GATE Civil Engineering
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A rigid member ACB is shown in the figure. The member is supported at A and B by pinned and guided roller supports, respectively. A force $\color{Red}{P}$ acts at $C$ as shown. Let $R_{Ah}$ and $R_{Bh}$ be the horizontal reactions at supports $A$ and $B$, respectively, and $R_{Av}$ be the vertical reaction at support $A$. Self-weight of the member may be ignored.

Which one of the following sets gives the correct magnitudes of $R_{AV}, \: R_{Bh}$ and $R_{Ah}$?

  1. $R_{Av}=0; \: R_{Bh} = \dfrac{1}{3}P; \text{ and } R_{Ah} = \dfrac{2}{3} P \\$
  2. $R_{Av}=0; \: R_{Bh} = \dfrac{2}{3}P; \text{ and } R_{Ah} = \dfrac{1}{3} P \\$
  3. $R_{Av}=P; \: R_{Bh} = \dfrac{3}{8}P; \text{ and } R_{Ah} = \dfrac{1.5}{8} P \\$
  4. $R_{Av}=P; \: R_{Bh} = \dfrac{1.5}{8}P; \text{ and } R_{Ah} = \dfrac{1.5}{8} P$
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