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

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

PLANE STRESS SITUATION Principal stresses in the plane become

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

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

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

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

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

SUBSTITUTING FOR STRESS ELEMENTS Yields

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.

SHAFT DESIGN EQUATION BENDING AND TORSION Design equation becomes

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