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  2. Euler–Bernoulli beam theory - Wikipedia

    en.wikipedia.org/wiki/Euler–Bernoulli_beam_theory

    Besides deflection, the beam equation describes forces and moments and can thus be used to describe stresses. For this reason, the Euler–Bernoulli beam equation is widely used in engineering, especially civil and mechanical, to determine the strength (as well as deflection) of beams under bending.

  3. Deflection (engineering) - Wikipedia

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

    The deflection of beam elements is usually calculated on the basis of the Euler–Bernoulli beam equation while that of a plate or shell element is calculated using plate or shell theory. An example of the use of deflection in this context is in building construction. Architects and engineers select materials for various applications.

  4. Timoshenko–Ehrenfest beam theory - Wikipedia

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

    The two equations that describe the deformation of a Timoshenko beam have to be augmented with boundary conditions if they are to be solved. Four boundary conditions are needed for the problem to be well-posed. Typical boundary conditions are: Simply supported beams: The displacement is

  5. Macaulay's method - Wikipedia

    en.wikipedia.org/wiki/Macaulay's_method

    The starting point is the relation from Euler-Bernoulli beam theory = 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 if the value of as a function of is known.

  6. Moment-area theorem - Wikipedia

    en.wikipedia.org/wiki/Moment-Area_Theorem

    The moment-area theorem is an engineering tool to derive the slope, rotation and deflection of beams and frames. This theorem was developed by Mohr and later stated namely by Charles Ezra Greene in 1873.

  7. 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 ...

  8. Bending - Wikipedia

    en.wikipedia.org/wiki/Bending

    The beam is originally straight and slender, and any taper is slight; The material is isotropic (or orthotropic), linear elastic, and homogeneous across any cross section (but not necessarily along its length) Only small deflections are considered; In this case, the equation describing beam deflection can be approximated as:

  9. Beam (structure) - Wikipedia

    en.wikipedia.org/wiki/Beam_(structure)

    A beam of PSL lumber installed to replace a load-bearing wall. The primary tool for structural analysis of beams is the Euler–Bernoulli beam equation. This equation accurately describes the elastic behaviour of slender beams where the cross sectional dimensions are small compared to the length of the beam.