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### INTRODUCTION

When a straight beam is subjected to an axial moment, each cross section twists around its torsional center. Shear stresses occur within the cross sectional planes of the beam.

For a torsionally loaded beam, the angular twist is described by:

is the shear modulus. The relation between the shear modulus and the elastic modulus is defined by the following formula:

(For most metals)

The rotational stiffness of a torsionally loaded beam is:

For a torsionally loaded beam, the maximum torque load can be calculated with:

is the torsion constant. It is equal to the polar moment of inertia if the cross section is circular.

For non-circular cross sections warping occurs which reduces the effective torsion constant. For these shapes, approximate solutions of the torsion constant are given in the table below.

**Cross section**

**Torsion constant **

**Cross section**

**Torsion constant **

**Cross section**

**Torsion constant **

**Cross section**

**Torsion constant **

**Cross section**

**Torsion constant **

**With h>w**

**Cross section**

**Torsion constant **

This page uses QuickLaTeX to display formulas.