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Principle Stresses: Example 1

Question:

The direct stresses on an element of material, on orthogonal planes are 75 N/mm^2 (tensile) and 45 N/mm^2 (compressive) together with a shear stress of 30 N/mm^2. Calculate the magnitude and location of the principle and maximum shear stresses.


Answer:

Firstly, a diagram to help visualize the problem:


Remember, no shear stress on principle planes.

Theta 1 has to lie between 0° and 90°, when shear stress is positive.

Max Shear Stress acts at 45° from principle planes (58.28°, 148.28°)

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