3-D stress in mechanical design august 2000 copyright ó

3-D STRESS IN MECHANICAL
DESIGN

August 2000
Copyright © 2000 C. E. Knight

PURPOSE OF THE TUTORIAL
This tutorial is designed to introduce and place strong emphasis on the role of 3-D stress in the process of mechanical design. Students in engineering are normally introduced to stress in its simplest onecomponent form defined by load divided by area of cross section.. This is a valid definition of a pure 1-D state of stress, but in many cases it seems to establish a baseline safe position for which many students don’t want to venture forth. Carrying this attitude through the mechanical design process is a recipe for failure. Everything in the mechanical design realm has solid 3-D characteristics. The same is true for the state of stress in the solid. In many simple cases the effective state of stress can be reduced to 2-D or 1-D, but only after careful consideration. In the early stages of mechanical design, the locations of most likely stress failure and the corresponding stress components acting at those locations must be identified. Once all the stress components at a given location are determined, they may then be combined to find principal stresses, maximum shear stress or other measures that are useful for predicting design success or failure. It is very important to remember that stress components for one location in a machine part should never be combined with stress components for a different location in the same part.
One of the interesting developments in visualizing the combining of 2 stress components was the
-D
creation of Mohr’s circle. This graphical representation of the 2-D stress transformation equations provides a quick, accurate and visual protrayal of the 2 state of stress. It finds the principal stresses and a
-D
maximum shear stress (although this maximum shear stress may be quite misleading in 3-D stress).
Review of Two-Dimensional Mohr’s Circle - Graphical Approach
The beginning of a Mohr’s circle representation