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Endpoint force derivative of clamped-free beam energy

For the clamped-free beam under uniform load and endpoint force, the additional minimized internal energy is

E (F) = \frac{F ^{2} L ^{3}}{6 A} .

Its derivative is the endpoint displacement caused by the endpoint force:

\frac{d E}{d F} = \frac{F L ^{3}}{3 A} = h .

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