The GATE Grind

GATE 2017 CE (CE2) – Question 42

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

Three prismatic cantilevers have clamped supports P, Q, R and loads shown. Given $E=2.5\times10^4$ MPa and $I=8\times10^8$ mm⁴, compare support shear-force magnitudes S and bending-moment magnitudes M.

Diagram for GATE 2017 CE (CE2) question 42
  1. $S_P<S_Q<S_R;\ M_P=M_Q=M_R$
  2. $S_P=S_Q>S_R;\ M_P=M_Q>M_R$
  3. $S_P<S_Q>S_R;\ M_P=M_Q=M_R$
  4. $S_P<S_Q<S_R;\ M_P<M_Q<M_R$

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Show answer and explanation

Correct answer: (C) $S_P<S_Q>S_R;\ M_P=M_Q=M_R$

Explanation

For the point load, $S_P=80$ N and $M_P=80(8)=640$ N m. For the UDL, $S_Q=20(8)=160$ N and $M_Q=20(8^2)/2=640$ N m. An end couple produces $S_R=0$, $M_R=640$ N m. Thus $S_P<S_Q>S_R$ and all moments are equal (C).