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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. Fixed end moment - Wikipedia

    en.wikipedia.org/wiki/Fixed_end_moment

    The fixed end moments are reaction moments developed in a beam member under certain load conditions with both ends fixed. A beam with both ends fixed is statically indeterminate to the 3rd degree, and any structural analysis method applicable on statically indeterminate beams can be used to calculate the fixed end moments.

  4. 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.

  5. Macaulay's method - Wikipedia

    en.wikipedia.org/wiki/Macaulay's_method

    Macaulay's method (the double integration method) is a technique used in structural analysis to determine the deflection of Euler-Bernoulli beams.Use of Macaulay's technique is very convenient for cases of discontinuous and/or discrete loading.

  6. 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 ...

  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. Theorem of three moments - Wikipedia

    en.wikipedia.org/wiki/Theorem_of_three_moments

    The deflection downward positive. (Downward settlement positive) Let ABC is a continuous beam with support at A,B, and C. Then moment at A,B, and C are M1, M2, and M3, respectively. Let A' B' and C' be the final positions of the beam ABC due to support settlements. Figure 04-Deflection Curve of a Continuous Beam Under Settlement

  9. 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.