Torsion Calculations For Circular Members

This subject can be seemed like a very specific topic to understand in general engineering mechanics. But it is not. There are lots of kinds of applications in engineering that hollow or full shafts are used to transmit the power, by rotating around their longitudinal axes. 

So very strict engineering calculations to calculate their strength and safety in the working conditions. Torsion calculations are one of the most used calculation techniques in this aspect. 

Here, we explain how to make torsion calculations for circular shafts.  

What Is Torsion And How It Is Calculated?

Torsion is the twisting action because of the application of torque from the longitudinal axis of circular geometry. Torsion calculations are generally made for the shafts that are subjected to moment from one side, and the other side is built-in. 

Image Source: D. K. Singh – Strength of Materials-Springer, 2020, pg.321

As you see above, with the application of torque which is denoted as ‘T’ above, there are two angles are defined in the twisting action.
Say ‘l’ for the length of the shaft and
‘R’ is the radius of the shaft.
‘G’ is the shear modulus of the materials of the shaft.
‘ϕ’ is the shear strain of the twisting action.
‘?’ is the general symbol for the shear stress.
‘Φ’ is the angle of the center of the shaft.
All of these parameters must be defined to build the required equation for the torsion action on the shaft.

The general equation for the torsion is like the above. You can find out the required parameter related to the torsion phenomenon for the shafts.

Here, ‘J’ is the polar moment of inertia of the circular cross-section. The polar moment of inertia values can be calculated with the equations below.

The polar modulus of a solid shaft;

Here, ‘d’ is the diameter of the cross-section of the shaft.

The polar modulus of a hollow shaft;

‘d0’ is the external diameter of the hollow shaft and ‘di’ is the internal diameter of the hollow shaft. 

Torsion Calculator For Shafts

The use of the calculator above is very simple. What you need to do is, you need to enter the values inside the brackets with the given units inside the parentheses. Then click on the ‘Calculate!’ button to calculate the shear stress value. 

To make another calculation, click on the ‘Reset’ button and re-enter the value again.


This is the general information about the torsion calculations for solid shafts and hollow shafts. You can calculate the torque from the given parameters about a shaft. 

By using this torque value, you can also calculate the power transmission on that shaft.

Mechanicalland does not accept any responsibility for calculations made by users in calculators. A good engineer must check calculations again and again.

You can find out much more calculators like in Mechanicalland! Take a look at the other engineering calculators available in Mechanicalland!

Do not forget to leave your comments and questions below about the torsion calculations and calculator for shafts. 

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