load: base fixed: top free

Solid circular flat plate: simple bending: simply supported: with linearly increasing thickness: uniform load

Thin-walled cylindrical shell: Guided-guided: applied moment

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: point load: vertical: on girder left half

Fixed-free beam: on elastic foundation: distributed load: linearly varying: from 'a' to 'b'

Minimum thickness of: torispherical ends: under internal pressure

Beam under bending: with axial compression: left end fixed: right end supported: applied vertical displacement

Beam under bending: with held ends: left end fixed: right end free: distributed load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: point load: horizontal: on left post

Solid circular flat plate with uniform thickness: large deflections behaviour: clamped edge: uniform annular line load

Circular arch: uniform section: end A: pinned: end B: inclined slide: uniform load: tangential

Solid circular flat plate: simple bending: simply supported: with uniform thickness: distributed load

Beam under bending: with held ends: left end supported: right end supported: concentrated moment

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge fixed: uniform annular line moment

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge free: distributed load

Beam under bending: with axial compression: left end fixed: right end fixed: uniform load

Beam under bending: with axial compression: left end fixed: right end guided: applied angular displacement

Circular arch: uniform section: end A: fixed: end B: inclined guide: concentrated load: radial

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: uniform load: horizontal: on girder

Circular arch: uniform section: end A: fixed: end B: horiz.slide: uniform load: per unit vertical projection: horizontal: on left half arch

Small deflections of rectangular plates: 4 simply supported sides: concentrated load

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: free edge: center load

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: supported edge: center load + uniform load

Tapered fixed beam under simple bending: main inertia varying symmetrically with the 2nd power of x: resistance modulus varying with the 1st power of x: combined loads

Circular arch: uniform section: end A: pinned: end B: horiz.guide: uniform load: radial

Beam under simple bending: left end fixed: right end fixed: applied vertical displacement

Continuous beam: over 2 spans: in simple bending: combined loads

Small deflections of rectangular plates: 2 adjacent supported sides, 2 free: combined loads

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge guided: applied angular displacement

Continuous beam: over 5 spans: in simple bending: combined loads

Circular arch: uniform section: end A: fixed: end B: horiz.guide: distributed load: vertical: partial

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: uniform load: horizontal: on girder right half

Large deflections of rectangular plates: 4 supported & fully held sides: uniform load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: uniform load: horizontal: on girder right half

Semiinfinite beam: on elastic foundation: point load

Beam under bending+shear: left end supported: right end supported: uniform load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: distributed partial load: linearly varying: on right post

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end sliding: point load: on girder

Small deflections of rectangular plates: 2 simply supported opposite sides and 2 free: concentrated load

Circular arch: uniform section: end A: fixed: end B: pinned: distributed load: vertical: partial

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: guided edge: center load

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end sliding: right end fixed: point load: on girder

Beam under bending+shear: left end fixed: right end free: point load

Tapered simply supported beam under simple bending: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: linearly decreasing load

Circular arch: uniform section: end A: pinned: end B: inclined slide: uniform temperature change

Circular arch: uniform section: end A: fixed: end B: horiz.slide: distributed load: vertical: partial

Circular arch: uniform section: end A: fixed: end B: horiz.slide: distributed load: radial

Small deflections of rectangular plates: 2 adjacent supported sides, 2 free: distributed load: over a partial rectangular area

Circular arch: uniform section: end A: fixed: end B: vertical slide: combined loads

Beam under bending: with axial tension: left end fixed: right end supported: combined loads

Solid circular flat plate with uniform thickness: simple bending: on (mono)elastic foundation: supported edge: distributed + uniform load

Beam under bending+shear: left end fixed: right end supported: uniform load

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge supported: combined loads

Small deflections of triangular plates: equilateral: 2 supported sides, 1 free: distributed load: linearly varying: along height a

Solid circular flat plate: simple bending: simply supported: with uniform thickness: uniform annular line load

Circular arch: uniform section: end A: fixed: end B: pinned: concentrated load: horizontal

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: point load: horizontal: on girder

Small deflections of rectangular plates: bending + shear: 4 simply supported sides: uniform load

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 3rd power of x (n=3): under a single axial compressive load: base fixed: top fixed

Small deflections of rectangular plates: 4 free sides: supported at 4 corners: combined loads

Circular arch: uniform section: end A: pinned: end B: horiz.slide: concentrated moment

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge supported: uniform annular line moment

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: distributed partial load: linearly varying: vertical: on girder left half

Design rules for clamp connections: clamping faces parallel

Circular arch: uniform section: end A: fixed: end B: pinned: uniform load: per unit vertical projection: horizontal: on left half arch

Circular arch: uniform section: end A: pinned: end B: horiz.guide: uniform load: tangential

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end pinned: combined loads

Circular arch: uniform section: end A: pinned: end B: horiz.slide: uniform temperature change

Beam under bending: with axial tension: left end fixed: right end supported: applied vertical displacement

Thickness of shells and tubes: under external pressure

Small deflections of triangular plates: equilateral: 3 clamped sides: combined loads

Circular arch: uniform section: end A: fixed: end B: inclined guide: combined loads

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end sliding: right end fixed: uniform load: on post

Tapered simply supported beam under simple bending: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: concentrated moment

Thin-walled cylindrical shell: Guided-guided: radial load

Beam under bending: with axial compression: left end supported: right end guided: uniform load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: point load: vertical: on girder right half

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: distributed partial load: linearly varying: vertical: on girder right half

Simply supported beam: on elastic foundation: distributed load: linearly varying: from 'a' to 'b'

Two spheres in contact under load: Hertz's theory

Circular arch: uniform section: end A: pinned: end B: pinned: uniform load: per unit length of arch: horizontal

Beam under simple bending: large deflections: left end supported: right end supported: uniform load

Large deflections of rectangular plates: 4 clamped & held sides: uniform load

Beam under bending: with axial compression: left end supported: right end supported: combined loads

Beam under bending: with axial compression: left end fixed: right end supported: distributed load

Small deflections of triangular plates: equilateral: 2 clamped sides, 1 free: uniform load

Circular arch: uniform section: end A: fixed: end B: pinned: concentrated load: tangential

Circular arch: uniform section: end A: fixed: end B: free: uniform load: per unit vertical projection: horizontal: on left half arch

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: distributed partial load: linearly varying: vertical: on girder

Annular flat plate: with uniform thickness: simple bending: outer edge free: inner edge supported: distributed load

Beam under simple bending: left end supported: right end guided: applied angular displacement

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end pinned: distributed partial load: linearly varying: on girder

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: uniform load: horizontal: on girder left half

Beam under bending: with axial tension: left end supported: right end supported: combined loads

Small deflections of triangular plates: equilateral: 2 supported sides, 1 free: uniform load

Circular arch: uniform section: end A: fixed: end B: horiz.slide: concentrated moment

Circular arch: uniform section: end A: fixed: end B: vertical slide: concentrated moment

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: free edge: distributed + uniform load

Annular flat plate: with uniform thickness: simple bending: outer edge guided: inner edge fixed: uniform annular line moment

Circular arch: uniform section: end A: fixed: end B: horiz.guide: concentrated load: tangential

Circular arch: uniform section: end A: fixed: end B: horiz.slide: concentrated load: tangential

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: distributed partial load: linearly varying: horizontal: on right post

Full face flanges: with soft ring type gaskets: to internal pressure

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: concentrated load: horizontal

Thin-walled cylindrical shell: Free-guided: applied moment

Tapered simply supported beam under simple bending: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: concentrated load

Beam under simple bending: left end fixed: right end fixed: applied angular displacement

Beam under simple bending: left end fixed: right end fixed: uniform load

Tapered simply supported beam under simple bending: main inertia symmetrically varying with the 4th power of x: resistance modulus varying with the 3rd power of x: linearly decreasing load

Tapered simply supported beam under simple bending: main inertia symmetrically varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: uniform load

Supported-guided beam: on elastic foundation: concentrated moment

Circular arch: uniform section: end A: pinned: end B: inclined slide: hydrostatic load

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: uniform temperature change

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end sliding: distributed partial load: linearly varying: on post

Circular arch: uniform section: end A: fixed: end B: horiz.slide: uniform load: per unit vertical projection: horizontal

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end fixed: combined loads

Cylinder in contact on a flat plate under load: Hertz's theory

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: uniform load

Circular arch: uniform section: end A: pinned: end B: pinned: concentrated load: vertical

Continuous beam: over 2 spans: in simple bending: distributed load

Small deflections of rectangular plates: 2 opposite sides clamped, 2 free: distributed load linearly varying along side a

Beam under bending: with axial compression: left end supported: right end guided: concentrated load

Thin-walled cylindrical shell: Guided-guided: uniform radial pressure: from 'a' to B

Rectangular membranes: 4 fully held sides: uniform load

Small deflections of rectangular plates: 4 free sides: supported at 4 corners: uniform load

Tapered fixed beam under simple bending: main inertia varying symmetrically with the 3rd power of x: resistance modulus varying with the 2nd power of x: combined loads

Beam under simple bending: large deflections: left end supported: right end supported: concentrated load

Circular arch: uniform section: end A: pinned: end B: inclined guide: concentrated load: vertical

Small deflections of rectangular plates: 3 clamped sides, 1 supported: uniform load

Circular arch: uniform section: end A: fixed: end B: vertical guide: concentrated load: tangential

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge guided: combined loads

Beam under bending+shear: left end fixed: right end fixed: combined loads

Thin-walled cylindrical shell: Free-free: uniform radial pressure: from 'a' to 'b'

Circular arch: uniform section: end A: pinned: end B: pinned: uniform temperature gradient: across depth

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge supported: uniform annular line moment

Beam under simple bending: large deflections: left end fixed: right end free: concentrated load

Annular flat plate: with uniform thickness: simple bending: outer edge free: inner edge supported: parabolically increasing load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: uniform temperature change

Beam under bending: with axial tension: left end supported: right end guided: distributed load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: uniform load: horizontal: on left post

Annular flat plate: with uniform thickness: simple bending: outer edge guided: inner edge supported: distributed load

Supported-infinite beam: on elastic foundation: concentrated load

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge free: applied angular displacement

Circular arch: uniform section: end A: fixed: end B: fixed: concentrated moment

Thin-walled cylindrical shell: Guided-supported: uniform radial pressure: from 'a' to B

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge fixed: parabolically increasing load

Thin-walled cylindrical shell: Fixed-supported: linearly varying radial pressure

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge guided: uniform load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: distributed partial load: linearly varying: vertical: on girder left half

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: uniform load: horizontal: on right post

Small deflections of rectangular plates: 3 supported sides, 1 free: combined loads

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: combined loads

Circular arch: uniform section: end A: fixed: end B: fixed: distributed load: tangential

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: uniform pressure: on girder left half

Thin-walled cylindrical shell: Supported-guided: uniform radial pressure: from 'a' to B

Thin-walled cylindrical shell: Guided-fixed: radial load

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: guided edge: distributed load

Circular arch: uniform section: end A: pinned: end B: inclined slide: uniform load: per unit length of arch: horizontal

Beam under bending: with axial tension: left end fixed: right end fixed: uniform load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: distributed partial load: linearly varying: on left post

Small deflections of rectangular plates: 2 facing sides clamped, 2 supported: distributed load: over a partial rectangular area

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: point load: on girder

Fixed-free beam: on elastic foundation: point load

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end fixed: uniform load: on post

Beam under bending: with axial tension: left end fixed: right end free: concentrated moment

Tapered fixed beam under simple bending: main inertia varying symmetrically with the 1st power of x: resistance modulus varying with the 1st power of x: uniform load

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: concentrated load

Flat face flanges with metal-to-metal contact outside the bolt circle: analysis of an identical (Class 1) flange pair: same material: integral (Cat.1) flanges: hub of constant thickness: no spacer: self-sealing gasket with negligible loads

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge guided: distributed load

Small deflections of rectangular plates: 1 clamped side, 3 free: distributed load linearly varying along side a

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge supported: distributed load

Beam under bending: with held ends: left end fixed: right end fixed: uniform load

Circular arch: uniform section: end A: fixed: end B: vertical slide: uniform load: radial

Beam under bending: with axial compression: left end fixed: right end guided: concentrated moment

Beam under bending: with axial tension: left end fixed: right end supported: distributed load

Infinite beam: on elastic foundation: concentrated moment

Small deflections of rectangular plates: 2 adjacent supported sides, 2 free: point load

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: point load: vertical: on girder

Thin-walled cylindrical shell: Free-fixed: uniform radial pressure: from 'a' to 'b'

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: uniform load: vertical: on girder

Fixed-infinite beam: on elastic foundation: concentrated moment

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge guided: temperature differential across thickness

Beam: simple bending: with held ends: left end supported: right end supported: uniform load

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 3rd power of x (n=3): under a single axial compressive load: base fixed: top free

Beam under simple bending: left end fixed: right end supported: applied vertical displacement

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end fixed: point load: on post

Small deflections of rectangular plates: 1 clamped side, 2 supported and 1 free: distributed load: over a partial rectangular area

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: distributed load

Tapered simply supported beam under simple bending: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: uniform load

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end fixed: uniform load: on girder

Circular pipes: supported at bottom: filled with liquid

Annular flat plate: with uniform thickness: simple bending: outer edge simply fixed: inner edge fixed: uniform annular line load

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: concentrated moment

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: uniform load: horizontal: on girder left half

Circular arch: uniform section: end A: fixed: end B: horiz.guide: distributed load: radial

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: uniform load: vertical: on girder left half

Simply supported beam: on elastic foundation: point load

Beam under bending: with axial tension: left end fixed: right end guided: combined loads

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: point load: on girder

Minimum thickness of cylindrical shells under internal pressure: e/De<=0.16: Calculation based on inner diameter

Circular arch: uniform section: end A: fixed: end B: inclined slide: concentrated load: horizontal

Beam under bending: with axial tension: left end fixed: right end fixed: concentrated load

Tapered cantilever under simple bending: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: distributed load

Beam under bending: with axial compression: left end supported: right end supported: uniform load

Elastic stability of a beam-column: with two stepped sections: under two axial compressive loads: base fixed: top free

Beam under simple bending: left end fixed: right end supported: temperature gradient: across depth: linearly varying

Circular flat flanges without hubs: loose, welded: to internal pressure: gasket laying inside inner edge of bolt holes

Solid circular flat plate with uniform thickness: large deflections behaviour: simply supported: distributed load

Annular flat plate: with uniform thickness: simple bending: outer edge free: inner edge fixed: parabolically increasing load

Circular arch: uniform section: end A: fixed: end B: inclined guide: uniform temperature change

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: uniform load: vertical: on girder

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: distributed partial load: linearly varying: on girder

Small deflections of rectangular plates: 3 clamped sides, 1 supported: distributed load linearly varying along side a: starting at x0

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge fixed: uniform annular line load

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: distributed partial load: linearly varying: horizontal: on left post

Thin-walled cylindrical shell: Free-supported: linearly varying radial pressure

Thin-walled cylindrical shell: Free-supported: uniform radial pressure: from 'a' to 'b'

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: point load: vertical: on girder left half

Tapered simply supported beam under simple bending: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: uniform load

Circular arch: uniform section: end A: pinned: end B: horiz.guide: concentrated load: tangential

Large deflections of rectangular plates: 4 supported & held sides: distributed load linearly varying along side a: starting at x0

Thin-walled cylindrical shell: Guided-free: uniform radial pressure: from 'a' to B

Circular ring beam: supported at bottom: load at top

Large deflections of rectangular plates: 4 clamped & held sides: distributed load linearly varying along side a: starting at x0

Supported-free beam: on elastic foundation: distributed load: linearly varying: from 'a' to 'b'

Circular flanges with hub: hub with constant thickness: loose, welded: fig.2-4(3): to internal pressure: gasket laying inside inner edge of bolt holes: with bolt spacing correction

Circular arch: uniform section: end A: fixed: end B: vertical slide: hydrostatic load

Circular arch: uniform section: end A: fixed: end B: free: concentrated load: tangential

Circular arch: uniform section: end A: fixed: end B: fixed: hydrostatic load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: uniform temperature change

Tapered simply supported beam under simple bending: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: combined loads

Solid circular flat plate: simple bending: clamped: with uniform thickness: distributed load

Tapered cantilever under simple bending: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: linearly decreasing load

Beam under bending: with axial compression: left end fixed: right end supported: concentrated moment

Circular arch: uniform section: end A: fixed: end B: inclined guide: distributed load: tangential

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: free edge: center load + uniform load

Circular ring beam: supported at bottom: 2 tangential loads

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: uniform load: horizontal: on girder left half

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: point load: horizontal: on left post

Circular arch: uniform section: end A: fixed: end B: free: distributed load: tangential

Solid circular flat plate with uniform thickness: large deflections behaviour: clamped & held: uniform distributed load

Elastic stability of a beam-column: with two stepped sections: under two axial compressive loads: base fixed: top supported

Circular arch: uniform section: end A: fixed: end B: inclined guide: uniform load: per unit vertical projection: horizontal: on left half arch

Circular arch: uniform section: end A: pinned: end B: inclined slide: concentrated load: vertical

Beam under simple bending: left end fixed: right end fixed: concentrated moment

Supported-infinite beam: on elastic foundation: distributed load: linearly varying: from 'a' to 'b'

Beam under bending: with held ends: left end supported: right end guided: applied angular displacement

Guided-free beam: on elastic foundation: concentrated moment

Circular arch: uniform section: end A: pinned: end B: horiz.guide: uniform load: per unit length of arch: vertical

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: uniform load: per unit length of arch: vertical

Small deflections of rectangular plates: 3 clamped sides, 1 supported: combined loads

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end pinned: distributed partial load: linearly varying: on post

Small deflections of rectangular plates: 2 adjacent clamped sides, 2 free: distributed load linearly varying along side a: starting at x0

Thin-walled cylindrical shell: Guided-free: radial load

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: point load: horizontal: on right post

Beam under bending+shear: left end fixed: right end fixed: distributed load

Continuous beam: over 2 spans: in simple bending: uniform load

Circular arch: uniform section: end A: pinned: end B: inclined guide: distributed load: vertical: partial

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: point load: horizontal: on girder left half

Circular ring beam: supported at bottom: 2 radial loads

Beam under simple bending: large deflections: left end fixed: right end free: uniform load

Circular arch: uniform section: end A: fixed: end B: vertical slide: uniform load: per unit length of arch: horizontal

Circular arch: uniform section: end A: fixed: end B: vertical guide: uniform load: per unit length of arch: horizontal

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end sliding: combined loads

Continuous beam: over 3 spans: in simple bending: uniform load

Circular arch: uniform section: end A: fixed: end B: pinned: uniform load: per unit length of arch: vertical

Solid circular flat plate with uniform thickness: simple bending: on (mono)elastic foundation: free edge: annular line load + uniform load

Solid circular flat plate with uniform thickness: simple bending: on (mono)elastic foundation: guided edge: distributed + uniform load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: uniform load: on girder

Circular arch: uniform section: end A: fixed: end B: pinned: hydrostatic load

Beam under bending: with axial tension: left end fixed: right end fixed: applied vertical displacement

Small deflections of rectangular plates: 2 adjacent clamped sides, 2 free: uniform load

Continuous beam: over 4 spans: in simple bending: uniform load

Small deflections of triangular plates: equilateral: 2 clamped sides, 1 free: combined loads

Circular arch: uniform section: end A: fixed: end B: fixed: concentrated load: radial

Small deflections of rectangular plates: 1 clamped side, 2 supported and 1 free: distributed load linearly varying along side a

Circular arch: uniform section: end A: fixed: end B: vertical slide: uniform temperature gradient: across depth

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: uniform load

Thin-walled cylindrical shell: Supported-supported: applied moment

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end pinned: uniform temperature change

Circular arch: uniform section: end A: pinned: end B: horiz.slide: uniform load: tangential

Circular arch: uniform section: end A: pinned: end B: inclined slide: distributed load: radial

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 1st power of x (n=1): under a single axial compressive load: base fixed: top fixed

Circular arch: uniform section: end A: pinned: end B: pinned: hydrostatic load

Small deflections of rectangular plates: 1 clamped side, 3 free: combined loads

Small deflections of rectangular plates: 2 adjacent clamped sides, 2 supported: distributed load linearly varying along side a: starting at x0

Annular flat plate: with uniform thickness: simple bending: outer edge free: inner edge supported: temperature differential across thickness

Circular arch: uniform section: end A: pinned: end B: pinned: concentrated load: radial

Small deflections of triangular plates: equilateral: 3 clamped sides: uniform load

Beam under bending: with held ends: left end supported: right end supported: applied vertical displacement

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge free: combined loads

Circular arch: uniform section: end A: fixed: end B: free: hydrostatic load

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: supported edge: annular line load + uniform load

Tapered cantilever under simple bending: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: concentrated load

Beam under bending+shear: left end fixed: right end supported: point load

Thin-walled cylindrical shell: Supported-supported: uniform radial pressure: from 'a' to 'b'

Circular arch: uniform section: end A: pinned: end B: inclined guide: concentrated load: tangential

Beam under bending: with axial tension: left end supported: right end guided: temperature gradient: across depth: linearly varying

Circular arch: uniform section: end A: pinned: end B: inclined slide: combined loads

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: uniform temperature change

Elastic stability of a beam-column: prismatic: under a single axial compressive load: base fixed: top fixed

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: distributed partial load: linearly varying: horizontal: on left post

Required thickness of conical shells: under internal pressure: Calculation based on inside diameter

Annular flat plate: with uniform thickness: simple bending: outer edge guided: inner edge fixed: distributed load

Beam under bending: with axial tension: left end supported: right end supported: distributed load

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end fixed: distributed partial load: linearly varying: on post

Thin-walled cylindrical shell: Free-guided: uniform radial pressure: from 'a' to B

Thin-walled cylindrical shell: Guided-fixed: uniform radial pressure: from 'a' to B

Beam under simple bending: left end supported: right end supported: uniform load

Tapered simply supported beam under simple bending: main inertia symmetrically varying with the 1st power of x: resistance modulus varying with the 1st power of x: concentrated moment

Rectangular membranes: 4 held sides: uniform load

Circular arch: uniform section: end A: fixed: end B: pinned: uniform temperature change

Beam under bending: with axial compression: left end fixed: right end guided: distributed load

Small deflections of rectangular plates: 2 facing sides clamped, 2 supported: distributed load linearly varying along side a

Thin-walled cylindrical shell: Guided-supported: radial load

Guided-infinite beam: on elastic foundation: distributed load: linearly varying: from 'a' to 'b'

Beam under simple bending: large deflections: left end fixed: right end guided: uniform load

Tapered fixed beam under simple bending: main inertia varying symmetrically with the 4th power of x: resistance modulus varying with the 3rd power of x: uniform load

Circular arch: uniform section: end A: fixed: end B: horiz.slide: concentrated load: horizontal

Tapered cantilever under simple bending: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: concentrated load

Beam under simple bending: left end supported: right end guided: temperature gradient: across depth: linearly varying

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: concentrated load

Beam under simple bending: left end fixed: right end supported: concentrated load

Circular arch: uniform section: end A: fixed: end B: vertical guide: uniform load: radial

Beam under bending: with axial compression: left end fixed: right end fixed: temperature gradient: across depth: linearly varying

Solid circular flat plate with uniform thickness: large deflections behaviour: clamped & held: distributed load

Solid circular flat plate with uniform thickness: large deflections behaviour: clamped: distributed load

Circular arch: uniform section: end A: fixed: end B: vertical guide: concentrated load: horizontal

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: distributed partial load: linearly varying: vertical: on girder left half

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: point load: on right post

Tapered simply supported beam under simple bending: main inertia symmetrically varying with the 4th power of x: resistance modulus varying with the 3rd power of x: concentrated moment

Circular pipes: supported at bottom: load at top

Thin-walled cylindrical shell: Fixed-fixed: applied moment

Annular flat plate: with uniform thickness: simple bending: outer edge guided: inner edge supported: uniform annular line moment

Circular pipes: supported at bottom: uniform radial pressure: over an arc

Circular arch: uniform section: end A: pinned: end B: inclined slide: uniform load: per unit horizontal projection: vertical

Circular arch: uniform section: end A: pinned: end B: horiz.slide: uniform load: per unit vertical projection: horizontal

Circular arch: uniform section: end A: fixed: end B: inclined guide: distributed load: vertical: partial

Solid circular flat plate: simple bending: clamped: with uniform thickness: combined loads

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: point load: horizontal: on girder

Continuous beam: over 4 spans: in simple bending: distributed load

Supported-guided beam: on elastic foundation: concentrated load

Circular arch: uniform section: end A: pinned: end B: horiz.guide: distributed load: tangential

Beam under simple bending: left end fixed: right end guided: applied angular displacement

Elastic stability of a beam-column: prismatic: under a single axial compressive load: base fixed: top guided

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge guided: parabolically increasing load

Beam under bending: with axial tension: left end fixed: right end free: applied angular displacement

Guided-guided beam: on elastic foundation: distributed load: linearly varying: from 'a' to 'b'

Small deflections of rectangular plates: 3 clamped sides, 1 free: distributed load linearly varying along side a: starting at x0

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge fixed: temperature differential across thickness

Annular flat plate: with uniform thickness: simple bending: outer edge free: inner edge fixed: temperature differential across thickness

Beam under simple bending: left end fixed: right end guided: concentrated moment

Thin-walled cylindrical shell: Fixed-free: uniform radial pressure: from 'a' to 'b'

Tapered fixed beam under simple bending: main inertia symmetrically varying with the 2nd power of x: resistance modulus varying with the 1st power of x: concentrated moment

Thin-walled cylindrical shell: Free-fixed: linearly varying radial pressure

Circular arch: uniform section: end A: pinned: end B: inclined guide: uniform load: radial

Tapered fixed beam under simple bending: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: combined loads

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: distributed load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: combined loads

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: concentrated moment

Supported-fixed beam: on elastic foundation: concentrated load

Beam under bending: with axial compression: left end supported: right end guided: temperature gradient: across depth: linearly varying

Beam under bending: with held ends: left end fixed: right end supported: applied vertical displacement

Circular arch: uniform section: end A: pinned: end B: horiz.guide: concentrated load: horizontal

Solid circular flat plate: simple bending: clamped: with uniform thickness: uniform annular line load

Solid circular flat plate with uniform thickness: large deflections behaviour: supported & held: distributed load

Tapered fixed beam under simple bending: main inertia varying symmetrically with the 2nd power of x: resistance modulus varying with the 1st power of x: uniform load

Solid circular flat plate with uniform thickness: large deflections behaviour: simply supported: uniform annular line load

Thin-walled cylindrical shell: Supported-guided: linearly varying radial pressure

Circular pipes: supported at bottom: 2 facing horizontal line loads

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: combined loads

Beam under bending: with axial compression: left end fixed: right end fixed: combined loads

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: uniform load: on left post

Circular arch: uniform section: end A: fixed: end B: horiz.guide: concentrated load: radial

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: point load: horizontal: on right post

Tapered fixed beam under simple bending: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: concentrated moment

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 2nd power of x (n=2): under a single axial compressive load: base fixed: top supported

Small deflections of rectangular plates: 1 clamped side, 2 supported(adjacent) and 1 free: distributed load: over a partial rectangular area

Tapered cantilever under simple bending: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: uniform load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: uniform load: vertical: on girder right half

Small deflections of rectangular plates: 4 simply supported sides: uniform load

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: uniform load: horizontal: on girder

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 1st power of x (n=1): under a single axial compressive load: base supported: top supported

Beam under bending: with held ends: left end fixed: right end guided: concentrated moment

Annular flat plate: with uniform thickness: simple bending: outer edge clamped: inner edge clamped: combined loads

Tapered fixed beam under simple bending: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: linearly decreasing load

Beam under bending: with held ends: left end fixed: right end fixed: distributed load

Tapered fixed beam under simple bending: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: distributed load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: uniform load: on left post

Tapered fixed beam under simple bending: main inertia symmetrically varying with the 1st power of x: resistance modulus varying with the 1st power of x: concentrated load

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: uniform load: horizontal: on left post

Circular arch: uniform section: end A: fixed: end B: free: concentrated load: horizontal

Circular arch: uniform section: end A: fixed: end B: vertical slide: uniform load: per unit vertical projection: horizontal: on left half arch

Circular arch: uniform section: end A: fixed: end B: inclined slide: concentrated load: tangential

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: combined loads

Circular arch: uniform section: end A: fixed: end B: fixed: uniform load: per unit length of arch: horizontal

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: uniform load: vertical: on girder left half

Tapered fixed beam under simple bending: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: linearly decreasing load

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge fixed: parabolically increasing load

Circular arch: uniform section: end A: fixed: end B: vertical guide: distributed load: radial

Circular arch: uniform section: end A: pinned: end B: inclined guide: uniform temperature change

Circular arch: uniform section: end A: fixed: end B: inclined slide: uniform load: per unit length of arch: vertical

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: uniform load: on left post

Annular flat plate: with uniform thickness: simple bending: outer edge simply fixed: inner edge supported: uniform annular line load

Tapered simply supported beam under simple bending: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: uniform load

Continuous beam: over 3 spans: in simple bending: point load

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: point load: vertical: on girder

Small deflections of rectangular plates: on elastic foundation: free: concentrated load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: point load: on left post

Beam under bending: with axial compression: left end fixed: right end free: concentrated moment

Circular arch: uniform section: end A: pinned: end B: horiz.slide: uniform load: radial

Thin-walled cylindrical shell: Fixed-fixed: linearly varying radial pressure

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: point load: on left post

Circular arch: uniform section: end A: fixed: end B: horiz.guide: uniform load: per unit horizontal projection: vertical

Beam under bending: with held ends: left end supported: right end supported: applied angular displacement

Beam under bending: with axial compression: left end supported: right end guided: concentrated moment

Solid circular flat plate: simple bending: clamped: with uniform thickness: distributed parabolically increasing load

Beam under bending: with axial compression: left end fixed: right end fixed: concentrated load

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: point load: horizontal: on left post

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: combined loads

Circular arch: uniform section: end A: pinned: end B: inclined slide: concentrated load: radial

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: uniform load: horizontal: on right post

Thin-walled cylindrical shell: Fixed-guided: uniform radial pressure: from 'a' to 'b'

Thin-walled cylindrical shell: Supported-fixed: uniform radial pressure: from 'a' to B

Tapered fixed beam under simple bending: main inertia symmetrically varying with the 4th power of x: resistance modulus varying with the 3rd power of x: concentrated load

Beam under bending+shear: left end supported: right end supported: combined loads

Supported-fixed beam: on elastic foundation: concentrated moment

Annular flat plate: with uniform thickness: simple bending: outer edge free: inner edge supported: combined loads

Tapered fixed beam under simple bending: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: distributed load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: combined loads

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge free: uniform annular line load

Tapered simply supported beam under simple bending: main inertia symmetrically varying with the 4th power of x: resistance modulus varying with the 3rd power of x: concentrated load

Circular arch: uniform section: end A: fixed: end B: fixed: combined loads

Circular arch: uniform section: end A: pinned: end B: pinned: uniform load: per unit horizontal projection: vertical

Beam under bending: with axial compression: left end fixed: right end supported: applied angular displacement

Annular flat plate: with uniform thickness: simple bending: outer edge simply fixed: inner edge guided: uniform annular line load

Circular arch: uniform section: end A: pinned: end B: horiz.guide: uniform load: per unit horizontal projection: vertical

Spheres in contact with a spherical socket under load: Hertz's theory

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 4th power of x (n=4): under a single axial compressive load: base fixed: top guided

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: concentrated load: tangential

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: point load: horizontal: on right post

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: point load: vertical: on girder right half

Circular arch: uniform section: end A: fixed: end B: fixed: uniform load: per unit length of arch: vertical

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: distributed load: radial

Beam under simple bending: left end supported: right end supported: applied angular displacement

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: uniform load: per unit vertical projection: horizontal

Elastic stability of a beam-column: prismatic: under a single axial compressive load: base supported: top supported

Tapered fixed beam under simple bending: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: linearly decreasing load

Circular arch: uniform section: end A: fixed: end B: pinned: combined loads

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge guided: parabolically increasing load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: uniform temperature change

Circular arch: uniform section: end A: pinned: end B: inclined guide: concentrated moment

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: uniform pressure: on girder left half

Circular arch: uniform section: end A: fixed: end B: horiz.guide: uniform load: tangential

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end sliding: right end fixed: point load: on post

Circular arch: uniform section: end A: fixed: end B: fixed: concentrated load: horizontal

Circular arch: uniform section: end A: fixed: end B: horiz.guide: combined loads

Beam under simple bending: left end supported: right end guided: uniform load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: uniform load: on girder

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: point load: horizontal: on right post

Thin-walled cylindrical shell: Free-guided: radial load

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end sliding: uniform load: on post

Small deflections of rectangular plates: 2 simply supported opposite sides and 2 free: uniform load

Junction between the large end of a cone and a cylinder: with knuckle: cone and cylinder with constant thicknesses: under internal pressure

Beam under bending: with held ends: left end fixed: right end guided: temperature gradient: across depth: linearly varying

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge fixed: temperature differential across thickness

Circular flanges with hub: integral with hub slope 1/3 max: WN or LWN type: to internal pressure: gasket laying inside inner edge of bolt holes

Small deflections of rectangular plates: 4 simply supported sides: distributed load: over a partial rectangular area

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: uniform load: horizontal: on right post

Beam under bending: with axial tension: left end supported: right end guided: combined loads

Beam under bending: with held ends: left end fixed: right end guided: uniform load

Small deflections of rectangular plates: 2 adjacent clamped sides, 2 supported: distributed load linearly varying along side a

Circular arch: uniform section: end A: pinned: end B: inclined guide: uniform load: per unit length of arch: horizontal

Beam under bending+shear: left end fixed: right end free: combined loads

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: uniform load: on right post

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge clamped: combined loads

Small deflections of rectangular plates: 3 supported sides, 1 clamped: combined loads

Beam under simple bending: left end supported: right end supported: point load

Solid circular flat plate with uniform thickness: pure membrane behaviour: simply supported: distributed load

Beam under bending: with held ends: left end fixed: right end free: concentrated load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: distributed partial load: linearly varying: on left post

Tapered cantilever under simple bending: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: linearly decreasing load

Beam: simple bending: with held ends: left end supported: right end supported: uniform load

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: guided edge: uniform annular line load

Solid circular flat plate with uniform thickness: simple bending: on (mono)elastic foundation: supported edge: center load + uniform load

Circular arch: uniform section: end A: fixed: end B: horiz.guide: uniform load: per unit length of arch: horizontal

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: uniform load: horizontal: on left post

Small deflections of rectangular plates: 4 free sides: supported at 4 corners: concentrated load

Small deflections of rectangular plates: 4 clamped sides: combined loads

Tapered simply supported beam under simple bending: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: linearly decreasing load

Thin-walled cylindrical shell: Free-fixed: radial load

Circular arch: uniform section: end A: fixed: end B: inclined slide: uniform load: per unit vertical projection: horizontal

Circular arch: uniform section: end A: pinned: end B: horiz.guide: uniform temperature gradient: across depth

Disc springs: stack in series: with or without bearing flats

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: uniform load: horizontal: on left post

Circular arch: uniform section: end A: fixed: end B: pinned: uniform load: per unit horizontal projection: vertical

Tapered cantilever under simple bending: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: combined loads

Circular arch: uniform section: end A: fixed: end B: vertical slide: distributed load: vertical: partial

Circular arch: uniform section: end A: fixed: end B: free: uniform load: radial

Beam under bending: with held ends: left end fixed: right end supported: applied angular displacement

Circular arch: uniform section: end A: pinned: end B: horiz.slide: distributed load: vertical: partial

Thin-walled cylindrical shell: Supported-free: uniform radial pressure: from 'a' to B

Circular arch: uniform section: end A: pinned: end B: pinned: concentrated moment

Beam under bending: with axial compression: left end fixed: right end fixed: applied angular displacement

Beam under simple bending: left end fixed: right end free(cantilever): combined loads

Elastic stability of a beam-column: with two stepped sections: under two axial compressive loads: base fixed: top fixed

Small deflections of rectangular plates: on elastic foundation: free: distributed load: over a partial rectangular area

Annular flat plate: with uniform thickness: simple bending: outer edge free: inner edge fixed: distributed load

Disc springs: stack in parallel: with or without bearing flats

Beam under bending: with held ends: left end fixed: right end fixed: concentrated moment

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: uniform load: horizontal: on right post

Fixed-fixed beam: on elastic foundation: distributed load: linearly varying: from 'a' to 'b'

Tapered simply supported beam under simple bending: main inertia symmetrically varying with the 4th power of x: resistance modulus varying with the 3rd power of x: combined loads

Circular arch: uniform section: end A: pinned: end B: horiz.guide: uniform load: per unit length of arch: horizontal

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: uniform load: vertical: on girder

Tapered fixed beam under simple bending: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: uniform load

Circular arch: uniform section: end A: pinned: end B: inclined guide: hydrostatic load

Beam under bending: with axial tension: left end supported: right end supported: concentrated moment

Tapered simply supported beam under simple bending: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: distributed load

Beam under simple bending: large deflections: left end fixed: right end guided: concentrated load

Circular arch: uniform section: end A: fixed: end B: pinned: uniform load: per unit length of arch: horizontal

Thin-walled cylindrical shell: Fixed-free: linearly varying radial pressure

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: concentrated moment

Circular arch: uniform section: end A: fixed: end B: vertical guide: uniform temperature gradient: across depth

Circular arch: uniform section: end A: fixed: end B: free: concentrated moment

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: linearly decreasing load

Circular arch: uniform section: end A: fixed: end B: inclined slide: uniform load: per unit horizontal projection: vertical

Tapered fixed beam under simple bending: main inertia symmetrically varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: concentrated load

Annular flat plate: with uniform thickness: simple bending: outer edge guided: inner edge fixed: applied angular displacement

Solid circular flat plate with uniform thickness: pure membrane behaviour: supported & held: distributed load

Circular arch: uniform section: end A: pinned: end B: horiz.guide: concentrated moment

Tapered cantilever under simple bending: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: distributed load

Small deflections of rectangular plates: 2 opposite sides clamped, 2 free: combined loads

Small deflections of triangular plates: equilateral: 3 supported sides: distributed load: linearly varying: along height a

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: concentrated moment

Beam under simple bending: large deflections: left end supported: right end guided: concentrated load

Circular arch: uniform section: end A: fixed: end B: inclined slide: uniform load: per unit length of arch: horizontal

Tapered simply supported beam under simple bending: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: distributed load

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 2nd power of x (n=2): under a single axial compressive load: base supported: top supported

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 4th power of x (n=4): under a single axial compressive load: base fixed: top free

Small deflections of rectangular plates: 1 clamped side, 3 free: distributed load: over a partial rectangular area

Tapered simply supported beam under simple bending: main inertia symmetrically varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: concentrated moment

Circular arch: uniform section: end A: fixed: end B: horiz.slide: concentrated load: vertical

Circular arch: uniform section: end A: fixed: end B: inclined guide: uniform load: per unit length of arch: vertical

Solid circular flat plate: simple bending: simply supported: with uniform thickness: distributed parabolically increasing load

Circular arch: uniform section: end A: pinned: end B: inclined slide: uniform load: radial

Tapered cantilever under simple bending: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: concentrated load

Continuous beam: over 5 spans: in simple bending: distributed load

Circular arch: uniform section: end A: pinned: end B: inclined guide: combined loads

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: point load: horizontal: on girder left half

Solid circular flat plate with uniform thickness: simple bending: on (mono)elastic foundation: fixed edge: center load + uniform load

Beam under simple bending: left end fixed: right end free(cantilever): uniform load

Guided-infinite beam: on elastic foundation: concentrated moment

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge supported: parabolically increasing load

Beam under bending: with held ends: left end fixed: right end fixed: applied angular displacement

Circular arch: uniform section: end A: pinned: end B: horiz.slide: concentrated load: radial

Beam under bending: with held ends: left end fixed: right end supported: uniform load

Circular flat flanges without hubs: loose, welded: to internal pressure: gasket laying inside inner edge of bolt holes: with bolt spacing correction

Small deflections of rectangular plates: 3 supported sides, 1 free: uniform load

Small deflections of rectangular plates: 4 clamped sides: distributed load: linearly varying: along side a: starting at x0

Tapered simply supported beam under simple bending: main inertia symmetrically varying with the 2nd power of x: resistance modulus varying with the 1st power of x: combined loads

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end fixed: combined loads

Beam under bending: with axial compression: left end supported: right end supported: concentrated moment

Thin-walled cylindrical shell: Fixed-fixed: radial load

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge supported: temperature differential across thickness

Beam under bending: with held ends: left end supported: right end guided: concentrated moment

Circular arch: uniform section: end A: fixed: end B: inclined guide: distributed load: radial

Annular flat plate: with uniform thickness: simple bending: outer edge guided: inner edge supported: combined loads

Circular arch: uniform section: end A: pinned: end B: horiz.slide: distributed load: tangential

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: supported: distributed load

Beam under bending: with axial tension: left end fixed: right end fixed: temperature gradient: across depth: linearly varying

Full face flanges with soft ring type gaskets: external pressure

Beam under simple bending: large deflections: left end fixed: right end fixed: distributed load

Circular arch: uniform section: end A: fixed: end B: free: uniform temperature gradient: across depth

Circular arch: uniform section: end A: pinned: end B: pinned: uniform load: per unit length of arch: vertical

Circular arch: uniform section: end A: fixed: end B: inclined guide: uniform load: per unit horizontal projection: vertical

Annular flat plate: with uniform thickness: simple bending: outer edge guided: inner edge supported: applied angular displacement

Circular ring beam: supported at bottom: 2 vertical loads

Solid circular flat plate with uniform thickness: simple bending: on (mono)elastic foundation: guided edge: annular line load + uniform load

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end pinned: point load: on girder

Circular arch: uniform section: end A: fixed: end B: vertical guide: distributed load: tangential

Fixed-infinite beam: on elastic foundation: point load

Fixed-guided beam: on elastic foundation: concentrated moment

Solid circular flat plate: simple bending: simply supported: with linearly increasing thickness: center load

Circular arch: uniform section: end A: fixed: end B: horiz.slide: distributed load: tangential

Circular arch: uniform section: end A: fixed: end B: inclined slide: uniform temperature gradient: across depth

Beam under simple bending: left end supported: right end guided: distributed load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: uniform pressure: on girder left half

Beam under bending+shear: left end supported: right end guided: distributed load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: distributed partial load: linearly varying: horizontal: on left post

Infinite beam: on elastic foundation: concentrated load

Circular arch: uniform section: end A: pinned: end B: pinned: uniform load: per unit vertical projection: horizontal: on left half arch

Circular arch: uniform section: end A: fixed: end B: horiz.slide: uniform load: per unit horizontal projection: vertical

Beam under simple bending: left end fixed: right end supported: distributed load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: uniform pressure: on girder right half

Circular arch: uniform section: end A: fixed: end B: horiz.slide: uniform load: radial

Beam under bending+shear: left end supported: right end guided: combined loads

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end pinned: uniform load: on post

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: point load: horizontal: on girder right half

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 2nd power of x (n=2): under a single axial compressive load: base fixed: top guided

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 3rd power of x (n=3): under a single axial compressive load: base fixed: top guided

Tapered simply supported beam under simple bending: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: concentrated moment

Semi-infinite beam: on elastic foundation: concentrated moment

Thin-walled cylindrical shell: Supported-guided: uniform radial pressure: from 'a' to 'b'

Thin-walled cylindrical shell: Fixed-guided: applied moment

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: uniform load: horizontal: on left post

Beam under bending+shear: left end fixed: right end supported: distributed load

Tapered fixed beam under simple bending: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: concentrated moment

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge free: uniform annular line moment

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: distributed load: tangential

Thin-walled cylindrical shell: Fixed-supported: applied moment

Minimum thickness of: ellipsoidal ends: under internal pressure

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: linearly decreasing load

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end sliding: right end fixed: uniform load: on girder

Tapered simply supported beam under simple bending: main inertia symmetrically varying with the 2nd power of x: resistance modulus varying with the 1st power of x: concentrated load

Beam under bending+shear: left end fixed: right end guided: point load

Beam under bending: with axial tension: left end fixed: right end guided: concentrated load

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: point load: horizontal: on left post

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: distributed partial load: linearly varying: horizontal: on right post

Fixed-free beam: on elastic foundation: concentrated moment

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: distributed load

Circular arch: uniform section: end A: fixed: end B: fixed: uniform temperature change

Small deflections of rectangular plates: 2 simply supported opposite sides and 2 free: distributed load: over a partial rectangular area

Annular flat plate: with uniform thickness: simple bending: outer edge clamped: inner edge supported: uniform load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: distributed partial load: linearly varying: on girder

Annular flat plate: with uniform thickness: simple bending: outer edge clamped: inner edge guided: uniform load

Continuous beam: over 3 spans: in simple bending: concentrated moment

Circular flat flanges without hubs: lap joint: to internal pressure: gasket laying inside inner edge of bolt holes: split ring: along a diameter: with bolt spacing correction

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: concentrated moment

Circular arch: uniform section: end A: fixed: end B: horiz.slide: uniform load: tangential

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: uniform load: tangential

Circular arch: uniform section: end A: pinned: end B: horiz.guide: distributed load: radial

Spheres in contact: with a grooved outer ring: under load: Hertz's theory

Allowable external pressure: of cylindrical shells: circularity within tolerance

Beam under bending+shear: left end supported: right end supported: distributed load

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: supported edge: center load

Circular arch: uniform section: end A: fixed: end B: horiz.slide: uniform load: per unit length of arch: horizontal

Two cylinders in contact under load: axes at right angles: Hertz's theory

Circular arch: uniform section: end A: fixed: end B: fixed: distributed load: vertical: partial

Spheres in contact: with a grooved inner ring: under load: Hertz's theory

Beam under bending: with axial compression: left end fixed: right end free: applied angular displacement

Beam under bending: with axial tension: left end supported: right end supported: temperature gradient: across depth: linearly varying

Circular arch: uniform section: end A: pinned: end B: horiz.guide: uniform load: per unit vertical projection: horizontal

Solid circular flat plate with uniform thickness: large deflections behaviour: supported & held: uniform annular line load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: distributed partial load: linearly varying: horizontal: on right post

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: uniform load: on left post

Small deflections of rectangular plates: 2 simply supported opposite sides and 2 free: concentrated load at center

Rectangular membranes: 3 held sides, 1 free: uniform load

Solid circular flat plate with uniform thickness: simple bending: on (mono)elastic foundation: supported edge: annular line load + uniform load

Beam under simple bending: left end fixed: right end fixed: combined loads

Beam under bending: with axial compression: left end supported: right end guided: applied angular displacement

Solid circular flat plate: simple bending: simply supported: with uniform thickness: combined loads

Large deflections of rectangular plates: 4 simply supported sides: distributed load linearly varying along side a

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: point load: horizontal: on girder left half

Circular arch: uniform section: end A: pinned: end B: horiz.guide: concentrated load: radial

Large deflections of rectangular plates: 4 clamped & held sides: distributed load linearly varying along side a

Circular arch: uniform section: end A: fixed: end B: pinned: distributed load: radial

Beam under bending: with axial compression: left end fixed: right end guided: temperature gradient: across depth: linearly varying

Small deflections of rectangular plates: bending + shear: 4 simply supported sides: distributed load linearly varying along side a: starting at x0

Circular arch: uniform section: end A: pinned: end B: inclined slide: uniform load: per unit vertical projection: horizontal: on left half arch

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end fixed: uniform load: on post

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end sliding: point load: on post

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge free: uniform load

Circular arch: uniform section: end A: pinned: end B: inclined guide: uniform load: per unit horizontal projection: vertical

Beam under simple bending: large deflections: left end fixed: right end supported: distributed load

Small deflections of rectangular plates: 1 clamped side, 2 supported and 1 free: uniform load

Solid circular flat plate: simple bending: simply supported: with linearly increasing thickness: combined loads

Circular arch: uniform section: end A: pinned: end B: pinned: uniform load: radial

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: uniform load: on left post

Small deflections of triangular plates: equilateral: 2 supported sides, 1 free: combined loads

Circular arch: uniform section: end A: pinned: end B: inclined guide: distributed load: radial

Tapered fixed beam under simple bending: main inertia varying symmetrically with the 4th power of x: resistance modulus varying with the 3rd power of x: combined loads

Circular arch: uniform section: end A: fixed: end B: horiz.guide: concentrated load: vertical

Supported-free beam: on elastic foundation: concentrated moment

Beam under simple bending: left end supported: right end supported: combined loads

Solid circular flat plate: simple bending: simply supported: with uniform thickness: uniform line moment

Circular arch: uniform section: end A: fixed: end B: inclined guide: concentrated load: tangential

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge fixed: applied vertical displacement

Circular arch: uniform section: end A: fixed: end B: inclined guide: uniform load: tangential

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: fixed edge: uniform annular line load

Thin-walled cylindrical shell: Fixed-guided: linearly varying radial pressure

Beam under bending: with axial compression: left end fixed: right end guided: combined loads

Beam under bending: with held ends: left end supported: right end guided: distributed load

Circular pipes: supported at bottom: loaded by self weight: directed upwards

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end fixed: point load: on post

Thin-walled cylindrical shell: Supported-free: applied moment

Thin-walled cylindrical shell: Guided-guided: linearly varying radial pressure

Circular arch: uniform section: end A: pinned: end B: pinned: distributed load: tangential

Beam under simple bending: left end fixed: right end guided: distributed load

Beam under bending: with axial tension: left end fixed: right end supported: concentrated moment

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: uniform load: horizontal: on right post

Small deflections of rectangular plates: 2 adjacent supported sides, 2 free: distributed load linearly varying along side a

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: distributed load

Circular arch: uniform section: end A: fixed: end B: free: concentrated load: radial

Small deflections of rectangular plates: 1 clamped side, 3 free: point load: over a partial rectangular area

Annular flat plate: with uniform thickness: simple bending: outer edge free: inner edge fixed: uniform annular line moment

Small deflections of rectangular plates: 4 simply supported sides: concentrated load at center

Solid circular flat plate with uniform thickness: simple bending: on (mono)elastic foundation: fixed edge: annular line load + uniform load

Small deflections of rectangular plates: 3 supported sides, 1 clamped: distributed load: over a partial rectangular area

Circular arch: uniform section: end A: pinned: end B: inclined slide: concentrated moment

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: uniform load: horizontal: on right post

Annular flat plate: with uniform thickness: simple bending: outer edge clamped: inner edge clamped: uniform load

Annular flat plate: with uniform thickness: simple bending: outer edge free: inner edge supported: uniform load

Thin-walled cylindrical shell: Fixed-supported: uniform radial pressure: from 'a' to 'b'

Circular arch: uniform section: end A: fixed: end B: fixed: uniform load: per unit vertical projection: horizontal: on left half arch

Tapered fixed beam under simple bending: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: combined loads

Beam under bending: with axial compression: left end supported: right end supported: applied vertical displacement

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: combined loads

Beam under bending: with held ends: left end fixed: right end supported: concentrated load

Circular arch: uniform section: end A: pinned: end B: inclined guide: concentrated load: radial

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: clamped edge: center load

Circular arch: uniform section: end A: fixed: end B: inclined slide: distributed load: radial

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge free: temperature differential across thickness

Beam under simple bending: left end fixed: right end free: concentrated moment

Beam under bending: with axial tension: left end fixed: right end guided: temperature gradient: across depth: linearly varying

Beam under bending: with held ends: left end fixed: right end supported: concentrated moment

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: combined loads

Circular arch: uniform section: end A: pinned: end B: inclined guide: uniform load: per unit vertical projection: horizontal: on left half arch

Circular arch: uniform section: end A: fixed: end B: horiz.guide: uniform temperature gradient: across depth

Beam under bending+shear: left end supported: right end guided: uniform load

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge fixed: uniform annular line moment

Tapered simply supported beam under simple bending: main inertia symmetrically varying with the 1st power of x: resistance modulus varying with the 1st power of x: linearly decreasing load

Beam under bending+shear: left end fixed: right end guided: distributed load

Circular arch: uniform section: end A: fixed: end B: vertical guide: uniform load: per unit vertical projection: horizontal

Small deflections of rectangular plates: 4 clamped sides: uniform load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: point load: on right post

Circular arch: uniform section: end A: fixed: end B: pinned: concentrated load: vertical

Circular arch: uniform section: end A: fixed: end B: horiz.slide: uniform temperature gradient: across depth

Circular arch: uniform section: end A: fixed: end B: vertical guide: concentrated moment

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: point load: vertical: on girder left half

Thin-walled cylindrical shell: Guided-supported: applied moment

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end fixed: distributed partial load: linearly varying: on post

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 4th power of x (n=4): under a single axial compressive load: base fixed: top supported

Tapered fixed beam under simple bending: main inertia varying symmetrically with the 3rd power of x: resistance modulus varying with the 2nd power of x: uniform load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: point load: on girder

Flat face flanges with metal-to-metal contact outside the bolt circle: analysis of a flange cover assembly (Class 3): integral (Cat.1) flange: hub of constant thickness: no spacer: self-sealing gasket with negligible loads

Circular arch: uniform section: end A: fixed: end B: vertical guide: hydrostatic load

Tapered cantilever under simple bending: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: combined loads

Circular arch: uniform section: end A: fixed: end B: fixed: uniform load: radial

Small deflections of rectangular plates: 2 opposite sides clamped, 2 free: concentrated load

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: distributed partial load: linearly varying: horizontal: on left post

Beam under bending: with axial tension: left end fixed: right end free: uniform load

Beam under bending: with axial compression: left end fixed: right end supported: uniform load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: point load: on right post

Supported-infinite beam: on elastic foundation: concentrated moment

Circular arch: uniform section: end A: fixed: end B: inclined slide: distributed load: tangential

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: combined loads

Circular arch: uniform section: end A: fixed: end B: vertical slide: distributed load: radial

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: distributed partial load: linearly varying: horizontal: on left post

Beam under bending: with axial tension: left end supported: right end guided: uniform load

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge supported: applied vertical displacement

Beam under bending: with axial compression: left end supported: right end supported: applied angular displacement

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: uniform temperature change

Thin-walled cylindrical shell: Guided-fixed: applied moment

Circular arch: uniform section: end A: pinned: end B: horiz.slide: uniform load: per unit length of arch: vertical

Solid circular flat plate: simple bending: clamped: with uniform thickness: uniform line moment

Circular arch: uniform section: end A: fixed: end B: vertical slide: distributed load: tangential

Beam under bending: with axial compression: left end fixed: right end free: distributed load

Circular arch: uniform section: end A: fixed: end B: free: distributed load: vertical: partial

Tapered simply supported beam under simple bending: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: distributed load

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end pinned: distributed partial load: linearly varying: on girder

Small deflections of rectangular plates: 2 adjacent clamped sides, 2 free: combined loads

Continuous beam: over 5 spans: in simple bending: uniform load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: uniform load: vertical: on girder left half

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: guided edge: center load + uniform load

Infinite beam: on elastic foundation: distributed load: linearly varying over 'a'

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end fixed: uniform load: on girder

Beam under bending: with axial compression: left end supported: right end guided: combined loads

Small deflections of rectangular plates: 3 supported sides, 1 free: distributed load linearly varying along side a: starting at x0

Beam under simple bending: large deflections: left end fixed: right end guided: distributed load

Beam under simple bending: left end fixed: right end fixed: distributed load

Thin-walled cylindrical shell: Fixed-free: radial load

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end fixed: point load: on girder

Circular arch: uniform section: end A: fixed: end B: vertical slide: concentrated load: tangential

Fixed-infinite beam: on elastic foundation: distributed load: linearly varying: from 'a' to 'b'

Small deflections of rectangular plates: 1 clamped side, 3 free: distributed load linearly varying along side a: starting at x0

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: distributed partial load: linearly varying: on right post

Beam: simple bending: with held ends: left end supported: right end supported: distributed load

Small deflections of rectangular plates: 2 adjacent clamped sides, 2 supported: combined loads

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 1st power of x (n=1): under a single axial compressive load: base fixed: top guided

Circular arch: uniform section: end A: fixed: end B: vertical slide: concentrated load: horizontal

Beam under bending: with axial tension: left end fixed: right end free: concentrated load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: distributed partial load: linearly varying: on girder

Circular arch: uniform section: end A: fixed: end B: vertical guide: distributed load: vertical: partial

Circular arch: uniform section: end A: pinned: end B: pinned: combined loads

Thin-walled cylindrical shell: Free-fixed: uniform radial pressure: from 'a' to B

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge supported: uniform load

Thin-walled cylindrical shell: Guided-free: applied moment

Circular flat flanges without hubs: lap joint: to internal pressure: gasket laying inside inner edge of bolt holes

Tapered fixed beam under simple bending: main inertia symmetrically varying with the 1st power of x: resistance modulus varying with the 1st power of x: linearly decreasing load

Annular flat plate: with uniform thickness: simple bending: outer edge clamped: inner edge guided: combined loads

Beam under bending: with axial tension: left end fixed: right end guided: applied angular displacement

Tapered fixed beam under simple bending: main inertia symmetrically varying with the 2nd power of x: resistance modulus varying with the 1st power of x: linearly decreasing load

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: fixed: distributed load

Fixed-guided beam: on elastic foundation: point load

Continuous beam: over 4 spans: in simple bending: concentrated moment

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: combined loads

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 3rd power of x (n=3): under a single axial compressive load: base supported: top supported

Beam under simple bending: left end fixed: right end supported: combined loads

Beam under simple bending: large deflections: left end fixed: right end free: distributed load

Large deflections of rectangular plates: 4 simply supported sides: uniform load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: uniform temperature change

Beam under bending: with axial tension: left end fixed: right end fixed: concentrated moment

Circular arch: uniform section: end A: pinned: end B: horiz.guide: concentrated load: vertical

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: distributed partial load: linearly varying: horizontal: on left post

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: uniform load: vertical: on girder right half

Circular pipes: supported at bottom: partially filled with liquid

Circular arch: uniform section: end A: fixed: end B: vertical slide: uniform load: per unit length of arch: vertical

Solid circular flat plate with uniform thickness: large deflections behaviour: simply supported: uniform distributed load

Tapered fixed beam under simple bending: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: combined loads

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: free edge: uniform annular line load

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: distributed partial load: linearly varying: vertical: on girder

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: distributed partial load: linearly varying: on left post

Small deflections of triangular plates: equilateral: 3 supported sides: combined loads

Circular arch: uniform section: end A: pinned: end B: pinned: distributed load: radial

Solid circular flat plate: simple bending: clamped: with uniform thickness: uniform load

Circular arch: uniform section: end A: fixed: end B: vertical slide: uniform load: per unit vertical projection: horizontal

Circular flanges with hub: integral with hub slope 1/3 max: WN or LWN type: to internal pressure: gasket laying inside inner edge of bolt holes: with bolt spacing correction

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: uniform load: vertical: on girder left half

Circular arch: uniform section: end A: fixed: end B: inclined slide: concentrated load: radial

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: uniform load: on girder

Circular ring beam: supported at bottom: loaded by uniform vertical load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: point load: vertical: on girder right half

Circular arch: uniform section: end A: fixed: end B: vertical guide: uniform load: tangential

Small deflections of triangular plates: equilateral: 3 clamped sides: distributed load: linearly varying: along height a

Elastic stability of a beam-column: with two stepped sections: under two axial compressive loads: base supported: top supported

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: uniform load: per unit vertical projection: horizontal: on left half arch

Tapered simply supported beam under simple bending: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: concentrated load

Beam under simple bending: left end fixed: right end supported: applied angular displacement

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 3rd power of x (n=3): under a single axial compressive load: base fixed: top supported

Thin-walled cylindrical shell: Guided-fixed: linearly varying radial pressure

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 1st power of x (n=1): under a single axial compressive load: base fixed: top free

Free-free beam: on elastic foundation: distributed load: linearly varying: from 'a' to 'b'

Beam under bending: with axial compression: left end fixed: right end supported: temperature gradient: across depth: linearly varying

Annular flat plate: with uniform thickness: simple bending: outer edge free: inner edge clamped: combined loads

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: uniform pressure: on girder right half

Minimum thickness of: spherical shells: spherical parts of shells: hemispherical ends: central zone of torispherical ends: spherical knuckles of cones to cylinders: under internal pressure: e/De<=0.16: Calculation based on outer radius

Circular arch: uniform section: end A: pinned: end B: pinned: uniform temperature change

Beam under bending: with held ends: left end supported: right end guided: temperature gradient: across depth: linearly varying

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: point load: horizontal: on right post

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge supported: parabolically increasing load

Circular arch: uniform section: end A: fixed: end B: inclined guide: uniform temperature gradient: across depth

Tapered fixed beam under simple bending: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: combined loads

Beam under simple bending: left end supported: right end supported: concentrated moment

Circular arch: uniform section: end A: pinned: end B: inclined slide: uniform temperature gradient: across depth

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: combined loads

Thin-walled cylindrical shell: Free-free: uniform radial pressure: from 'a' to B

Beam under simple bending: left end fixed: right end fixed: concentrated load

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: uniform load: vertical: on girder

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: point load: horizontal: on left post

Tapered simply supported beam under simple bending: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: concentrated load

Circular arch: uniform section: end A: fixed: end B: inclined guide: concentrated load: horizontal

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: uniform load: horizontal: on right post

Annular flat plate: with uniform thickness: simple bending: outer edge free: inner edge supported: uniform annular line load

Beam under simple bending: left end fixed: right end fixed: temperature gradient: across depth: linearly varying

Circular arch: uniform section: end A: fixed: end B: pinned: uniform load: per unit vertical projection: horizontal

Circular arch: uniform section: end A: pinned: end B: horiz.slide: uniform temperature gradient: across depth

Full faced flanges with soft ring type gaskets: non metallic gaskets not less than 1.5 mm thick

Small deflections of rectangular plates: 2 adjacent clamped sides, 2 free: distributed load: over a partial rectangular area

Circular arch: uniform section: end A: pinned: end B: pinned: uniform load: per unit vertical projection: horizontal

Tapered simply supported beam under simple bending: main inertia symmetrically varying with the 2nd power of x: resistance modulus varying with the 1st power of x: linearly decreasing load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: uniform load: on right post

Circular arch: uniform section: end A: pinned: end B: inclined guide: uniform load: per unit vertical projection: horizontal

Circular arch: uniform section: end A: fixed: end B: inclined slide: hydrostatic load

Small deflections of rectangular plates: 4 simply supported sides: distributed load: linearly varying: along side a

Circular arch: uniform section: end A: fixed: end B: free: concentrated load: vertical

Annular flat plate: with uniform thickness: simple bending: outer edge simply guided: inner edge fixed: uniform annular line load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: point load: horizontal: on right post

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge fixed: applied angular displacement

Small deflections of rectangular plates: 3 clamped sides, 1 free: distributed load: over a partial rectangular area

Small deflections of rectangular plates: 2 adjacent clamped sides, 2 free: distributed load linearly varying along side a

Circular arch: uniform section: end A: pinned: end B: inclined slide: uniform load: per unit length of arch: vertical

Tapered simply supported beam under simple bending: main inertia symmetrically varying with the 2nd power of x: resistance modulus varying with the 1st power of x: uniform load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: uniform pressure: on girder left half

Tapered cantilever under simple bending: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: concentrated moment

Circular arch: uniform section: end A: pinned: end B: inclined slide: distributed load: vertical: partial

Thin-walled cylindrical shell: Free-supported: applied moment

Small deflections of triangular plates: equilateral: 2 clamped sides, 1 free: distributed load: linearly varying: along height a

Tapered fixed beam under simple bending: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: distributed load

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: point load: horizontal: on right post

Beam under bending: with axial tension: left end supported: right end supported: applied vertical displacement

Solid circular flat plate with uniform thickness: large deflections behaviour: clamped & held: uniform annular line load

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end fixed: uniform temperature change

Beam under bending: with axial compression: left end fixed: right end supported: concentrated load

Circular arch: uniform section: end A: pinned: end B: horiz.slide: uniform load: per unit vertical projection: horizontal: on left half arch

Small deflections of rectangular plates: 1 clamped side, 2 supported(adjacent) and 1 free: combined loads

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end pinned: point load: on post

Small deflections of rectangular plates: 2 opposite sides clamped, 2 free: distributed load linearly varying along side a: starting at x0

Continuous beam: over 2 spans: in simple bending: concentrated moment

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: uniform load: per unit length of arch: horizontal

Thin-walled cylindrical shell: Guided-fixed: uniform radial pressure: from 'a' to 'b'

Cylinder in contact in a cylindrical socket under load: Hertz's theory

Circular arch: uniform section: end A: fixed: end B: fixed: concentrated load: tangential

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge guided: temperature differential across thickness

Supported-guided beam: on elastic foundation: distributed load: linearly varying: from 'a' to 'b'

Circular pipes: supported at bottom: combined loads

Beam under bending: with axial tension: left end supported: right end guided: concentrated load

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: supported edge: uniform load

Rectangular membranes: 4 fully held sides: distributed load linearly varying along side a

Beam under bending+shear: left end fixed: right end free: distributed load

Tapered cantilever under simple bending: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: linearly decreasing load

Circular arch: uniform section: end A: pinned: end B: horiz.guide: uniform load: per unit vertical projection: horizontal: on left half arch

Beam under bending+shear: left end fixed: right end fixed: point load

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: point load: vertical: on girder

Beam under simple bending: large deflections: left end fixed: right end supported: concentrated load

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end sliding: distributed partial load: linearly varying: on girder

Minimum thickness of: spherical shells: spherical parts of shells: hemispherical ends: central zone of torispherical ends: spherical knuckles of cones to cylinders: under internal pressure: e/De<=0.16: Calculation based on inner radius

Tapered simply supported beam under simple bending: main inertia symmetrically varying with the 1st power of x: resistance modulus varying with the 1st power of x: combined loads

Solid circular flat plate: simple bending: simply supported: with uniform thickness: center load

Thin-walled cylindrical shell: Supported-fixed: radial load

Small deflections of rectangular plates: 1 clamped side, 2 supported(adjacent) and 1 free: distributed load linearly varying along side a

Circular arch: uniform section: end A: pinned: end B: inclined guide: distributed load: tangential

Circular arch: uniform section: end A: fixed: end B: free: uniform load: tangential

Beam under bending: with axial tension: left end supported: right end guided: concentrated moment

Simply supported beam: on elastic foundation: concentrated moment

Tapered simply supported beam under simple bending: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: concentrated moment

Small deflections of rectangular plates: 2 facing sides clamped, 2 supported: distributed load linearly varying along side a: starting at x0

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: distributed partial load: linearly varying: horizontal: on left post

Circular arch: uniform section: end A: pinned: end B: pinned: concentrated load: horizontal

Circular arch: uniform section: end A: pinned: end B: horiz.slide: distributed load: radial

Small deflections of rectangular plates: 4 simply supported sides: combined loads

Tapered simply supported beam under simple bending: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: uniform load

Beam under bending: with axial tension: left end fixed: right end supported: uniform load

Thin-walled cylindrical shell: Free-fixed: applied moment

Annular flat plate: with uniform thickness: simple bending: outer edge guided: inner edge supported: uniform load

Thin-walled cylindrical shell: Guided-guided: uniform radial pressure: from 'a' to 'b'

Circular arch: uniform section: end A: fixed: end B: free: uniform load: per unit horizontal projection: vertical

Circular arch: uniform section: end A: fixed: end B: inclined guide: concentrated load: vertical

Thin-walled cylindrical shell: Guided-supported: uniform radial pressure: from 'a' to 'b'

Design rules for clamp connections: clamping faces parallel: hub calculated as loose flange

Small deflections of rectangular plates: 2 simply supported opposite sides and 2 free: distributed load linearly varying along side a: starting at x0

Small deflections of rectangular plates: 3 clamped sides, 1 supported: distributed load linearly varying along side a

Guided-guided beam: on elastic foundation: concentrated moment

Circular pipes: supported at bottom: 2 vertical line loads: symmetric

Circular arch: uniform section: end A: fixed: end B: inclined slide: uniform load: radial

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: uniform load: horizontal: on girder

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: concentrated load: radial

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: uniform load: horizontal: on girder left half

Beam under bending: with axial compression: left end supported: right end guided: distributed load

Thin-walled cylindrical shell: Supported-supported: linearly varying radial pressure

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: distributed partial load: linearly varying: on right post

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: uniform load: per unit horizontal projection: vertical

Small deflections of rectangular plates: 3 clamped sides, 1 free: uniform load

Beam under simple bending: left end fixed: right end guided: combined loads

Beam under bending+shear: left end fixed: right end guided: uniform load

Circular arch: uniform section: end A: fixed: end B: fixed: uniform load: tangential

Circular pipes: supported at bottom: 2 radial line loads: symmetric

Thin-walled cylindrical shell: Fixed-supported: radial load

Circular arch: uniform section: end A: fixed: end B: vertical guide: concentrated load: radial

Beam under bending: with axial tension: left end fixed: right end free: temperature gradient: across depth: linearly varying

Tapered fixed beam under simple bending: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: concentrated load

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: guided edge: distributed + uniform load

Circular arch: uniform section: end A: fixed: end B: horiz.guide: uniform load: radial

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: distributed partial load: linearly varying: on girder

Circular arch: uniform section: end A: fixed: end B: free: distributed load: radial

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: point load: horizontal: on right post

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: uniform temperature change

Small deflections of rectangular plates: 4 clamped sides: distributed load: over a partial rectangular area

Circular arch: uniform section: end A: fixed: end B: horiz.guide: uniform load: per unit vertical projection: horizontal

Circular arch: uniform section: end A: fixed: end B: inclined slide: distributed load: vertical: partial

Beam under simple bending: large deflections: left end supported: right end supported: distributed load

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge free: parabolically increasing load

Free-free beam: on elastic foundation: point load

Tapered simply supported beam under simple bending: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: linearly decreasing load

Tapered fixed beam under simple bending: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: uniform load

Small deflections of rectangular plates: 3 clamped sides, 1 free: distributed load linearly varying along side a

Tapered simply supported beam under simple bending: main inertia symmetrically varying with the 4th power of x: resistance modulus varying with the 3rd power of x: uniform load

Annular flat plate: with uniform thickness: simple bending: outer edge simply guided: inner edge supported: uniform annular line load

Thin-walled cylindrical shell: Fixed-free: uniform radial pressure: from 'a' to B

Thin-walled cylindrical shell: Supported-guided: applied moment

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: distributed partial load: linearly varying: horizontal: on left post

Minimum thickness of cylindrical shells under internal pressure: e/De<=0.16: Calculation based on outer diameter

Beam under simple bending: left end fixed: right end guided: temperature gradient: across depth: linearly varying

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: point load: horizontal: on girder right half

Beam under bending: with held ends: left end fixed: right end free: temperature gradient: across depth: linearly varying

Small deflections of rectangular plates: 3 supported sides, 1 clamped: distributed load: linearly varying: along side a

Solid circular flat plate: simple bending: simply supported: with uniform thickness: uniform load

Circular arch: uniform section: end A: fixed: end B: horiz.guide: concentrated moment

Beam under simple bending: large deflections: left end fixed: right end fixed: uniform load

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 2nd power of x (n=2): under a single axial compressive load: base fixed: top fixed

Small deflections of rectangular plates: 3 clamped sides, 1 supported: distributed load: over a partial rectangular area

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: uniform load: on girder

Beam under bending: with held ends: left end fixed: right end guided: concentrated load

Thin-walled cylindrical shell: Free-supported: radial load

Allowable external pressure: of cylindrical shells: circularity outside tolerance

Circular arch: uniform section: end A: fixed: end B: inclined slide: concentrated moment

Beam under simple bending: large deflections: left end fixed: right end supported: uniform load

Annular flat plate: with uniform thickness: simple bending: outer edge guided: inner edge clamped: combined loads

Continuous beam: over 4 spans: in simple bending: point load

Small deflections of rectangular plates: 1 clamped side, 3 free: uniform load

Tapered fixed beam under simple bending: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: uniform load

Beam under bending: with held ends: left end fixed: right end free: applied angular displacement

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 1st power of x (n=1): under a single axial compressive load: base fixed: top supported

Solid circular flat plate with uniform thickness: simple bending: on (mono)elastic foundation: free edge: distributed + uniform load

Circular arch: uniform section: end A: fixed: end B: inclined slide: uniform load: per unit vertical projection: horizontal: on left half arch

Tapered fixed beam under simple bending: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: concentrated load

Tapered cantilever under simple bending: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: uniform load

Circular arch: uniform section: end A: fixed: end B: free: combined loads

Beam under simple bending: left end fixed: right end free: temperature gradient: across depth: linearly varying

Circular ring beam: supported at bottom: 2 horizontal loads

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge fixed: distributed load

Tapered fixed beam under simple bending: main inertia symmetrically varying with the 1st power of x: resistance modulus varying with the 1st power of x: concentrated moment

Small deflections of triangular plates: equilateral: 3 supported sides: uniform load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: distributed partial load: linearly varying: vertical: on girder right half

Circular arch: uniform section: end A: fixed: end B: vertical slide: uniform load: tangential

Beam under bending: with axial tension: left end fixed: right end supported: applied angular displacement

Beam under bending: with axial compression: left end fixed: right end supported: combined loads

Small deflections of rectangular plates: 4 free sides: supported at 4 corners: distributed load linearly varying along side a: starting at x0

Beam under bending: with held ends: left end fixed: right end fixed: concentrated load

Circular flat flanges without hubs: lap joint: to internal pressure: gasket laying inside inner edge of bolt holes: with bolt spacing correction

Circular arch: uniform section: end A: pinned: end B: inclined guide: uniform temperature gradient: across depth

Beam under simple bending: left end supported: right end supported: temperature gradient: across depth: linearly varying

Fixed-fixed beam: on elastic foundation: concentrated moment

Guided-free beam: on elastic foundation: point load

Tapered simply supported beam under simple bending: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: combined loads

Beam under bending: with axial tension: left end fixed: right end fixed: distributed load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: point load: on girder

Circular arch: uniform section: end A: pinned: end B: horiz.slide: concentrated load: tangential

Beam under bending+shear: left end fixed: right end fixed: uniform load

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: uniform temperature change

Circular arch: uniform section: end A: fixed: end B: pinned: concentrated load: radial

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge supported: applied vertical displacement

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: combined loads

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end pinned: uniform temperature change

Tapered fixed beam under simple bending: main inertia symmetrically varying with the 4th power of x: resistance modulus varying with the 3rd power of x: linearly decreasing load

Thin-walled cylindrical shell: Guided-free: linearly varying radial pressure

Thin-walled cylindrical shell: Free-free: radial load

Required thickness of conical shells: under internal pressure: Calculation based on outside diameter

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge guided: uniform annular line load

Beam under simple bending: left end supported: right end guided: combined loads

Beam under simple bending: large deflections: left end supported: right end guided: uniform load

Circular arch: uniform section: end A: fixed: end B: inclined guide: uniform load: per unit vertical projection: horizontal

Thin-walled cylindrical shell: Free-guided: linearly varying radial pressure

Small deflections of rectangular plates: 2 opposite sides clamped, 2 free: uniform load

Small deflections of rectangular plates: 1 clamped side, 2 supported and 1 free: distributed load linearly varying along side a: starting at x0

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: uniform load: horizontal: on girder right half

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: combined loads

Solid circular flat plate with uniform thickness: simple bending: on (mono)elastic foundation: guided edge: center load + uniform load

Circular arch: uniform section: end A: fixed: end B: pinned: uniform load: tangential

Tapered cantilever under simple bending: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: linearly decreasing load

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge supported: distributed load

Beam under bending: with axial tension: left end fixed: right end guided: uniform load

Annular flat plate: with uniform thickness: simple bending: outer edge guided: inner edge clamped: uniform load

Beam under bending: with axial tension: left end fixed: right end fixed: combined loads

Beam under bending: with axial compression: left end supported: right end supported: distributed load

Thin-walled cylindrical shell: Supported-free: radial load

Circular flanges with hub: hub with constant thickness: loose, welded: fig.2-4(3): to internal pressure: gasket laying inside inner edge of bolt holes

Tapered fixed beam under simple bending: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: concentrated moment

Thin-walled cylindrical shell: Free-supported: uniform radial pressure: from 'a' to B

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end pinned: distributed partial load: linearly varying: on post

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: combined loads

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: distributed partial load: linearly varying: vertical: on girder left half

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: hydrostatic load

Small deflections of rectangular plates: 1 clamped side, 2 supported and 1 free: combined loads

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: point load: horizontal: on girder right half

Circular arch: uniform section: end A: pinned: end B: inclined slide: distributed load: tangential

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge free: temperature differential across thickness

Circular arch: uniform section: end A: pinned: end B: horiz.guide: hydrostatic load

Circular arch: uniform section: end A: fixed: end B: vertical guide: uniform load: per unit length of arch: vertical

Circular arch: uniform section: end A: pinned: end B: inclined slide: concentrated load: horizontal

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: linearly decreasing load

Two cylinders in contact under load: parallel axes: Hertz's theory

Beam under bending: with axial compression: left end supported: right end supported: concentrated load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: uniform load: vertical: on girder right half

Annular flat plate: with uniform thickness: simple bending: outer edge free: inner edge supported: uniform annular line moment

Circular arch: uniform section: end A: fixed: end B: free: uniform load: per unit length of arch: vertical

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end sliding: uniform temperature change

Narrow face gasketed flanges: integral method: with hub: WN or LWN type: to internal pressure

Solid circular flat plate with uniform thickness: large deflections behaviour: clamped: uniform distributed load

Small deflections of rectangular plates: bending + shear: 4 simply supported sides: concentrated load

Circular arch: uniform section: end A: fixed: end B: horiz.slide: hydrostatic load

Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: supported edge: uniform annular line load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: point load: vertical: on girder right half

Solid circular flat plate: simple bending: simply supported: with linearly decreasing thickness: uniform load

Thin-walled cylindrical shell: Supported-supported: uniform radial pressure: from 'a' to B

Circular arch: uniform section: end A: pinned: end B: pinned: distributed load: vertical: partial

Tapered cantilever under simple bending: main inertia varying with the 2nd power of x: resistance modulus varying with the 1st power of x: concentrated moment

Beam under simple bending: left end supported: right end guided: concentrated moment

Tapered simply supported beam under simple bending: main inertia symmetrically varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: linearly decreasing load

Beam under bending: with axial tension: left end supported: right end guided: applied angular displacement

Tapered cantilever under simple bending: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: distributed load

Circular arch: uniform section: end A: fixed: end B: horiz.guide: concentrated load: horizontal

Tapered simply supported beam under simple bending: main inertia varying with the 1st power of x: resistance modulus varying with the 1st power of x: combined loads

Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge free: distributed load

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end pinned: uniform load: on girder

Thin-walled cylindrical shell: Fixed-guided: radial load

Small deflections of rectangular plates: 2 adjacent clamped sides, 2 supported: distributed load: over a partial rectangular area

Rectangular membranes: 4 held sides: liquid filled+self weight

Small deflections of rectangular plates: 4 free sides: supported at 4 corners: distributed load linearly varying along side a

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end pinned: combined loads

Tapered beam under simple bending: a fixed end and a supported one: main inertia varying with the 4th power of x: resistance modulus varying with the 3rd power of x: uniform load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: point load: horizontal: on girder right half

Beam under simple bending: left end supported: right end supported: distributed load

Continuous beam: over 2 spans: in simple bending: point load

Annular flat plate: with uniform thickness: simple bending: outer edge clamped: inner edge free: uniform load

Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge guided: distributed load

Beam under bending: with axial compression: left end fixed: right end guided: concentrated load

Beam under bending+shear: left end fixed: right end supported: combined loads

Circular arch: uniform section: end A: fixed: end B: free: uniform load: per unit vertical projection: horizontal

Circular arch: uniform section: end A: fixed: end B: horiz.slide: concentrated load: radial

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: distributed partial load: linearly varying: vertical: on girder right half

Circular arch: uniform section: end A: fixed: end B: vertical guide: uniform load: per unit horizontal projection: vertical

Circular arch: uniform section: end A: fixed: end B: fixed: concentrated load: vertical