An accurate solution for stress fields strongly varied across the adhesive thickness in soffit plate-strengthened beams

Abstract

A closed form solution and a finite difference formulation are developed for an accurate prediction of adhesive shear and normal stresses in soffit plate flexural-strengthened beams. First, three statically admissible stress fields (i.e., longitudinal normal, transverse shear and normal stresses) are derived and expressed in terms of four unknown interfacial shear and normal stresses. Then, a modified complementary strain energy is written in which the energy contributions of the transverse normal stress fields in the beam and in the plate, and the transverse shear stresses in the beam are omitted. Based on an energy variational principle, compatibility equations and corresponding boundary conditions are obtained. A closed form solution and a finite difference formulation are finally developed. Through validations, the adhesive shear and normal stresses near the plate ends predicted by the present study are in excellently agreements with those provided in several experimental and numerical studies. Also, the present study excellently captures stress fields strongly varied across the adhesive thickness, especially the transverse normal stresses. Based on the present theory, a parametric study is conducted to quantify the effects of the plate longitudinal modulus and the thickness on the interfacial shear and normal stresses. The parametric study indicates that the peak normal stresses are significantly higher than the peak shear stresses in the adhesive layer. The present study is applicable to predict the adhesive shear and normal stresses highly concentrated near the plate ends in plate-strengthened beams with general applied loads and force boundary conditions.