Question

Three principal stresses at a point in a material are 300 MPa, 250 MPa, and 100 MPa. If the yielding just starts at that point, the yield strength (in MPa) of the material as per Tresca criterion is ............ 

Hint:

In the Tresca criterion, the yield strength is determined by twice the maximum shear stress, which is the difference between the maximum and minimum principal stresses divided by 2.

Answer 1

According to the Tresca criterion, the yield strength is determined by the maximum shear stress. The maximum shear stress (\( \tau_{{max}} \)) is given by: \[ \tau_{{max}} = \frac{1}{2} \left( \sigma_1 - \sigma_3 \right) \] where \( \sigma_1 \) and \( \sigma_3 \) are the maximum and minimum principal stresses, respectively. In this case, the maximum principal stress is \( 300 \, {MPa} \), and the minimum principal stress is \( 100 \, {MPa} \). Therefore, the maximum shear stress is: \[ \tau_{{max}} = \frac{1}{2} \left( 300 - 100 \right) = 100 \, {MPa} \] The yield strength, as per Tresca criterion, is twice the maximum shear stress: \[ {Yield strength} = 2 \times \tau_{{max}} = 2 \times 100 = 200 \, {MPa} \] Thus, the yield strength lies between 199 to 201 MPa.