### First: Torsion

** Torsion **in members of circular cross section area such as

**occurs when these members are subjected to**

*shafts***(i.e. two torques "T" having the same magnitudes but opposite senses as shown above). This**

*twisting couples***can be calculate from the following equation:**

*torsion*Note that: ** Shafts **can be either solid or hollow. In a hollow

**, the maximum torque (and therefore, the maximum**

*shaft***) occurs on the outer surface, and the minimum torque (and therefore, the minimum**

*shearing stress***) occurs on the inner surface. This is shown in the following image**

*shearing stress*Image source: F. Beer. Mechanics of Materials, Sixth Edition |

Therefore; the minimum ** shearing stress** in a hollow

**could be calculated from the following equation:**

*shaft*The ** polar moment of inertia** can be calculated from the following equations

- In the case of a
**solid circular shaft**of radius c. Theis*polar moment of inertia*Image source: F. Beer. Mechanics of Materials, Sixth Edition - In the case of a
**hollow circular shaft**of inner radius c1 and outer radius c2, Theis*polar moment of inertia*

### Second: Angle of twist

Image source: F. Beer. Mechanics of Materials, Sixth Edition |

When a

**is applied to a***torsion***, a***shaft***will form as shown above. This angle can be calculated from the following equation:***twist angle*Then, we change from Radians to degrees according to the following correlation:

Similarly, we can convert from degrees to Radians

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