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They don't always become a curved shape.

A SFD will only become a curved shape if you have a distributed load that is changing over time.

A BMD will only become a curved shape if the related shear force diagram is changing over time (not a flat line)

however because the SFD is the integral of the force applied and the BMD is the integral of the SFD, generally as you keep going to a higher order, you will start getting more curvy lines.

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Q: Why shearforce diagram and bending moment diagram become curve shape?
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