Question

A load P is applied horizontally while the other end is fixed to a structure. A load P is applied horizontally while the other end is fixed to a structure. How many bolts are required to make the assembly safe? Use 8 mm bolts (M8-1.25) that yield at 0.5 MPa. (You must provide an answer before moving to the next part.)

Answer 1

Answer:

The number of bolt is 4.

Explanation:

Given that,

$\tau = 0.5\ MPa$

distance = 8 mm

Suppose, Load P = 205 N

We need to calculate the shear area of bolt

Using formula of shear stress

$\tau=\dfrac{P}{A}$

Here is double shear.

So, $\tau$ will be double.

$A=\dfrac{P}{2\tau}$

Put the value into the formula

$A=\dfrac{205}{2\times0.5\times10^{6}}$

$A=205\times10^{-6}\ m^2$

We need to calculate the area of one bolt

Using formula of area

$A'=\dfrac{\pi}{4}d^2$

Put the value into the formula

$A'=\dfrac{\pi}{4}\times(8\times10^{-3})^2$

$A'=50.26\times10^{-6}\ m^2$

We need to calculate the number of bolt

Using formula of number of bolt

$n=\dfrac{A}{A'}$

Put the value into the formula

$n=\dfrac{205\times10^{-6}}{50.26\times10^{-6}}$

$n=4.0$

Hence, The number of bolt is 4.