Torsion equation or torsion constant is defined as the geometrical property of a bar’s cross-section that is involved in the axis of the bar that has a relationship between the angle of twist and applied torque whose SI unit is m4. The torsion equation is given as follows:
Torsion equation derivation
Following are the assumptions made for the derivation of torsion equation:
- The material is homogeneous (elastic property throughout)
- The material should follow Hooke’s law
- The material should have shear stress proportional to shear strain
- The cross-sectional area should be plane
- The circular section should be circular
- Every diameter of the material should rotate through the same angle
- The stress of the material should not exceed the elastic limit
Consider a solid circular shaft with radius R that is subjected to a torque T at one end and the other end under the same torque.
Angle in radius =
Arc AB = RӨ = Lγ
A and B: two fixed points on the circular shaft
γ: angle subtended by AB
𝞃: shear stress
γ: shear strain
Consider a small strip of radius with thickness dr that is subjected to shear stress.
r: radius of small strip
dr: thickness of the strip
γ: shear stress
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Frequently Asked Questions – FAQs
What is torsion?
What is torque?
Define torsion constant.
Write a few assumptions made for the derivation of the torsion equation.
The material should follow Hooke’s law.
The material should have shear stress proportional to shear strain.
The circular section should be circular.
The stress of the material should not exceed the elastic limit.