## Q. 2.11

A cylinder that has a sealed cover plate attached (Figure 2.22(a)) with steel bolts contains a gas under pressure of 2 N/mm². The diameter d of the bolts is 5 mm and the allowable tensile stress in the bolts is 150 N/mm². If the inside diameter of the cylinder is 100 mm, find the number of bolts needed to fasten the cover plate.

## Verified Solution

The top covering plate will always have the tendency to be blown-off due to inside pressure acting on the bottom surface of the plate in upward direction. While the bolts hold the plate against this kind of tendency, sustains tension.

The force tending to lift the lid up = pressure × area of the plate

$=\frac{2 \times \pi \times 100^2}{4}=15707.9 N$

The force of tension that can be permitted in the bolt

= allowable stress × area of cross section of bolt

$=\frac{150 \times \pi \times 100^2}{4}=2945.24 N$

∴        $\text { No. of bolts }=\frac{\text { Total force to be sustained }}{\text { Force allowed in each bolt }}=\frac{15707.9}{2945.24}=5.33 \text { say } 6 \text { No. s }$