Strengthening of composite beams with external tendons using a rating factor equation

Abstract

The prestressing technique using external tendons can be considered an effective method of strengthening bridges that are deteriorating due to increasing overloading and progressive structural aging. This technique is not only easy to perform but it is also convenient to maintain the tendon because it is exposed in the air; it is a practical and cost-effective strengthening method (Troitsky et al. 1989). The advantages of the technique are the enlargement of the elastic range of behavior, the increment of the ultimate capacity, and improvement of the fatigue and fracture strength (Saadatmanesh et al. 1989a, b, c). Therefore, prestressing is applied to the reinforcement of many concrete girders (Harajli 1993, Ng 2003). In order to achieve an more economical and effective strengthening, design variables such as configuration of tendon, the number of tendons and the initial tendon force have to be determined effectively to reinforce an existing bridge with external tendons. In this paper, external tendons are used for strengthening of steel-concrete composite beams. An analytic expression for the increment in the initial tendon force is derived using the virtual work method for configurations of straight and draped tendons under external loads. Considering the initial tendon force and its increment under external loads, a new rating factor equation is introduced. A systematic procedure has been developed to calculate the number of tendons and the initial tendon force using the proposed rating factor equation. A design example is given to demonstrate the effect of the proposed equation on increasing load-carrying capacity in existing steel-concrete composite bridges. Stress distribution in any cross section of a composite beam strengthened with external tendons under each stage of loading is calculated. Dead load and live load cause compressive stresses in the concrete slab and top flange, and tensile stress in the bottom flange of the simply supported beam. Tendon force causes compressive stresses in all cross section of the composite beam; the negative moment due to tendon force causes compressive stresses in the upper cross section and tensile stresses in the lower cross section of the neutral axis. Under live loading, there is an increment in the initial tendon force. Accordingly, the increment of tendon force causes stresses in the cross section of the composite beam. An analytic expression for the increment in the initial tendon force for configurations of straight and draped tendons under external loads is determined using the virtual work (Saadatmanesh et al. 1989c, Troitsky 1990). External loads used are truck load (DB) and lane load (DL) that are prescribed in KHBS (2005). The finite element program, LUSAS (2005), was performed to compare with the virtual work method. The results show little difference between the two methods. Considering the initial tendon force and its increment under external loads, a new rating factor equation is introduced. In the allowable stress method, in-service bridges strengthened with external tendons are evaluated by a rating factor equation as follows: RF′ = f a - (fDL + fT)/ (fLL + f ΔT)(1 + i) where fa = allowable stress of the member; fDL = stress due to dead load; fLL = stress due to live load; i = impact factor (15/(40 + span length)); fT = stress due to tendon force; and fAT = stress due to increment of tendon force. A systematic procedure has been described to determine both the number of tendons and the initial tendon force using the proposed rating factor equation after the material and configuration of the external tendon are selected. A design example of a plate girder bridge constructed in 1973 with a span of 40 m was selected for enhancing load carrying capacity by introducing straight external tendons under the bottom of the lower flange. The existing bridge was originally designed for DB-18 truck loading. The number of tendon and initial tendon force are calculated using the proposed rating factor equation for upgrading the bridge that have a target rating factor of 1.2 for DB-24 truck loading. The effects of the proposed equation for increasing load-carrying capacity in existing steel-concrete composite bridge are summarized as follows: (1) the stress in the lower flange due to increment in the initial tendon force is 5.1% ofthat due to initial tendon force; (2) the rating factor considering the increment in the initial tendon force is 1.20, whereas it is 1.18 if the increment is neglected. In this study, the increment in the initial tendon force for configurations of straight and draped tendons under external loads are derived in an analytic expression. And a systematic procedure has been described to calculate the number of tendons and the initial tendon force using the proposed rating factor equation.