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  2. Euler–Bernoulli beam theory - Wikipedia

    en.wikipedia.org/wiki/Euler–Bernoulli_beam_theory

    Both the bending moment and the shear force cause stresses in the beam. The stress due to shear force is maximum along the neutral axis of the beam (when the width of the beam, t, is constant along the cross section of the beam; otherwise an integral involving the first moment and the beam's width needs to be evaluated for the particular cross ...

  3. Macaulay's method - Wikipedia

    en.wikipedia.org/wiki/Macaulay's_method

    Where is the deflection and is the bending moment. This equation [ 7 ] is simpler than the fourth-order beam equation and can be integrated twice to find w {\displaystyle w} if the value of M {\displaystyle M} as a function of x {\displaystyle x} is known.

  4. Bending stiffness - Wikipedia

    en.wikipedia.org/wiki/Bending_stiffness

    The bending stiffness is the resistance of a member against bending deflection/deformation. It is a function of the Young's modulus E {\displaystyle E} , the second moment of area I {\displaystyle I} of the beam cross-section about the axis of interest, length of the beam and beam boundary condition.

  5. Bending - Wikipedia

    en.wikipedia.org/wiki/Bending

    Cross-sections of the beam remain plane during bending. Deflection of a beam deflected symmetrically and principle of superposition. Compressive and tensile forces develop in the direction of the beam axis under bending loads. These forces induce stresses on the beam. The maximum compressive stress is found at the uppermost edge of the beam ...

  6. Flexural modulus - Wikipedia

    en.wikipedia.org/wiki/Flexural_modulus

    For a 3-point test of a rectangular beam behaving as an isotropic linear material, where w and h are the width and height of the beam, I is the second moment of area of the beam's cross-section, L is the distance between the two outer supports, and d is the deflection due to the load F applied at the middle of the beam, the flexural modulus: [1]

  7. Cantilever method - Wikipedia

    en.wikipedia.org/wiki/Cantilever_method

    The cantilever method is an approximate method for calculating shear forces and moments developed in beams and columns of a frame or structure due to lateral loads. The applied lateral loads typically include wind loads and earthquake loads, which must be taken into consideration while designing buildings.

  8. Cantilever - Wikipedia

    en.wikipedia.org/wiki/Cantilever

    Like other structural elements, a cantilever can be formed as a beam, plate, truss, or slab. When subjected to a structural load at its far, unsupported end, the cantilever carries the load to the support where it applies a shear stress and a bending moment. [1] Cantilever construction allows overhanging structures without additional support.

  9. Timoshenko–Ehrenfest beam theory - Wikipedia

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

    A cantilever Timoshenko beam under a point load at the free end For a cantilever beam , one boundary is clamped while the other is free. Let us use a right handed coordinate system where the x {\displaystyle x} direction is positive towards right and the z {\displaystyle z} direction is positive upward.