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. This method is advantageous when we solve problems involving beams, especially for those subjected to a series of concentrated loadings or having segments with different moments of inertia. If we draw the moment diagram for the beam and then divided it by the flexural rigidity(EI), the 'M/EI diagram' results by the following equation

${\displaystyle \theta =\int \left({\frac {M}{EI}}\right)dx}$

The change in slope between any two points on the elastic curve equals the area of the M/EI diagram between these two points.

${\displaystyle \theta _{AB}={\int _{A}}^{B}{\frac {M}{EI}}f(x)dx}$

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