Question

The principal stresses at a point in a critical section of a machine component are ${\sigma }_1=60MPa.$
${\sigma }_2=5MPa.$ and ${\sigma }_3=-40MPa.$ For the material of the component, the tensile yield strength is ${\sigma }_y=200MPa$. According to the maximum shear stress theory, the factor of safety is

• A. 1.67
• B. 2.00
• C. 3.60
• D. 4.00

Answer 1

The correct option is B 2.00

As per maximum shear stress theory, safe condition for design,
Absolute ${\tau }_{max}=\frac{S_{ys}}{N}or\frac{S_{yt}}{2N}$
Absolute ${\tau }_{max}$ = larger of
$[\left|\frac{{\sigma }_1-{\sigma }_2}{2}\right|,\left|\frac{{\sigma }_2-{\sigma }_3}{2}\right|,\left|\frac{{\sigma }_3-{\sigma }_1}{2}\right|]$
$=\left|\frac{{\sigma }_3-{\sigma }_1}{2}\right|$
$[\because {\sigma }_{1}and{\sigma }_3\text{are unlike in nature}]$
$=\left|\frac{-40-60}{2}\right|=50MPa$
Hence, $50=\frac{200}{2\left(N\right)}$
$N=2$