Question

The state of stress at a point in a body is given by σxx = −8MPa,τxy = −6MPa,τ xz = 0,σ yy = 12MPa,τ yz =0, and σ zz =0 a) Use the stress transformation equations to find the stresses on an element oriented at 30∘ counterclockwise from the current orientation. b) Compare your answers for a) with Mohr's circle.

Answer 1

The question involves calculating stress transformation for a 30° counterclockwise rotation using equations and then comparing the result using Mohr's circle.

Step-by-step explanation:

The question deals with stress transformation at a point in a material, specifically how the state of stress changes when the material is oriented at a different angle from its original orientation. To find the new stresses after a 30° counterclockwise rotation, we use stress transformation equations for plane stress. The original stresses given are σxx = −8 MPa, τxy = −6 MPa, τxz = 0 MPa, σyy = 12 MPa, τyz = 0 MPa, and σzz = 0 MPa. For part (b), we will compare the transformed stresses to the ones obtained via Mohr's circle, which is a graphical method for finding principal stresses and stress transformation.