# Effect of Prestress Levels and Jacking Methods on Friction Losses in Curved Prestressed Tendons
## 1 Introduction  
Prestressed concrete (PSC) is used extensively in bridges, multistory buildings, and many other important parts of today's modern infrastructure. In particular, prestressing systems are essential for long-span bridges that use concrete as the main material. Prestressing systems are generally divided into pre- and post-tensioning methods [1]. In the post-tensioning methods, prestressing tendons pre-mounted in a sheath are extended using tensioning devices and fixed to anchorages pre-installed at the ends of the concrete members. Then, the prestress force is transferred to the concrete. However, the tensioning force at the prestressing tendon inevitably decreases during or after prestressing, i.e., a prestress loss occurs. The losses at the prestressing tendon can be divided into instantaneous losses that occur during prestressing and time-dependent losses after prestressing [2]. The instantaneous losses that occur in PSC girders manufactured by the post-tensioning method are caused by three factors: creep and shrinkage of concrete, and relaxation of the prestressing steel. An exact determination of the magnitude of the time-dependent losses is not feasible because they depend on a multiplicity of interrelated factors. Thus, many empirical methods are used to estimate time-dependent losses. The instantaneous lossesare caused by three factors: anchorage slip, friction between the prestressing tendon and sheath, and elastic shortening of concrete [3]. Among these factors, the friction loss has the greatest effect on the initial prestress force of the tendon [4]. The friction loss can affect even the midspan of the girder, whereas the loss resulting from anchorage slip is limited to the vicinity of the end anchorage. The elastic shortening of concrete may cause substantial losses. In a post-tensioning system, concrete is elastically shortened during the jacking process, but this is compensated for because the prestressing tendon is tensioned until the required prestress force is obtained. Therefore, there are almost no losses from elastic shortening to be allowed for at jacking. Owing to these instantaneous losses, the prestress force of the tendon is not constant and is smallest at midspan. It is critical to determine the initial force of the prestressing tendon accurately in order to achieve initial usability and stability of PSC structures. The service load capacity of the structure may not besufficient if the introduced prestress force is greatly reduced by instantaneous losses, particularly the friction loss at midspan, which has the greatest bending moment. Therefore, the friction loss has higher importance than the other instantaneous losses, and the improved accuracy of friction loss models will assist structural engineers designing PSC structures. Many researchers have studied the instantaneous losses of steel tendons, but most of them have focused on the anchorage slip [5] and elastic shortening of concrete [6]. Furthermore, almost all of the test specimens used in the previous studies were limited to small-scale concrete members [7; 8; 9]. There are a few reports on friction loss tests using full-scale concrete girders. [PERSON] [10] and [PERSON] [11] conducted friction tests using 22.3 m concrete beams, and eight 54 mm galvanized steel ducts were used in each beam. The beams used by [PERSON] weremonolithically fabricated, whereas those used by [PERSON] were segmentally fabricated. [PERSON]'s tests were conducted using unoiled tendons and tendons coiled with four emulsifiable oils for corrosion protection and lubrication, selected from a preliminary test performed by [PERSON] et al. [12]. [PERSON] tests, on the other hand, were conducted using unoiled tendons and tendons oiled with Wright 502 (a type of emulsifiable oil). Based on the results of these tests, both researchers reported that the unoiled tendons showed almost no increase or decrease in friction coefficient, whereas the oiled tendons showed an 8-25% decrease. [PERSON] et al.