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:
![](https://static.wixstatic.com/media/20c892_640a49293be34d9f89e1a30c1d4ec85d~mv2.png/v1/fill/w_49,h_26,al_c,q_85,usm_0.66_1.00_0.01,blur_2,enc_auto/20c892_640a49293be34d9f89e1a30c1d4ec85d~mv2.png)
Remember, no shear stress on principle planes.
![](https://static.wixstatic.com/media/20c892_dd2978361af44ec4ba98a975af676c08~mv2.png/v1/fill/w_47,h_24,al_c,q_85,usm_0.66_1.00_0.01,blur_2,enc_auto/20c892_dd2978361af44ec4ba98a975af676c08~mv2.png)
![](https://static.wixstatic.com/media/20c892_b83d85645c2a46248932a64e26ece50c~mv2.png/v1/fill/w_47,h_15,al_c,q_85,usm_0.66_1.00_0.01,blur_2,enc_auto/20c892_b83d85645c2a46248932a64e26ece50c~mv2.png)
Theta 1 has to lie between 0° and 90°, when shear stress is positive.
![](https://static.wixstatic.com/media/20c892_3370d65e1292488ba996605de0574f0a~mv2.png/v1/fill/w_46,h_11,al_c,q_85,usm_0.66_1.00_0.01,blur_2,enc_auto/20c892_3370d65e1292488ba996605de0574f0a~mv2.png)
Max Shear Stress acts at 45° from principle planes (58.28°, 148.28°)