List of top Applied Mechanics and Design Questions on Fatigue asked in GATE ME

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 rigid uniform annular disc is pivoted on a knife edge A in a uniform gravitational field as shown, such that it can execute small amplitude simple harmonic motion in the plane of the figure without slip at the pivot point. The inner radius \( r \) and outer radius \( R \) are such that \( r^2 = R^2/2 \), and the acceleration due to gravity is \( g \). If the time period of small amplitude simple harmonic motion is given by \[ T = \beta \pi \sqrt{\frac{R}{g}}, \] where \( \pi \) is the ratio of circumference to diameter of a circle, then \( \beta = \) ________________ (round off to 2 decimal places).