# Torsion and the modulus of rigidity

• Confusedbiomedeng
In summary, the conversation discusses determining the modulus of rigidity for a material tested in a torsion testing machine. The specimen was 12.5mm in diameter and the gauge length was 0.75m. Using the given values for torque and angle of twist, the modulus of rigidity was calculated to be approximately 126x10^7 GPa. There was a discrepancy with the calculation of the polar moment of inertia, which should have been ∏(0.0125)^4/32 instead of ∏(0.025)^4/32.
Confusedbiomedeng

## Homework Statement

A specimen tested in a simple torsion testing machine , the specimen was 12.5mm in diameter and the angles were read over a gauge length of 0.75m Determine the modulus of rigidity of the material taking the torque T as 4.5Nm and the angle of twist as 4.0 degrees

T/J=τMax/R=Gθ\L

## The Attempt at a Solution

J=∏(0.025)4/32
J=3.8349x10^-8

4.0degress=0.0698132

4.5/3.8349x10^-8=G(0.0698132)/0.75
=>G=126x10^7
Wondering if this looks correct ??

Last edited by a moderator:
Where does the factor (0.025)^4 come from?

Don't you want pi*r^4/2 for this?

Dr.D said:
Where does the factor (0.025)^4 come from?

Don't you want pi*r^4/2 for this?
So I have for the polar moment of inertia to be ∏d^4/32
I did just see however I wrote 0.025 instead of 0.0125 which is the 12.5mm in m

## 1. What is torsion?

Torsion is a type of stress or strain that occurs when an object is twisted or rotated. It is caused by a force acting on one end of an object, while the other end remains fixed.

## 2. What is the modulus of rigidity?

The modulus of rigidity, also known as the shear modulus, is a measure of a material's resistance to shear stress. It is defined as the ratio of shear stress to shear strain.

## 3. How is torsion related to the modulus of rigidity?

Torsion and the modulus of rigidity are directly related. The amount of torsion in an object is determined by its modulus of rigidity and the amount of force applied to it. The higher the modulus of rigidity, the more resistant the object is to torsion.

## 4. What factors affect the modulus of rigidity?

The modulus of rigidity is affected by the material's composition, structure, and temperature. Different materials have different moduli of rigidity, and certain structures, such as crystalline structures, may have higher moduli of rigidity.

## 5. How is the modulus of rigidity measured?

The modulus of rigidity is typically measured using a torsion test, where a sample of the material is twisted and the resulting deformation and applied torque are measured. The ratio of these values gives the modulus of rigidity for the material.

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