1. DEPARTMENT OF MECHANICAL AND MANUFACTURING ENGINEERING
UNIVERSITY OF NAIROBI
DEPARTMENT OF MECHANICAL AND MANUFACTURING ENGINEERING
ENGINEERING DESIGN II
FME 461
PART 7
GO NYANGASI
November 2008

2. PLANE STRESS SITUATION
Three stresses exists on one plane and stresses on the third dimension are zero
CASE OF SOLID CIRCULAR SHAFT SUBJECT TO TORSION COMBINED WITH BENDING

3. PLANE STRESS SITUATION
Principal stresses in the plane become

4. MAXIMUM SHEAR STRESS AT LOCATION
When principal stresses in the x-y plane are of opposite sign,
The maximum shear stress in the plane, is the maximum shear stress at the location
Maximum Shear stress at location is

5. BENDING AND TORSION OF SOLID CIRCULAR SHAFT
In the case of combined torsion and bending, the stress elements in the plane stress situation are:

6. MAXIMUM SHEAR STRESS AT LOCATION
PLANE STRESS SITUATION
With zero normal stress in y direction
Maximum shear stress at location is

7. MAXIMUM SHEAR STRESS AT LOCATION
SOLID CIRCULAR SHAFT SUBJECT TO BENDING AND TORSION

8. SUBSTITUTING FOR STRESS ELEMENTS
Substituting in equation for maximum shear stress with the values of stress elements

9. SUBSTITUTING FOR STRESS ELEMENTS
Yields

10. MAXIMUM SHEAR STRESS Theory of failure states
When Yielding occurs in any material
The maximum shear stress at the point of failure
Equals or Exceeds
The maximum shear stress when yielding occurs
In the tension test specimen.

11. SHAFT DESIGN EQUATION BENDING AND TORSION
Design equation becomes

12. SHAFT DESIGN EQUATION BENDING AND TORSION
The required dimension of the shaft can be expressed in terms of the loads, factor of safety, and material strength