Simplified Calculation of Shear Rotations for First-Order Shear Deformation Theory in Deep Bridge Beams

Abstract

Nodal rotations are produced by bending and shear effects and bending rotations can be easily calculated using Euler–Bernoulli’s stiffness matrix method. Nevertheless, shear rotations are traditionally neglected, as their effects are practically negligible in most structures. This assumption might lead to significant errors in the simulation of the rotations in some structures, as well as the wrong identification of the mechanical properties in inverse analysis. Despite its important role, no other works studying the calculation of shear rotations in deep beams were found in the literature. To fill this gap, after illustrating the errors of commercial software regarding calculating the rotations in deep beams, this study proposed a simple and intuitive method to calculate shear rotations in both isostatic and statically redundant beams. The new method calculates the shear rotation for all segments separately and introduces the result to the total rotation of the structure. This method can be applied to find the shear rotation in a redundant structure as well. A parametric study was carried out to calculate slenderness ratios to determine in what structural systems the shear rotations can be neglected. In addition, the errors in the inverse analysis of deep beams were parametrically studied to determine the role of shear rotation in different structural systems. Finally, to validate the application of the method in actual structures, a construction stage of a composite bridge was analyzed.