A uniform beam $(E I=$ constant $) P Q$ 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, $\delta_{q},$ at the loaded point $Q$ is given by: $\delta_{q}=\beta\left(\frac{W R^{3}}{E I}\right) .$ Find the value of $\beta($ correct to 4 -decimal places).

A uniform beam $(E I=$ constant $) P Q$ 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, $\delta_{q},$ at the loaded point $Q$ is given by: $\delta_{q}=\beta\left(\frac{W R^{3}}{E I}\right) .$ Find the value of $\beta($ correct to 4 -decimal places).

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