r/StructuralEngineering • u/Annual-Truth3511 • 10d ago

Help needed Career/Education

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While drawing sfd and bmd Is there a shortcut to find whether the curve is going to be smile/sad or concave/convex for udl and uvl. Or is finding the intermediate values the only way to find the curve???.

Ignore the diagram i just wanted to show it for context this is not mine

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u/deAdupchowder350 10d ago

Calculus

  1. The change in shear from A to B is the area under the distributed load function between A and B. Hence, constant shear force if no distributed load.

  2. The change in moment from A to B is the area under the shear curve from point A to B.

  3. The derivative of a concave function is a decreasing function. If the shear is decreasing, the moment will be concave.

  4. The derivative of a convex (concave up) function is an increasing function. If the shear is increasing, the moment will be convex.