TORSIONAL STRESS CALCULATOR of SHAFTS

A shaft is a rotation member usually with cylindrical shape which is used to transmit torque, power and motion between various elements such as electric or combustion motor to gear sets, wheels, cams, flywheels, pulleys, or from turbine to an electric generator. The shafts can be solid or hollow. During the power transmission, the shafts twist and stresses and deformations are taking placed.

Torsion is the twisting of an object due to an applied torque.  When the shaft twists, one end rotates relative to the other and shear stress is produced on any cross section.

The shear stress is zero on the axis passing through the center of the shaft and maximum at the outside surface of the shaft. On the element where shear stress is maximum, normal stresses are 0. This element where maximum shear stresses occurred is 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.

Torsional stress of shafts

Torsional stress calculator is developed to calculate shear stress, angle of twist and polar moment of inertia  parameters of a shaft. Calculator is only valid for solid/hollow circular shafts and can be used for the sizing of the shafts. The formulas used for the calculations are given in the List of Equations section.

Torsional stress calculator is developed to calculate shear stress, angle of twist and polar moment of inertia  parameters of a shaft. Calculator is only valid for solid/hollow circular shafts and can be used for the sizing of the shafts. The formulas used for the calculations are given in the List of Equations section.

Author's Note: The main reference that used during the development of this calculator is Shigley's Mechanical Engineering Design Please refer to latest version of the reference if further information is needed.

Calculator:

Torsional stress of solid shaft Torsional stress of hollow shaft
Shaft style
 INPUT PARAMETERS
Parameter Symbol Value Unit Link
Torque T  
Rotation speed w rpm  
Shaft outer radius c2  
Shaft inner radius c1
Shaft length L
Modulus of rigidity G  
Stress concentration factor Kt --- Info

Note: Use dot "." as decimal separator.

 


 RESULTS
Parameter Symbol Value Unit
Maximum shear stress (includes Kt) τmax ---
Angle of twist θ ---
Power requirement P ---
Polar moment of inertia J ---


Definitions:

Angle of Twist: The angle through which a part of an object such as a shaft is rotated from its normal position when a torque is applied.

Modulus of rigidity (modulus of elasticity in shear): The rate of change of unit shear stress with respect to unit shear strain for the condition of pure shear within the proportional limit. Typical values Aluminum 6061-T6: 24 GPa, Structural Steel: 79.3 GPa.

Polar Moment of Inertia: A geometric property of the cross section. Measure of ability how a beam resists torsion.

Stress Concentration Factor: Dimensional changes and discontinuities of a member in a loaded structure causes variations of stress and high stresses concentrate near these dimensional changes. This situation of high stresses near dimensional changes and discontinuities of a member (holes, sharp corners, cracks etc.) is called stress concentration. The ratio of peak stress near stress riser to average stress over the member is called stress concentration factor.

Supplements:

Link Usage
Stress concentration factors Stress concentration factor for different types of stress raisers can be calculated for tension, bending and torsional loading type.

List of Equations:

Step Parameter/Condition Symbol Equation
1 Shear stress τ Equation for shear stress for shaft torsion
2 Angle of twist θ Equation for angle of twist for shaft torsion
3 Maximum shear stress τmax Equation for maximum shear stress for shaft torsion
4 Polar moment of inertia of solid shaft Equation for polar moment of inertia of solid shaft
5 Polar moment of inertia of hollow shaft J Equation for polar moment of inertia of hollow shaft
6 Power P

Symbol Parameter
T Torque to be transmitted
J Polar moment of inertia
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

Examples:

Link Usage
Torsion Of Solid Shaft An example about the calculation of torsional stress on stepped shaft. After calculation of torsional stress, principal stresses are calculated and evaluation of yield criteria of material is done with these stresses.

Reference:
  • Budynas.R , Nisbett.K . (2008) . Shigley's Mechanical Engineering Design . 8th edition.  McGraw-Hill
  • Beer.F.P. , Johnston.E.R. (1992). Mechanics of Materials , 2nd edition. McGraw-Hill