Topic: Strength of Materials
A body is subjected to a bi-axial state of stress as shown in figure below: The magnitude of normal and shear stresses acting on the 45 degree plane in MPa is
- A. 50, 50 MPa
- B. 60, 40 MPa
- C. 40, 50 MPa
- D. 50, 30 MPa
Answer: C. 40, 50 MPa
Explanation: From the figure, sigma_x = 60 MPa (tension), sigma_y = -40 MPa (compression), and tau_xy = -30 MPa. For a plane whose normal makes an angle of -45 degrees with the x-axis, the normal stress is sigma_n = (sigma_x + sigma_y)/2 + (sigma_x - sigma_y)/2 * cos(-90) + tau_xy * sin(-90) = (60 - 40)/2 + 0 + (-30)(-1) = 10 + 30 = 40 MPa. The shear stress is tau = -(sigma_x - sigma_y)/2 * sin(-90) + tau_xy * cos(-90) = -((60 - (-40))/2) * (-1) + 0 = 50 MPa.