Analysis of Steel Beams Strengthened with Adhesively - Bonded GFRP Plates - Phe, Pham Van (Université d'Ottawa / University of Ottawa, 2018)
Glass Fiber-Reinforced Polymer (GFRP) plates offer a light-weight, corrosion-resistant and cost-effective alternative to steel plates for strengthening steel members. Typically, GFRP plates are bonded to steel members through a relatively soft adhesive layer. The large difference between the mechanical properties of the three materials involved is generally associated with relative slip at the steel-GFRP interface and is thus associated with partial interaction between the two materials. Available full interaction models aimed at fully composite systems tend to overestimate the strength of GFRP-strengthened steel beams. Also, quantifying the strength of the resulting steel-adhesive-GFRP composite represents a technical challenge as it involves several potential modes of failure (e.g., local buckling, lateral-torsional buckling, cross-sectional strength, GFRP rupture, adhesive shear failure, adhesive peeling failure, excessive deflections, adhesive loss of strength due to thermal effects). Within the above context, the present research aims at formulating a number of analytical/numerical solutions to quantify the strength of GFRP-strengthened steel beams, and assessing the validity of the models through 3D finite element analyses in commercial software. Towards this goal, the study contributes to the solution of the problem by developing a series of models that incorporate partial interaction effects between the steel and GFRP. The models are intended to determine: (1) the linear static analysis response, (2) the elastic lateral-torsional buckling capacity, (3) the ultimate moment resistance and propose classification considerations for local buckling, (4) quantifying the detrimental effect of pre-existing load on the added capacity of strengthening GFRP plates, (5) developing an advanced beam theory that captures transverse normal stresses in homogeneous beams (in addition to longitudinal and shear stresses in common beam theories), and (6) generalizing the beam theory to multi-layered beams to model sandwich structures and GFRP-strengthened steel beams. In contribution 1, a super-convergent finite element formulation is developed for the linear static analysis for steel beams strengthened with a single GFRP plate subjected to general transverse loads. The shear deformation effect is captured in the formulation. The element is shown to circumvent discretization errors in conventional finite elements based on polynomial interpolation functions and to accurately predict displacements and stresses while keeping the number of degrees of freedom to a minimum. The model is then adopted to (a) determine the elastic flexural resistance of strengthened steel beams with class 3 (subcompact) sections based on a first yield mode of failure, (b) quantify deflection limits and (c) conduct the pre-buckling analysis required for subsequent elastic lateral torsional buckling analysis. In contribution 2, a variational principle and two finite elements are developed for the elastic lateral torsional buckling analysis of steel beams strengthened with a single GFRP plate. The formulation accounts for global and local warping, shear deformation due to bending and twist, partial interaction, and load elevation effects. The study provides a basis to quantify key design information including critical moments, buckling modes, moment gradients, and load elevation effects. In contribution 3, analytical models are developed to determine the ultimate moment resistance for Class 1 and 2 (compact) sections for steel beams strengthened with a single GFRP plate on the tension side. The models account for the elasto-plastic behaviour of steel, the adhesive shear capacity, and the GFRP tensile strength. Attention is given to relatively strong adhesives (e.g., common adhesives at room temperature) as well as weak adhesives (adhesive at elevated temperatures). Also, a methodology for classifying GFRP-strengthened steel sections is proposed to ensure that local buckling does not occur prior the attainment of the ultimate moment resistance. In contribution 4, a closed form solution is developed for the linear static analysis of a pre-loaded steel beam strengthened with two GFRP plates bonded to both flanges and then subjected to additional loads. The solution provides means to determine the elastic flexural resistance of strengthened steel beams with class 3 (subcompact) sections based on a first yield mode of failure and to quantify deflection limits. In contribution 5, a family of higher order beam solutions is developed for the analysis of homogeneous beams with a mono-symmetrical cross-section. The distinctive features of the solution are: (a) it is based on the complementary energy variational principle and thus offers advantages in quantifying stresses when compared to common displacement based formulations, (b) it captures the transverse normal stresses in addition to longitudinal and shear stresses, (c) it is based on a polynomial expansion of the stress fields which enables the analyst to increase the accuracy of the predictions by specifying the order of the polynomial. The governing field equations and boundary conditions are formulated and a closed-form solution scheme is developed. The ability of the theory to capture transverse stresses is key in extending the work to non-homogeneous systems such as GFRP-strengthened steel beams in which the peeling of the adhesive represents a possible mode of failure. Finally, contribution 6 extends the developments of contribution 5 in two respects: (1) generalizing the solution to multilayer beams, and (2) developing a finite element formulation able to handle general boundary conditions. The solution developed is then applied to a number of applications involving sandwich beams and GFRP-strengthened steel beams where it is shown to capture the peeling stresses at the steel-GFRP interface.
Keywords: GFRP strengthening; steel beams; Lateral Torsional Buckling; Ultimate Moment Capacity; Preloaded beams; Failure modes