Question

For a plane stress problem, the principal stresses are 100 MPa and 50 MPa. The magnitude of maximum shear stress (in MPa) in the material is ............... (rounded off to one decimal place).

Hint:

Maximum shear stress in 2D is always half the difference between principal stresses. On Mohr’s circle, it corresponds to the radius.

Answer 1

Correct Answer: 49.5

Step 1: Recall formula for maximum shear stress.
\[ \tau_{max} = \frac{\sigma_1 - \sigma_2}{2} \]
Step 2: Substitute values.
\[ \sigma_1 = 100 \, MPa, \sigma_2 = 50 \, MPa \] \[ \tau_{max} = \frac{100 - 50}{2} = \frac{50}{2} = 25 \, MPa \] Final Answer: \[ \boxed{25.0 \, MPa} \]