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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Properties of plane area: Standard beams with parallel-faced flanges: IPE, HE and others: longitudinally cut beam

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

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

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

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

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

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

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

Cylindrical vessel: horizontal: with two ellipsoidal heads: filled volume: as a function of content height

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

User defined section: by means of a pixel map or image

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

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

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

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

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

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

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

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

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

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 pressure: on girder left half

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: combined loads

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

Cylindrical vessel: vertical: with two hemispherical heads: filled volume: as a function of content height

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

Circular arch: uniform section: end A: pinned: end B: inclined 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: uniform load: on girder

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

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: pinned: uniform load: tangential

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

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

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

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

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

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

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

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

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

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 fixed: right end pinned: supports at same elevation: uniform load: horizontal: on right post

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Circular ring beam: supported at bottom: combined loads

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

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

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

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

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

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

Circular arch: uniform section: end A: fixed: end B: 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 fixed: right end pinned: supports at same elevation: uniform load: horizontal: on left post

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Cylindrical vessel: horizontal: with two hemispherical heads: filled volume: as a function of content height

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: pinned: end B: inclined guide: hydrostatic load

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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: pinned: end B: horiz.slide: distributed load: tangential

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

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

Full face flanges with soft ring type gaskets: external pressure

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

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

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

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

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

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: inclined guide: uniform load: per unit horizontal projection: vertical

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

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

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

Circular ring beam: supported at bottom: 2 vertical loads

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

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

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

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

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

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

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

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

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

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

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

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: 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

Circular arch: uniform section: end A: fixed: end B: inclined slide: 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 left post

Beam under bending+shear: left end supported: right end guided: distributed 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: pinned: uniform load: per unit vertical projection: horizontal: on left half arch

Circular arch: uniform section: end A: fixed: end B: horiz.slide: uniform load: 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 pressure: on girder right half

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

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

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

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

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

Beam under bending: with held ends: left end fixed: right end 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 temperature change

Properties of plane area: hollow structural sections: round

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

Cylindrical vessel: horizontal: with two torispherical heads: filled volume: as a function of content height

Circular arch: uniform section: end A: fixed: 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: uniform load: horizontal: on left post

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

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

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

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+shear: left end fixed: right end guided: point load

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

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

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

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

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

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

Small deflections of rectangular plates: 2 simply supported opposite sides and 2 free: distributed load: over a partial rectangular area

Beam under bending: with axial tension: left end fixed: 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: distributed partial load: linearly varying: on girder

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

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: hydrostatic load

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

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

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

Cylindrical vessel: vertical: with two torispherical heads: filled volume: as a function of content height

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

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

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

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

Spheres in contact: with a grooved outer ring: under load: Hertz's theory

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

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

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

Two cylinders in contact under load: axes at right angles: Hertz's theory

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

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

Spheres in contact: with a grooved inner ring: under load: Hertz's theory

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

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

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

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

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

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

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

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

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

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

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

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: fixed: end B: pinned: uniform temperature gradient: across depth

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Beam under bending: with axial compression: left end supported: 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 pinned: point load: on post

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

Circular arch: uniform section: end A: pinned: end B: inclined guide: 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 pinned: supports at same elevation: distributed partial load: linearly varying: horizontal: on right post

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

Properties of plane area: Standard channels: with tapered flanges: two beams face-to-face

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

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

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

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

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

Circular arch: uniform section: end A: fixed: end B: inclined 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 load: horizontal: on left post

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

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

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

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

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

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

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

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

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

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

Circular arch: uniform section: end A: pinned: end B: pinned: distributed 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 load: horizontal: on right post

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

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

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

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

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

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: point load: over a partial rectangular area

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Sections derived from elliptical shapes

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Circular arch: uniform section: end A: pinned: end B: horiz.guide: uniform 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: point load: vertical: on girder left half

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

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

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

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

Standard beams with parallel-faced flanges

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

Flat face flanges with metal-to-metal contact outside the bolt circle: analysis of a flange cover assembly (Class 3): integral (Cat.1) flange: hub of constant thickness: no spacer: self-sealing gasket with negligible loads

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Circular arch: uniform section: end A: pinned: 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: distributed partial load: linearly varying: horizontal: on left post

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

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

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

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

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

Properties of plane area: hollow structural sections: elliptical

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

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

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: uniform temperature change

Beam under bending+shear: left end fixed: right end supported: uniform 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: fixed: end B: pinned: concentrated load: horizontal

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

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

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

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

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

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

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

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

Cylindrical vessel: vertical: with two ellipsoidal heads: filled volume: as a function of content height

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

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

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

Design rules for clamp connections: clamping faces parallel

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Sections derived from circular shape

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

Circular flat flanges without hubs: lap joint: to internal pressure: gasket laying inside inner edge of bolt holes

Two spheres in contact under load: Hertz's theory

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Properties of plane area: hollow structural sections: rectangular

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

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

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

Properties of plane area: Standard channels: with tapered flanges

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

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: hydrostatic 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 fixed: distributed partial load: linearly varying: 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 temperature change

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

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

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

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

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

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

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

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

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

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

Circular ring beam: supported at bottom: loaded by uniform vertical load

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Circular arch: uniform section: end A: fixed: end B: 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 pressure: on girder right half

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

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

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

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

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

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: fixed: distributed load: tangential

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

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

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

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

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

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

Properties of plane area: Standard channels: with parallel faced flanges

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

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

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

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

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

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

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

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

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

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

Cylindrical vessel: vertical: with two spherically dished heads: filled volume: as a function of content height

Standard beams with tapered flanges

Full faced flanges with soft ring type gaskets: non metallic gaskets not less than 1.5 mm thick

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

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

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

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

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

Circular arch: uniform section: end A: fixed: end B: free: 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: point load: horizontal: on right post

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

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

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

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

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

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

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

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

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

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

Beam: simple bending: with held ends: 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 pinned: right end fixed: supports at same elevation: point load: horizontal: 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 fixed: right end fixed: point load: on post

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

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

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

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

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 pinned: right end pinned: point load: on post

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: 2 opposite sides clamped, 2 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: horizontal: on girder left half

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Properties of plane area: hollow structural sections: square

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Circular ring beam: supported at bottom: load at top

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

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

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

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

Design rules for clamp connections: clamping faces parallel: hub calculated as loose flange

Small deflections of rectangular plates: 2 simply supported opposite sides and 2 free: distributed load linearly varying along side a: starting at x0

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

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

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

Properties of plane area: Standard channels: with tapered flanges: two beams full penetration welded to form a closed section

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

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

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

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

Properties of plane area: Standard channels: with tapered flanges: two beams back-to-back

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

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

Circular ring beam: supported at bottom: 2 tangential loads

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

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

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

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

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

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

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

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

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

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

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

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

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

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 bending: with axial tension: 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

Beam under bending+shear: left end fixed: right end fixed: 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: point load: horizontal: on right post

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

Circular ring beam: supported at bottom: 2 radial 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: point load: horizontal: on girder left half

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

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

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: pinned: uniform load: per unit length of arch: vertical

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Sections with quadrangular, rectangular or square shape

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Circular ring beam: supported at bottom: 2 horizontal loads

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

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

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

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

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

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

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

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

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

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

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

Circular flat flanges without hubs: lap joint: to internal pressure: gasket laying inside inner edge of bolt holes: with bolt spacing correction

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

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

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

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

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

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

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

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

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

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

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

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: inclined guide: distributed load: vertical: partial

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

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

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: combined loads

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

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

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

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

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

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

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

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

Cylindrical vessel: horizontal: with two spherically dished heads: filled volume: as a function of content height

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

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

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

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

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

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

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

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

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

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

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

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

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

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: hydrostatic 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: vertical: on girder left half

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

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

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

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

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

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

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

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

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

Two cylinders in contact under load: parallel axes: Hertz's theory

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

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

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

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

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

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

Narrow face gasketed flanges: integral method: with hub: WN or LWN type: to internal pressure

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Properties of plane area: Standard Tee beams

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

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

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

Beam under bending+shear: left end fixed: right end supported: 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 left half

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Properties of plane area: Standard beams with parallel-faced flanges: IPE, HE and others: longitudinally cut beam

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

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

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

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

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

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

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

Cylindrical vessel: horizontal: with two ellipsoidal heads: filled volume: as a function of content height

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

User defined section: by means of a pixel map or image

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

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

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

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

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

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

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

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

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

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 pressure: on girder left half

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: combined loads

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

Cylindrical vessel: vertical: with two hemispherical heads: filled volume: as a function of content height

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

Circular arch: uniform section: end A: pinned: end B: inclined 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: uniform load: on girder

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

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: pinned: uniform load: tangential

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

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

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

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

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

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

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

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

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

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 fixed: right end pinned: supports at same elevation: uniform load: horizontal: on right post

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Circular ring beam: supported at bottom: combined loads

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

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

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

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

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

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

Circular arch: uniform section: end A: fixed: end B: 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 fixed: right end pinned: supports at same elevation: uniform load: horizontal: on left post

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Cylindrical vessel: horizontal: with two hemispherical heads: filled volume: as a function of content height

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: pinned: end B: inclined guide: hydrostatic load

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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: pinned: end B: horiz.slide: distributed load: tangential

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

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

Full face flanges with soft ring type gaskets: external pressure

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

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

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

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

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

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: inclined guide: uniform load: per unit horizontal projection: vertical

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

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

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

Circular ring beam: supported at bottom: 2 vertical loads

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

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

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

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

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

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

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

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

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

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

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

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: 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

Circular arch: uniform section: end A: fixed: end B: inclined slide: 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 left post

Beam under bending+shear: left end supported: right end guided: distributed 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: pinned: uniform load: per unit vertical projection: horizontal: on left half arch

Circular arch: uniform section: end A: fixed: end B: horiz.slide: uniform load: 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 pressure: on girder right half

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

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

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

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

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

Beam under bending: with held ends: left end fixed: right end 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 temperature change

Properties of plane area: hollow structural sections: round

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

Cylindrical vessel: horizontal: with two torispherical heads: filled volume: as a function of content height

Circular arch: uniform section: end A: fixed: 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: uniform load: horizontal: on left post

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

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

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

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+shear: left end fixed: right end guided: point load

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

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

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

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

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

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

Small deflections of rectangular plates: 2 simply supported opposite sides and 2 free: distributed load: over a partial rectangular area

Beam under bending: with axial tension: left end fixed: 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: distributed partial load: linearly varying: on girder

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

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: hydrostatic load

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

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

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

Cylindrical vessel: vertical: with two torispherical heads: filled volume: as a function of content height

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

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

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

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

Spheres in contact: with a grooved outer ring: under load: Hertz's theory

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

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

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

Two cylinders in contact under load: axes at right angles: Hertz's theory

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

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

Spheres in contact: with a grooved inner ring: under load: Hertz's theory

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

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

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

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

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

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

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

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

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

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

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

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: fixed: end B: pinned: uniform temperature gradient: across depth

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

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

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

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

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

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

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

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

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

Beam under bending: with axial tension: left end fixed: right end fixed: applied angular displacement

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: distributed partial load: linearly varying: on right post

Beam under bending: with held ends: left end fixed: right end supported: distributed load

W.R.C. Bulletin 297-Aug.84,Supplement to WRC Bulletin No. 107: Local Stresses in Cylindrical Shells Due to External Loadings on a Radial Flush Nozzle: Loads specified at nozzle/wall intersection

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end fixed: uniform load: on post

Beam under bending: with axial compression: left end supported: 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 pinned: point load: on post

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end sliding: point load: on post

Circular arch: uniform section: end A: pinned: end B: inclined guide: 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 pinned: supports at same elevation: distributed partial load: linearly varying: horizontal: on right post

Circular arch: uniform section: end A: pinned: end B: pinned: uniform load: radial

Properties of plane area: Standard channels: with tapered flanges: two beams face-to-face

Circular arch: uniform section: end A: fixed: end B: vertical slide: concentrated load: radial

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: uniform load: on left post

Circular arch: uniform section: end A: pinned: end B: inclined guide: distributed load: radial

Circular arch: uniform section: end A: fixed: end B: horiz.guide: concentrated load: vertical

Circular arch: uniform section: end A: fixed: end B: inclined guide: concentrated load: tangential

Circular arch: uniform section: end A: fixed: end B: inclined 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 load: horizontal: on left post

Circular arch: uniform section: end A: pinned: end B: horiz.slide: hydrostatic load

Circular arch: uniform section: end A: pinned: end B: horiz.slide: combined loads

Beam under bending: with axial compression: left end fixed: right end guided: combined loads

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: uniform load: on right post

Beam under bending: with held ends: left end supported: right end guided: distributed load

Beam under bending: with axial tension: left end supported: right end supported: applied angular displacement

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: uniform load: on right post

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: concentrated load: vertical

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end fixed: point load: on 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: vertical: on girder right half

Spheres in contact with a cylindrical socket under load: Hertz's theory

Circular arch: uniform section: end A: pinned: end B: pinned: distributed 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 load: horizontal: on right post

Beam under bending: with axial tension: left end fixed: right end supported: concentrated moment

Beam under bending: with axial compression: left end fixed: right end free: combined loads

Beam under bending: with axial compression: left end fixed: right end fixed: distributed load

Beam under bending+shear: left end supported: right end guided: point load

Circular arch: uniform section: end A: fixed: end B: free: 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

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: point load: over a partial rectangular area

Small deflections of rectangular plates: 1 clamped side, 2 supported(adjacent) and 1 free: distributed load linearly varying along side a: starting at x0

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: point load: horizontal: on girder

Small deflections of rectangular plates: 3 supported sides, 1 clamped: distributed load: over a partial rectangular area

Circular arch: uniform section: end A: pinned: end B: inclined slide: concentrated moment

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: uniform load: horizontal: on right post

Beam under bending: with held ends: left end fixed: right end fixed: applied vertical displacement

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: uniform temperature change

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: uniform load: vertical: on girder

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: point load: horizontal: on girder left half

Circular arch: uniform section: end A: fixed: end B: fixed: uniform load: per unit vertical projection: horizontal: on left half arch

Small deflections of rectangular plates: 3 supported sides, 1 free: distributed load: over a partial rectangular area

Beam under bending+shear: left end fixed: right end guided: combined loads

Circular arch: uniform section: end A: fixed: end B: horiz.guide: hydrostatic load

Beam under bending: with axial compression: left end supported: right end supported: applied vertical displacement

Sections derived from elliptical shapes

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: combined loads

Circular arch: uniform section: end A: pinned: end B: inclined guide: concentrated load: radial

Beam under bending: with held ends: left end fixed: right end supported: concentrated load

Elastic stability of a beam-column: prismatic: under a single axial compressive load: base fixed: top free

Circular arch: uniform section: end A: fixed: end B: inclined slide: distributed load: radial

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: point load: vertical: on girder left half

Beam under bending: with axial tension: left end fixed: right end guided: temperature gradient: across depth: linearly varying

Beam under bending: with held ends: left end fixed: right end supported: concentrated moment

Circular arch: uniform section: end A: pinned: end B: inclined guide: uniform load: per unit vertical projection: horizontal: on left half arch

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: combined loads

Beam under bending: with axial compression: left end fixed: right end supported: applied vertical displacement

Circular arch: uniform section: end A: fixed: end B: horiz.guide: uniform temperature gradient: across depth

Beam under bending: with held ends: left end fixed: right end free: distributed load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: point load: horizontal: on left post

Circular arch: uniform section: end A: pinned: end B: inclined slide: uniform load: tangential

Beam under bending+shear: left end supported: right end guided: uniform load

Beam under bending: with held ends: left end supported: right end supported: concentrated moment

Beam under bending: with axial compression: left end fixed: right end fixed: uniform load

Beam under bending: with axial compression: left end fixed: right end guided: applied angular displacement

Circular arch: uniform section: end A: fixed: end B: inclined guide: concentrated load: radial

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: uniform load: horizontal: on girder

Beam under bending+shear: left end fixed: right end guided: distributed load

Circular arch: uniform section: end A: fixed: end B: vertical guide: uniform load: per unit vertical projection: horizontal

Circular arch: uniform section: end A: fixed: end B: horiz.slide: uniform load: per unit vertical projection: horizontal: on left half arch

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: point load: on right post

Circular arch: uniform section: end A: fixed: end B: pinned: concentrated load: vertical

Circular arch: uniform section: end A: fixed: end B: horiz.slide: uniform temperature gradient: across depth

Circular arch: uniform section: end A: fixed: end B: vertical guide: concentrated moment

Circular arch: uniform section: end A: pinned: end B: horiz.guide: uniform 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: point load: vertical: on girder left half

Circular arch: uniform section: end A: fixed: end B: horiz.guide: distributed load: vertical: partial

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end fixed: distributed partial load: linearly varying: on post

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 4th power of x (n=4): under a single axial compressive load: base fixed: top supported

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

Standard beams with parallel-faced flanges

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: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: point load: on girder

Flat face flanges with metal-to-metal contact outside the bolt circle: analysis of a flange cover assembly (Class 3): integral (Cat.1) flange: hub of constant thickness: no spacer: self-sealing gasket with negligible loads

Circular arch: uniform section: end A: fixed: end B: vertical guide: hydrostatic load

Beam under bending+shear: left end supported: right end supported: uniform load

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end sliding: point load: on girder

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

Circular arch: uniform section: end A: fixed: end B: fixed: uniform load: radial

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

Circular arch: uniform section: end A: fixed: end B: pinned: distributed load: vertical: partial

Beam under bending+shear: left end fixed: right end free: point load

Beam under bending: with axial tension: left end fixed: right end free: uniform load

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end sliding: right end fixed: 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 right post

Beam under bending: with axial compression: left end fixed: right end supported: uniform load

Circular arch: uniform section: end A: fixed: end B: inclined slide: distributed load: tangential

Circular arch: uniform section: end A: fixed: end B: vertical slide: distributed load: radial

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: combined loads

Circular arch: uniform section: end A: pinned: 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: distributed partial load: linearly varying: horizontal: on left post

Circular arch: uniform section: end A: fixed: end B: horiz.slide: distributed load: vertical: partial

Circular arch: uniform section: end A: fixed: end B: horiz.slide: distributed load: radial

Beam under bending: with axial tension: left end supported: right end guided: uniform load

Small deflections of rectangular plates: 2 adjacent supported sides, 2 free: distributed load: over a partial rectangular area

Circular arch: uniform section: end A: fixed: end B: vertical slide: combined loads

Properties of plane area: hollow structural sections: elliptical

Beam under bending: with axial tension: left end fixed: right end supported: combined loads

Beam under bending: with axial compression: left end supported: right end supported: applied angular displacement

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: uniform temperature change

Beam under bending+shear: left end fixed: right end supported: uniform 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: fixed: end B: pinned: concentrated load: horizontal

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: point load: horizontal: on girder

Circular arch: uniform section: end A: fixed: end B: vertical slide: distributed load: tangential

Circular arch: uniform section: end A: fixed: end B: free: distributed load: vertical: partial

Beam under bending: with axial compression: left end fixed: right end free: distributed load

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end pinned: distributed partial load: linearly varying: on girder

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

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

Circular arch: uniform section: end A: pinned: end B: horiz.slide: concentrated moment

Cylindrical vessel: vertical: with two ellipsoidal heads: filled volume: as a function of content height

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end fixed: uniform load: on girder

Beam under bending: with axial compression: left end supported: right end guided: combined loads

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: distributed partial load: linearly varying: vertical: on girder left half

Design rules for clamp connections: clamping faces parallel

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: fixed: end B: pinned: uniform load: per unit vertical projection: horizontal: on left half arch

Circular arch: uniform section: end A: pinned: end B: horiz.guide: uniform load: tangential

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end pinned: combined loads

Circular arch: uniform section: end A: pinned: end B: horiz.slide: uniform temperature change

Beam under bending: with axial tension: left end fixed: right end supported: applied vertical displacement

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end fixed: point load: on girder

Circular arch: uniform section: end A: fixed: end B: vertical slide: concentrated load: tangential

Small deflections of rectangular plates: 1 clamped side, 3 free: distributed load linearly varying along side a: starting at x0

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: distributed partial load: linearly varying: on right post

Circular arch: uniform section: end A: fixed: end B: inclined guide: combined loads

Beam: simple bending: with held ends: left end supported: right end supported: distributed load

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end sliding: right end fixed: uniform load: on post

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 1st power of x (n=1): under a single axial compressive load: base fixed: top guided

Circular arch: uniform section: end A: fixed: end B: vertical slide: concentrated load: horizontal

Beam under bending: with axial tension: left end fixed: right end free: concentrated load

Beam under bending: with axial compression: left end supported: right end guided: uniform load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: distributed partial load: linearly varying: on girder

Circular arch: uniform section: end A: fixed: end B: vertical guide: distributed load: vertical: partial

Circular arch: uniform section: end A: pinned: end B: pinned: combined loads

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

Sections derived from circular shape

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

Circular flat flanges without hubs: lap joint: to internal pressure: gasket laying inside inner edge of bolt holes

Two spheres in contact under load: Hertz's theory

Circular arch: uniform section: end A: pinned: end B: pinned: uniform load: per unit length of arch: horizontal

Beam under bending: with axial tension: left end fixed: right end guided: applied angular displacement

Beam under bending: with axial compression: left end supported: right end supported: combined loads

Beam under bending: with axial compression: left end fixed: right end supported: distributed load

Circular arch: uniform section: end A: fixed: end B: pinned: concentrated load: tangential

Circular arch: uniform section: end A: fixed: end B: free: uniform load: per unit vertical projection: horizontal: on left half arch

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: distributed partial load: linearly varying: vertical: on girder

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end pinned: distributed partial load: linearly varying: on girder

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: uniform load: horizontal: on girder left half

Beam under bending: with axial tension: left end supported: right end supported: combined loads

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: combined loads

Circular arch: uniform section: end A: fixed: end B: horiz.slide: concentrated moment

Circular arch: uniform section: end A: fixed: end B: vertical slide: concentrated moment

Circular arch: uniform section: end A: fixed: end B: horiz.guide: concentrated load: tangential

Circular arch: uniform section: end A: fixed: end B: horiz.slide: concentrated load: tangential

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

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: uniform temperature change

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: distributed partial load: linearly varying: horizontal: on right post

Full face flanges: with soft ring type gaskets: to internal pressure

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: concentrated load: horizontal

Beam under bending: with axial tension: left end fixed: right end fixed: concentrated moment

Properties of plane area: hollow structural sections: rectangular

Circular arch: uniform section: end A: pinned: end B: horiz.guide: concentrated load: vertical

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: distributed partial load: linearly varying: horizontal: on left post

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: uniform load: vertical: on girder right half

Properties of plane area: Standard channels: with tapered flanges

Circular arch: uniform section: end A: fixed: end B: vertical slide: uniform load: per unit length of arch: vertical

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: hydrostatic 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 fixed: distributed partial load: linearly varying: 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 temperature change

Circular arch: uniform section: end A: pinned: end B: pinned: distributed load: radial

Circular arch: uniform section: end A: fixed: end B: horiz.slide: uniform load: per unit vertical projection: horizontal

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end fixed: combined loads

Circular arch: uniform section: end A: fixed: end B: vertical slide: uniform load: per unit vertical projection: horizontal

Cylinder in contact on a flat plate under load: Hertz's theory

Circular flanges with hub: integral with hub slope 1/3 max: WN or LWN type: to internal pressure: gasket laying inside inner edge of bolt holes: with bolt spacing correction

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: uniform load: vertical: on girder left half

Circular arch: uniform section: end A: pinned: end B: pinned: concentrated load: vertical

Circular arch: uniform section: end A: fixed: end B: inclined slide: concentrated load: radial

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: uniform load: on girder

Circular ring beam: supported at bottom: loaded by uniform vertical load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: point load: vertical: on girder right half

Circular arch: uniform section: end A: fixed: end B: vertical guide: uniform load: tangential

Beam under bending: with axial compression: left end supported: right end guided: concentrated load

Elastic stability of a beam-column: with two stepped sections: under two axial compressive loads: base supported: top supported

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: uniform load: per unit vertical projection: horizontal: on left half arch

Circular arch: uniform section: end A: pinned: end B: inclined guide: concentrated load: vertical

Circular arch: uniform section: end A: fixed: end B: vertical guide: concentrated load: tangential

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

Beam under bending+shear: left end fixed: right end fixed: combined loads

Circular arch: uniform section: end A: pinned: end B: pinned: uniform temperature gradient: across depth

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

Beam under bending: with axial tension: left end supported: right end guided: distributed load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: 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 fixed: supports at same elevation: uniform load: horizontal: on left post

Beam under bending: with axial compression: left end fixed: right end supported: temperature gradient: across depth: linearly varying

Circular arch: uniform section: end A: fixed: end B: 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 pressure: on girder right half

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: distributed partial load: linearly varying: vertical: on girder left half

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: uniform load: horizontal: on right post

Circular arch: uniform section: end A: pinned: end B: pinned: uniform temperature change

Beam under bending: with held ends: left end supported: right end guided: temperature gradient: across depth: linearly varying

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: point load: horizontal: on right post

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: fixed: distributed load: tangential

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: uniform pressure: on girder left half

Circular arch: uniform section: end A: pinned: end B: inclined slide: uniform temperature gradient: across depth

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: combined loads

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: uniform load: vertical: on girder

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: point load: horizontal: on left post

Circular arch: uniform section: end A: pinned: end B: inclined slide: uniform load: per unit length of arch: horizontal

Properties of plane area: Standard channels: with parallel faced flanges

Beam under bending: with axial tension: left end fixed: right end fixed: uniform load

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: distributed partial load: linearly varying: on left post

Circular arch: uniform section: end A: fixed: end B: inclined guide: concentrated load: horizontal

Small deflections of rectangular plates: 2 facing sides clamped, 2 supported: distributed load: over a partial rectangular area

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: uniform load: horizontal: on right post

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: point load: on girder

Circular arch: uniform section: end A: fixed: end B: pinned: uniform load: per unit vertical projection: horizontal

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end fixed: uniform load: on post

Beam under bending: with axial tension: left end fixed: right end free: concentrated moment

Circular arch: uniform section: end A: pinned: end B: horiz.slide: uniform temperature gradient: across depth

Cylindrical vessel: vertical: with two spherically dished heads: filled volume: as a function of content height

Standard beams with tapered flanges

Full faced flanges with soft ring type gaskets: non metallic gaskets not less than 1.5 mm thick

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

Circular arch: uniform section: end A: pinned: end B: pinned: uniform load: per unit vertical projection: horizontal

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: uniform load: on right post

Circular arch: uniform section: end A: pinned: end B: inclined guide: uniform load: per unit vertical projection: horizontal

Circular arch: uniform section: end A: fixed: end B: inclined slide: hydrostatic load

Circular arch: uniform section: end A: fixed: end B: free: 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: point load: horizontal: on right post

Small deflections of rectangular plates: 3 clamped sides, 1 free: distributed load: over a partial rectangular area

Circular arch: uniform section: end A: pinned: end B: inclined slide: uniform load: per unit length of arch: vertical

Beam under bending: with held ends: left end fixed: right end fixed: uniform load

Circular arch: uniform section: end A: fixed: end B: vertical slide: uniform load: radial

Beam under bending: with axial compression: left end fixed: right end guided: concentrated moment

Beam under bending: with axial tension: left end fixed: right end supported: distributed load

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

Circular arch: uniform section: end A: pinned: end B: inclined slide: distributed load: vertical: partial

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

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

Beam: simple bending: with held ends: 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 pinned: right end fixed: supports at same elevation: point load: horizontal: 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 fixed: right end fixed: point load: on post

Beam under bending: with axial tension: left end supported: right end supported: applied vertical displacement

Small deflections of rectangular plates: 1 clamped side, 2 supported and 1 free: distributed load: over a partial rectangular area

Beam under bending: with axial compression: left end fixed: right end supported: concentrated load

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end fixed: uniform temperature change

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 pinned: right end pinned: point load: on post

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: 2 opposite sides clamped, 2 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: horizontal: on girder left half

Circular arch: uniform section: end A: fixed: end B: horiz.guide: distributed load: radial

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: uniform load: per unit length of arch: horizontal

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: uniform load: vertical: on girder left half

Cylinder in contact in a cylindrical socket under load: Hertz's theory

Circular arch: uniform section: end A: fixed: end B: fixed: concentrated load: tangential

Beam under bending: with axial tension: left end fixed: right end guided: combined loads

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: point load: on girder

Circular arch: uniform section: end A: fixed: end B: inclined slide: concentrated load: horizontal

Beam under bending: with axial tension: left end fixed: right end fixed: concentrated load

Beam under bending: with axial tension: left end supported: right end guided: concentrated load

Beam under bending: with axial compression: left end supported: right end supported: uniform load

Beam under bending+shear: left end fixed: right end free: distributed load

Circular arch: uniform section: end A: pinned: end B: horiz.guide: uniform load: per unit vertical projection: horizontal: on left half arch

Elastic stability of a beam-column: with two stepped sections: under two axial compressive loads: base fixed: top free

Beam under bending+shear: left end fixed: right end fixed: point load

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: point load: vertical: on girder

Circular flat flanges without hubs: loose, welded: to internal pressure: gasket laying inside inner edge of bolt holes

Properties of plane area: hollow structural sections: square

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

Circular arch: uniform section: end A: fixed: end B: inclined guide: uniform temperature change

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: uniform load: vertical: on girder

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: distributed partial load: linearly varying: on girder

Small deflections of rectangular plates: 3 clamped sides, 1 supported: distributed load linearly varying along side a: starting at x0

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

Circular arch: uniform section: end A: pinned: end B: inclined guide: distributed load: tangential

Circular arch: uniform section: end A: fixed: end B: free: uniform load: tangential

Beam under bending: with axial tension: left end supported: right end guided: concentrated moment

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

Small deflections of rectangular plates: 2 facing sides clamped, 2 supported: distributed load linearly varying along side a: starting at x0

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: distributed partial load: linearly varying: horizontal: on left post

Circular arch: uniform section: end A: pinned: end B: pinned: concentrated load: horizontal

Circular arch: uniform section: end A: pinned: end B: horiz.slide: distributed load: radial

Circular arch: uniform section: end A: pinned: end B: horiz.guide: concentrated load: tangential

Beam under bending: with axial tension: left end fixed: right end supported: uniform load

Circular ring beam: supported at bottom: load at top

Circular flanges with hub: hub with constant thickness: loose, welded: fig.2-4(3): to internal pressure: gasket laying inside inner edge of bolt holes: with bolt spacing correction

Circular arch: uniform section: end A: fixed: end B: vertical slide: hydrostatic load

Circular arch: uniform section: end A: fixed: end B: free: uniform load: per unit horizontal projection: vertical

Circular arch: uniform section: end A: fixed: end B: inclined guide: concentrated load: vertical

Design rules for clamp connections: clamping faces parallel: hub calculated as loose flange

Small deflections of rectangular plates: 2 simply supported opposite sides and 2 free: distributed load linearly varying along side a: starting at x0

Circular arch: uniform section: end A: fixed: end B: free: concentrated load: tangential

Circular arch: uniform section: end A: fixed: end B: inclined slide: uniform load: radial

Circular arch: uniform section: end A: fixed: end B: fixed: hydrostatic 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 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: uniform temperature change

Properties of plane area: Standard channels: with tapered flanges: two beams full penetration welded to form a closed section

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: concentrated load: radial

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: uniform load: horizontal: on girder left half

Beam under bending: with axial compression: left end fixed: right end supported: concentrated moment

Beam under bending: with axial compression: left end supported: right end guided: distributed load

Properties of plane area: Standard channels: with tapered flanges: two beams back-to-back

Circular arch: uniform section: end A: fixed: end B: inclined guide: distributed load: tangential

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: distributed partial load: linearly varying: on right post

Circular ring beam: supported at bottom: 2 tangential loads

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: uniform load: horizontal: on girder left half

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: point load: horizontal: on left post

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: uniform load: per unit horizontal projection: vertical

Circular arch: uniform section: end A: fixed: end B: free: distributed load: tangential

Elastic stability of a beam-column: with two stepped sections: under two axial compressive loads: base fixed: top supported

Circular arch: uniform section: end A: fixed: end B: inclined guide: uniform load: per unit vertical projection: horizontal: on left half arch

Circular arch: uniform section: end A: pinned: end B: inclined slide: concentrated load: vertical

Beam under bending: with held ends: left end supported: right end guided: applied angular displacement

Beam under bending+shear: left end fixed: right end guided: uniform load

Circular arch: uniform section: end A: fixed: end B: fixed: uniform load: tangential

Circular arch: uniform section: end A: pinned: end B: horiz.guide: uniform load: per unit length of arch: vertical

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: uniform load: per unit length of arch: vertical

Circular arch: uniform section: end A: fixed: end B: vertical guide: concentrated load: radial

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 bending: with axial tension: 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

Beam under bending+shear: left end fixed: right end fixed: 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: point load: horizontal: on right post

Circular arch: uniform section: end A: pinned: end B: inclined guide: distributed load: vertical: partial

Circular ring beam: supported at bottom: 2 radial 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: point load: horizontal: on girder left half

Circular arch: uniform section: end A: fixed: end B: vertical slide: uniform load: per unit length of arch: horizontal

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end sliding: combined loads

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: pinned: uniform load: per unit length of arch: vertical

Circular arch: uniform section: end A: fixed: end B: horiz.guide: uniform load: radial

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: distributed partial load: linearly varying: on girder

Circular arch: uniform section: end A: fixed: end B: free: distributed load: radial

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: point load: horizontal: on right post

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: uniform load: on girder

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: uniform temperature change

Small deflections of rectangular plates: 4 clamped sides: distributed load: over a partial rectangular area

Circular arch: uniform section: end A: fixed: end B: horiz.guide: uniform load: per unit vertical projection: horizontal

Circular arch: uniform section: end A: fixed: end B: inclined slide: distributed load: vertical: partial

Circular arch: uniform section: end A: fixed: end B: pinned: hydrostatic load

Beam under bending: with axial tension: left end fixed: right end fixed: applied vertical displacement

Circular arch: uniform section: end A: fixed: end B: fixed: concentrated load: radial

Circular arch: uniform section: end A: fixed: end B: vertical slide: uniform temperature gradient: across depth

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end pinned: uniform temperature change

Circular arch: uniform section: end A: pinned: end B: horiz.slide: uniform load: tangential

Circular arch: uniform section: end A: pinned: end B: inclined slide: distributed load: radial

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 1st power of x (n=1): under a single axial compressive load: base fixed: top fixed

Circular arch: uniform section: end A: pinned: end B: pinned: hydrostatic load

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

Small deflections of rectangular plates: 2 adjacent clamped sides, 2 supported: distributed load linearly varying along side a: starting at x0

Circular arch: uniform section: end A: pinned: end B: pinned: concentrated load: radial

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: point load: horizontal: on girder right half

Beam under bending: with held ends: left end supported: right end supported: applied vertical displacement

Beam under bending: with held ends: left end fixed: right end free: temperature gradient: across depth: linearly varying

Circular arch: uniform section: end A: fixed: end B: horiz.guide: concentrated moment

Circular arch: uniform section: end A: fixed: end B: free: hydrostatic load

Sections with quadrangular, rectangular or square shape

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 2nd power of x (n=2): under a single axial compressive load: base fixed: top fixed

Small deflections of rectangular plates: 3 clamped sides, 1 supported: distributed load: over a partial rectangular area

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: uniform load: on girder

Beam under bending+shear: left end fixed: right end supported: point load

Beam under bending: with held ends: left end fixed: right end guided: concentrated load

Circular arch: uniform section: end A: fixed: end B: inclined slide: concentrated moment

Circular arch: uniform section: end A: pinned: end B: inclined guide: concentrated load: tangential

Beam under bending: with axial tension: left end supported: right end guided: temperature gradient: across depth: linearly varying

Circular arch: uniform section: end A: pinned: end B: inclined slide: combined loads

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: uniform temperature change

Elastic stability of a beam-column: prismatic: under a single axial compressive load: base fixed: top fixed

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: distributed partial load: linearly varying: horizontal: on left post

Beam under bending: with held ends: left end fixed: right end free: applied angular displacement

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 1st power of x (n=1): under a single axial compressive load: base fixed: top supported

Circular arch: uniform section: end A: fixed: end B: inclined slide: uniform load: per unit vertical projection: horizontal: on left half arch

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end fixed: distributed partial load: linearly varying: on post

Beam under bending: with axial tension: left end supported: right end supported: distributed load

Circular arch: uniform section: end A: fixed: end B: free: combined loads

Circular ring beam: supported at bottom: 2 horizontal loads

Circular arch: uniform section: end A: fixed: end B: pinned: uniform temperature change

Beam under bending: with axial compression: left end fixed: right end guided: distributed load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: distributed partial load: linearly varying: vertical: on girder right half

Circular arch: uniform section: end A: fixed: end B: vertical slide: uniform load: tangential

Beam under bending: with axial tension: left end fixed: right end supported: applied angular displacement

Beam under bending: with axial compression: left end fixed: right end supported: combined loads

Small deflections of rectangular plates: 4 free sides: supported at 4 corners: distributed load linearly varying along side a: starting at x0

Circular arch: uniform section: end A: fixed: end B: horiz.slide: concentrated load: horizontal

Beam under bending: with held ends: left end fixed: right end fixed: concentrated load

Circular arch: uniform section: end A: fixed: end B: vertical guide: uniform load: radial

Beam under bending: with axial compression: left end fixed: right end fixed: temperature gradient: across depth: linearly varying

Circular flat flanges without hubs: lap joint: to internal pressure: gasket laying inside inner edge of bolt holes: with bolt spacing correction

Circular arch: uniform section: end A: pinned: end B: inclined guide: uniform temperature gradient: across depth

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

Circular arch: uniform section: end A: fixed: end B: vertical guide: concentrated load: horizontal

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

Beam under bending: with axial tension: left end fixed: right end fixed: distributed load

Circular arch: uniform section: end A: pinned: end B: horiz.slide: concentrated load: tangential

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: point load: on girder

Circular arch: uniform section: end A: pinned: end B: inclined slide: uniform load: per unit horizontal projection: vertical

Beam under bending+shear: left end fixed: right end fixed: uniform load

Circular arch: uniform section: end A: pinned: end B: horiz.slide: uniform load: per unit vertical projection: horizontal

Circular arch: uniform section: end A: fixed: end B: pinned: concentrated load: radial

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: inclined guide: distributed load: vertical: partial

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

Circular arch: uniform section: end A: pinned: end B: horiz.guide: distributed load: tangential

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: combined loads

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end pinned: uniform temperature change

Elastic stability of a beam-column: prismatic: under a single axial compressive load: base fixed: top guided

Beam under bending: with axial tension: left end fixed: right end free: applied angular displacement

Circular arch: uniform section: end A: fixed: end B: inclined guide: uniform load: per unit vertical projection: horizontal

Small deflections of rectangular plates: 3 clamped sides, 1 free: distributed load linearly varying along side a: starting at x0

Small deflections of rectangular plates: 1 clamped side, 2 supported and 1 free: distributed load linearly varying along side a: starting at x0

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: supports at same elevation: uniform load: horizontal: on girder right half

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: combined loads

Cylindrical vessel: horizontal: with two spherically dished heads: filled volume: as a function of content height

Circular arch: uniform section: end A: pinned: end B: inclined guide: uniform load: radial

Circular arch: uniform section: end A: fixed: end B: pinned: uniform load: tangential

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: combined loads

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: concentrated moment

Beam under bending: with axial tension: left end fixed: right end guided: uniform load

Beam under bending: with axial compression: left end supported: right end guided: temperature gradient: across depth: linearly varying

Beam under bending: with axial tension: left end fixed: right end fixed: combined loads

Beam under bending: with axial compression: left end supported: right end supported: distributed load

Beam under bending: with held ends: left end fixed: right end supported: applied vertical displacement

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

Circular arch: uniform section: end A: pinned: end B: horiz.guide: concentrated load: horizontal

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end pinned: distributed partial load: linearly varying: on post

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: combined loads

Circular arch: uniform section: end A: fixed: end B: restrained against rotation only: hydrostatic 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: vertical: on girder left half

Circular arch: uniform section: end A: pinned: end B: inclined slide: distributed load: tangential

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: point load: horizontal: on girder right half

Circular arch: uniform section: end A: pinned: end B: horiz.guide: hydrostatic load

Circular arch: uniform section: end A: pinned: end B: inclined slide: concentrated load: horizontal

Circular arch: uniform section: end A: fixed: end B: vertical guide: uniform load: per unit length of arch: vertical

Beam under bending: with axial compression: left end fixed: right end fixed: combined loads

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: combined loads

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end pinned: right end pinned: uniform load: on left post

Circular arch: uniform section: end A: fixed: end B: horiz.guide: concentrated load: radial

Two cylinders in contact under load: parallel axes: Hertz's theory

Beam under bending: with axial compression: left end supported: right end supported: concentrated load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: uniform load: vertical: on girder right half

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

Circular arch: uniform section: end A: fixed: end B: free: uniform load: per unit length of arch: 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 supported

Small deflections of rectangular plates: 1 clamped side, 2 supported(adjacent) and 1 free: distributed load: over a partial rectangular area

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end fixed: right end sliding: uniform temperature change

Narrow face gasketed flanges: integral method: with hub: WN or LWN type: to internal pressure

Circular arch: uniform section: end A: fixed: end B: horiz.slide: hydrostatic load

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end pinned: right end fixed: supports at same elevation: 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

Circular arch: uniform section: end A: pinned: end B: pinned: distributed load: vertical: partial

Portal frame: vertical left post: sloped girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: uniform load: horizontal: on girder

Elastic stability of a beam-column: tapered over a portion of length: inertia varying with the 1st power of x (n=1): under a single axial compressive load: base supported: top supported

Beam under bending: with held ends: left end fixed: right end guided: concentrated moment

Beam under bending: with axial tension: left end supported: right end guided: applied angular displacement

Circular arch: uniform section: end A: fixed: end B: horiz.guide: concentrated load: horizontal

Beam under bending: with held ends: left end fixed: right end fixed: distributed load

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end pinned: uniform load: on girder

Small deflections of rectangular plates: 2 adjacent clamped sides, 2 supported: distributed load: over a partial rectangular area

Portal frame: vertical left post: horizontal girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: uniform load: on left 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: uniform load: horizontal: on left post

One leg frame: vertical post: horizontal girder: under bending+shear+normal load: left end pinned: right end pinned: combined loads

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end pinned: supports at same elevation: point load: horizontal: on girder right half

Circular arch: uniform section: end A: fixed: end B: free: concentrated load: horizontal

Circular arch: uniform section: end A: fixed: end B: vertical slide: uniform load: per unit vertical projection: horizontal: on left half arch

Properties of plane area: Standard Tee beams

Circular arch: uniform section: end A: fixed: end B: inclined slide: concentrated load: tangential

Beam under bending: with axial compression: left end fixed: right end guided: concentrated load

Circular arch: uniform section: end A: fixed: end B: fixed: uniform load: per unit length of arch: horizontal

Beam under bending+shear: left end fixed: right end supported: 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 left half

Circular arch: uniform section: end A: fixed: end B: free: uniform load: per unit vertical projection: horizontal

Circular arch: uniform section: end A: fixed: end B: horiz.slide: concentrated load: radial

Circular arch: uniform section: end A: fixed: end B: vertical guide: distributed load: radial

Circular arch: uniform section: end A: pinned: end B: inclined guide: uniform temperature change

Portal frame: vertical left post: symmetrically gabled girder: vertical right post: under bending+shear+normal load: left end fixed: right end fixed: supports at same elevation: distributed partial load: linearly varying: vertical: on girder right half

Circular arch: uniform section: end A: fixed: end B: fixed: concentrated load: vertical

Circular arch: uniform section: end A: fixed: end B: inclined slide: uniform load: per unit length of arch: vertical

Circular arch: uniform section: end A: fixed: end B: vertical guide: uniform load: per unit horizontal projection: vertical