Question

The details of the principal stresses at a certain point in a steel member are as follows :
Major principal stress ${\sigma }_1=180N/m{m}^2$ (Tensile)
Minor principal stress ${\sigma }_2$ is Compressive.
If the uniaxial tensile yield stress is 240 $N/m{m}^2$, according to maximum shear stress theory, what would be the value of ${\sigma }_2$ in $N/m{m}^2$ at which yielding will commence?

• A. 120 tension
• B. 90 tension
• C. 80 compression
• D. 60 compression

Answer 1

The correct option is D 60 compression

As per maximum shear stress theory

$\frac{{\sigma }_1-{\sigma }_2}{2}=\frac{{\sigma }_y}{2}$

$\Rightarrow {\sigma }_1-{\sigma }_2={\sigma }_y$

$\Rightarrow 180-(-{\sigma }_2)=240$

$\Rightarrow {\sigma }_2=240-180$

$\Rightarrow {\sigma }_2=60N/m{m}^2$