How are the stress components transformed?
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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How are the stress components transformed?
Expert Solution

Step 1
Consider a plane truss.
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,
Step 2
Assume the plane is rotated by an angle θ.
After the rotation σ’x and σ’y are the new normal stresses and ?’xy is the new shear stress acting on the plane.
The free body diagram of the transformed plane is,
Here, ΔA is represented as the area were the corresponding stresses act.
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