Torsional stress

Torsional stress is the main topic of this article and I am sure many of you have some problems understanding its meaning. So go through this article to easily learn about it. At the end of this article you will find an example that challenges you to practice.

What causes torsional stress

In many cases the structural members are subjected to stress due to twisting like figure below. When we tighten a screw for example, we apply two equal and opposite parallel forces causing torsional stress in the body of the bolt. Now, Let’s have a closer look at what happens inside a the members under torsion.

Creating torsional stress

How torsional stress is distributed

As you can see in the next figure, the cross section are subjected to torsional stresses. The points that are closer to the center will experience a lower amount of torsional stress.In other words torsional stress start from zero at the center, and gets larger as it take distance.  So if the material remain elastic, we have a linear distribution of torsional stress on any radius of this circle. Here is the formula to calculate the torsional stress.

Torsional stress distribution on circular cross sections

Torsional stress formula

In this equation T is the amount of internal torque. And for those of you who are not familiar with the word “torque”, its exactly the same as moment.  C is the distance between the point  and the center. And finally J polar moment of inertia.

As you probably know, polar moment of inertia is an indicator of resistance against twisting. Please don’t mix it up with area moment of inertia which is about resistance against bending moment. You can find the amount of polar moment of inertia in the table below.

Polar moment of inertial

Positive or negative?

And about convention of positive direction, we assume a clockwise torque as positive. So counter clockwise is negative. Needless to say, it is just a simplification assumption and you can change it based on your will.

Positive convention for Torque


This solid shaft is under 3 different torques. Find the maximum amount of torsional stress.

Step1: draw the free body diagram.

Step2: draw the magnitude of internal torsion alongside the shaft.

Step3: calculate the amount of torsional stresses


As always you can challenge yourself by this mini-quiz and send your answers to be corrected by our team.

Quize og this lesson

Online class with Vahid

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