Amr Shaat, Waleed Safwat El Sayed Fahmy and Amir Fam

Department of Civil Engineering, Queen’s University, Kingston, Ontario, Canada
E-mail: fam@civil. queens. ca


This paper describes an analytical model developed to predict the behaviour of axially loaded slender members composed of steel hollow structural sections (HSS), retrofitted with carbon-fibre reinforced polymer (CFRP) composite sheets. A previous experimental study by the authors showed that gain in strength due to CFRP retrofitting was highly sensitive to the specimen’s imperfection. As such, developing an analytical model was necessary to uncouple the effects of imperfection and number of CFRP layers. The model predicts the load versus axial and lateral displacements, and accounts for steel plasticity, the built-in through-thickness residual stresses, geometric non-linearity, including initial imperfection, and the contribution of CFRP sheets. The model was verified against results of the experimental program and showed reasonable agreement. The model was then used in a parametric study. The study demonstrated that retrofitting slender HSS columns using CFRP sheets increased both the axial strength and stiffness substantially.


The progressive aging and deterioration, combined with the requirements for higher load capacity, results in an increase in the number of bridges which do not meet the current code standards. Conventional retrofitting techniques for steel members, in general, involve bolting or welding additional steel plates. These techniques have a number of shortcomings, including the added self weight of steel plates, the installation time, and the need for an elaborate and expensive shoring system. Fiber-reinforced polymers (FRP) are rapidly gaining acceptance as an effective material for retrofitting a wide range of structures, particularly due to their excellent corrosion resistance and fatigue properties (Hollaway and Cadei, 2002 and Shaat et al., 2004).

The majority of applications of these materials, so far, have been flexural members such as beams and bridge girders where bonding of FRP on the tension side is very effective in upgrading the structural performance of such members. Nevertheless, the failure mode of axially loaded steel members such as columns or truss members with medium to high slenderness ratios is generally governed by overall buckling, which is essentially a flexural problem. Therefore, bonding FRP sheets or strips of adequate stiffness in the longitudinal direction of slender members could be quite effective.

An experimental study was performed (Shaat and Fam, 2006) to investigate the effect of adhesively bonded carbon-FRP (CFRP) sheets on the behaviour of axially loaded HSS columns. The column’s cross sectional shape is shown in Fig. 1(a) and the column length was 2380 mm, such that slenderness ratio was 68. In slender columns, where overall buckling governs, it is anticipated that the ultra-high modulus CFRP sheets would contribute to the flexural stiffness of the column, and at large deflections, may resist some tension on the outer surface. It was shown experimentally that CFRP sheets have indeed increased the columns’ strengths by up to 23 percent. The study, however, revealed the sensitivity of axially loaded slender columns to their inherent geometric out-of-straightness and alignment (imperfections), which affects both the ultimate strength and stiffness of the specimens. Residual stresses are also an important factor, which can affect the behaviour of cold-formed sections. While the major parameter intended in the experimental investigation was the effect of number of CFRP layers, it is believed that geometric imperfections have also varied among the specimens. As such, no specific correlation could be established between the amount of strength gain and the amount of CFRP.


M. Pandey et al. (eds), Advances in Engineering Structures, Mechanics & Construction, 227-238. © 2006 Springer. Printed in the Netherlands.

A theoretical study including finite element analysis and analytical modeling is being developed by the authors to assess the exclusive contribution of CFRP sheets to the strength and stiffness of slender HSS steel members and understand their behaviour. The objective of this paper, which is the first phase in the analytical program, is to introduce a simplified analytical model to predict the load versus axial and lateral displacement responses of axially loaded HSS members retrofitted with CFRP. It is anticipated that further refinement of this approach will be needed in the future. The model is verified using the experimental results and is used to uncouple the effect of geometric imperfections from the effect of CFRP retrofitting. In the following sections, a brief summary of the experimental research program is given, followed by a detailed description of the analytical model. The model verification, using the experimental load-lateral displacement, load-axial displacement and load-axial strain responses, is then presented. Finally, the parametric study is presented.