A shear deformable theory for the analysis of steel beams reinforced with GFRP plates

• Starting with the principle of stationary potential energy, a shear deformable theory is developed for the analysis of steel beams reinforced with a GFRP plate.
• The theory yields two coupled systems of differential equations involving ten displacement fields. The first system governs the longitudinal-transverse response of the system and consists of four displacement fields. The second system governs the lateral-torsional response and involves six displacement fields.
• Expressions for associated boundary conditions are obtained as a by-product of the formulation.
• The equations are numerically solved using the central finite difference technique for a variety of problems. A thorough comparison with 3D FEA results is then conducted. The theory is shown to yield reliable displacement and stress predictions with a minimal computational effort.
• A comparison of the results based on non-shear deformable theory demonstrates the importance of incorporating shear deformation effects when capturing predominantly torsional responses.

A shear deformable thin-walled beam theory is developed for the analysis of steel beams reinforced with a GFRP plate to one of the flanges. Starting with the principle of stationary potential energy, the governing equilibrium equations and boundary conditions are formulated for the problem. The theory results in two sets of fully coupled systems of equilibrium equations. The first system describes the longitudinal-flexural response of the system and involves four generalized displacement fields and the second system governs the lateral-torsional response and involves six generalized displacement fields. The resulting coupled systems are then solved numerically for practical problems. Detailed comparisons with three dimensional and shell solutions under ABAQUS show that the present theory provides reliable predictions for displacements and stresses. A comparison with results from a non-shear deformable theory illustrates the necessity of incorporating shear deformation effects in cases involving predominantly twisting responses.