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

factor of safety = 0.8

Step-by-step 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

`(t)/(do) =(6)/(200)`

so we can see that that is
`<(1)/(20)`

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

σ =
`(p* do)/(2t)` .......................1

put here value and we get

σ =
`(10* 200)/(2* 2)`

σ = 500 MPa

so factor of safety will be express as

factor of safety =
`(\sigma U)/(\sigma)` ..........2

factor of safety =
`(400)/(500)`

factor of safety = 0.8