Stress-Deformation Theories for the Analysis of Steel Beams Reinforced with GFRP Plates

Abstract

A theory is developed for the analysis of composite systems consisting of steel wide flange sections reinforced with GFRP plates connected to one of the flanges through a layer of adhesive. The theory is based on an extension of the Gjelsvik theory and thus incorporates local and global warping effects but omits shear deformation effects. The theory captures the longitudinal transverse response through a system of three coupled differential equations of equilibrium and the lateral-torsional response through another system of three coupled differential equations. Closed form solutions are developed and a super-convergent finite element is formulated based under the new theory. A comparison to 3D FEA results based on established solid elements in Abaqus demonstrates the validity of the theory when predicting the longitudinal-transverse response, but showcases its shortcomings in predicting the torsional response of the composite system. The comparison sheds valuable insight on means of improving the theory. A more advanced theory is subsequently developed based on enriched kinematics which incorporates shear deformation effects. The shear deformable theory captures the longitudinal-transverse response through a system of four coupled differential equations of equilibrium and the lateral-torsional response through another system of six coupled differential equations. A finite difference approximation is developed for the new theory and a new finite element formulation is subsequently to solve the new system of equations. A comparison to 3D FEA illustrates the validity of the shear deformable theory in predicting the longitudinal-transverse response as well as the lateral-torsional response. Both theories are shown to be computationally efficient and reduce the modelling and running time from several hours per run to a few minutes or seconds while capturing the essential features of the response of the composite system.