Answer: Solving Torque Problems: Shaft Diameter & Stress

[confusedkarl]

1. Homework Statement

The steel shaft of a socket wrench is 18mm diameter and 450mm long. If the allowable shear stree is 70 MN/m^2.

2. Homework Equations
i) What is the maximum permissible torque T that may be extered with the wrench?
ii) Through what angle (theta) in radians will the shaft twist under the action of the maximum torque?
iii) Through what angle (theta) in degrees will the shaft twist under the action of the maximum torque? G = 80 GN/m^2


3. The Attempt at a Solution

Im pretty happy how to do the radians to degress conversion but haven't a clue on the forumulae or process I need for i and ii =(

 

[brewnog]

For a shaft of uniform cross section:

$$\frac{T}{J} = \frac{\tau}{R} = \frac{G \theta}{l}$$

Where T is torque applied, J is the polar second moment of area, Tau is shear stress, R is radius, G is modulus of rigidity, and Theta the angle of twist. All SI units.