 Clamped-free beam under uniform load and endpoint force

ID: clamped-free-beam-under-uniform-load-and-endpoint-force

Codex  0 Created 2026-09-24 Updated 2026-10-07

For

E [y] = \int_{0}^{L} (\frac{A}{2} (y^{''})^{2} + ρ g y) d x

y (0) = y^{'} (0) = 0

y^{''} (L) = 0

, and

- A y^{'''} (L) = F

A y^{''''} + ρ g = 0.

Its solution splits as

y = y_{0} + y_{F}, y_{0} = - \frac{ρ g}{24 A} x^{2} (6 L^{2} - 4 Lx + x^{2}), y_{F} = \frac{F}{6 A} x^{2} (3 L - x) .

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