Answer to Question #217840 in Mechanical Engineering for john Smith

Question

A pressurised cylindrical container has a sealed cover plate fastened with steel bolts as shown below. The internal pressure p in the thin cylinder is 1900 kPa, the inside diameter D of the cylinder is 250 mm and the diameter db of the bolts is 12 mm.

4.1 If the allowable tensile stress in the bolts is 70 MPa, find the number of bolts needed to fasten the cover plate. /3/

4.2 If the diametral change of the cylinder shell is limited to 0,025mm, determine the thickness of the shell plate required. (ESteel = 200 GPa) /3/

From the range of sizes given below select the minimum standard thickness of plate to be purchased for the manufacture of the cylinder. /1/ 8mm; 10mm; 12mm; 16mm; 20mm; 25mm; 30mm; 35mm

Answer 1

4.1

$F= P*\frac{\pi}{4}D^2\\ F= 1900*10^3*\frac{\pi}{4}*0.25^2\\ F=93266N\\ F= \sigma_b*n*\frac{\pi}{4}d_b^2\\ 93266= 70*n*\frac{\pi}{4}*12^2\\ n=11.78 n=12$

The number of bolts should be 12 to bear the pressure.

4.2

$e_h=\frac{\Delta D}{D}=\frac{0.025}{250}=0.0001\\ \sigma_h=e_hE=0.0001*200*10^3\\ \sigma_h=\frac{PD}{2t}\\ 20*10^6=\frac{1900*10^3*250}{2t}\\ t=11.875 mm$

From the range of sizes given, 12 mm thickness plate to be purchased for manufacturing the cylinder.

4.3

$53.5*10^6= \frac{\rho \pi tr \omega^2}{2t}\\ \omega = \sqrt{\frac{2*53.5*10^6}{7800*\pi*0.125}}\\ \omega = 186.9 rad/s\\ f= \frac{60*186.*}{2\pi}=1785$

f = 1785 r/min