Subject: Machine Design -I

Topic: Basic properties of Machine design and theories of failure

Difficulty: Medium

• Mean stress as well as stress amplitude exist when a component is subjected to fluctuating stresses.
• It has been observed that the mean stress component has an effect on fatigue failure when it is present in combination with an alternating component.
• The fatigue diagram for this general case is shown in Fig. below. In this diagram, the mean stress is plotted on the abscissa and stress amplitude on ordinate.
• The magnitudes of mean stress and stress amplitude depend upon the magnitudes of maximum and minimum force acting on the component.
• When stress amplitude is zero, the load is purely static and the criterion of failure is Sut or Syt. These limits are plotted on the abscissa.
• When the mean stress is zero, the stress is completely reversing and the criterion of failure is the endurance limit Se that is plotted on the ordinate.
• When the component is subjected to both components of stress, the actual failure occurs at different scattered points shown in the figure.
• There exists a border, which divides safe region from unsafe region for various combinations of mean stress and stress amplitude.
• Different criterion are proposed to construct the borderline dividing safe zone and failure zone. They include Gerber line, Soderberg line and Goodman line.

• Gerber Line: A parabolic curve joining Se on the ordinate to Sut on the abscissa is called the Gerber line.
• Soderberg Line A straight line joining Se on the ordinate to Syt on the abscissa is called the Soderberg line.
• Goodman Line A straight line joining Se on the ordinate to Sut on the abscissa is called the Goodman line.