TABLE OF CONTENTS Figure 8.1 shows failure surfaces of aluminum and cast iron members under axial and torsional loads. Why do different materials under similar loading produce different failure surfaces? If we had a combined loading of axial and torsion, then what would be the failure surface, and which stress component would cause the failure? The answer to this question is critical for the successful design of solid members that are subjected to combined axial, torsional, and bending loads. In Chapter 10 we will study combined loading and failure theories that relate maximum normal and shear stresses to material strength. In this chapter we develop procedures and equations that transform stress components from one coordinate system to another at a given point.
Stress transformation can also be viewed as relating stresses on different planes form the axes of a coordinate system. Thus relating stresses on different planes is equivalent to relating stresses on different planes is equivalent to relating stresses in different coordinate systems. We will use both viewpoints in this chapter of stress transformation.
The two major learning objectives of this chapter are:
Learn the equations and procedures of relating stresses (on different planes) in different coordinate systems at a point.
Develop the ability to visualize planes passing through a point on which stresses are given or are being found, in particular the planes of maximum normal stress and maximum...
