In a shaft the following significant stresses occur.
1. A maximum shear stress occurs on the cross-section of the shaft at its outermost surface.
2. The maximum longitudinal shear stress occurs at the surface of the shaft on the longitudinal planes passing through the longitudinal axis of the shaft.
3. The maximum tensile stress (i.e. major principal stress) occurs at planes 45º to the maximum shearing stress planes at the surface of the shaft. This stress is equal to the maximum shear stress on the cross section of the shaft.
4. The maximum compressive stress (i.e. minor principal stress) occurs on the planes at 45º to the longitudinal and the cross-sectional planes at the surface of the shaft. This stress is equal to the maximum shear stress on the cross section.
5. These stresses are important/ significant because they govern the failure of the shaft. These stresses develop simultaneously and therefore they should be considered simultaneously for design purposes.
6. For most engineering materials, fortunately the shear strength is the smallest as compared to the tensile and compressive stresses and in such cases only the maximum shear stress on the crosssection of the shaft is the significant stress for design.
7. For materials for which tensile and compressive strengths are lower than the shear strength, the shaft design should be carried for the lowest strength.