OVERVIEW

In Chapters 9, 10 and 11 we investigated the strength of beams in terms of the stresses produced by the action of bending, shear and torsion, respectively. An associated problem is the determination of the deflections of beams caused by different loads for, in addition to strength, a beam must possess sufficient stiffness so that excessive deflections do not have an adverse effect on adjacent structural members. In many cases, maximum allowable deflections are specified by Codes of Practice in terms of the dimensions of the beam, particularly the span; typical values are quoted in Section 8.7. We also saw in Section 8.7 that beams may be designed using either elastic or plastic analysis. However, since beam deflections must always occur within the elastic limit of the material of a beam they are determined using elastic theory.

There are several different methods of obtaining deflections in beams, the choice depending upon the type of problem being solved. For example, the double integration method gives the complete shape of a beam whereas the moment-area method can only be used to determine the deflection at a particular beam section. The latter method, however, is also useful in the analysis of statically indeterminate beams.

Generally beam deflections are caused primarily by the bending action of applied loads. In some instances, however, where a beam's cross-sectional dimensions are not small compared with its length, deflections due to shear become significant and must be calculated. We shall consider beam deflections due to...