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GATE 2020 PI – Question 20

General Engineering · Applied Mechanics · 1 mark · Multiple choice

The illustrated one-rivet joint carries transverse force F. Ignore rivet bending; allowable shear stress is τ and rivet diameter d. Find minimum d. All quantities use SI units.

Diagram for GATE 2020 PI question 20
  1. $\sqrt{F/(\pi\tau)}$
  2. $\sqrt{2F/(\pi\tau)}$
  3. $\sqrt{4F/(\pi\tau)}$
  4. $\sqrt{8F/(\pi\tau)}$

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Show answer and explanation

Correct answer: (B) $\sqrt{2F/(\pi\tau)}$

Explanation

The forked outer member places the rivet in double shear. Total resisting area is2(πd²/4)=πd²/2. Set F/(πd²/2)=τ and solve d=√[2F/(πτ)], B. Single-shear sizing would use only one circular area.

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