# Free twisting of round bars

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.

1. Designation of Mr

1. Determining the torque graph (internal forces)The entire length of the rod
1. Diameter determination

1. Stress value in section 1-1

1. Torsion angle