TABLE OF CONTENTS The analysis presented in Chapters 16 20 relies on elementary theory for the determination of stresses and displacements produced by axial loads, shear forces and bending moments and torsion. No allowance is made for the effects of restrained warping produced by structural or loading discontinuities in the torsion of open or closed section beams, or for the effects of shear strains on the calculation of direct and shear stresses in beams subjected to bending and shear.
In this chapter we shall examine some relatively simple examples of the above effects; more complex cases require analysis by computer-based techniques such as the finite element method.
Structural constraint stresses in either closed or open beams result from a restriction on the freedom of any section of the beam to assume its normal displaced shape under load. Such a restriction arises when one end of the beam is built-in although the same effect may be produced practically, in a variety of ways. For example, the root section of a beam subjected to torsion is completely restrained from warping into the displaced shape indicated by Eq. (18.5) and a longitudinal stress system is induced which, in a special case discussed later, is proportional to the free warping of the beam.
A slightly different situation arises when the beam supports shear loads. The stress system predicted by elementary bending theory relies on the basic assumption of plane sections remaining plane...
