How are the stress components transformed?

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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How are the stress components transformed?

Expert Solution
Step 1

Consider a plane truss.

Mechanical Engineering homework question answer, step 1, image 1

Let, σx and σy be the normal stress acting along x and y-axis, respectively. And let ?xy be the shear stress acting on the plane.

The stress system can be represented as,

Mechanical Engineering homework question answer, step 1, image 2

Step 2

Assume the plane is rotated by an angle θ.

Mechanical Engineering homework question answer, step 2, image 1

After the rotation σ’x and σ’y are the new normal stresses and ?’xy is the new shear stress acting on the plane.

Mechanical Engineering homework question answer, step 2, image 2

The free body diagram of the transformed plane is,

Mechanical Engineering homework question answer, step 2, image 3

Here, ΔA is represented as the area were the corresponding stresses act.

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