engineering core courses

Solid Mechanics I
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Solid Mechanics I
 Course homepage
C3: Torsion
3.1 Torsion Formula
- Theory - Example - Question 1 - Question 2
3.2 Power Transmission
- Theory - Example - Question 1
3.3 Angle of Twist
- Theory - Example - Question 1 - Question 2
3.4 Statically Indeterminate Analysis with Torque
- Theory - Example - Question 1 - Question 2

C3.3 Angle of Twist

Similar to elastic deformation, we have deformation due to torsion as well: twisting. The degree of twisting needs to be quantified to ensure that shafts are designed within safe twisting limits.

Angle of twist

The angle of twist due to a torque loading can be calculated using the following formula:


Angle of twist formula
Note:
  • T is the internal torque (Nm), L is the length of segment (m), J is the polar moment of inertia (m4) and G is the shear modulus (GPa).
  • Answer obtained is in radians (rad), but we usually convert it to degrees.

C3.3 Angle of Twist

Similar to elastic deformation, we have deformation due to torsion as well: twisting. The degree of twisting needs to be quantified to ensure that shafts are designed within safe twisting limits.

Angle of twist

The angle of twist due to a torque loading can be calculated using the following formula:


Angle of twist formula
Note:
  • T is the internal torque (Nm), L is the length of segment (m), J is the polar moment of inertia (m4) and G is the shear modulus (GPa).
  • Answer obtained is in radians (rad), but we usually convert it to degrees.

We also present to you the general formula for angle of twist, for completeness sake:

General formula for angle of twist

Angle of twist along a shaft, torque diagram

Often a shaft has a few torque loadings and we want to quantify the total angle of twist:

Shaft loaded with torque to find angle of twist

To do that, we first obtain our torque diagram, which considers the internal torque for each shaft segment:


Torque diagram used to find angle of twist

Using these internal torque values, we calculate the angle of twist for each segment, and sum them up successively with respect to one end of the shaft:

Total angle of twist along the shaft

And remember the sign convention; the angle of twist follows the right-hand rule as well. Let’s look at an example now.

We also present to you the general formula for angle of twist, for completeness sake:

General formula for angle of twist

Angle of twist along a shaft, torque diagram

Often a shaft has a few torque loadings and we want to quantify the total angle of twist:

Shaft loaded with torque to find angle of twist

To do that, we first obtain our torque diagram, which considers the internal torque for each shaft segment:


Torque diagram used to find angle of twist

Using these internal torque values, we calculate the angle of twist for each segment, and sum them up successively with respect to one end of the shaft:

Total angle of twist along the shaft

And remember the sign convention; the angle of twist follows the right-hand rule as well. Let’s look at an example now.

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