Question

A rotating steel shaft is supported at the ends. It is subjected to a point load at the center. The maxium bending stress developed is 100 MPa. If the yield, ultimate and corrected endurance strength of the shaft material are 300 MPa, 500 MPa and 200 MPa, respectively, then the factor of safety for the shaft is .

• A. 2

Answer 1

The correct option is A 2
Same fiber under point load at the centre of a rotating steel shaft supported at ends is subjected to reversal of stresses. Here only maximum stress is given, its sign (nature) is not given
$\therefore {\sigma }_{min}=-100MPa$

${\sigma }_{max}=100MPa$

${\sigma }_m=\frac{{\sigma }_{max}+{\sigma }_{min}}{2}=0$

${\sigma }_a=\frac{{\sigma }_{max}-{\sigma }_{min}}{2}$

$=\frac{100+100}{2}=100MPa$

As the steel is ductile material, Soderberg criteria will be applied.

$\therefore \frac{{\sigma }_m}{{\sigma }_y}+\frac{{\sigma }_a}{{\sigma }_e}=\frac{1}{n}$

$or0+\frac{100}{200}=\frac{1}{n}\Rightarrow n=2$