Stress Distribution in Beams of Varying Depth

Beams of varying depth are widely used in civil engineering structures, and are particularly suitable for large span prestressed concrete bridges. It is well known that the distribution of shear stress and hence principal tensile stress may be considerably affected by the variation in depth. A review is made of the various elastic analytical methods available, and their assumptions are discussed. The accuracy of each analysis is assessed on a plane wedge under separate application of normal force, shear, and bending moment, for a range of slopes and curvatures. The effect of curvature is shown to be unimportant for the values associated with bridges. The approximate forms of the solutions reached by Boussinesq and Wysiatycki are shown to be identical. These expressions are simple and give good agreement with the exact solution. Photo-elastic and finite element models are used to examine the accuracy of the various analytical methods applied to box-sections.

Gwynnes Davies, Richard S. Lamb and Cyril Snell