TABLE OF CONTENTS In Chapters 7, 9, 10 and 11 we determined stress distributions produced separately by axial load, bending moment, shear force and torsion. However, in many practical situations some or all of these force systems act simultaneously so that the various stresses are combined to form complex systems which may include both direct and shear stresses. In such cases it is no longer a simple matter to predict the mode of failure of a structural member, particularly since, as we shall see, the direct and shear stresses at a point due to, say, bending and torsion combined are not necessarily the maximum values of direct and shear stress at that point.
Therefore as a preliminary to the investigation of the theories of elastic failure in Section 14.10 we shall examine states of stress and strain at points in structural members subjected to complex loading systems.
We have seen that, generally, stress distributions in structural members vary throughout the member. For example the direct stress in a cantilever beam carrying a point load at its free end varies along the length of the beam and throughout its depth. Suppose that we are interested in the state of stress at a point lying in the vertical plane of symmetry and on the upper surface of the beam mid-way along its span. The direct stress at this point on planes perpendicular to the axis of the beam can be calculated using Eq. (9.9). This stress may...
