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GATE 2022 ME (ME1) – Question 40

Machine Design · Bolted, riveted and welded joints · 2 marks · Multiple choice

A bracket is attached to a vertical column by means of two identical rivets U and V separated by a distance of $2a = 100$ mm, as shown in the figure. The permissible shear stress of the rivet material is 50 MPa. If a load $P = 10$ kN is applied at an eccentricity $e = 3\sqrt{7}a$, the minimum cross-sectional area of each of the rivets to avoid failure is ___________ mm$^2$.

a bracket on a column, fastened by two rivets U (above) and V (below) separated by $2a$. The load $P$ acts downwards at the horizontal distance $e$ from the line of the rivets.
  1. 800
  2. 25
  3. $100\sqrt{7}$
  4. 200

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Correct answer: (A) 800

Explanation

The direct shear on each rivet is $\frac{P}{2} = 5$ kN, acting vertically. The moment $Pe = 10 \times 3\sqrt{7}a = 30\sqrt{7}a$ kN is carried by the two rivets as a couple, each at the distance $a$ from the centre, so each gets the force $\frac{Pe}{2a} = 15\sqrt{7}$ kN, acting horizontally. For one rivet the resultant is $\sqrt{5^2 + (15\sqrt{7})^2} = \sqrt{25 + 1575} = 40$ kN. The area is $\frac{40000}{50} = 800$ mm².