Question

the maximum gage presuure is known to be 10 mpa in a spherical steel pressure vessel having a 200 mm outer diameter and a 6 mm wall thickness. knowing that the ultimate stress in the steel used is 400 mpa determine the factor of safety with respect to tensile failure

Answer 1

Answer:

$FOS=2.39$

Explanation:

Given:

maximum gauge pressure in the steel , $p=10\ MPa$

outer diameter of the vessel, $d_o=200\ mm$

wall thickness of the vessel, $t=6\ mm$

ultimate stress of the steel, $\sigma_u=400\ MPa$

We first check the type of shell:

$\frac{t}{d_o} =\frac{6}{200}<\frac{1}{20}$

so the vessel is a thin shell.

Now the maximum tensile stress in the vessel due to maximum pressure is given as:

$\sigma=\frac{p.d_o}{2t}$

$\sigma=\frac{10\times 200}{2\times 6}$

$\sigma=166.67\ MPa$

Now the factor of safety:

$FOS=\frac{\sigma_u}{\sigma}$

$FOS=\frac{400}{166.67}$

$FOS=2.39$