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 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:
Note: Use dot "." as decimal separator.
RESULTS 
Parameter 
Symbol 
Value 
Unit 
Maximum shear stress (includes K_{t}) 
τ_{max} 



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 6061T6: 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 

2 
Angle of twist 
θ 

3 
Maximum shear stress 
τ_{max} 

4 
Polar moment of inertia of solid shaft 
J 

5 
Polar moment of inertia of hollow shaft 
J 

6 
Power 
P 

Symbol 
Parameter 
T 
Torque to be transmitted 
J 
Polar moment of inertia 
p 
Radial distance to center of shaft 
c_{1} 
Hollow shaft inner radius 
c_{2} 
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. McGrawHill

Beer.F.P. , Johnston.E.R. (1992). Mechanics of Materials , 2nd edition. McGrawHill