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  2. Euler–Bernoulli beam theory - Wikipedia

    en.wikipedia.org/wiki/Euler–Bernoulli_beam_theory

    Download as PDF; Printable version; ... [5] The bending moments, shear forces, and deflections of such a beam are listed below: ... is the axial load, () is the ...

  3. Bending moment - Wikipedia

    en.wikipedia.org/wiki/Bending_moment

    If clockwise bending moments are taken as negative, then a negative bending moment within an element will cause "hogging", and a positive moment will cause "sagging". It is therefore clear that a point of zero bending moment within a beam is a point of contraflexure—that is, the point of transition from hogging to sagging or vice versa.

  4. Conjugate beam method - Wikipedia

    en.wikipedia.org/wiki/Conjugate_beam_method

    A M/EI diagram is a moment diagram divided by the beam's Young's modulus and moment of inertia. To make use of this comparison we will now consider a beam having the same length as the real beam, but referred here as the "conjugate beam." The conjugate beam is "loaded" with the M/EI diagram derived from the load on the real beam.

  5. Shear and moment diagram - Wikipedia

    en.wikipedia.org/wiki/Shear_and_moment_diagram

    Shear and Bending moment diagram for a simply supported beam with a concentrated load at mid-span. Shear force and bending moment diagrams are analytical tools used in conjunction with structural analysis to help perform structural design by determining the value of shear forces and bending moments at a given point of a structural element such as a beam.

  6. Structural engineering theory - Wikipedia

    en.wikipedia.org/wiki/Structural_engineering_theory

    The bending moment at a particular cross section varies linearly with the second derivative of the deflected shape at that location. The beam is composed of an isotropic material. The applied load is orthogonal to the beam's neutral axis and acts in a unique plane. A simplified version of Euler–Bernoulli beam equation is:

  7. Influence line - Wikipedia

    en.wikipedia.org/wiki/Influence_line

    An influence line for a given function, such as a reaction, axial force, shear force, or bending moment, is a graph that shows the variation of that function at any given point on a structure due to the application of a unit load at any point on the structure. An influence line for a function differs from a shear, axial, or bending moment diagram.

  8. Timoshenko–Ehrenfest beam theory - Wikipedia

    en.wikipedia.org/wiki/Timoshenko–Ehrenfest_beam...

    The bending moment applied to the beam also has to be specified. The rotation φ {\displaystyle \varphi } and the transverse shear force Q x {\displaystyle Q_{x}} are not specified. Clamped beams : The displacement w {\displaystyle w} and the rotation φ {\displaystyle \varphi } are specified to be zero at the clamped end.

  9. Flexural rigidity - Wikipedia

    en.wikipedia.org/wiki/Flexural_rigidity

    where is the flexural modulus (in Pa), is the second moment of area (in m 4), is the transverse displacement of the beam at x, and () is the bending moment at x. The flexural rigidity (stiffness) of the beam is therefore related to both E {\displaystyle E} , a material property, and I {\displaystyle I} , the physical geometry of the beam.