Elastic sectional stress analysis of variable section piers subjected to three-dimensional loads

Abstract

The elastic stress analysis of beam-column structures of uniaxial symmetrical variable cross-sections is developed using an extension of Euler–Bernoulli beam theory. The applied loads are general considering axial (P), flexure (Mx–My), shear (Vx–Vy), and torsion (T). Three-dimensional analytical solutions for normal and shear stresses are derived using sectional analysis with warping functions for variable boundaries in elevation. The differential equations of equilibrium and deformations are accounting for the variations in the geometrical properties of the cross-section and related boundary conditions. The strong form solution is then written in a weak form that is implemented in a 2D sectional finite element (FE) code assuming linear normal stress distribution. Three application examples are presented to validate the proposed sectional approach and illustrate its accuracy by comparing with results from full 3D FE analyses: (a) a slender rectangular section pier with a sloped boundary, (b) a bulk rectangular section buttress with unsymmetrical slopes, and (c) a pier (squat wall) for a hydraulic structure. When the assumption of linear distribution for normal flexural stress is satisfied, the proposed sectional approach produces results within 1% of 3D FE with much reduced computational efforts. For bulk and squat walls the stress field distribution are very similar to 3D FE while the stress intensity shows some variations. This is of major practical significance because the proposed approach allows performing first a series of simplified yet acceptable sectional analyses in safety assessment of the three-dimensional type of structures considered herein.