GATE Civil Engineering (CE) 2013 Solved Paper

A uniform beam (EI = constant) PQ in the form of a quarter-circle of radius R is fixed at end P and free at the end Q, where a load W is applied as shown. The vertical downward displacement, δ_q, at the loaded point Q is given by: ${\mathit{\delta }}_{\mathit{q}}=\mathit{\beta }\left(\frac{\mathit{W}{\mathit{R}}^3}{\mathit{E}\mathit{I}}\right)$. Find the value of β (correct to 4-decimal places). __________