A hollow shaft of 60-mm outer diameter and 30-mm inner diameter is acted on by an axial...

Calculate the normal stress due to bending moment.

Substitute for , for I for a hollow shaft and for.

Substitute for and for.

Calculate the stress in x-direction.

Substitute for , and for .

Calculate the shearing stress due to the applied torque.

Here r is the radius of the shaft and J is the polar moment of inertia.

Substitute for J for a hollow shaft and for.

Substitute for T, for and for.

Define point A using the normal stress and shearing stress.

Here, normal stress in the x-direction is and the shearing stress is.

Substitute for and for.

Define point B using the normal stress and shearing stress.

Here, the normal stress in the y-direction is and the shearing stress is.

Substitute for and for.

Define point C, the center of the circle.

Substitute forand for.

Draw the Mohr’s circle by use of points A, B and C.

Write the steps for construction of Mohr’s Circle.

1. Locate the point C (16.8, 0) on the horizontal -axis from the origin O, with a suitable scale.

2. Now take C as center and draw a circle of radius CA, touching points A and B.

3. Now draw a line at an angle with respect to.

Sketch a right triangle using either points A and C or B and C.

Determine the radius R.

Determine the maximum principal stress.

Substitute for C and for R.

Determine the minimum principal stress.

Substitute for C and for R.

Therefore, the principal stresses are and.

Determine the principal direction by use of Mohr’s circle.

Determine the principal direction.

Therefore, the principal directions are and.