Question

The maximum gage pressure is known to be 10 MPa in a spherical steel pressure vessel having a 200 mm outer diameter and a(n) 2 mm wall thickness. Knowing that the ultimate stress in the steel used is σU = 400 MPa, determine the factor of safety with respect to tensile failure.

Answer 1

Answer:

factor of safety = 0.8

Explanation:

given data

maximum gauge pressure in steel p = 10 MPa

outer diameter do = 200  mm

wall thickness t = 2 mm

ultimate stress of the steel σU = 400 MPa

solution

We check the type of shell that is

$\frac{t}{do} =\frac{6}{200}$

so we can see that that is    

so that it mean vessel is a thin shell now we can we get maximum pressure by the maximum tensile stress is

σ = $\frac{p\times do}{2t}$     .......................1

put here value and we get

σ =  $\frac{10\times 200}{2\times 2}$  

σ =  500 MPa  

so factor of safety will be express as

factor of safety = $\frac{\sigma U}{\sigma}$     ..........2

factor of safety = $\frac{400}{500}$  

factor of safety = 0.8