Other than double integration method, we can also use moment area theorem to determine the deflection and slope of beam. The main assumptions for this theorem are isotropic beam and consistent beam cross section.
There are two principles in moment area theorem, where the first one helps us to determine the change in slope between two points on beam elastic curve. The second one helps us to determine the deviation of tangent at two points, and eventually helps us calculate the deflection at any point.
To use this method, we need to produce bending moment diagram for the entire beam and divide it by EI. Based on the shape of M/EI diagram, we calculate the area under curve between two points to determine the change in their slopes. The moment of that area on the other hand, signifying the vertical deviation of tangent at both points.
The following introduces the calculation of beam deflection using moment area theorem. Watch the video above for full details.
Beam overview
Beam support reactions
Internal moment function and bending moment diagram
First principle of moment area theorem to calculate slope
Second principle of moment area theorem to calculate deflection
Final result
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