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, 400 MPa respectively. The factor of safety as per Goodman's relation is

(a) 2.0
(b) 1.6
(c) 1.4
(d) 1.2

Answer 1

To calculate the factor of safety as per Goodman's relation for a thin spherical pressure vessel, we need to compare the alternating stress with the endurance strength of the material. However, the options provided in the question do not include the correct answer.

Step-by-step explanation:

To calculate the factor of safety as per Goodman's relation, we need to compare the alternating stress with the endurance strength of the material.

The alternating stress (Sa) is given by Sa = (Pd)/(4t), where P is the internal pressure, d is the diameter of the vessel, and t is the thickness of the vessel.

The endurance strength (Su) is the maximum stress at which the material can withstand an infinite number of load cycles without failure.

The factor of safety (FS) is given by FS = Su / (Sa + Sy), where Sy is the yield strength of the material.

Substituting the given values, we can calculate the factor of safety:

Alternate stress Sa = (8-4) * 10^6 * (0.1) / (4 * (0.001)) = 200 MPa

Factor of safety FS = 400 / (200 + 600) = 0.57

Therefore, the correct answer is not provided in the options given. The factor of safety is 0.57, which is not listed.