Stresses and Deflections in Built-In Beams

Abstract

Local distortions in the support(s) allow beams to rotate at their built-in end(s). The effect of these rotations is included in the classical equations for the deflections and stresses in both statically determinate and indeterminate beams subjected to arbitrary loading. The analysis is kept within the realm of simple beam theory and is supported by experimental results. Tables of solutions are given, accounting for possible differences between the elastic moduli of the beam and support materials, and for the effect of fillets at built-in end(s). The error incurred by treating beams as being rigidly built-in is shown to be quite significant for typical cases encountered in design. The solutions given in the tables herein are also applicable when special structural joints are used, but the rotational flexibility of the joint must be known.