What is the solution for this question for the of plane stress given determine the principal planes principal stresses and maximum shear stressshear max equals 50mpashear x equals 100mpashear y equ?

Answer 1

To determine the principal stresses and maximum shear stress for a plane stress condition with given shear stress ((\tau_{max} = 50 , \text{MPa})), (\sigma_x = 100 , \text{MPa}), and (\sigma_y = 0 , \text{MPa}), we first calculate the principal stresses using the equations:

[ \sigma_1, \sigma_2 = \frac{\sigma_x + \sigma_y}{2} \pm \sqrt{\left(\frac{\sigma_x - \sigma_y}{2}\right)^2 + \tau_{xy}^2} ]

Substituting the values yields (\sigma_1 = 125 , \text{MPa}) and (\sigma_2 = -25 , \text{MPa}). The maximum shear stress can be calculated as (\tau_{max} = \frac{\sigma_1 - \sigma_2}{2} = 75 , \text{MPa}).