Question

A steel tie of gross cross-sectional area \(800\,\mathrm{mm^2}\) has a hole of \(20\,\mathrm{mm}\) diameter for a bolt. If the plate thickness is \(10\,\mathrm{mm}\) and the tensile load is \(140\,\mathrm{kN}\), the net tensile stress in the member is

• A. \(210.10\,\mathrm{MPa}\)
• B. \(225.25\,\mathrm{MPa}\)
• C. \(233.33\,\mathrm{MPa}\)
• D. \(250.25\,\mathrm{MPa}\)

Hint:

Net area of a tension member is \[ \boxed{ A_n=A_g-dt, } \] where \(d\) is the bolt-hole diameter and \(t\) is the plate thickness.

Answer 1

The Correct Option is C

Step 1: Calculate the net cross-sectional area. Area removed by the bolt hole \[ =d\times t =20\times10 =200\,\mathrm{mm^2}. \] Therefore, \[ A_n = 800-200 = 600\,\mathrm{mm^2}. \]

Step 2: Calculate the net tensile stress. \[ \sigma_t = \frac{P}{A_n} = \frac{140\times10^3}{600} = 233.33\,\mathrm{N/mm^2}. \] Since \[ 1\,\mathrm{N/mm^2}=1\,\mathrm{MPa}, \] \[ \boxed{\sigma_t=233.33\,\mathrm{MPa}}. \] Hence, \[ \boxed{(C)} \] is the correct answer.