Problem 5: Principal Stresses (2D Case)

For the following stress state of stress occurring at a point on the free surface of a solid body:

Ox=50 MPa, Gy= 10 MPa, and Txy=-15 MPa

a. Use the transformation equations to evaluate the two principal normal stresses (01, 02) and

the principal directions (rotations) 0p. Also, sketch a stress element to indicate the element

orientation based on the principal normal directions and show 61 and 02.

b. Evaluate maximum shear stress tmax, the normal average stress Gavg, and the corresponding

direction (rotation) 0₁. Also, sketch a stress element to indicate the element orientation

based on the principal shear directions and show tmax and Gavg.