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  2. 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

  3. Euler–Bernoulli beam theory - Wikipedia

    en.wikipedia.org/wiki/Euler–Bernoulli_beam_theory

    Euler–Bernoulli beam theory (also known as engineer's beam theory or classical beam theory) [1] is a simplification of the linear theory of elasticity which provides a means of calculating the load-carrying and deflection characteristics of beams.

  4. 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.

  5. 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.

  6. 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.

  7. Moment distribution method - Wikipedia

    en.wikipedia.org/wiki/Moment_distribution_method

    The moment distribution method is a structural analysis method for statically indeterminate beams and frames developed by Hardy Cross. It was published in 1930 in an ASCE journal. [ 1 ] The method only accounts for flexural effects and ignores axial and shear effects.

  8. Influence line - Wikipedia

    en.wikipedia.org/wiki/Influence_line

    The bending moment diagram and the influence line for bending moment at the centre of the left-hand span, B, are shown. In engineering, an influence line graphs the variation of a function (such as the shear, moment etc. felt in a structural member) at a specific point on a beam or truss caused by a unit load placed at any point along the ...

  9. Müller-Breslau's principle - Wikipedia

    en.wikipedia.org/wiki/Müller-Breslau's_principle

    Using the beam sign convention and cutting the beam at B, we can deduce the figure shown. Part (e) of the figure shows the influence line for the bending moment at point B. Again making a cut through the beam at point B and using the beam sign convention, we can deduce the figure shown.