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