Question

If the principal stresses in a plane stress problem are ${\sigma }_1=100$ MPa, ${\sigma }_2=40$ MPa, the magnitude of the maximum shear stress (in MPa) will be

• A. 60
• B. 50
• C. 30
• D. 20

Answer 1

The correct option is B 50

In plane stress problem principal stresses,
${\sigma }_1=100MPa$ and ${\sigma }_2=40$ MPa
Magnitude of the maximum shear stress in plane stress case is given by
${\tau }_{\text{max}}=\text{Maximum of}[\left|\frac{{\sigma }_1}{2}\right|,\left|\frac{{\sigma }_2}{2}\right|,\left|\frac{{\sigma }_1-{\sigma }_2}{2}\right|]$
$=\text{Maximum of}[\left|\frac{100}{2}\right|,\left|\frac{40}{2}\right|,\left|\frac{100-40}{2}\right|]$
$=50MPa$