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In this case, in planes located at an angle of 45° to the shaft axis, only normal (main) stresses act. Moreover, normal and tangential stresses are equal in magnitude with each other, i.e.
σ1 = τ, σ3 = -τ
When torsion of a round shaft in planes perpendicular to its longitudinal axis, and in planes passing through this axis, only shear stresses arise, i.e. stress state at all points is pure shear (Figure 1).
Figure 1. Analysis of the stress state during torsion
Figure 2. The nature of the destruction of samples of various materials during torsion:
a – cast iron; b – steel; c – tree
By the nature of the torsional failure, it is possible to judge which stresses (normal or tangential) the material of which the shaft is made is less resistant.
So, a shaft of brittle material that is less resistant to stretching than compression, for example, from cast iron, usually collapses along a helical line from the action of the main tensile stresses (Figure 2, a).
A shaft made of ductile steel is destroyed along the cross section (Figure 2, b), since normal stresses are less dangerous for him than tangents.
When a wooden shaft is destroyed, shearing occurs along the generatrix, since wood poorly resists the action of shear stresses along the fibers (Figure 2, c).
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