An accurate solution for stress fields strongly varied across the adhesive thickness in soffit plate-strengthened beams
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An accurate solution for stress fields strongly varied across the adhesive thickness in soffit plate‑strengthened beams Phe Van Pham1 Received: 16 April 2020 / Accepted: 16 July 2020 © Springer Nature Switzerland AG 2020
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. Keywords Complementary energy · Variational principle · Finite difference · Layered beams · Interfacial shear and normal stresses
1 Introduction In soffit plate-strengthened beams, the adhesive shear and normal stresses near the plate ends are significant [1–3]. At such locations, the geometry of materials in a longitudinaltransverse plane is changed and thus stress flows transferred between the plate and the beam are narrowed, that leads to a stress concentration [4–7]. Because the strength of adhesive layer is small compared to those of the beam
and the plate [2], adhesive failure mode occurring at the plate ends was observed in several experimental studies (e.g., [8–12]). There were many analytical solutions developed in order to predict the high stresses concentrated near the plate ends. The majority of the analytical solutions were based on the postulation of the continuity of displacement and strain fields at material interfaces. Tounsi and Benyoucef [13] assumed that interfacial stresses were linearly
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s42452-020-03216-w) c
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