Circular arch: uniform section: end A: fixed: end B: vertical guide: 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: point load: on right post
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
One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end sliding: right end fixed: uniform temperature change
Circular arch: uniform section: end A: fixed: end B: horiz.slide: uniform load: per unit length of arch: horizontal
Beam under bending: with held ends: left end supported: right end supported: concentrated moment
Solid circular flat plate with uniform thickness: simple bending: on (mono)elastic foundation: guided edge: center load + uniform load
Beam: simple bending: with held ends: left end supported: right end supported: uniform load
Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge free: applied angular displacement
Beam under simple bending: large deflections: left end fixed: right end fixed: 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 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 right post
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
Circular arch: uniform section: end A: fixed: end B: horiz.slide: uniform load: per unit length of arch: vertical
Circular pipes: supported at bottom: load at top
Circular arch: uniform section: end A: fixed: end B: free: hydrostatic 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: 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 load: horizontal: on right post
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
Guided-infinite beam: on elastic foundation: distributed load: linearly varying: from 'a' to 'b'
Free-free beam: on elastic foundation: point load
Beam under bending: with held ends: left end supported: right end guided: concentrated moment
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: fixed: hydrostatic load
Circular arch: uniform section: end A: fixed: end B: free: uniform load: per unit vertical projection: horizontal: on left half arch
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
Small deflections of rectangular plates: 2 opposite sides clamped, 2 free: concentrated load at center
Beam under bending: with held ends: left end supported: right end guided: uniform load
Large deflections of rectangular plates: 4 clamped & held sides: 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 right post
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
One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end sliding: right end fixed: distributed partial load: linearly varying: on girder
Small deflections of rectangular plates: 1 clamped side, 2 supported and 1 free: distributed load linearly varying along side a
Beam under bending: with held ends: left end fixed: right end free: concentrated load
Circular arch: uniform section: end A: pinned: end B: horiz.slide: uniform load: radial
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
Circular arch: uniform section: end A: pinned: end B: horiz.guide: uniform load: per unit vertical projection: horizontal: on left half arch
Annular flat plate: with uniform thickness: simple bending: outer edge guided: inner edge clamped: uniform load
Beam under bending: with held ends: left end fixed: right end fixed: temperature gradient: across depth: linearly varying
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
Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: guided edge: center load
Required thickness of conical shells: under internal pressure: Calculation based on outside diameter
Small deflections of rectangular plates: 4 free sides: supported at 4 corners: uniform load
Circular arch: uniform section: end A: pinned: end B: horiz.guide: uniform load: per unit horizontal projection: vertical
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
Circular ring beam: supported at bottom: 2 horizontal 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
Spheres in contact with a spherical socket under load: Hertz's theory
Solid circular flat plate with uniform thickness: large deflections behaviour: supported & held: uniform distributed load
Circular pipes: supported at bottom: partially filled with liquid
Circular arch: uniform section: end A: pinned: end B: inclined slide: combined loads
One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end fixed: uniform load: 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
Circular arch: uniform section: end A: pinned: end B: inclined guide: uniform load: radial
Elastic stability of a beam-column: prismatic: under a single axial compressive load: base fixed: top supported
Beam under bending: with held ends: left end fixed: right end guided: concentrated load
Small deflections of rectangular plates: 3 clamped sides, 1 free: uniform 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: distributed 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
Circular arch: uniform section: end A: pinned: end B: inclined slide: uniform load: tangential
Circular arch: uniform section: end A: fixed: end B: vertical slide: concentrated load: vertical
Circular arch: uniform section: end A: fixed: end B: inclined guide: uniform load: radial
Circular arch: uniform section: end A: fixed: end B: horiz.slide: distributed load: vertical: partial
Annular flat plate: with uniform thickness: simple bending: outer edge clamped: inner edge free: combined loads
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
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
One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end pinned: uniform load: on post
One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end sliding: combined loads
Small deflections of rectangular plates: 1 clamped side, 2 supported(adjacent) and 1 free: uniform load
Circular arch: uniform section: end A: fixed: end B: free: concentrated load: radial
Circular pipes: supported at bottom: uniform radial pressure: over an arc
Circular arch: uniform section: end A: fixed: end B: pinned: hydrostatic load
One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end fixed: point load: on girder
Thin-walled cylindrical shell: Free-supported: radial load
Small deflections of rectangular plates: 2 opposite sides clamped, 2 free: distributed load linearly varying along side a
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
Circular arch: uniform section: end A: pinned: end B: horiz.guide: uniform 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: uniform 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 left post
Supported-fixed beam: on elastic foundation: distributed load: linearly varying: from 'a' to 'b'
Beam under bending: with held ends: left end fixed: right end fixed: 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: uniform temperature change
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
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: pinned: end B: horiz.guide: combined loads
Circular arch: uniform section: end A: fixed: end B: vertical guide: distributed load: tangential
Thin-walled cylindrical shell: Free-supported: uniform radial pressure: from 'a' to 'b'
Beam under bending: with held ends: 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 pinned: right end pinned: supports at same elevation: point load: horizontal: on left post
Thin-walled cylindrical shell: Free-fixed: applied moment
Beam under simple bending: large deflections: left end supported: right end supported: concentrated load
Circular arch: uniform section: end A: pinned: end B: pinned: reverse hydrostatic load
One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end pinned: combined loads
One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end sliding: uniform load: on post
Circular arch: uniform section: end A: pinned: end B: inclined slide: uniform load: per unit horizontal projection: vertical
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
Circular arch: uniform section: end A: fixed: end B: vertical slide: uniform temperature gradient: across depth
Thin-walled cylindrical shell: Free-guided: uniform radial pressure: from 'a' to B
Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge free: distributed load
Circular arch: uniform section: end A: fixed: end B: horiz.slide: uniform load: per unit vertical projection: horizontal
Small deflections of rectangular plates: bending + shear: 4 simply supported sides: distributed load linearly varying along side a: starting at x0
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
Solid circular flat plate with uniform thickness: large deflections behaviour: simply supported: distributed load
Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: distributed load: vertical: partial
Supported-guided beam: on elastic foundation: concentrated load
Circular arch: uniform section: end A: pinned: end B: inclined slide: uniform load: per unit vertical projection: horizontal: on left half arch
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
One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end fixed: combined loads
Solid circular flat plate with uniform thickness: large deflections behaviour: clamped & held: distributed load
Supported-guided beam: on elastic foundation: 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: vertical guide: uniform load: per unit vertical projection: horizontal
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: horiz.guide: hydrostatic load
Small deflections of triangular plates: equilateral: 2 clamped sides, 1 free: uniform load
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
Circular arch: uniform section: end A: fixed: end B: vertical guide: uniform load: per unit length of arch: horizontal
Circular arch: uniform section: end A: fixed: end B: free: 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: distributed load
Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: concentrated load: horizontal
Beam under bending: with held ends: left end supported: right end supported: temperature gradient: across depth: linearly varying
Circular arch: uniform section: end A: fixed: end B: vertical slide: concentrated moment
Circular arch: uniform section: end A: fixed: end B: inclined slide: distributed load: radial
Beam under simple bending: large deflections: left end fixed: right end free: uniform load
Circular arch: uniform section: end A: fixed: end B: horiz.slide: concentrated moment
Large deflections of rectangular plates: 4 supported & held sides: distributed load linearly varying along side a
Cylinder in contact in a cylindrical socket under load: Hertz's theory
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
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
Disc springs: stack in series: with or without bearing flats
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
Design rules for clamp connections: clamping faces parallel: hub calculated as loose flange
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 pinned: supports at same elevation: uniform load: vertical: on girder
Elastic stability of a beam-column: with two stepped sections: under two axial compressive loads: base fixed: top supported
Beam under bending: with held ends: left end fixed: right end supported: applied angular displacement
Semiinfinite beam: on elastic foundation: point load
Small deflections of triangular plates: equilateral: 3 clamped sides: distributed load: linearly varying: along height a
Thin-walled cylindrical shell: Free-free: linearly varying radial pressure
Beam under bending: with held ends: left end supported: right end guided: temperature gradient: across depth: linearly varying
Beam under simple bending: large deflections: left end fixed: right end guided: uniform load
Circular ring beam: supported at bottom: combined loads
Circular pipes: supported at bottom: filled with liquid
Beam under simple bending: large deflections: left end fixed: right end supported: distributed load
Fixed-fixed beam: on elastic foundation: point load
Circular arch: uniform section: end A: fixed: end B: horiz.slide: concentrated load: radial
Circular arch: uniform section: end A: fixed: end B: free: concentrated load: tangential
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
Small deflections of triangular plates: equilateral: 2 supported sides, 1 free: uniform load
Small deflections of rectangular plates: 1 clamped side, 3 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 pinned: combined loads
Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: concentrated load: radial
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
Circular arch: uniform section: end A: fixed: end B: horiz.slide: combined loads
Narrow face gasketed flanges: integral method: with hub: WN or LWN type: to internal pressure
Elastic stability of a beam-column: prismatic: under a single axial compressive load: base fixed: top free
Beam under bending: with held ends: left end fixed: right end guided: uniform load
One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: 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: combined loads
Small deflections of triangular plates: equilateral: 3 clamped sides: 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 load: vertical: on girder
Circular arch: uniform section: end A: fixed: end B: horiz.slide: uniform load: tangential
Solid circular flat plate: simple bending: simply supported: with linearly decreasing thickness: center load
Circular arch: uniform section: end A: pinned: end B: inclined slide: distributed load: vertical: partial
Beam under bending: with held ends: left end fixed: right end guided: concentrated moment
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
Circular arch: uniform section: end A: fixed: end B: vertical guide: combined loads
Elastic stability of a beam-column: prismatic: under a single axial compressive load: base fixed: top fixed
Beam under bending: with held ends: left end fixed: right end supported: distributed load
Circular ring beam: supported at bottom: 2 radial loads
Beam under bending: with held ends: left end fixed: right end free: uniform load
Spheres in contact with a cylindrical socket under load: Hertz's theory
Minimum thickness of cylindrical shells under internal pressure: e/De<=0.16: Calculation based on outer diameter
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
Beam under bending: with held ends: left end fixed: right end free: concentrated moment
Circular ring beam: supported at bottom: loaded by uniform vertical load
Circular arch: uniform section: end A: pinned: end B: horiz.guide: 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: linearly decreasing load
Solid circular flat plate: simple bending: clamped: with uniform thickness: uniform load
Two spheres in contact under load: Hertz's theory
Circular arch: uniform section: end A: fixed: end B: horiz.guide: uniform load: radial
One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end fixed: point load: on 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 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
Beam under bending: with held ends: left end fixed: right end fixed: applied vertical displacement
Thin-walled cylindrical shell: Fixed-free: linearly varying radial pressure
Circular pipes: supported at bottom: 2 facing horizontal line loads
Annular flat plate: with uniform thickness: simple bending: outer edge free: inner edge fixed: applied angular displacement
Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: uniform load: per unit vertical projection: horizontal: on left half arch
Circular pipes: supported at bottom: 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
Elastic stability of a beam-column: with two stepped sections: under two axial compressive loads: base fixed: top guided
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
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
Beam under bending: with held ends: left end supported: right end guided: concentrated load
Annular flat plate: with uniform thickness: simple bending: outer edge free: inner edge supported: applied angular displacement
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
Circular arch: uniform section: end A: pinned: end B: horiz.guide: concentrated moment
Solid circular flat plate with uniform thickness: pure membrane behaviour: supported & held: distributed load
Circular arch: uniform section: end A: pinned: end B: pinned: uniform load: radial
Circular pipes: supported at bottom: loaded by self weight: directed upwards
Circular arch: uniform section: end A: pinned: end B: inclined slide: uniform load: per unit length of arch: horizontal
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
Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: hydrostatic load
Circular arch: uniform section: end A: pinned: end B: horiz.guide: concentrated load: radial
Small deflections of rectangular plates: bending + shear: 4 simply supported sides: 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: point load: on right 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 free
Beam under simple bending: large deflections: left end fixed: right end fixed: uniform load
Beam: simple bending: with held ends: left end supported: right end supported: uniform load
Circular arch: uniform section: end A: pinned: end B: inclined slide: uniform load: per unit length of arch: vertical
Circular arch: uniform section: end A: fixed: end B: pinned: uniform load: radial
One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end sliding: right end fixed: point load: on girder
Beam under simple bending: large deflections: left end fixed: right end guided: concentrated load
Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: concentrated load: tangential
Elastic stability of a beam-column: with two stepped sections: under two axial compressive loads: base fixed: top free
Circular arch: uniform section: end A: fixed: end B: inclined guide: hydrostatic 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
Circular arch: uniform section: end A: pinned: end B: horiz.guide: uniform load: per unit length of arch: vertical
Small deflections of rectangular plates: 4 clamped sides: uniform load
Fixed-free beam: on elastic foundation: point load
Elastic stability of a beam-column: with two stepped sections: under two axial compressive loads: base fixed: top fixed
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
Circular arch: uniform section: end A: pinned: end B: horiz.guide: uniform load: per unit length of arch: horizontal
Circular arch: uniform section: end A: pinned: end B: inclined guide: hydrostatic load
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
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 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: inclined slide: concentrated load: radial
Two cylinders in contact under load: axes at right angles: Hertz's theory
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
Disc springs: stack in series and in parallel: with or without bearing flats
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
Beam under simple bending: large deflections: left end fixed: right end free: concentrated load
Circular arch: uniform section: end A: pinned: end B: inclined slide: concentrated moment
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
Circular arch: uniform section: end A: fixed: end B: inclined slide: uniform load: per unit horizontal projection: vertical
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
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
Disc springs: single: with or without bearing flats
Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge guided: uniform load
Two cylinders in contact under load: parallel axes: Hertz's theory
Circular arch: uniform section: end A: fixed: end B: inclined slide: uniform 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: uniform load: vertical: on girder
Circular arch: uniform section: end A: fixed: end B: free: 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: linearly decreasing load
Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: uniform temperature change
Circular arch: uniform section: end A: pinned: end B: horiz.slide: hydrostatic load
Circular arch: uniform section: end A: fixed: end B: horiz.slide: uniform load: per unit horizontal projection: vertical
Circular arch: uniform section: end A: pinned: end B: inclined 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: distributed partial load: linearly varying: on girder
Annular flat plate: with uniform thickness: simple bending: outer edge free: inner edge supported: uniform annular line load
One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end pinned: combined loads
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
Solid circular flat plate with uniform thickness: large deflections behaviour: clamped: 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: Pressure stresses per BS5500 G.2.3.5.2(a): (radial load should not include pressure end 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 free: inner edge supported: uniform annular line moment
Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: combined loads
Circular arch: uniform section: end A: fixed: end B: horiz.slide: uniform load: per unit vertical projection: horizontal: on left half arch
Circular arch: uniform section: end A: fixed: end B: free: distributed load: vertical: partial
Rectangular membranes: 4 held sides: liquid filled+self weight
Annular flat plate: with uniform thickness: simple bending: outer edge free: inner edge fixed: uniform annular line load
Circular arch: uniform section: end A: fixed: end B: fixed: uniform load: radial
Beam under bending: with held ends: left end fixed: 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 1st power of x: resistance modulus varying with the 1st power of x: combined loads
Elastic stability of a beam-column: prismatic: under a single axial compressive load: base fixed: top guided
Beam under simple bending: large deflections: 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 moment
Thin-walled cylindrical shell: Free-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: combined loads
Circular arch: uniform section: end A: pinned: end B: horiz.guide: distributed load: vertical: partial
Small deflections of rectangular plates: 2 adjacent clamped sides, 2 supported: distributed load linearly varying along side a: starting at x0
Circular ring beam: supported at bottom: 2 tangential loads
Thin-walled cylindrical shell: Free-guided: applied moment
Small deflections of rectangular plates: bending + shear: 4 simply supported sides: concentrated 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
Spheres in contact: with a grooved inner ring: under load: Hertz's theory
Small deflections of rectangular plates: 2 adjacent clamped sides, 2 supported: distributed load: over a partial rectangular area
Supported-infinite beam: on elastic foundation: distributed load: linearly varying: from 'a' to 'b'
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
Beam under bending: with held ends: left end fixed: right end free: temperature gradient: across depth: linearly varying
Small deflections of rectangular plates: 2 adjacent clamped sides, 2 free: distributed load linearly varying along side a: starting at x0
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
Small deflections of rectangular plates: 2 adjacent clamped sides, 2 free: distributed load: over a partial rectangular area
Beam under simple bending: large deflections: left end supported: right end supported: 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: point load: horizontal: on left post
One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end fixed: uniform temperature change
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
Circular arch: uniform section: end A: fixed: end B: vertical guide: uniform load: tangential
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 symmetrically varying with the 3rd power of x: resistance modulus varying with the 2nd power of x: combined loads
Beam under bending: with held ends: left end fixed: right end fixed: concentrated 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 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: horizontal: on girder right half
Full face flanges: with soft ring type gaskets: to internal pressure
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
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
Circular arch: uniform section: end A: fixed: end B: pinned: concentrated load: horizontal
Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge guided: applied angular displacement
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
Beam under bending+shear: left end fixed: right end free: distributed load
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: fixed: uniform temperature change
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
Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: distributed load: radial
Circular arch: uniform section: end A: fixed: end B: vertical slide: uniform load: tangential
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
Small deflections of triangular plates: equilateral: 3 supported sides: combined loads
Beam under bending: with axial tension: left end fixed: right end fixed: applied angular displacement
Circular arch: uniform section: end A: fixed: end B: free: uniform load: radial
One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end pinned: uniform load: on girder
Solid circular flat plate: simple bending: simply supported: with linearly increasing thickness: center load
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
Small deflections of rectangular plates: 2 facing sides clamped, 2 supported: distributed load: over a partial rectangular area
Thin-walled cylindrical shell: Supported-fixed: applied moment
Circular arch: uniform section: end A: fixed: end B: inclined slide: concentrated load: horizontal
Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: uniform temperature change
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
Minimum thickness of cylindrical shells under internal pressure: e/De<=0.16: Calculation based on inner diameter
Beam under bending+shear: left end fixed: right end supported: combined loads
Circular arch: uniform section: end A: pinned: end B: pinned: concentrated load: vertical
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
Beam under bending+shear: left end fixed: right end guided: distributed load
Beam under simple bending: left end fixed: right end fixed: uniform load
Small deflections of rectangular plates: 4 clamped sides: combined loads
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
Solid circular flat plate: simple bending: clamped: with uniform thickness: distributed load
Beam under bending+shear: left end fixed: right end supported: uniform load
Beam under simple bending: left end fixed: right end fixed: concentrated moment
Circular arch: uniform section: end A: fixed: end B: horiz.guide: uniform temperature gradient: across depth
Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge fixed: uniform annular line 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: linearly decreasing load
Thin-walled cylindrical shell: Supported-supported: applied 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: point load: vertical: on girder left half
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: horiz.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 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 pinned: right end pinned: point load: on left post
Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge guided: uniform annular line moment
Circular arch: uniform section: end A: fixed: end B: inclined guide: concentrated load: tangential
Small deflections of rectangular plates: 3 supported sides, 1 clamped: combined loads
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
Continuous beam: over 3 spans: in simple bending: distributed load
Beam under bending: with axial compression: left end supported: right end supported: applied vertical displacement
Small deflections of rectangular plates: 2 adjacent clamped sides, 2 free: uniform 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: distributed partial load: linearly varying: horizontal: on right post
Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge supported: uniform annular line load
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: pinned: end B: inclined guide: concentrated load: tangential
Beam under bending: with axial compression: left end supported: right end supported: combined loads
Beam under simple bending: left end supported: right end guided: temperature gradient: across depth: linearly varying
Infinite beam: on elastic foundation: distributed load: linearly varying over 'a'
Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge fixed: applied vertical displacement
Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge supported: uniform annular line moment
Beam under simple bending: left end fixed: right end supported: applied angular displacement
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: pinned: uniform temperature change
Beam under bending: with axial tension: left end fixed: right end free: distributed load
Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge free: uniform annular line load
Circular arch: uniform section: end A: pinned: end B: horiz.slide: distributed load: radial
Thin-walled cylindrical shell: Guided-free: applied moment
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
Beam under bending: with axial compression: left end fixed: right end guided: temperature gradient: across depth: linearly varying
Small deflections of rectangular plates: 2 adjacent clamped sides, 2 supported: uniform load
Beam under bending: with axial tension: left end fixed: right end supported: uniform load
Thin-walled cylindrical shell: Supported-guided: radial 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
Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: free edge: distributed + 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: horizontal: on girder right half
Beam under simple bending: left end fixed: right end guided: combined loads
Annular flat plate: with uniform thickness: simple bending: outer edge free: inner edge clamped: uniform load
Small deflections of rectangular plates: 2 adjacent supported sides, 2 free: point load
Beam under bending: with axial compression: left end supported: right end guided: combined loads
Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge fixed: parabolically increasing load
Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge guided: combined loads
Small 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: inclined guide: 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 supported: top supported
Beam under simple bending: left end supported: right end supported: 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 fixed: supports at same elevation: uniform load: horizontal: on girder right half
Small deflections of rectangular plates: 2 simply supported opposite sides and 2 free: distributed load: over a partial rectangular area
Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: supported: distributed + uniform load
Beam under bending: with axial tension: left end fixed: right end guided: distributed load
Beam under bending: with axial compression: left end fixed: right end free: temperature gradient: across depth: linearly varying
Circular arch: uniform section: end A: fixed: end B: inclined slide: distributed load: vertical: partial
Thin-walled cylindrical shell: Fixed-supported: uniform radial pressure: from 'a' to 'b'
Circular arch: uniform section: end A: pinned: end B: inclined guide: distributed load: radial
Thin-walled cylindrical shell: Supported-guided: linearly varying radial pressure
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 fixed: right end pinned: supports at same elevation: point load: vertical: on girder right half
Small deflections of rectangular plates: 3 supported sides, 1 free: distributed load linearly varying along side a: starting at x0
Circular arch: uniform section: end A: pinned: end B: horiz.slide: concentrated load: tangential
Beam under bending: with axial compression: left end fixed: right end fixed: concentrated load
Circular arch: uniform section: end A: fixed: end B: pinned: uniform temperature gradient: across depth
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
Annular flat plate: with uniform thickness: simple bending: outer edge free: inner edge supported: uniform load
Thin-walled cylindrical shell: Fixed-fixed: uniform radial pressure: from 'a' to B
Fixed-guided beam: on elastic foundation: point load
Solid circular flat plate: simple bending: clamped: with uniform thickness: center 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 left post
Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge fixed: applied vertical displacement
Beam under simple bending: left end supported: right end guided: uniform load
Thin-walled cylindrical shell: Guided-free: radial load
Beam under bending: with axial compression: left end fixed: right end guided: 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: linearly decreasing load
Solid circular flat plate with uniform thickness: simple bending: on (mono)elastic foundation: fixed edge: annular line load + uniform load
Fixed-guided beam: on elastic foundation: concentrated moment
Thin-walled cylindrical shell: Guided-supported: uniform radial pressure: from 'a' to B
Beam under bending: with axial tension: left end supported: right end supported: applied angular displacement
Beam under simple bending: left end supported: right end guided: concentrated moment
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
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
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
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
Annular flat plate: with uniform thickness: simple bending: outer edge simply guided: inner edge supported: uniform annular line load
Small deflections of rectangular plates: 4 clamped sides: distributed load: linearly varying: along side a
Beam under bending: with axial compression: left end fixed: right end supported: distributed load
Fixed-free beam: on elastic foundation: concentrated moment
Circular arch: uniform section: end A: pinned: end B: pinned: concentrated moment
Thin-walled cylindrical shell: Guided-free: linearly varying radial pressure
Beam under bending: with axial compression: left end fixed: right end guided: concentrated moment
Thin-walled cylindrical shell: Fixed-guided: uniform radial pressure: from 'a' to B
Beam under bending: with axial compression: left end fixed: right end free: uniform 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: 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 pressure: on girder left half
Beam under simple bending: left end supported: right end supported: uniform load
Thin-walled cylindrical shell: Free-supported: linearly varying radial 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: concentrated moment
Continuous beam: over 5 spans: in simple bending: 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: horizontal: on girder
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
Circular arch: uniform section: end A: fixed: end B: fixed: concentrated load: horizontal
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 simple bending: left end supported: right end supported: concentrated moment
Beam under bending: with axial tension: left end supported: right end guided: 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 pressure: on girder left half
Beam under bending: with axial compression: left end fixed: right end free: 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: uniform 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: linearly decreasing load
Thin-walled cylindrical shell: Supported-guided: applied moment
Beam under bending: with axial tension: left end fixed: right end supported: 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 fixed: supports at same elevation: distributed partial load: linearly varying: horizontal: on left post
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 guided: distributed load
Circular arch: uniform section: end A: fixed: end B: pinned: uniform temperature change
Thin-walled cylindrical shell: Guided-guided: uniform radial pressure: from 'a' to B
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
Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge fixed: parabolically increasing load
Thin-walled cylindrical shell: Free-free: radial load
Continuous beam: over 2 spans: in simple bending: distributed load
Beam under bending: with axial compression: left end fixed: right end fixed: applied vertical displacement
Solid circular flat plate: simple bending: simply supported: with uniform thickness: distributed parabolically increasing load
Guided-guided beam: on elastic foundation: concentrated moment
Small deflections of rectangular plates: 3 supported sides, 1 clamped: distributed load: over a partial rectangular area
Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: supported edge: uniform load
Small deflections of rectangular plates: 2 simply supported opposite sides and 2 free: combined loads
Thin-walled cylindrical shell: Supported-fixed: radial load
Circular arch: uniform section: end A: fixed: end B: horiz.slide: concentrated load: vertical
Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge guided: parabolically increasing 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
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
Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge supported: parabolically increasing load
Beam under bending: with axial compression: left end supported: right end guided: concentrated load
Guided-guided beam: on elastic foundation: concentrated load
Circular arch: uniform section: end A: fixed: end B: fixed: 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 fixed: supports at same elevation: point load: horizontal: on left post
Thin-walled cylindrical shell: Free-free: uniform radial pressure: from 'a' to 'b'
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: distributed load
Beam under bending: with axial compression: left end fixed: right end fixed: combined loads
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 simple bending: left end fixed: right end guided: concentrated load
Rectangular membranes: 4 held sides: uniform load
Circular arch: uniform section: end A: fixed: end B: horiz.slide: distributed load: tangential
Thin-walled cylindrical shell: Supported-fixed: linearly varying radial pressure
Continuous beam: over 4 spans: in simple bending: distributed load
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 (bi)elastic foundation: free edge: uniform annular line load
Thin-walled cylindrical shell: Supported-supported: radial load
Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge supported: applied vertical displacement
Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge fixed: uniform annular line moment
Small deflections of rectangular plates: 2 adjacent supported sides, 2 free: combined loads
Supported-free beam: on elastic foundation: concentrated 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
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
Beam under bending: with axial compression: left end supported: right end supported: concentrated load
Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: supported edge: uniform annular line load
Small deflections of rectangular plates: 2 simply supported opposite sides and 2 free: concentrated load
Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge guided: temperature differential across thickness
Beam under simple bending: left end fixed: right end free: concentrated load
Circular arch: uniform section: end A: fixed: end B: vertical slide: combined loads
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
Circular arch: uniform section: end A: fixed: end B: horiz.guide: uniform temperature change
Supported-free beam: on elastic foundation: concentrated moment
Beam under simple bending: left end fixed: right end fixed: temperature gradient: across depth: linearly varying
Thin-walled cylindrical shell: Supported-supported: linearly varying radial pressure
Solid circular flat plate with uniform thickness: simple bending: on (mono)elastic foundation: guided edge: distributed + 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
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
Circular arch: uniform section: end A: fixed: end B: horiz.guide: concentrated load: tangential
Beam under bending: with axial tension: left end fixed: right end supported: 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: point load: vertical: on girder right half
Thin-walled cylindrical shell: Supported-guided: uniform radial pressure: from 'a' to B
Solid circular flat plate: simple bending: simply supported: with uniform thickness: uniform annular line 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 supported: top supported
Thin-walled cylindrical shell: Guided-guided: applied moment
Beam under bending: with axial compression: left end fixed: right end fixed: concentrated moment
Fixed-infinite beam: on elastic foundation: distributed load: linearly varying: from 'a' to 'b'
Circular arch: uniform section: end A: fixed: end B: inclined guide: concentrated load: horizontal
Small deflections of rectangular plates: 3 supported sides, 1 clamped: distributed load: linearly varying: along side a: starting at x0
Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge supported: parabolically increasing load
Circular arch: uniform section: end A: pinned: end B: inclined guide: concentrated load: horizontal
Thin-walled cylindrical shell: Guided-fixed: 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 right half
Thin-walled cylindrical shell: Fixed-guided: applied moment
Small deflections of rectangular plates: 4 simply supported sides: 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 supported: inner edge free: parabolically increasing load
Beam under bending+shear: left end supported: right end guided: distributed 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 girder
Beam under bending: with axial compression: left end fixed: right end fixed: uniform load
Circular arch: uniform section: end A: fixed: end B: horiz.guide: distributed load: radial
Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge free: temperature differential across thickness
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
Thin-walled cylindrical shell: Guided-supported: 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 temperature change
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
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
Free-free beam: on elastic foundation: concentrated moment
Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge fixed: uniform annular line load
Circular arch: uniform section: end A: fixed: end B: vertical guide: concentrated moment
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
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
Circular arch: uniform section: end A: fixed: end B: vertical slide: 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: horizontal: on right post
Continuous beam: over 3 spans: in simple bending: uniform load
Small deflections of rectangular plates: 4 simply supported sides: concentrated load
Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge 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: supports at same elevation: uniform temperature change
Beam under bending+shear: left end supported: right end supported: distributed load
Small deflections of rectangular plates: 3 supported sides, 1 free: combined loads
Continuous beam: over 3 spans: in simple bending: concentrated moment
Circular arch: uniform section: end A: pinned: end B: horiz.slide: concentrated load: horizontal
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
Thin-walled cylindrical shell: Fixed-fixed: applied moment
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
Simply supported beam: on elastic foundation: point load
Beam under bending: with axial compression: left end supported: right end supported: temperature gradient: across depth: linearly varying
Circular arch: uniform section: end A: pinned: end B: pinned: distributed load: vertical: partial
Beam under simple bending: left end fixed: right end free: temperature gradient: across depth: linearly varying
Required thickness of conical shells: under internal pressure: Calculation based on inside diameter
Circular arch: uniform section: end A: fixed: end B: pinned: concentrated load: tangential
Annular flat plate: with uniform thickness: simple bending: outer edge guided: inner edge fixed: 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: distributed load
Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: guided edge: center load + uniform load
Circular arch: uniform section: end A: pinned: end B: horiz.slide: uniform temperature gradient: across depth
Beam under simple bending: left end fixed: right end fixed: concentrated load
Circular arch: uniform section: end A: fixed: end B: vertical guide: uniform temperature gradient: across depth
Circular arch: uniform section: end A: pinned: end B: horiz.guide: distributed load: tangential
Beam under bending: with axial tension: left end supported: 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: linearly decreasing load
Circular arch: uniform section: end A: fixed: end B: vertical slide: uniform load: per unit vertical projection: horizontal
Beam under bending+shear: left end fixed: right end supported: point load
Solid circular flat plate with uniform thickness: large deflections behaviour: supported & held: uniform annular line load
Continuous beam: over 4 spans: in simple bending: combined loads
Simply supported beam: on elastic foundation: concentrated moment
Beam under bending: with axial compression: left end fixed: right end guided: 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: uniform load
Circular arch: uniform section: end A: pinned: end B: horiz.guide: concentrated load: vertical
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
Beam under simple bending: left end supported: right end guided: combined loads
Annular flat plate: with uniform thickness: simple bending: outer edge guided: inner edge supported: uniform annular line moment
Circular arch: uniform section: end A: fixed: end B: inclined slide: concentrated load: tangential
Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: uniform load: radial
Circular arch: uniform section: end A: fixed: end B: pinned: distributed load: radial
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
Beam under simple bending: left end supported: right end supported: combined loads
Beam under bending: with axial compression: left end supported: right end guided: temperature gradient: across depth: linearly varying
Small deflections of rectangular plates: 3 clamped sides, 1 free: distributed load linearly varying along side a
Beam under bending: with axial compression: left end fixed: right end supported: applied angular displacement
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
Circular arch: uniform section: end A: fixed: end B: inclined slide: 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: point load: horizontal: on girder right half
Circular arch: uniform section: end A: pinned: end B: pinned: concentrated load: radial
Small deflections of rectangular plates: 4 free sides: supported at 4 corners: combined loads
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
One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end fixed: uniform load: on girder
Circular arch: uniform section: end A: fixed: end B: free: distributed load: radial
Beam under bending: with axial tension: left end supported: right end supported: distributed load
Thin-walled cylindrical shell: Fixed-free: radial load
Circular arch: uniform section: end A: pinned: end B: inclined guide: uniform temperature gradient: across depth
Beam under simple bending: left end fixed: right end guided: temperature gradient: across depth: linearly varying
Continuous beam: over 2 spans: in simple bending: 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: point load: horizontal: on girder right half
Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: uniform load: per unit horizontal projection: vertical
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: fixed: end B: inclined guide: uniform temperature gradient: across depth
Circular arch: uniform section: end A: fixed: end B: vertical slide: distributed load: tangential
Beam under simple bending: left end supported: right end supported: applied vertical displacement
Thin-walled cylindrical shell: Fixed-free: uniform radial pressure: from 'a' to 'b'
Small deflections of rectangular plates: 3 clamped sides, 1 supported: distributed load: over a partial rectangular area
One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end pinned: uniform load: on girder
Beam under bending: with axial compression: left end fixed: right end free: 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: uniform load: horizontal: on left post
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
Beam under bending: with axial compression: left end supported: right end supported: concentrated moment
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
Circular arch: uniform section: end A: pinned: end B: horiz.slide: uniform temperature change
Beam under simple bending: left end fixed: right end free: concentrated moment
Solid circular flat plate: simple bending: simply supported: with uniform thickness: uniform line moment
Continuous beam: over 4 spans: in simple bending: uniform 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 left half
Circular arch: uniform section: end A: fixed: end B: inclined slide: uniform load: per unit vertical projection: horizontal: on left half arch
Annular flat plate: with uniform thickness: simple bending: outer edge simply fixed: inner edge guided: uniform annular line 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 right post
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 fixed: right end guided: applied angular displacement
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
Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge supported: uniform annular line moment
Thin-walled cylindrical shell: Supported-supported: uniform radial pressure: from 'a' to B
Small deflections of rectangular plates: 2 opposite sides clamped, 2 free: uniform load
Beam under simple bending: left end fixed: right end free(cantilever): uniform load
Annular flat plate: with uniform thickness: simple bending: outer edge guided: inner edge clamped: combined loads
Annular flat plate: with uniform thickness: simple bending: outer edge simply fixed: inner edge supported: uniform annular line load
Continuous beam: over 4 spans: in simple bending: concentrated moment
Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: fixed edge: uniform annular line load
Beam under bending: with axial compression: left end supported: right end supported: uniform 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 right post
Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge free: uniform annular line moment
Circular arch: uniform section: end A: fixed: end B: vertical guide: concentrated load: vertical
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
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
Beam under bending: with axial compression: left end supported: right end guided: concentrated moment
Continuous beam: over 2 spans: in simple bending: uniform load
Beam under bending: with axial tension: left end fixed: right end supported: combined loads
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
Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: free edge: distributed load
Beam under bending: with axial tension: left end fixed: right end free: applied angular displacement
One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end sliding: uniform load: on girder
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
Beam under simple bending: left end fixed: right end supported: distributed load
Small deflections of rectangular plates: 2 adjacent supported sides, 2 free: distributed load: over a partial rectangular area
Thin-walled cylindrical shell: Supported-fixed: uniform radial pressure: from 'a' to B
Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: fixed edge: uniform load
Small deflections of rectangular plates: 4 simply supported sides: distributed load: over a partial rectangular area
Annular flat plate: with uniform thickness: simple bending: outer edge clamped: inner edge free: uniform 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
Circular arch: uniform section: end A: pinned: end B: inclined slide: concentrated load: vertical
Guided-free beam: on elastic foundation: distributed load: linearly varying: from 'a' to 'b'
Circular arch: uniform section: end A: pinned: end B: inclined guide: uniform temperature change
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
Beam under simple bending: left end fixed: right end guided: concentrated moment
Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: supported: distributed load
Small deflections of rectangular plates: 2 simply supported opposite sides and 2 free: distributed load linearly varying along side a: starting at x0
Continuous beam: over 2 spans: in simple bending: concentrated moment
Beam under bending+shear: left end fixed: right end fixed: distributed load
Circular arch: uniform section: end A: fixed: end B: inclined guide: uniform temperature change
Beam under bending: with axial compression: left end supported: right end guided: uniform load
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
Small deflections of rectangular plates: 3 supported sides, 1 free: distributed load: over a partial rectangular area
Circular arch: uniform section: end A: pinned: end B: inclined slide: distributed load: tangential
Beam under simple bending: left end fixed: right end guided: uniform load
Circular arch: uniform section: end A: fixed: end B: inclined slide: hydrostatic load
Solid circular flat plate: simple bending: simply supported: with uniform thickness: combined loads
Beam under bending: with axial tension: left end fixed: right end supported: applied vertical displacement
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
Beam under simple bending: left end supported: right end supported: point 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
Thin-walled cylindrical shell: Fixed-guided: radial load
Beam under bending: with axial compression: left end fixed: right end free: concentrated load
Circular arch: uniform section: end A: fixed: end B: fixed: distributed load: radial
Small deflections of rectangular plates: 1 clamped side, 2 supported(adjacent) and 1 free: distributed load: over a partial rectangular area
Thin-walled cylindrical shell: Guided-guided: linearly varying radial pressure
Beam under bending: with axial compression: left end fixed: right end fixed: temperature gradient: across depth: linearly varying
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
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
Thin-walled cylindrical shell: Fixed-guided: linearly varying radial pressure
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
Annular flat plate: with uniform thickness: simple bending: outer edge guided: inner edge supported: parabolically increasing load
Large deflections of rectangular plates: 4 supported & held sides: 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: 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 guided
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: Guided-guided: radial load
Circular arch: uniform section: end A: fixed: end B: inclined slide: concentrated load: radial
Small deflections of rectangular plates: 2 facing sides clamped, 2 supported: distributed load linearly varying along side a: starting at x0
Annular flat plate: with uniform thickness: simple bending: outer edge simply guided: inner edge supported: temperature differential across thickness
Beam under simple bending: left end supported: right end guided: concentrated load
Thin-walled cylindrical shell: Guided-supported: linearly varying radial pressure
Solid circular flat plate with uniform thickness: simple bending: on (mono)elastic foundation: free 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 moment
Thin-walled cylindrical shell: Supported-free: uniform radial pressure: from 'a' to 'b'
Beam under bending: with axial tension: left end fixed: right end fixed: distributed load
Semi-infinite beam: on elastic foundation: concentrated moment
Beam under simple bending: left end fixed: right end fixed: combined loads
Small deflections of triangular plates: equilateral: 3 supported sides: distributed load: linearly varying: along height a
Circular arch: uniform section: end A: fixed: end B: fixed: concentrated load: tangential
Thin-walled cylindrical shell: Guided-free: uniform radial pressure: from 'a' to B
Beam under bending: with axial compression: left end fixed: right end guided: concentrated load
Circular arch: uniform section: end A: fixed: end B: vertical slide: uniform load: per unit length of arch: vertical
Small deflections of rectangular plates: 4 free sides: supported at 4 corners: distributed load linearly varying along side a: starting at x0
Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: guided edge: annular line load + uniform load
Beam under simple bending: left end fixed: right end fixed: applied vertical displacement
Annular flat plate: with uniform thickness: simple bending: outer edge guided: inner edge 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: uniform load: on left post
Solid circular flat plate with uniform thickness: simple bending: on (mono)elastic foundation: supported edge: annular line load + uniform load
Thin-walled cylindrical shell: Guided-supported: radial load
Small deflections of rectangular plates: 3 clamped sides, 1 supported: combined loads
Continuous beam: over 3 spans: in simple bending: combined loads
Small deflections of rectangular plates: 4 free sides: supported at 4 corners: distributed load: over a partial rectangular area
Annular flat plate: with uniform thickness: simple bending: outer edge simply fixed: inner edge fixed: uniform annular line load
Fixed-fixed beam: on elastic foundation: concentrated moment
Beam under bending: with axial tension: left end fixed: right end guided: temperature gradient: across depth: linearly varying
Thin-walled cylindrical shell: Free-free: uniform radial pressure: from 'a' to B
Beam under simple bending: left end supported: right end supported: distributed load
Beam under bending: with axial compression: left end fixed: right end free: distributed 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 moment
Thin-walled cylindrical shell: Fixed-supported: applied moment
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
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
Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge free: distributed 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
Small deflections of rectangular plates: 4 free sides: supported at 4 corners: concentrated load
Circular arch: uniform section: end A: fixed: end B: vertical guide: concentrated 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: point load: horizontal: on girder
Beam under bending: with axial tension: left end supported: right end supported: combined loads
Continuous beam: over 5 spans: in simple bending: uniform load
Allowable external pressure: of cylindrical shells: circularity outside tolerance
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
Guided-guided beam: on elastic foundation: distributed load: linearly varying: from 'a' to 'b'
Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: combined loads
Beam under bending: with axial tension: left end supported: right end supported: 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 pressure: on girder left half
Continuous beam: over 5 spans: in simple bending: 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: horizontal: on girder
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
Large deflections of rectangular plates: 4 supported & fully held sides: uniform load
Circular arch: uniform section: end A: pinned: end B: inclined slide: 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: fixed: end B: horiz.slide: concentrated load: horizontal
Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge supported: distributed load
Beam under simple bending: left end supported: right end guided: distributed load
Solid circular flat plate: simple bending: simply supported: with uniform thickness: center load
One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end sliding: right end fixed: uniform load: on girder
Beam under bending: with axial tension: left end fixed: right end fixed: concentrated load
Thin-walled cylindrical shell: Supported-free: uniform radial pressure: from 'a' to B
Beam under bending: with axial compression: left end fixed: right end supported: concentrated moment
Small deflections of rectangular plates: 3 supported sides, 1 free: distributed load: linearly varying: along side a
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
Beam under bending: with axial tension: left end fixed: right end free: temperature gradient: across depth: linearly varying
Supported-free beam: on elastic foundation: distributed load: linearly varying: from 'a' to 'b'
Thin-walled cylindrical shell: Guided-free: uniform radial pressure: from 'a' to 'b'
Beam under bending: with axial compression: left end fixed: right end guided: distributed load
Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: fixed edge: annular line load + uniform load
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
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
Beam under bending: with axial tension: left end supported: right end guided: combined loads
Circular arch: uniform section: end A: pinned: end B: inclined slide: concentrated load: tangential
Beam under bending: with axial compression: left end fixed: right end supported: uniform load
Small deflections of rectangular plates: 4 simply supported sides: distributed load: linearly varying: along side a
Small deflections of rectangular plates: 1 clamped side, 2 supported(adjacent) and 1 free: 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 supported
Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: combined loads
Thin-walled cylindrical shell: Free-guided: linearly varying radial pressure
Fixed-guided beam: on elastic foundation: distributed load: linearly varying: from 'a' to 'b'
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
Beam under bending: with axial compression: left end fixed: right end fixed: applied angular displacement
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
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
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
Thin-walled cylindrical shell: Supported-supported: uniform radial pressure: from 'a' to 'b'
Circular arch: uniform section: end A: fixed: end B: inclined slide: concentrated load: vertical
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
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
Annular flat plate: with uniform thickness: simple bending: outer edge guided: inner edge fixed: parabolically increasing load
Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: guided edge: uniform annular line load
Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: combined loads
Small deflections of triangular plates: equilateral: 3 supported sides: uniform load
Circular arch: uniform section: end A: fixed: end B: vertical guide: uniform load: per unit vertical projection: horizontal: on left half arch
Solid circular flat plate: simple bending: simply supported: with linearly increasing thickness: combined loads
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
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
Circular arch: uniform section: end A: fixed: end B: horiz.slide: uniform temperature gradient: across depth
Solid circular flat plate: simple bending: clamped: with uniform thickness: distributed parabolically increasing 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
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
Beam under simple bending: left end fixed: right end supported: 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: vertical: on girder
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
Annular flat plate: with uniform thickness: simple bending: outer edge simply guided: inner edge fixed: temperature differential across thickness
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
Thin-walled cylindrical shell: Supported-fixed: uniform radial pressure: from 'a' to 'b'
Circular arch: uniform section: end A: fixed: end B: vertical guide: hydrostatic load
Circular arch: uniform section: end A: fixed: end B: fixed: distributed load: tangential
Rectangular membranes: 3 held sides, 1 free: uniform load
Circular arch: uniform section: end A: fixed: end B: free: uniform load: per unit length of arch: vertical
Beam under bending+shear: left end fixed: right end fixed: point 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: horizontal: on left 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
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
Small deflections of rectangular plates: 3 clamped sides, 1 free: combined loads
Circular arch: uniform section: end A: fixed: end B: fixed: concentrated load: vertical
Annular flat plate: with uniform thickness: simple bending: outer edge guided: inner edge supported: applied angular displacement
Beam under bending+shear: left end fixed: right end guided: uniform 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 right post
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
Minimum thickness of: ellipsoidal ends: under internal pressure
Beam under bending: with axial tension: left end fixed: right end fixed: combined loads
Circular arch: uniform section: end A: fixed: end B: horiz.guide: distributed load: tangential
Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: uniform temperature change
Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: fixed edge: center load + uniform load
Infinite beam: on elastic foundation: concentrated moment
Small deflections of rectangular plates: 4 simply supported sides: concentrated load at center
Beam under simple bending: left end fixed: right end fixed: distributed load
Circular arch: uniform section: end A: fixed: end B: vertical guide: concentrated load: tangential
Beam under bending: with axial tension: left end supported: right end guided: concentrated load
Solid circular flat plate with uniform thickness: large deflections behaviour: clamped edge: uniform annular line load
Beam under bending+shear: left end fixed: right end supported: distributed load
Small deflections of rectangular plates: 4 free sides: supported at 4 corners: distributed load linearly varying along side a
Circular arch: uniform section: end A: fixed: end B: horiz.guide: concentrated load: vertical
Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: uniform temperature change
Infinite beam: on elastic foundation: concentrated load
Solid circular flat plate: simple bending: simply supported: with uniform thickness: distributed load
Beam under bending+shear: left end fixed: right end guided: 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 fixed: top fixed
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
Circular arch: uniform section: end A: fixed: end B: inclined slide: uniform temperature gradient: across depth
Circular flat flanges without hubs: loose, welded: to internal pressure: gasket laying inside inner edge of bolt holes: with bolt spacing correction
Beam under bending: with axial tension: left end fixed: right end fixed: applied vertical displacement
Small deflections of rectangular plates: 1 clamped side, 2 supported and 1 free: uniform load
Circular arch: uniform section: end A: fixed: end B: horiz.slide: uniform temperature change
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
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
Small deflections of rectangular plates: 1 clamped side, 2 supported(adjacent) and 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 pinned: supports at same elevation: distributed partial load: linearly varying: vertical: on girder left half
Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge supported: applied angular displacement
Thin-walled cylindrical shell: Fixed-fixed: uniform radial pressure: from 'a' to 'b'
Beam under bending+shear: left end fixed: right end free: uniform load
Beam under bending: with axial tension: 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 pinned: 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: free: uniform load: per unit length of arch: horizontal
Circular arch: uniform section: end A: fixed: end B: vertical guide: uniform temperature change
Thin-walled cylindrical shell: Fixed-fixed: radial 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
Beam under bending+shear: left end fixed: right end free: combined loads
Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge free: applied angular displacement
Solid circular flat plate with uniform thickness: simple bending: on (mono)elastic foundation: fixed edge: distributed + uniform load
Beam under bending: with axial tension: left end fixed: right end guided: 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 load: horizontal: on girder right half
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
Thin-walled cylindrical shell: Supported-guided: uniform radial pressure: from 'a' to 'b'
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
Beam under bending: with axial tension: 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 fixed: right end pinned: supports at same elevation: uniform load: vertical: on girder right half
Circular arch: uniform section: end A: fixed: end B: pinned: distributed load: tangential
Thin-walled cylindrical shell: Fixed-supported: linearly varying radial pressure
Beam under simple bending: left end fixed: right end free(cantilever): combined loads
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
Annular flat plate: with uniform thickness: simple bending: outer edge guided: inner edge supported: distributed load
Small deflections of rectangular plates: 4 clamped sides: distributed load: linearly varying: along side a: starting at x0
Beam under simple bending: left end fixed: right end supported: combined loads
Fixed-free beam: on elastic foundation: distributed load: linearly varying: from 'a' to 'b'
Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge supported: temperature differential across thickness
Beam under bending: with axial compression: left end supported: right end supported: applied angular displacement
Circular arch: uniform section: end A: fixed: end B: free: uniform load: per unit vertical projection: horizontal
Circular arch: uniform section: end A: pinned: end B: horiz.guide: concentrated load: tangential
Thin-walled cylindrical shell: Guided-fixed: uniform radial pressure: from 'a' to B
Beam under simple bending: left end fixed: right end supported: applied vertical displacement
Thin-walled cylindrical shell: Fixed-supported: radial load
Circular arch: uniform section: end A: fixed: end B: pinned: concentrated load: vertical
Beam under bending: with axial tension: left end fixed: right end guided: uniform load
Junction between the large end of a cone and a cylinder: with knuckle: cone and cylinder with constant thicknesses: under internal pressure
Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: guided edge: distributed + 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: distributed 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 right post
Annular flat plate: with uniform thickness: simple bending: outer edge guided: inner edge fixed: uniform annular line moment
Continuous beam: over 5 spans: in simple bending: combined loads
Beam under bending+shear: left end supported: right end guided: point load
Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge free: combined loads
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
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
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
Beam under simple bending: left end fixed: right end guided: applied angular displacement
Circular arch: uniform section: end A: pinned: end B: pinned: distributed load: radial
Circular arch: uniform section: end A: fixed: end B: free: distributed 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: linearly decreasing 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
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
Beam under bending: with axial compression: left end fixed: right end supported: temperature gradient: across depth: linearly varying
Small deflections of rectangular plates: 3 clamped sides, 1 supported: distributed load linearly varying along side a
Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge guided: uniform annular line load
Circular arch: uniform section: end A: pinned: 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 pinned: right end pinned: supports at same elevation: distributed partial load: linearly varying: horizontal: on right post
Beam under bending: with axial tension: left end fixed: right end free: concentrated moment
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: 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
Beam under bending: with axial compression: left end supported: right end guided: applied angular displacement
Thin-walled cylindrical shell: Fixed-free: applied moment
Circular arch: uniform section: end A: pinned: end B: pinned: distributed load: tangential
Solid circular flat plate with uniform thickness: pure membrane behaviour: simply supported: 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 left 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: uniform pressure: on girder right half
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: 3 clamped sides, 1 free: distributed load: over a partial rectangular area
Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: uniform load: tangential
Circular arch: uniform section: end A: fixed: end B: vertical slide: distributed load: radial
Beam under bending+shear: left end supported: right end supported: point 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: concentrated moment
Circular arch: uniform section: end A: fixed: end B: inclined slide: 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: uniform load: horizontal: on girder left half
Beam under bending: with axial tension: left end fixed: right end free: 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: horizontal: on right post
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
Beam under bending+shear: 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: distributed partial load: linearly varying: on girder
Continuous beam: over 2 spans: in simple bending: point 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
Circular arch: uniform section: end A: pinned: end B: inclined slide: uniform temperature gradient: across depth
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
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 bending: with axial tension: left end fixed: right end guided: 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: distributed partial load: linearly varying: vertical: on girder
Small deflections of rectangular plates: 4 clamped sides: distributed load: over a partial rectangular area
Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: uniform load: per unit length of arch: vertical
Beam under simple bending: left end fixed: right end supported: uniform load
Annular flat plate: with uniform thickness: simple bending: outer edge clamped: inner edge guided: combined loads
Beam under bending: with axial compression: 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: point load: horizontal: on left post
Beam under bending+shear: left end fixed: right end fixed: uniform load
Junction between the large end of a cone and a cylinder: without a knuckle: cone and cylinder with constant thicknesses: under internal pressure
Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge supported: temperature differential across thickness
Annular flat plate: with uniform thickness: simple bending: outer edge simply guided: inner edge fixed: uniform annular line load
Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: guided edge: distributed 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: distributed load
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
Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge fixed: applied angular displacement
Solid circular flat plate: simple bending: clamped: with uniform thickness: combined loads
Beam under simple bending: left end fixed: right end supported: concentrated moment
Rectangular membranes: 4 fully held sides: uniform load
Beam under simple bending: left end fixed: right end guided: distributed load
Beam under bending: with axial tension: left end supported: right end supported: 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 fixed: supports at same elevation: distributed partial load: linearly varying: vertical: on girder
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
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: simple bending: clamped: with uniform thickness: uniform line moment
Continuous beam: over 4 spans: in simple bending: point load
Beam under bending: with axial tension: left end fixed: right end free: combined loads
Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: combined loads
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
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
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
Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge guided: uniform annular line 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: 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: 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 pinned: right end pinned: supports at same elevation: point load: horizontal: on right post
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
Circular arch: uniform section: end A: pinned: end B: horiz.guide: uniform temperature change
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
Beam under bending: with axial compression: left end supported: right end supported: distributed load
Small deflections of rectangular plates: 3 clamped sides, 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 fixed: supports at same elevation: uniform load: vertical: on girder left half
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
Beam under simple bending: left end fixed: right end free: distributed load
Thin-walled cylindrical shell: Free-fixed: linearly varying radial pressure
Beam under bending: with axial tension: left end fixed: right end supported: applied angular displacement
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
Beam under bending: with axial tension: left end supported: right end guided: temperature gradient: across depth: linearly varying
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
Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: free edge: annular line load + uniform load
Beam under bending: with axial tension: left end fixed: right end fixed: uniform load
Thin-walled cylindrical shell: Supported-free: radial load
Thin-walled cylindrical shell: Free-free: applied moment
Circular expansion joints: single: unreinforced bellows: without collar: to internal pressure: zero corrosion allowance: cyclic movement due to thermal expansion
Thin-walled cylindrical shell: Guided-supported: uniform radial pressure: from 'a' to 'b'
Solid circular flat plate with uniform thickness: simple bending: on (mono)elastic foundation: guided edge: annular line load + uniform load
Thin-walled cylindrical shell: Supported-free: linearly varying radial pressure
Beam under bending: with axial tension: left end fixed: right end fixed: concentrated moment
Small deflections of rectangular plates: 2 simply supported opposite sides and 2 free: concentrated load at center
Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: supported edge: annular line load + 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 supported
Fixed-infinite beam: on elastic foundation: concentrated moment
Beam under bending: with axial compression: left end fixed: right end supported: concentrated load
Small deflections of rectangular plates: 3 supported sides, 1 clamped: distributed load: linearly varying: along side a
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: fixed: end B: horiz.slide: concentrated load: tangential
Thin-walled cylindrical shell: Fixed-guided: uniform radial pressure: from 'a' to 'b'
Thin-walled cylindrical shell: Guided-fixed: applied moment
Circular arch: uniform section: end A: fixed: end B: free: combined loads
Large deflections of rectangular plates: 4 clamped & held sides: uniform 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 guided
Annular flat plate: with uniform thickness: simple bending: outer edge free: inner edge fixed: temperature differential across thickness
Continuous beam: over 5 spans: in simple bending: distributed load
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
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
Small deflections of rectangular plates: on elastic foundation: free: concentrated load
Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge guided: applied angular displacement
Guided-free beam: on elastic foundation: point load
Beam under simple bending: left end fixed: right end fixed: applied angular displacement
Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge supported: applied angular displacement
Free-free beam: on elastic foundation: distributed load: linearly varying: from 'a' to 'b'
Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge fixed: temperature differential across thickness
Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge fixed: distributed load
Circular arch: uniform section: end A: fixed: end B: horiz.slide: distributed load: radial
Thin-walled cylindrical shell: Guided-guided: uniform radial pressure: from 'a' to 'b'
Circular arch: uniform section: end A: pinned: end B: inclined slide: concentrated load: horizontal
Guided-free beam: on elastic foundation: concentrated moment
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
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
Large deflections of rectangular plates: 4 simply supported sides: uniform load
Annular flat plate: with uniform thickness: simple bending: outer edge free: inner edge supported: temperature differential across thickness
Simply supported beam: on elastic foundation: distributed load: linearly varying: from 'a' to 'b'
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
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
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
Circular arch: uniform section: end A: fixed: end B: vertical slide: uniform 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 temperature change
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
Continuous beam: over 3 spans: in simple bending: point load
Small deflections of rectangular plates: 4 clamped sides: 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: uniform load: horizontal: on right post
Beam under bending+shear: left end supported: right end supported: 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: 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: uniform load
Circular arch: uniform section: end A: pinned: end B: horiz.guide: concentrated load: horizontal
Circular arch: uniform section: end A: fixed: end B: free: uniform 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: distributed partial load: linearly varying: horizontal: on right 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: uniform load: horizontal: on girder left half
Small deflections of rectangular plates: 2 facing sides clamped, 2 supported: distributed load linearly varying along side a
Circular arch: uniform section: end A: fixed: end B: vertical slide: uniform load: per unit horizontal projection: vertical
Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge guided: temperature differential across thickness
Thin-walled cylindrical shell: Supported-free: applied moment
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
Beam under bending: with axial tension: left end fixed: right end fixed: temperature gradient: across depth: linearly varying
Beam under bending: with axial tension: left end fixed: right end free: concentrated 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: horizontal: on girder left half
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
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
Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: distributed load: tangential
Beam under bending+shear: left end supported: right end supported: uniform load
Thin-walled cylindrical shell: Guided-fixed: linearly varying radial pressure
Solid circular flat plate: simple bending: clamped: with uniform thickness: 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 pinned: supports at same elevation: uniform load: vertical: 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: uniform load: on right post
Circular arch: uniform section: end A: fixed: end B: vertical guide: distributed load: vertical: partial
Solid circular flat plate with uniform thickness: simple bending: on (mono)elastic foundation: supported edge: distributed + uniform load
Large deflections of rectangular plates: 4 free sides: supported at 4 (sliding) corners: uniform load
Beam under bending+shear: left end supported: right end guided: 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: point load: on girder
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
Fixed-fixed beam: on elastic foundation: distributed load: linearly varying: from 'a' to 'b'
Thin-walled cylindrical shell: Fixed-free: uniform radial pressure: from 'a' to B
Solid circular flat plate: simple bending: simply supported: with linearly increasing thickness: uniform load
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 fixed: inner edge fixed: distributed load
Beam under bending: with axial tension: left end fixed: right end guided: concentrated load
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
Solid circular flat plate with uniform thickness: simple bending: on (mono)elastic foundation: free edge: distributed + uniform load
Thin-walled cylindrical shell: Fixed-supported: uniform radial pressure: from 'a' to B
Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: uniform load: per unit vertical projection: horizontal
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
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
Thin-walled cylindrical shell: Guided-fixed: radial load
Semiinfinite beam: on elastic foundation: distributed load: linearly varying: from 'a' to 'b'
Beam under bending: with axial compression: 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
Beam under bending+shear: 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 fixed: supports at same elevation: point load: horizontal: on girder right half
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
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 fixed: inner edge supported: distributed load
Circular arch: uniform section: end A: pinned: end B: inclined slide: uniform temperature change
Circular arch: uniform section: end A: pinned: end B: inclined guide: concentrated load: vertical
Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: uniform load: per unit length of arch: horizontal
Beam under bending: with axial tension: left end supported: right end supported: uniform load
Circular arch: uniform section: end A: fixed: end B: inclined guide: distributed load: tangential
Circular arch: uniform section: end A: fixed: end B: vertical guide: concentrated load: horizontal
Beam under bending+shear: left end fixed: right end free: point load
Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge fixed: applied angular displacement
Circular arch: uniform section: end A: pinned: end B: inclined guide: distributed load: tangential
Beam under bending: with axial compression: left end fixed: right end guided: applied angular displacement
Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge guided: distributed load
Beam under simple bending: 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 fixed: right end fixed: uniform load: on girder
Small deflections of rectangular plates: 1 clamped side, 3 free: uniform load
Beam under bending: with axial tension: left end supported: right end supported: concentrated moment
Beam under simple bending: left end supported: right end guided: applied angular displacement
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
Circular arch: uniform section: end A: fixed: end B: inclined guide: concentrated load: vertical
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 symmetrically varying with the 1st power of x: resistance modulus varying with the 1st 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 pinned: uniform temperature change
Small deflections of rectangular plates: 2 simply supported opposite sides and 2 free: distributed load linearly varying along side a
Beam under bending: with axial compression: left end fixed: right end supported: applied vertical displacement
Solid circular flat plate with uniform thickness: large deflections behaviour: clamped & held: uniform annular line load
Beam under bending+shear: left end fixed: right end guided: point load
Beam under bending: with axial tension: left end supported: right end guided: uniform 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
Circular arch: uniform section: end A: pinned: end B: horiz.slide: concentrated load: vertical
Small deflections of rectangular plates: bending + shear: 4 simply supported sides: uniform load
Circular arch: uniform section: end A: pinned: end B: horiz.guide: uniform temperature gradient: across depth
Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: free edge: center load + uniform load
Solid circular flat plate with uniform thickness: large deflections behaviour: simply supported: uniform annular line load
Beam under bending: with axial compression: left end fixed: right end free: applied angular displacement
Circular arch: uniform section: end A: pinned: end B: horiz.slide: distributed load: tangential
Beam under bending: with axial compression: left end fixed: right end supported: combined loads
Small deflections of rectangular plates: 2 adjacent supported sides, 2 free: distributed load linearly varying along side a
Beam under simple bending: left end supported: right end supported: applied angular displacement
Beam under bending: with axial tension: left end supported: right end guided: concentrated moment
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: fixed: end B: inclined guide: uniform load: tangential
Circular flat flanges without hubs: lap joint: to internal pressure: gasket laying inside inner edge of bolt holes: split ring: along a diameter
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
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
Circular arch: uniform section: end A: pinned: end B: inclined slide: uniform load: radial
Circular arch: uniform section: end A: fixed: end B: pinned: 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 fixed: combined loads
Circular arch: uniform section: end A: pinned: end B: inclined guide: combined loads
Solid circular flat plate with uniform thickness: large deflections behaviour: supported & held: distributed 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: uniform load
Small deflections of rectangular plates: 2 adjacent clamped sides, 2 free: combined loads
Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: combined loads
Circular arch: uniform section: end A: fixed: end B: inclined guide: combined loads
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
Circular arch: uniform section: end A: fixed: end B: fixed: uniform load: per unit vertical projection: horizontal
Rectangular membranes: 4 fully held sides: distributed load linearly varying along side a
Small deflections of rectangular plates: 2 adjacent clamped sides, 2 supported: combined loads
Circular arch: uniform section: end A: pinned: end B: inclined guide: uniform load: tangential
Circular arch: uniform section: end A: fixed: end B: pinned: uniform load: per unit length of arch: 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: concentrated load
Circular arch: uniform section: end A: fixed: end B: vertical slide: concentrated load: horizontal
Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: concentrated moment
Circular arch: uniform section: end A: pinned: end B: horiz.slide: combined loads
One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end pinned: point load: on girder
Circular arch: uniform section: end A: pinned: end B: pinned: hydrostatic load
Circular arch: uniform section: end A: fixed: end B: horiz.guide: distributed load: vertical: partial
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 slide: uniform load: tangential
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
Circular arch: uniform section: end A: pinned: end B: horiz.slide: uniform load: tangential
One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end fixed: point 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: distributed partial load: linearly varying: vertical: on girder right half
Annular flat plate: with uniform thickness: simple bending: outer edge free: inner edge supported: parabolically increasing load
One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end pinned: uniform temperature change
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
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
Circular arch: uniform section: end A: pinned: end B: pinned: uniform load: per unit length of arch: vertical
Beam under bending: with held ends: left end fixed: right end fixed: distributed load
Beam under simple bending: large deflections: left end fixed: right end guided: distributed load
Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: uniform temperature gradient: across depth
Thin-walled cylindrical shell: Free-supported: uniform radial pressure: from 'a' to B
Circular pipes: supported at bottom: 2 vertical line loads: symmetric
Circular arch: uniform section: end A: fixed: end B: horiz.guide: uniform load: per unit length of arch: vertical
Circular arch: uniform section: end A: fixed: end B: vertical slide: distributed load: vertical: partial
Circular arch: uniform section: end A: pinned: end B: pinned: uniform load: per unit length of arch: horizontal
Circular arch: uniform section: end A: fixed: end B: fixed: concentrated load: radial
Supported-fixed beam: on elastic foundation: concentrated load
Annular flat plate: with uniform thickness: simple bending: outer edge free: inner edge supported: combined loads
Fixed-infinite beam: on elastic foundation: point load
Beam under simple bending: large deflections: left end fixed: right end supported: uniform load
Small deflections of rectangular plates: 3 supported sides, 1 clamped: uniform 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 free: inner edge clamped: combined loads
Circular arch: uniform section: end A: fixed: end B: horiz.guide: uniform load: per unit length of arch: horizontal
Supported-fixed beam: on elastic foundation: concentrated moment
Thickness of shells and tubes: under external pressure
Small deflections of rectangular plates: on elastic foundation: free: distributed load: over a partial rectangular area
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
Large deflections of rectangular plates: 4 clamped & held sides: distributed load linearly varying along side a
Small deflections of rectangular plates: 1 clamped side, 3 free: distributed load linearly varying along side a: starting at x0
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
Spheres in contact: with a grooved outer ring: under load: Hertz's theory
Thin-walled cylindrical shell: Free-guided: radial load
Beam under bending: with held ends: left end fixed: right end supported: applied vertical displacement
Circular arch: uniform section: end A: fixed: end B: vertical guide: uniform load: radial
Circular arch: uniform section: end A: fixed: end B: pinned: distributed load: vertical: partial
Beam under simple bending: large deflections: left end fixed: right end free: distributed load
Circular ring beam: supported at bottom: 2 vertical loads
Supported-guided beam: on elastic foundation: distributed load: linearly varying: from 'a' to 'b'
Small deflections of rectangular plates: 1 clamped side, 3 free: point load: over a partial rectangular area
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
Thin-walled cylindrical shell: Free-guided: uniform radial pressure: from 'a' to 'b'
Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge clamped: 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: combined loads
Large deflections of rectangular plates: 4 simply supported sides: distributed load linearly varying along side a
Design rules for clamp connections: clamping faces parallel
Beam under bending: with held ends: left end fixed: right end free: applied angular displacement
Circular arch: uniform section: end A: fixed: end B: fixed: concentrated moment
Circular arch: uniform section: end A: fixed: end B: vertical guide: uniform load: per unit horizontal projection: vertical
Large deflections of rectangular plates: 4 supported & held sides: distributed load linearly varying along side a: starting at x0
Small deflections of rectangular plates: 2 adjacent clamped sides, 2 supported: distributed load linearly varying along side a
One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end pinned: point load: on post
Small deflections of triangular plates: equilateral: 2 clamped sides, 1 free: combined loads
Small deflections of rectangular plates: 2 facing sides clamped, 2 supported: uniform load
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
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
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
Small deflections of rectangular plates: 2 adjacent clamped sides, 2 free: distributed load linearly varying along side a
Circular arch: uniform section: end A: fixed: end B: horiz.guide: concentrated moment
Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: concentrated load: vertical
Beam under bending: with held ends: left end supported: right end guided: distributed load
Circular arch: uniform section: end A: fixed: end B: horiz.slide: hydrostatic 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
Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge supported: combined loads
Thin-walled cylindrical shell: Fixed-fixed: linearly varying radial pressure
Circular arch: uniform section: end A: pinned: end B: pinned: uniform load: per unit vertical projection: horizontal
Circular arch: uniform section: end A: fixed: end B: horiz.guide: concentrated load: radial
Annular flat plate: with uniform thickness: simple bending: outer edge free: inner edge supported: distributed load
Annular flat plate: with uniform thickness: simple bending: outer edge clamped: inner edge clamped: uniform load
Solid circular flat plate: simple bending: simply supported: with linearly decreasing thickness: uniform 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: fixed: 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: point load: on right post
Small deflections of triangular plates: equilateral: 2 supported sides, 1 free: distributed load: linearly varying: along height a
Beam: simple bending: with held ends: left end supported: right end supported: distributed load
Circular arch: uniform section: end A: fixed: end B: fixed: uniform load: per unit length of arch: horizontal
Annular flat plate: with uniform thickness: simple bending: outer edge free: inner edge fixed: distributed load
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: fixed: end B: pinned: uniform load: per unit vertical projection: horizontal
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: pinned: concentrated load: horizontal
Circular flat flanges without hubs: lap joint: to internal pressure: gasket laying inside inner edge of bolt holes
Circular arch: uniform section: end A: fixed: end B: fixed: distributed load: vertical: partial
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
Annular flat plate: with uniform thickness: simple bending: outer edge clamped: inner edge supported: uniform load
Circular arch: uniform section: end A: fixed: end B: inclined slide: combined loads
Circular arch: uniform section: end A: pinned: end B: inclined guide: uniform load: per unit horizontal projection: vertical
One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end fixed: uniform load: on post
Annular flat plate: with uniform thickness: simple bending: outer edge clamped: inner edge guided: uniform load
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: 2 opposite sides clamped, 2 free: distributed load linearly varying along side a: starting at x0
Circular arch: uniform section: end A: fixed: end B: inclined guide: uniform load: per unit horizontal projection: vertical
Circular arch: uniform section: end A: fixed: end B: pinned: concentrated moment
Circular arch: uniform section: end A: pinned: end B: inclined guide: uniform load: per unit vertical projection: horizontal: on left half arch
Beam under bending: with held ends: left end fixed: right end supported: concentrated load
Guided-infinite beam: on elastic foundation: point load
Circular arch: uniform section: end A: fixed: end B: pinned: concentrated load: radial
Circular arch: uniform section: end A: pinned: end B: horiz.slide: uniform load: per unit horizontal projection: vertical
Solid circular flat plate with uniform thickness: large deflections behaviour: clamped & held: uniform distributed load
Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: supported edge: center load
Small deflections of rectangular plates: 2 simply supported opposite sides and 2 free: 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 load
Small deflections of rectangular plates: 2 adjacent supported sides, 2 free: uniform 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 girder left half
Circular arch: uniform section: end A: pinned: end B: horiz.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 sliding: point load: on girder
Circular arch: uniform section: end A: pinned: end B: horiz.guide: uniform load: radial
Guided-infinite beam: on elastic foundation: concentrated moment
Circular arch: uniform section: end A: pinned: end B: pinned: concentrated load: tangential
Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge free: uniform annular line load
Small deflections of rectangular plates: 1 clamped side, 3 free: combined loads
Small deflections of rectangular plates: bending + shear: 4 simply supported sides: distributed load linearly varying along side a
Solid circular flat plate with uniform thickness: large deflections behaviour: simply supported: uniform distributed load
Circular arch: uniform section: end A: fixed: end B: horiz.guide: uniform load: per unit vertical projection: horizontal
Solid circular flat plate with uniform thickness: simple bending: on (bi)elastic foundation: free edge: center load
Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge free: uniform load
Thin-walled cylindrical shell: Free-supported: applied 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: combined loads
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
Allowable external pressure: of cylindrical shells: circularity within tolerance
Circular arch: uniform section: end A: pinned: end B: inclined guide: uniform load: per unit length of arch: horizontal
Circular arch: uniform section: end A: fixed: end B: inclined guide: uniform load: per unit length of arch: vertical
Thin-walled cylindrical shell: Free-fixed: uniform radial pressure: from 'a' to 'b'
Circular arch: uniform section: end A: pinned: end B: horiz.guide: hydrostatic load
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
Circular arch: uniform section: end A: fixed: end B: pinned: uniform load: tangential
Circular arch: uniform section: end A: fixed: end B: inclined slide: uniform load: per unit length of arch: horizontal
Cylinder in contact on a flat plate under load: Hertz's theory
Circular arch: uniform section: end A: fixed: end B: inclined guide: uniform load: per unit length of arch: horizontal
Circular arch: uniform section: end A: pinned: end B: inclined guide: uniform load: per unit length of arch: vertical
Small deflections of rectangular plates: 2 opposite sides clamped, 2 free: distributed load: over a partial rectangular area
Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge supported: uniform load
Disc springs: stack in parallel: with or without bearing flats
Circular arch: uniform section: end A: fixed: end B: vertical guide: distributed load: radial
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
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
Thin-walled cylindrical shell: Free-fixed: radial load
Circular arch: uniform section: end A: fixed: end B: pinned: combined loads
Elastic stability of a beam-column: with two stepped sections: under two axial compressive loads: base supported: top supported
Circular pipes: supported at bottom: 2 radial line loads: symmetric
Small deflections of rectangular plates: 1 clamped side, 2 supported and 1 free: distributed load linearly varying along side a: starting at x0
Small deflections of rectangular plates: 3 supported sides, 1 free: uniform load
Circular arch: uniform section: end A: pinned: end B: horiz.slide: uniform load: per unit length of arch: horizontal
Supported-infinite beam: on elastic foundation: concentrated moment
Annular flat plate: with uniform thickness: simple bending: outer edge clamped: inner edge clamped: combined loads
Small deflections of rectangular plates: 1 clamped side, 2 supported and 1 free: distributed load: over a partial rectangular area
Circular arch: uniform section: end A: pinned: end B: pinned: uniform load: tangential
One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end sliding: right end fixed: uniform load: on post
Supported-infinite beam: on elastic foundation: concentrated load
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 fixed: inner edge free: uniform annular line moment
Beam under simple bending: large deflections: left end fixed: right end supported: concentrated load
Small deflections of rectangular plates: 4 simply supported sides: uniform load
Circular arch: uniform section: end A: fixed: end B: free: uniform temperature gradient: across depth
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
Circular arch: uniform section: end A: pinned: end B: horiz.slide: uniform load: per unit length of arch: vertical
Circular arch: uniform section: end A: pinned: end B: pinned: uniform temperature gradient: across depth
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
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
One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end pinned: point load: on girder
Small deflections of triangular plates: equilateral: 2 supported sides, 1 free: combined loads
Circular arch: uniform section: end A: fixed: end B: inclined slide: distributed load: tangential
Annular flat plate: with uniform thickness: simple bending: outer edge clamped: inner edge supported: 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 bending: with held ends: left end supported: right end supported: applied angular displacement
Circular arch: uniform section: end A: fixed: end B: horiz.guide: uniform 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: uniform temperature change
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
Small deflections of triangular plates: equilateral: 3 clamped sides: 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: distributed partial load: linearly varying: vertical: on girder right half
Circular arch: uniform section: end A: pinned: end B: horiz.slide: distributed load: vertical: partial
Solid circular flat plate: simple bending: simply supported: with linearly decreasing thickness: combined loads
Full faced flanges with soft ring type gaskets: non metallic gaskets not less than 1.5 mm thick
Circular arch: uniform section: end A: fixed: end B: vertical slide: uniform temperature change
Circular arch: uniform section: end A: fixed: end B: free: 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: concentrated 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: fixed: end B: horiz.guide: combined loads
Beam under simple bending: large deflections: left end supported: right end supported: distributed load
Circular arch: uniform section: end A: fixed: end B: vertical slide: concentrated load: tangential
Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: combined loads
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
Circular arch: uniform section: end A: fixed: end B: fixed: uniform load: per unit vertical projection: horizontal: on left half arch
Circular arch: uniform section: end A: fixed: end B: horiz.slide: uniform load: radial
Circular arch: uniform section: end A: fixed: end B: inclined guide: distributed load: vertical: partial
Beam under bending: with held ends: left end supported: right end guided: applied angular displacement
Circular arch: uniform section: end A: fixed: end B: inclined slide: uniform load: per unit vertical projection: horizontal
Beam under bending: with held ends: left end fixed: right end supported: temperature gradient: across depth: linearly varying
Circular arch: uniform section: end A: fixed: end B: fixed: uniform load: per unit horizontal projection: vertical
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
Small deflections of triangular plates: equilateral: 2 clamped sides, 1 free: distributed load: linearly varying: along height a
Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: 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: concentrated moment
Beam under simple bending: large deflections: left end supported: right end guided: distributed load
Circular arch: uniform section: end A: pinned: end B: inclined guide: distributed load: vertical: partial
Beam under bending: with held ends: left end fixed: right end free: distributed load
Circular arch: uniform section: end A: fixed: end B: vertical slide: hydrostatic load
Circular arch: uniform section: end A: pinned: end B: horiz.slide: uniform load: per unit vertical projection: horizontal
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
One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end sliding: uniform temperature change
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: horiz.guide: uniform load: per unit vertical projection: horizontal: on left half arch
Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge free: temperature differential across thickness
Minimum thickness of: torispherical ends: under internal pressure
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
Circular ring beam: supported at bottom: load at top
Small deflections of rectangular plates: 2 opposite sides clamped, 2 free: concentrated load
Circular arch: uniform section: end A: fixed: end B: horiz.guide: uniform load: per unit horizontal projection: vertical
One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end sliding: right end fixed: distributed partial load: linearly varying: on post
Solid circular flat plate with uniform thickness: large deflections behaviour: clamped: uniform distributed load
Sphere in contact with a flat plate under load: Hertz's theory
Solid circular flat plate: simple bending: simply supported: with uniform thickness: uniform load
Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: combined loads
Circular arch: uniform section: end A: fixed: end B: fixed: uniform load: tangential
Circular arch: uniform section: end A: pinned: end B: inclined guide: uniform load: per unit vertical projection: horizontal
Beam under bending: with held ends: left end fixed: right end guided: distributed load
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 3rd power of x: resistance modulus varying with the 2nd power of x: combined loads
Full face flanges with soft ring type gaskets: external pressure
Beam under bending: with held ends: left end fixed: right end supported: concentrated moment
Small deflections of rectangular plates: 2 opposite sides clamped, 2 free: combined loads
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
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 flat flanges without hubs: loose, welded: to internal pressure: gasket laying inside inner edge of bolt holes
Circular arch: uniform section: end A: fixed: end B: inclined guide: uniform load: per unit vertical projection: horizontal
Circular arch: uniform section: end A: fixed: end B: vertical slide: uniform load: per unit vertical projection: horizontal: on left half arch
Annular flat plate: with uniform thickness: simple bending: outer edge fixed: inner edge free: parabolically increasing 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: vertical: on girder
Circular arch: uniform section: end A: fixed: end B: fixed: combined loads
Beam under bending: with held ends: left end fixed: right end supported: uniform 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: inclined guide: concentrated moment
Annular flat plate: with uniform thickness: simple bending: outer edge guided: inner edge supported: 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 free
Solid circular flat plate with uniform thickness: simple bending: on (mono)elastic foundation: fixed edge: center load + uniform load
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: fixed: end B: inclined slide: uniform load: per unit length of arch: vertical
Beam under simple bending: large deflections: left end fixed: right end fixed: distributed load
Circular pipes: supported at bottom: loaded by self weight: directed downwards
Circular arch: uniform section: end A: fixed: end B: pinned: uniform load: per unit horizontal projection: vertical
Circular arch: uniform section: end A: fixed: end B: inclined guide: concentrated moment
Circular arch: uniform section: end A: pinned: end B: horiz.slide: concentrated load: radial
Small deflections of rectangular plates: 3 clamped sides, 1 supported: uniform load
Circular arch: uniform section: end A: fixed: end B: vertical slide: concentrated load: radial
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
One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end pinned: point load: on post
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
Circular arch: uniform section: end A: pinned: end B: horiz.slide: concentrated moment
Circular arch: uniform section: end A: fixed: end B: free: concentrated load: vertical
Circular arch: uniform section: end A: fixed: end B: inclined guide: concentrated load: radial
Circular arch: uniform section: end A: pinned: end B: pinned: 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 pinned: right end fixed: point load: on post
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
Circular arch: uniform section: end A: pinned: end B: inclined guide: concentrated load: radial
Solid circular flat plate with uniform thickness: pure membrane behaviour: simply supported: distributed load
One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end sliding: right end fixed: 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: concentrated load
Circular arch: uniform section: end A: pinned: end B: pinned: uniform load: per unit horizontal projection: vertical
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
Circular arch: uniform section: end A: pinned: end B: inclined slide: hydrostatic load
Annular flat plate: with uniform thickness: simple bending: outer edge supported: inner edge clamped: combined loads