Elastic Analysis of Steel Beams Strengthened with GFRP Plates Including Preexisting Loading Effects

Abstract

The present study develops a theory for the elastic analysis of a pre-loaded wide flange steel beam, strengthened with two Glass Fiber Reinforced Polymer (GFRP) plates bonded to both flanges, then subjected to additional loads. Starting with the principle of stationary potential energy, the governing equilibrium equations and corresponding boundary conditions are formulated prior to and after GFRP strengthening. The resulting theory involves four coupled equilibrium equations and 10 boundary conditions. A general closed form solution is then provided for general loading and boundary conditions. Detailed comparisons with three-dimensional finite element solutions show that the theory provides reliable predictions for the displacements and stresses. A parametric study is then developed to quantify the effects of strengthening, GFRP plate thicknesses, and pre-existing loads, on the capacity of the strengthened beam.