In this guide I will explain what it means to free twisting bars, give all the necessary formulas for calculating a bar with a circular or annular cross-section and at the same time I will carry out calculations for an exemplary task.

**Free twisting** – it is a torsion, in which the deplanations (warping) of neighboring cross-sections are free, that is, they do not press themselves. There is no normal stress.

In order for the rod to undergo free twisting, the need for a suitable shape, a proper method of fixing and proper application of loads.

Before starting to calculate an example bar, I will give all the necessary patterns. Let’s start with the formula for determining the diameter of the rod, it looks like this:

where:

– torque moment

– allowable stresses

– 3.14 …

Another pattern is used to calculate stresses:

where:

– torque moment

– moment of inertia when turning. Note, I will also place patterns for this because they depend on the section. Another is for circular and another for annular.

Formula for the moment of inertia when turning for a circular cross-section:

Formula for the moment of inertia when screwing for the ring section:

The last pattern has been left. This is a formula for the angle of twisting the rod, it looks like this:

where:

– torque moment

– length

– moment of inertia when turning

So much theory, now it’s time for some counting. I will choose the diameter of the rod, calculate the stresses in section 1-1 and the total angle of torsion on the cross-section below.

It is a steel rod with circular cross-section, fixed along its length.

Data:

We start calculating the given bar according to the following algorithm.

**Designation of Mr**

**Determining the torque graph**(internal forces)The entire length of the rod

**Diameter determination**

**Stress value in section 1-1**

**Torsion angle**