# Change of volume in pure torsion

• joltu
In summary, pure torsion is defined as the case where normal stresses are zero due to exterior forces producing only moments of torsion along the bar axis. This means that the change of volume in pure torsion is zero, as the three principal stresses evaluated in a plane with degree of 45 will sum up to zero due to the absence of normal stress.

#### joltu

why change of volume in pure torsion is zero?
if you consider stress in plane with degree of 45 there is normal stress
normal stress can lead to change of volume

define "pure torsion"...

Pure torsion appears when exterior forces acting perpendicular to the bar axis
produce only moments of torsion acting along the bar axis

i.e. pure torsion is defined to be the case where the normal stresses are zero.

joltu said:
why change of volume in pure torsion is zero?
if you consider stress in plane with degree of 45 there is normal stress
normal stress can lead to change of volume
See what you get if you evaluate the three principal stresses. Do they sum to zero?

joltu

## 1. What is pure torsion?

Pure torsion is a type of mechanical loading in which a material experiences twisting without any accompanying tensile or compressive forces. This is in contrast to other types of loading, such as tension or compression, which cause changes in the length or shape of the material.

## 2. What is the change of volume in pure torsion?

The change of volume in pure torsion refers to the change in the overall volume of a material as it is subjected to twisting forces. This change in volume is typically very small, as torsion primarily affects the shape and orientation of the material rather than its overall size.

## 3. How is the change of volume in pure torsion calculated?

The change of volume in pure torsion can be calculated using the formula ΔV = Vθ/L, where ΔV is the change in volume, V is the original volume, θ is the angle of twist, and L is the length of the material. This formula is based on the assumption that the material is incompressible and has a constant cross-sectional area.

## 4. What factors can affect the change of volume in pure torsion?

The change of volume in pure torsion can be affected by several factors, including the material's elastic properties, the magnitude of the twisting force, the length and shape of the material, and the speed at which the twisting force is applied. Additionally, any imperfections or defects in the material can also impact the change of volume.

## 5. Why is the change of volume in pure torsion important?

The change of volume in pure torsion is important because it can affect the material's overall performance and behavior under twisting forces. It is particularly relevant in designing and analyzing structures and components that are subjected to torsion, such as shafts, axles, and springs. Understanding the change of volume can help engineers predict how a material will behave and ensure the structural integrity of their designs.