-
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 Goodman's relation is
-
- 2.0
- 1.6
- 1.4
- 1.2
Correct Option: B
Stress induced,
| σ1 = σ2 = | |
| 2t |
| σ1max = | = 400MPa | |
| 2 × 1 |
| σ1min = | = 200MPa | |
| 2 × 1 |
σ2max = 400 MPa
σ2min = 200 MPa
σ1m = 300 MPa
σ1a = 100 MPa
σ2m = 300 MPa
σ2a = 100 MPa
Equivalent stress are as follows:
σme = √σ1m² + σ2m² − σ1mσ2m
= σme = √300² + 300² − 300 × 300
= 300 Mpa
Similarly, σae = 100 MPa
From Goodman equation,
| + | = | |||
| Se | Sut | n |
| ⇒ | + | = | |||
| 400 | 800 | n |
= n = 1.6
