Shear deformable super-convergent finite element for steel beams strengthened with glass-fiber reinforced polymer (GFRP) plate

The present study investigates the flexural behaviour of steel beams strengthened by adhesively bonding a glass-fiber reinforced polymer (GFRP) plate to one of the flanges. The model captures shear deformation effects and partial interaction between the steel and GFRP owing to the relative flexibility of the adhesive. A general closed form solution is first developed for the governing coupled system of differential equations. The solution is then used to formulate mechanics-based shape functions and develop a finite element with superior convergence characteristics. The model is used to investigate the response of multi-span continuous beams, determine the strength gained by GFRP strengthening, and quantify shear deformation effects on the response of strengthened beams. A technique capturing partial interaction effects is devised to characterize the flexural strength of Class 3 strengthened beams. A classification limit for strengthened Class 3 sections is also proposed within the framework of the Canadian Standard CAN-CSA S16 (2014).