A massless beam is fixed at one end and supported by a roller at the other. A downward force P acts at its midpoint, as shown. Find the roller reaction.
Remove the roller and enforce zero deflection at the released end. For uniform EI, a midpoint load produces $\delta_P=Pa^2(3L-a)/(6EI)=5PL^3/(48EI)$, with a = L/2. Upward end reaction gives $\delta_R=RL^3/(3EI)$. Equating yields **R = 5P/16, A**.
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