Question

The endurance limit of a specific grade of steel is same as its yield strength. The ultimate strength of this grade of steel is twice of its yield strength. A component made of this steel is loaded in tension and unloaded periodically. It is required that the component does NOT fail for at least \( 10^6 \) loading cycles, as per the Soderberg law. Considering a factor of safety of 2, the maximum applied tensile principal stress is:

• A. one-fourth of the endurance limit
• B. half of the endurance limit
• C. the endurance limit
• D. twice the endurance limit

Hint:

The Soderberg criterion is used to ensure that components under cyclic loading do not fail due to fatigue. It relates the applied stress to the material's endurance limit.

Answer 1

The Correct Option is B

The Soderberg criterion for a material under cyclic loading states that for a component to have a factor of safety \(n\), the maximum principal stress \( \sigma_{{max}} \) should be less than or equal to the endurance limit divided by the factor of safety: \[ \frac{\sigma_{{max}}}{{Endurance Limit}} \leq \frac{1}{n} \] where \( n \) is the factor of safety, and the endurance limit of the steel is the same as its yield strength. Given:
The factor of safety \( n = 2 \),
The ultimate strength is twice the yield strength, and the endurance limit is equal to the yield strength.
For a factor of safety of 2, the maximum principal stress should be: \[ \sigma_{{max}} = \frac{{Endurance Limit}}{2} \] Thus, the maximum applied tensile principal stress is half of the endurance limit.