Question

At a point in a steel member, the major principal stress is 200 MPa (tensile) and the minor principal stress is compressive. If the uniaxial tensile yield stress is 250 MPa, then according to the maximum shear stress theory, the magnitude of the minor principal stress (compressive) at which yielding will commence is

• A. 200 MPa
• B. 100 MPa
• C. 50 MPa
• D. 25 MPa

Answer 1

The correct option is C 50 MPa

Let minor principal stress is ${\sigma }_3$.
$\therefore$ Maximum shear stress $=\left(\frac{200+{\sigma }_3}{2}\right)$

$\therefore \left(\frac{200+{\sigma }_3}{2}\right)=\frac{250}{2}$ at yielding

$\Rightarrow {\sigma }_3=50MPa$