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deflection of continuous beam.

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The problem uses a continuous beam, but I'm unsure if I'm correct in solving for the max deflection between pts A and B (I've included the BM and SF diagrams btw pts A snd B, only). Deflection should be a maximum when SF = 0.

I've also formulated an equation to solve for max deflection using the second area-moment, where 'x' is measured as the distance from A. The BM at B ([latex] M_{B} [/latex]) is straight forward, but the BM due to load is non-linear, I believe this needs revision, but your thoughts.

[latex] \Sigma A\bar{x} = \int_{0}^{X}wx\frac{x}{2} \,dx - M_{B}\frac{x}{L}\frac{x}{2} [/latex]

BM cont beam.pdf

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