Vol. 16, No. 3, 2021

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An enriched model based on a complementary strain energy variational principle for stress analysis in FRP plate-strengthened beams

Phe van Pham and Xuan-Huy Nguyen

Vol. 16 (2021), No. 3, 237–262
Abstract

A finite difference formulation is developed for the stress analyses in orthotropic three-layer composite beams with mono-symmetrical cross-sections under various force boundary and loading conditions. Four interfacial shear and peeling stress fields at material interfaces are assumed as unknown functions. Based on shear stress flow equilibrium conditions, three groups of stress fields including transverse shear, transverse normal and longitudinal normal stresses in the beam, the plate and the adhesive layer are expressed in terms of the unknown functions. A set of compatibility equations and corresponding boundary conditions are then derived from a variational principle of complementary strain energy and solved by a finite difference technique. The present theory eliminates kinematic assumptions of equal curvatures for the beam and the plate, it satisfies the infinitesimal stress equilibrium conditions of the interfacial shear and peeling stresses at material interfaces, and it captures the longitudinal normal stresses in the adhesive. By comparing to numerical and analytical solutions, the present theory is a solution for the prediction of concentrated transverse shear and transverse normal (peeling) in the adhesive occurring near the plate ends. Based on the present theory, a parametric study is conducted to quantify the effects of the strengthening length, thickness, and elasticity moduli of the FRP plate and adhesive layer on the peak values of the interfacial shear and peeling stresses.

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Keywords
complementary energy, variational principle, finite difference, orthotropic material, layered beam, FRP strengthening, interfacial shear, interfacial peeling, adhesive longitudinal normal stress
Milestones
Received: 20 March 2020
Revised: 22 October 2020
Accepted: 31 October 2020
Published: 1 July 2021
Authors
Phe van Pham
Research and Application Center for Technology in Civil Engineering
University of Transport and Communications
Hanoi
Vietnam
Xuan-Huy Nguyen
Research and Application Center for Technology in Civil Engineering
University of Transport and Communications
Hanoi
Vietnam