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The rigid-jointed plane frame QRS shown in the figure is subjected to a load $P$ at the joint $R$. Let the axial deformations in the frame be neglected. If the support $S$ undergoes a settlement of $\Delta = \frac{PL^3}{\beta EI}$, the vertical reaction at the support $S$ will become zero when $\beta$ is equal to

  1. $0.1$
  2. $3.0$
  3. $7.5$
  4. $48.0$
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