The Rankine formula is a mathematical expression used in solid mechanics to determine the shear stress distribution within a column subjected to torsion. The fo...
The Rankine formula is a mathematical expression used in solid mechanics to determine the shear stress distribution within a column subjected to torsion. The formula expresses the shear stress as a function of the radial distance from the center of the column.
Where:
v is the shear stress in Pascals (Pa)
d is the radial distance from the center of the column in meters (m)
dr is the differential of the radial distance in meters
The shear stress is a measure of the shear force acting per unit area and is a function of the shear strain. The shear strain is the deformation of the material along the column in the direction of the applied torque.
The Rankine formula assumes that the material is isotropic, homogeneous, and linearly elastic. It also assumes that the column is fixed at its ends and subjected to a single torque.
The shear stress distribution obtained from the Rankine formula is typically used to analyze the behavior of columns subjected to torsion. It can be used to calculate the required shear force to cause failure or deformation in a column