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

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

Curved beam in bending: end A free: end B fixed: concentrated bending moment

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

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

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

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

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

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

Curved beam in bending: end A supported and slope guided: end B supported and slope guided: concentrated bending moment

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

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

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

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

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

Curved beam in bending: end A simply supported: end B supported and roll guided: distributed load

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

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

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

Supported-fixed beam: on elastic foundation: concentrated moment

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

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

Curved beam in bending: end A simply supported: end B supported and slope guided: uniform load

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

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

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

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

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

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

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

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

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

Curved beam in bending: end A supported and roll guided: end B supported and slope guided: concentrated twisting moment

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

Curved beam in bending: end A supported and roll guided: end B supported and roll guided: concentrated load

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

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

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

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

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

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

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

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

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

Curved beam in bending: end A supported and roll guided: end B supported and slope guided: distributed load

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

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

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

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

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

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

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

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

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

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

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

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

Curved beam in bending: end A simply supported: end B fixed: combined loads

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

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

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

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

Circular ring beam: supported at bottom: combined loads

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

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

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

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

Curved beam in bending: end A supported and slope guided: end B fixed: combined loads

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

Curved beam in bending: end A simply supported: end B fixed: distributed load

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

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

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

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

Curved beam in bending: end A supported and slope guided: end B supported and slope guided: concentrated twisting moment

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

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

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

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

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

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

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

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

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

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

Free-free beam: on elastic foundation: concentrated moment

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

Curved beam in bending: end A supported and roll guided: end B supported and roll guided: distributed load

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

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

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

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

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

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

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

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

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

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

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

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

Curved beam in bending: end A free: end B fixed: concentrated load

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

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

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

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

Beam under simple bending: left end fixed: right end free(cantilever): uniform load

Guided-infinite beam: on elastic foundation: concentrated moment

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

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

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

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

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

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

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

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

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

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

Fixed-fixed beam: on elastic foundation: point load

Circular ring beam: supported at bottom: 2 vertical loads

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

Fixed-infinite beam: on elastic foundation: point load

Fixed-guided beam: on elastic foundation: concentrated moment

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

Curved beam in bending: end A supported and roll guided: end B supported and slope guided: concentrated load

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

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

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

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

Infinite beam: on elastic foundation: concentrated load

Curved beam in bending: end A simply supported: end B supported and roll guided: uniform load

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

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

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

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

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

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

Supported-free beam: on elastic foundation: concentrated load

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

Curved beam in bending: end A supported and roll guided: end B fixed: distributed load

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

Semi-infinite beam: on elastic foundation: concentrated moment

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

Curved beam in bending: end A supported and slope guided: end B fixed: concentrated twisting moment

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

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

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

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

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

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

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

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

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

Fixed-free beam: on elastic foundation: concentrated moment

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

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

Continuous beam: over 3 spans: in simple bending: concentrated moment

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

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

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

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

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

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

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

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

Beam under bending: with axial compression: 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 2nd power of x (n=2): under a single axial compressive load: base fixed: top free

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

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

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

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

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

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

Beam under simple bending: left end fixed: right end fixed: combined loads

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

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

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

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

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

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

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

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

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

Curved beam in bending: end A supported and roll guided: end B supported and roll guided: concentrated twisting moment

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

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

Curved beam in bending: end A free: end B fixed: distributed load

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

Supported-free beam: on elastic foundation: concentrated moment

Beam under simple bending: left end supported: right end supported: combined loads

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

Curved beam in bending: end A simply supported: end B supported and slope guided: distributed load

Curved beam in bending: end A simply supported: end B fixed: concentrated bending moment

Curved beam in bending: end A simply supported: end B supported and roll guided: concentrated bending moment

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

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

Curved beam in bending: end A fixed: end B fixed: concentrated twisting moment

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

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

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

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

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

Curved beam in bending: end A simply supported: end B fixed: concentrated twisting moment

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

Guided-guided beam: on elastic foundation: concentrated load

Curved beam in bending: end A simply supported: end B supported and slope guided: concentrated load

Curved beam in bending: end A supported and slope guided: end B fixed: concentrated bending moment

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

Guided-infinite beam: on elastic foundation: point load

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

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

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

Curved beam in bending: end A supported and roll guided: end B supported and roll guided: concentrated bending moment

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Semiinfinite beam: on elastic foundation: point load

Curved beam in bending: end A simply supported: end B supported and roll guided: concentrated load

Curved beam in bending: end A simply supported: end B fixed: concentrated load

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

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

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

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

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

Curved beam in bending: end A supported and slope guided: end B supported and slope guided: uniform load

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

Supported-infinite beam: on elastic foundation: concentrated moment

Curved beam in bending: end A supported and roll guided: end B supported and slope guided: uniform load

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

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

Curved beam in bending: end A free: end B fixed: uniform load

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

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

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

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

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

Curved beam in bending: end A simply supported: end B supported and slope guided: concentrated bending moment

Infinite beam: on elastic foundation: distributed load: linearly varying over 'a'

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

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

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

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

Curved beam in bending: end A supported and slope guided: end B fixed: concentrated load

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

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

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

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

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

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

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

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

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

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

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

Fixed-guided beam: on elastic foundation: point load

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

Continuous beam: over 4 spans: in simple bending: concentrated moment

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

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

Beam under simple bending: left end fixed: right end supported: combined loads

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

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

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

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

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

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

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

Properties of plane area: Standard channels: with tapered flanges

Supported-guided beam: on elastic foundation: concentrated moment

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

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

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

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

Curved beam in bending: end A simply supported: end B supported and roll guided: combined loads

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

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

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

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

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

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

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

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

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

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

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

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

Supported-infinite beam: on elastic foundation: concentrated load

Curved beam in bending: end A supported and roll guided: end B fixed: concentrated bending moment

Curved beam in bending: end A fixed: end B fixed: distributed load

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

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

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

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

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

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

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

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

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

Fixed-free beam: on elastic foundation: point load

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

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

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

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

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

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

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

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

Infinite beam: on elastic foundation: concentrated moment

Curved beam in bending: end A supported and roll guided: end B fixed: uniform load

Fixed-infinite beam: on elastic foundation: concentrated moment

Curved beam in bending: end A simply supported: end B supported and slope guided: concentrated twisting moment

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

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

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

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

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

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

Curved beam in bending: end A supported and slope guided: end B fixed: distributed load

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

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

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

Continuous beam: over 2 spans: in simple bending: concentrated moment

Curved beam in bending: end A supported and roll guided: end B fixed: concentrated load

Simply supported beam: on elastic foundation: point load

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

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

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

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

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

Curved beam in bending: end A supported and slope guided: end B supported and slope guided: combined loads

Curved beam in bending: end A simply supported: end B supported and roll guided: concentrated twisting moment

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

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

Curved beam in bending: end A supported and roll guided: end B supported and roll guided: combined loads

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

Curved beam in bending: end A supported and roll guided: end B supported and slope guided: combined loads

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

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

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

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

Curved beam in bending: end A free: end B fixed: combined loads

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

Simply supported beam: on elastic foundation: concentrated moment

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

Curved beam in bending: end A fixed: end B fixed: uniform load

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

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

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

Circular ring beam: supported at bottom: load at top

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

Curved beam in bending: end A fixed: end B fixed: combined loads

Guided-guided beam: on elastic foundation: concentrated moment

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

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

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

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

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

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

Circular ring beam: supported at bottom: 2 tangential loads

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

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

Beam under simple bending: left end fixed: right end guided: combined loads

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

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

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

Guided-free beam: on elastic foundation: concentrated moment

Curved beam in bending: end A supported and roll guided: end B supported and slope guided: concentrated bending moment

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

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

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

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

Circular ring beam: supported at bottom: 2 radial loads

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

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

Curved beam in bending: end A simply supported: end B fixed: uniform load

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

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

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

Free-free beam: on elastic foundation: point load

Curved beam in bending: end A supported and slope guided: end B supported and slope guided: concentrated load

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

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

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

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

Curved beam in bending: end A supported and slope guided: end B fixed: uniform load

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

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

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

Sections with quadrangular, rectangular or square shape

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

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

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

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

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

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

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

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

Curved beam in bending: end A supported and roll guided: end B fixed: combined loads

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

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

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

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

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

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

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

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

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

Curved beam in bending: end A simply supported: end B supported and slope guided: combined loads

Circular ring beam: supported at bottom: 2 horizontal loads

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Curved beam in bending: end A fixed: end B fixed: concentrated load

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

Fixed-fixed beam: on elastic foundation: concentrated moment

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

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

Guided-free beam: on elastic foundation: point load

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

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

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

Supported-guided beam: on elastic foundation: concentrated load

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

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

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

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

Beam under simple bending: left end supported: right end guided: combined loads

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

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

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

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

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

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

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

Supported-fixed beam: on elastic foundation: concentrated load

Curved beam in bending: end A supported and roll guided: end B supported and roll 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 guided: uniform load

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

Curved beam in bending: end A free: end B fixed: concentrated twisting moment

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

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

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

Curved beam in bending: end A supported and roll guided: end B fixed: concentrated twisting moment

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

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

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

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

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

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

Curved beam in bending: end A supported and slope guided: end B supported and slope guided: distributed load

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

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

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

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

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

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

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

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

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

Curved beam in bending: end A fixed: end B fixed: concentrated bending moment

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

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

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

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

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

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

Properties of plane area: Standard Tee beams

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

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

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

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

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

Curved beam in bending: end A free: end B fixed: concentrated bending moment

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

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

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

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

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

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

Curved beam in bending: end A supported and slope guided: end B supported and slope guided: concentrated bending moment

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

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

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

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

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

Curved beam in bending: end A simply supported: end B supported and roll guided: distributed load

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

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

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

Supported-fixed beam: on elastic foundation: concentrated moment

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

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

Curved beam in bending: end A simply supported: end B supported and slope guided: uniform load

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

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

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

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

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

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

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

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

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

Curved beam in bending: end A supported and roll guided: end B supported and slope guided: concentrated twisting moment

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

Curved beam in bending: end A supported and roll guided: end B supported and roll guided: concentrated load

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

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

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

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

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

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

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

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

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

Curved beam in bending: end A supported and roll guided: end B supported and slope guided: distributed load

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

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

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

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

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

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

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

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

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

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

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

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

Curved beam in bending: end A simply supported: end B fixed: combined loads

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

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

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

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

Circular ring beam: supported at bottom: combined loads

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

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

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

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

Curved beam in bending: end A supported and slope guided: end B fixed: combined loads

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

Curved beam in bending: end A simply supported: end B fixed: distributed load

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

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

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

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

Curved beam in bending: end A supported and slope guided: end B supported and slope guided: concentrated twisting moment

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

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

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

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

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

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

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

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

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

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

Free-free beam: on elastic foundation: concentrated moment

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

Curved beam in bending: end A supported and roll guided: end B supported and roll guided: distributed load

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

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

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

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

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

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

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

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

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

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

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

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

Curved beam in bending: end A free: end B fixed: concentrated load

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

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

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

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

Beam under simple bending: left end fixed: right end free(cantilever): uniform load

Guided-infinite beam: on elastic foundation: concentrated moment

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

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

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

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

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

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

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

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

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

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

Fixed-fixed beam: on elastic foundation: point load

Circular ring beam: supported at bottom: 2 vertical loads

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

Fixed-infinite beam: on elastic foundation: point load

Fixed-guided beam: on elastic foundation: concentrated moment

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

Curved beam in bending: end A supported and roll guided: end B supported and slope guided: concentrated load

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

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

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

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

Infinite beam: on elastic foundation: concentrated load

Curved beam in bending: end A simply supported: end B supported and roll guided: uniform load

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

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

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

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

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

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

Supported-free beam: on elastic foundation: concentrated load

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

Curved beam in bending: end A supported and roll guided: end B fixed: distributed load

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

Semi-infinite beam: on elastic foundation: concentrated moment

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

Curved beam in bending: end A supported and slope guided: end B fixed: concentrated twisting moment

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

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

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

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

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

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

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

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

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

Fixed-free beam: on elastic foundation: concentrated moment

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

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

Continuous beam: over 3 spans: in simple bending: concentrated moment

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

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

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

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

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

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

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

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

Beam under bending: with axial compression: 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 2nd power of x (n=2): under a single axial compressive load: base fixed: top free

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

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

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

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

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

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

Beam under simple bending: left end fixed: right end fixed: combined loads

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

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

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

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

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

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

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

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

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

Curved beam in bending: end A supported and roll guided: end B supported and roll guided: concentrated twisting moment

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

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

Curved beam in bending: end A free: end B fixed: distributed load

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

Supported-free beam: on elastic foundation: concentrated moment

Beam under simple bending: left end supported: right end supported: combined loads

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

Curved beam in bending: end A simply supported: end B supported and slope guided: distributed load

Curved beam in bending: end A simply supported: end B fixed: concentrated bending moment

Curved beam in bending: end A simply supported: end B supported and roll guided: concentrated bending moment

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

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

Curved beam in bending: end A fixed: end B fixed: concentrated twisting moment

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

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

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

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

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

Curved beam in bending: end A simply supported: end B fixed: concentrated twisting moment

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

Guided-guided beam: on elastic foundation: concentrated load

Curved beam in bending: end A simply supported: end B supported and slope guided: concentrated load

Curved beam in bending: end A supported and slope guided: end B fixed: concentrated bending moment

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

Guided-infinite beam: on elastic foundation: point load

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

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

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

Curved beam in bending: end A supported and roll guided: end B supported and roll guided: concentrated bending moment

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Semiinfinite beam: on elastic foundation: point load

Curved beam in bending: end A simply supported: end B supported and roll guided: concentrated load

Curved beam in bending: end A simply supported: end B fixed: concentrated load

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

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

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

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

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

Curved beam in bending: end A supported and slope guided: end B supported and slope guided: uniform load

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

Supported-infinite beam: on elastic foundation: concentrated moment

Curved beam in bending: end A supported and roll guided: end B supported and slope guided: uniform load

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

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

Curved beam in bending: end A free: end B fixed: uniform load

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

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

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

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

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

Curved beam in bending: end A simply supported: end B supported and slope guided: concentrated bending moment

Infinite beam: on elastic foundation: distributed load: linearly varying over 'a'

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

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

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

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

Curved beam in bending: end A supported and slope guided: end B fixed: concentrated load

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

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

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

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

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

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

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

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

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

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

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

Fixed-guided beam: on elastic foundation: point load

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

Continuous beam: over 4 spans: in simple bending: concentrated moment

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

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

Beam under simple bending: left end fixed: right end supported: combined loads

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

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

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

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

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

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

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

Properties of plane area: Standard channels: with tapered flanges

Supported-guided beam: on elastic foundation: concentrated moment

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

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

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

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

Curved beam in bending: end A simply supported: end B supported and roll guided: combined loads

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

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

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

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

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

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

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

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

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

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

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

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

Supported-infinite beam: on elastic foundation: concentrated load

Curved beam in bending: end A supported and roll guided: end B fixed: concentrated bending moment

Curved beam in bending: end A fixed: end B fixed: distributed load

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

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

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

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

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

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

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

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

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

Fixed-free beam: on elastic foundation: point load

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

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

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

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

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

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

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

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

Infinite beam: on elastic foundation: concentrated moment

Curved beam in bending: end A supported and roll guided: end B fixed: uniform load

Fixed-infinite beam: on elastic foundation: concentrated moment

Curved beam in bending: end A simply supported: end B supported and slope guided: concentrated twisting moment

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

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

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

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

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

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

Curved beam in bending: end A supported and slope guided: end B fixed: distributed load

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

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

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

Continuous beam: over 2 spans: in simple bending: concentrated moment

Curved beam in bending: end A supported and roll guided: end B fixed: concentrated load

Simply supported beam: on elastic foundation: point load

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

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

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

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

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

Curved beam in bending: end A supported and slope guided: end B supported and slope guided: combined loads

Curved beam in bending: end A simply supported: end B supported and roll guided: concentrated twisting moment

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

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

Curved beam in bending: end A supported and roll guided: end B supported and roll guided: combined loads

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

Curved beam in bending: end A supported and roll guided: end B supported and slope guided: combined loads

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

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

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

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

Curved beam in bending: end A free: end B fixed: combined loads

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

Simply supported beam: on elastic foundation: concentrated moment

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

Curved beam in bending: end A fixed: end B fixed: uniform load

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

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

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

Circular ring beam: supported at bottom: load at top

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

Curved beam in bending: end A fixed: end B fixed: combined loads

Guided-guided beam: on elastic foundation: concentrated moment

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

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

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

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

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

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

Circular ring beam: supported at bottom: 2 tangential loads

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

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

Beam under simple bending: left end fixed: right end guided: combined loads

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

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

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

Guided-free beam: on elastic foundation: concentrated moment

Curved beam in bending: end A supported and roll guided: end B supported and slope guided: concentrated bending moment

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

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

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

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

Circular ring beam: supported at bottom: 2 radial loads

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

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

Curved beam in bending: end A simply supported: end B fixed: uniform load

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

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

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

Free-free beam: on elastic foundation: point load

Curved beam in bending: end A supported and slope guided: end B supported and slope guided: concentrated load

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

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

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

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

Curved beam in bending: end A supported and slope guided: end B fixed: uniform load

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

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

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

Sections with quadrangular, rectangular or square shape

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

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

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

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

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

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

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

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

Curved beam in bending: end A supported and roll guided: end B fixed: combined loads

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

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

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

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

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

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

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

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

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

Curved beam in bending: end A simply supported: end B supported and slope guided: combined loads

Circular ring beam: supported at bottom: 2 horizontal loads

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Curved beam in bending: end A fixed: end B fixed: concentrated load

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

Fixed-fixed beam: on elastic foundation: concentrated moment

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

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

Guided-free beam: on elastic foundation: point load

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

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

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

Supported-guided beam: on elastic foundation: concentrated load

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

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

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

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

Beam under simple bending: left end supported: right end guided: combined loads

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

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

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

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

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

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

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

Supported-fixed beam: on elastic foundation: concentrated load

Curved beam in bending: end A supported and roll guided: end B supported and roll 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 guided: uniform load

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

Curved beam in bending: end A free: end B fixed: concentrated twisting moment

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

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

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

Curved beam in bending: end A supported and roll guided: end B fixed: concentrated twisting moment

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

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

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

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

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

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

Curved beam in bending: end A supported and slope guided: end B supported and slope guided: distributed load

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

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

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

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

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

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

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

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

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

Curved beam in bending: end A fixed: end B fixed: concentrated bending moment

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

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

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

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

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

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

Properties of plane area: Standard Tee beams

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

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

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

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