Question

A machine component is subjected to fluctuating stress that varies from 60 to 120 MPa. The corrected endurance limit stress for the machine component is 270 MPa. The ultimate tensile strength and yield strengths are 590 MPa and 440 MPa respectively. The factor of safety according to the Soderberg theory will be _____. (correct up to two decimal places)

• A. 3.168

Answer 1

The correct option is A 3.168
${\sigma }_{\text{max}}=120\text{MPa,}{\sigma }_{\text{max}}=60\text{MPa,}$

$\text{Now}{\sigma }_{\text{in}}=\frac{{\sigma }_{\text{max}}+{\sigma }_{\text{min}}}{2}=\frac{120+60}{2}=90\text{MPa}$

$\text{amplitude stress,}{\sigma }_a=\frac{{\sigma }_{\text{max}}+{\sigma }_{\text{min}}}{2}=\frac{120-60}{2}=30\text{MPa}$

Now according to soderberg,

$\frac{{\sigma }_m}{s_{yt}}+\frac{{\sigma }_a}{s_c}=\frac{1}{N}$

$\frac{90}{440}+\frac{30}{270}=\frac{1}{N}$

$n=3.168$