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 motors and gear sets, wheels, cams, flywheels, pulleys, or turbines
and electric generators. Shafts can be solid or hollow. During power
transmission, shafts twist and stresses and deformations are taking place.
Torsion is twisting of an object due to an applied torque. When
a
shaft twists, one end rotates relative to the other and shear stresses are
produced on any cross section.
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
occurrs 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.

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