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Shaft Torsion Stress Calculator and Equations

Mechanics of Materials Table of Content

In solid mechanics , torsion is the twisting of an object due to an applied torque . It is expressed in newton meters(N·m) or foot-pound force (ft·lbf). In sections perpendicular to the torque axis, the resultant shear stress in this section is perpendicular to the radius.

Shear stress is zero on the axis passing through the center of a shaft and maximum at the outside surface of a shaft. On an element where shear stress is maximum, normal stress is 0. This element where maximum shear stress occursis oriented in such a way that its faces are either parallel or perpendicular to the axis of the shaft as shown in the figure. To obtain stress in other orientations, plane stress transformation is needed for shear stresses found with this calculator.

Related:
Structural Beam Deflection and Stress Formula and Calculation


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List of Equations:
Description
Symbol
Equation
Shear stress
τ
Equation for shear stress for shaft torsion
Angle of twist
θ
Equation for angle of twist for shaft torsion
Maximum shear stress
τ max
Equation for maximum shear stress for shaft torsion
Polar moment of inertia of solid shaft
J
Equation for polar moment of inertia of solid shaft
Polar moment of inertia of hollow shaft
J
Equation for polar moment of inertia of hollow shaft
Power
P

P = [(T/12) x w]/5252

Symbol
Description
T
Torque to be transmitted
J
Polar moment of inertia
p
Radial distance to center of shaft
c1
Hollow shaft inner radius
c2
Shaft outer radius
L
Length of the shaft
G
Modulus of rigidity
w
Rotation speed
P
Power
K
Stress concentration factor

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