Shear and torsion

Shear stress

Shear stress - the stress component tangential to the plane on which the forces act. Shear stress is expressed in shear force per unit of area (megapascals, pound-force per square inch).

Shear stress is highest in the most remote rivet from the center of sum area. There is practically no shear stress in the central rivet.

Torque transforms a square at the cylinder surface into a rhomb. Absolute values of shear stress at all side surfaces of the rhomb are equal. The stress state of pure shear is equivalent to bi-axial tension-compression state. Tensile stress can result in the brittle fracture of shafts under torsion. The figure shows typical failure of a cylindrical shaft made from brittle material.

There are two angles that help to describe torsion: shear angle g and angle of twist j. The shear angle does not depend on the length of a shaft with constant torque. The longer the shaft, the bigger the angle of twist.

A cross section without a sharp corner corresponds to uniform shear stress and effective use of the material. Rigidity depends on polar moment of inertia J which is proportional to r⁴. The bigger the radius r, the bigger the rigidity.

Rigidity of an open thin-walled shell is sufficiently smaller than rigidity of a closed section.

Torsional stress

Torsional stress - the shear stress on a transverse cross section resulting from a twisting action. Torsional stress is at a maximum at the surface. It is equal to zero in the center. The stress is proportional to the applied torque. For a rectangular cross section the maximum shear stress acts along the longer side, closest to the center point.

Shear stress is at a maximum for the shaft with the highest torque. The moment is the highest for the shaft with lowest rotation speed - the last shaft in the kinematic chain.