Question

A thin spherical pressure vessel of 200 mm diameter and 1 mm thickness is subjected to an internal pressure varying from 4 to 8 mpa. Assume that the yield, ultimate, and endurance strength of material are 600, 800 and 400 mpa respectively. The factor of safety as per goodmans relation is

Answer 1

Answer:

1.6

Step-by-step explanation:

Given A thin spherical pressure vessel of 200 mm diameter and 1 mm thickness is subjected to an internal pressure varying from 4 to 8 mpa. Assume that the yield, ultimate, and endurance strength of material are 600, 800 and 400 mpa respectively. The factor of safety as per goodmans relation is

Given D = 200 nm, t = 1 mm, σ y = 600 MPa, σ v = 800 MPa, σe = 400 MPa

Stress is same so σ h = PD / 4t

                         σmax = p max D / 4t

                                = 8 x 200 / 4 x 1

                                 = 400 MPa

Similarly in other direction we have,

                           Σmax = 400 MPa

                           Σmin = 200 MPa

So mean stress will be 400 + 200 / 2 = 300 MPa

We have variable stress

                         = 400 – 200 / 2

                         = 100 MPa

From the Goodman method we get

So σ m/σ u + σ v / σ e = 1 / F.S.

300 / 800 + 100 / 400 = 1 / F.S.

8 / 5 = 1/F.S.

F.S. = 1.6