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GATE 2016 CE (CE1) – Question 44

Solid Mechanics · Bending moment and shear force in statically determinate beams · 2 marks · Multiple choice

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 P acts at C as shown. Let RAh and RBh be the horizontal reactions at supports A and B, respectively, and RAv 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 RAv, RBh and RAh ?

Diagram for GATE 2016 CE (CE1) question 44
  1. $R_{Av}=0;\ R_{Bh}=P/3;\ R_{Ah}=2P/3$
  2. $R_{Av}=0;\ R_{Bh}=2P/3;\ R_{Ah}=P/3$
  3. $R_{Av}=P;\ R_{Bh}=3P/8;\ R_{Ah}=1.5P/8$
  4. $R_{Av}=P;\ R_{Bh}=1.5P/8;\ R_{Ah}=1.5P/8$

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Correct answer: (D) $R_{Av}=P;\ R_{Bh}=1.5P/8;\ R_{Ah}=1.5P/8$

Explanation

Take moments about A: the vertical load P has horizontal lever arm1.5m and the horizontal reaction at B has vertical lever arm8m. Hence RB=1.5P/8. Horizontal equilibrium gives an equal opposing horizontal reaction at A, and vertical equilibrium gives RAy=P. These components match **D**.