Question

2.
An eye bolt is to be used lifting a load of 70 KN and the
tensile stress is not to exceed 100 MPa. The core diameter of the
bolt will be given by:​

Answer 1

Given:

An eye bolt is to be used lifting a load of 70 KN and the tensile stress is not to exceed 100 MPa.

To find:

Core diameter of bolt

Calculation:

Considering circular cross-section of bolt, the radius be denoted as r and the diameter as d;

$\therefore \: \rm{pressure = \dfrac{force}{area} }$

$= > \: \rm{100 \times {10}^{6} = \dfrac{70 \times {10}^{3} }{\pi {r}^{2} } }$

$= > \: \rm{100 \times {10}^{2} = \dfrac{7}{\pi {r}^{2} } }$

$= > \: \rm{ {10}^{4} = \dfrac{7}{\pi {r}^{2} } }$

$= > \: \rm{ {r}^{2} = \dfrac{7}{\pi {(10)}^{4} } }$

$= > \: \rm{ {r}^{2} = \dfrac{7 \times {10}^{ - 4} }{\pi } }$

$= > r = 1.49 \times {10}^{ - 2} \: m$

$= > r = 1.49 \: cm$

$= > d = 2r =2 .98 \: cm$

So, diameter of bolt is 2.98 cm.