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  2. Euler–Bernoulli beam theory - Wikipedia

    en.wikipedia.org/wiki/Euler–Bernoulli_beam_theory

    Euler–Bernoulli beam theory can also be extended to the analysis of curved beams, beam buckling, composite beams, and geometrically nonlinear beam deflection. Euler–Bernoulli beam theory does not account for the effects of transverse shear strain. As a result, it underpredicts deflections and overpredicts natural frequencies.

  3. Deflection (engineering) - Wikipedia

    en.wikipedia.org/wiki/Deflection_(engineering)

    The deflection distance of a member under a load can be calculated by integrating the function that mathematically describes the slope of the deflected shape of the member under that load. Standard formulas exist for the deflection of common beam configurations and load cases at discrete locations.

  4. Sandwich theory - Wikipedia

    en.wikipedia.org/wiki/Sandwich_theory

    Bending of a sandwich beam. The total deflection is the sum of a bending part w b and a shear part w s Shear strains during the bending of a sandwich beam. Let the sandwich beam be subjected to a bending moment and a shear force . Let the total deflection of the beam due to these loads be .

  5. Moment distribution method - Wikipedia

    en.wikipedia.org/wiki/Moment_distribution_method

    Let one end (end A) of a fixed beam be released and applied a moment while the other end (end B) remains fixed. This will cause end A to rotate through an angle θ A {\displaystyle \theta _{A}} . Once the magnitude of M B {\displaystyle M_{B}} developed at end B is found, the carryover factor of this member is given as the ratio of M B ...

  6. Timoshenko–Ehrenfest beam theory - Wikipedia

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

    [4] [5] The model takes into account shear deformation and rotational bending effects, making it suitable for describing the behaviour of thick beams, sandwich composite beams, or beams subject to high-frequency excitation when the wavelength approaches the thickness of the beam.

  7. Structural engineering theory - Wikipedia

    en.wikipedia.org/wiki/Structural_engineering_theory

    Continuum mechanics is valid for a bending beam. The stress at a cross section varies linearly in the direction of bending, and is zero at the centroid of every cross section. 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 ...

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  9. Direct integration of a beam - Wikipedia

    en.wikipedia.org/wiki/Direct_integration_of_a_beam

    Simply supported beam with a constant 10 kN per meter load over a 15m length. Take the beam shown at right supported by a fixed pin at the left and a roller at the right. There are no applied moments, the weight is a constant 10 kN, and - due to symmetry - each support applies a 75 kN vertical force to the beam. Taking x as the distance from ...