Topic: Machine Design
Two plates subjected to tensile force of 50 kN, are fixed together by means of three rivets. The plates and rivets are made of same material. If the permissible shear stress in the rivets is 50 $N/mm^{2}$, what is the diameter of the rivets? (Neglect stress concentration effects)
- A. 14.75 mm
- B. 20.60 mm
- C. 24.38 mm
- D. 29.52 mm
Answer: B. 20.60 mm
Explanation: Force $P = 50~kN = 50000~N$. Since there are 3 rivets in single shear, the total shear resistance is $n \times \frac{\pi}{4} d^2 \times \tau = P$.
$3 \times \frac{\pi}{4} d^2 \times 50 = 50000$.
$d^2 = \frac{50000 \times 4}{3 \times \pi \times 50} = \frac{4000}{3\pi} \approx 424.41~mm^2$.
$d = \sqrt{424.41} \approx 20.60~mm$.