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I am trying to derive the strain at the base of a cantilever beam with a known deflection. I know the bending stress is equal to Mc/I, so the strain is Mc/IE, where c is the distance from the neutral axis. For a point load ,P, the strain would then be PL/IE. Since the deflection is known I need to find the point load ,P, for that deflection. From the moment curvature relationship I can derive the deflection,y, to be equal to -PL^3/3EI. Solving for P and substituting it into the previous eqation I can solve for the strain to be equal to -3yc/L^2.
This seems to be a roundabout way to solve for the strain. Is there a cleaner way to derive this relationship?
This seems to be a roundabout way to solve for the strain. Is there a cleaner way to derive this relationship?