Question

A bolt of diameter \(16\,\mathrm{mm}\) carries a shear force of \(40.2\,\mathrm{kN}\) in single shear. Shear stress in the bolt is

• A. \(150\,\mathrm{MPa}\)
• B. \(175\,\mathrm{MPa}\)
• C. \(200\,\mathrm{MPa}\)
• D. \(225\,\mathrm{MPa}\)

Hint:

For a bolt in single shear, \[ \boxed{ \tau=\frac{P}{\frac{\pi d^2}{4}}. } \]

Answer 1

The Correct Option is C

Step 1: Calculate the cross-sectional area of the bolt. \[ A = \frac{\pi d^2}{4} = \frac{\pi(16)^2}{4} = 201.06\,\mathrm{mm^2}. \]

Step 2: Calculate the shear stress. \[ \tau = \frac{P}{A} = \frac{40.2\times10^3}{201.06} \approx 200\,\mathrm{N/mm^2}. \] Since \[ 1\,\mathrm{N/mm^2}=1\,\mathrm{MPa}, \] \[ \boxed{\tau=200\,\mathrm{MPa}}. \] Hence, \[ \boxed{(C)} \] is the correct answer.