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GATE 2022 CE (CE1) – Question 37

Engineering Mechanics · Internal forces in structures · 2 marks · Multiple choice

A semi-circular bar of radius R m, in a vertical plane, is fixed at the end G, as shown in the figure. A horizontal load of magnitude P kN is applied at the end H. The magnitude of the axial force, shear force, and bending moment at point Q for θ = 45°, respectively, are

Circular curved bar of radius R with a horizontal end force P and section Q at 45 degrees. See the attached source image.
  1. $P/\sqrt2,\ P/\sqrt2,\ PR/\sqrt2$
  2. $P/\sqrt2,\ P/\sqrt2,\ 0$
  3. $0,\ P/\sqrt2,\ PR/\sqrt2$
  4. $P/\sqrt2,\ 0,\ PR/\sqrt2$

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Correct answer: (A) $P/\sqrt2,\ P/\sqrt2,\ PR/\sqrt2$

Explanation

Cut the bar at Q and isolate the portion ending at H. Resolve the horizontal load along the local tangent and normal at θ=45°: both force magnitudes are $P/\sqrt2$.

The perpendicular distance from Q to the load’s horizontal line is $R\sin45^\circ=R/\sqrt2$, so the bending moment magnitude is $PR/\sqrt2$. **Answer: A**.