Rotating Disc with central hole

[Mechaman]

Homework Statement

Problem and worked Example[/B]

Homework Equations

In worked example 1. Problem

The Attempt at a Solution

It's the part where I'm subtracting one stress from the other stress. I put it in parenthesis on the worked example. I don't think my method here is right, I've tried to subtract each like term from the other to get my B term. When I come to extract the 3.3/8 by 3.3/8 it should be 3.3/8 - (-3.3/8) giving + 3.3/8.

Also why is the radius term now divisible by the variables on the right?

Can anyone see what's going on here?

 

[nilesh_pat]

Worked Example 1. ProblemA circular cylinder of radius r and length l is subjected to an axial tensile stress σ1 = 7.3/8 MPa and a circumferential stress of σ2 = -3.3/8 MPa. Determine the maximum shear stress and its location.Solution:The maximum shear stress τmax will occur at the outer surface of the cylinder, at a distance r from the axis. The shear stress τ can be determined usingτ = (σ1 - σ2) / 2Substituting in the given values givesτmax = (7.3/8 - (-3.3/8)) / 2 = 5/8 MPaAt the outer surface of the cylinder, the maximum shear stress is 5/8 MPa.