Question

Two principal stresses at a point in the bar are 200 N/mm² (tensile) and 80 N/mm² (Compressive). What is the value of the maximum shear stress in the bar?

• A. 60 N/mm²
• B. 80 N/mm²
• C. 140 N/mm²
• D. 200 N/mm²

Hint:

The maximum shear stress is always calculated using the difference between the maximum and minimum principal stresses, divided by 2.

Answer 1

The Correct Option is C

Step 1: Formula for maximum shear stress.
The maximum shear stress \(\tau_{\text{max}}\) for a given point with two principal stresses \(\sigma_1\) and \(\sigma_2\) (where \(\sigma_1\) is the larger principal stress) is given by: \[ \tau_{\text{max}} = \frac{\sigma_1 - \sigma_2}{2} \]
Step 2: Substituting the values.
Here, \(\sigma_1 = 200 \, \text{N/mm}^2\) (tensile) and \(\sigma_2 = -80 \, \text{N/mm}^2\) (compressive). Substituting these into the formula: \[ \tau_{\text{max}} = \frac{200 - (-80)}{2} = \frac{200 + 80}{2} = \frac{280}{2} = 140 \, \text{N/mm}^2 \] Thus, the maximum shear stress is \(140 \, \text{N/mm}^2\).