Answer to Question #214575 in Mechanical Engineering for Nano

Question

A spherical pressure vessel is constructed by bolting two hemispheres together along rigid flanges as shown in the sketch. The sphere has an internal diameter of 1.5 m and the plate thickness is 5 mm. Allowable tensile stresses are 45 MPa in the shell and 80 MPa in the bolts.

 

1      Calculate the allowable gauge pressure.                                                        

2      Determine the number of bolts required if the bolt diameter is 25 mm        

           (Note: bolt root diameter = 0.84 × nominal bolt diameter)

Answer 1

Part 1

$S= \frac{PD}{2t}\\ S= \frac{45*1.5}{2*\frac{5}{1000}}\\ S= 6750 Nm^{-2}$

Part 2

$n(AS_w) = PA\\ n =\frac{ PA}{AS_w}\\ n =\frac{ 6750* 4\pi*0.75^2 }{\frac{\pi}{4} *0.025^2*80}\\ n= 121500 \space bolts$