Calculating the Maximum In-Plane Shear Stress and Associated Orientation for a Differential Plane Stress Element

February 27, 2017 Abdul Siraj, P.E.

In this post, I will go over the third example in our mechanics of materials course covering stress transformation. The goal of this example is to calculate the maximum in-plane shear stress and associated orientation for a differential plane stress element.

 

The engineering problem statement states,

 

The differential element shown in the figure below experiences a state of plane stress.

 

Stress in the normal x direction = -25 MPa
Stress in the normal y direction = 100 MPa
Shear stress in the x-y direction = 50 MPa

 

Find the maximum in-plane shear stress at this point, orientation, and associated average normal stress.