## 1 Introduction  
A two or multiple-I girder system has two or more steel I girders connected with diaphragms and composite with a concrete deck using shear studs. The steel girders are in tension and the concrete deck is in compression in the regions of positive moments (i.e., the sagging region) under vertical loads, which makes good use of material advantages of steel and concrete. While within the regions of negative moments (i.e., the hogging regions), the concrete deck is in tension under vertical loads and the tensile stress may increase due to concrete shrinkage and creep. Concrete cracking is a big issue for the hogging regions [1; 2; 3; 4; 5]. High performance concrete with larger tension strength can be used [6] but the cost is substantial. One common way to make concrete deck in compression with initial compressive stress to overcome the tensile stress induced by live load. One way is to arrange prestressed tendons in the concrete deck in the hogging regions. The prestressing compressive stress in the concrete is to overcome any additional tensile stress induced by vertical loads and additional second order effect of shrinkage and creep. [PERSON] et al. found that using external tendons could be considered an effective method of strengthening bridges deteriorating due to overloading [7]. [PERSON] and [PERSON] proposed a new prestressed concrete-steel composite girder, which uses pretensioned concrete bottom flange to provide initial compressive stress in the concrete deck [8; 9]. [PERSON] et al. investigated the behaviour of reinforced concrete strengthened with externally prestressed tendons and they found that the basalt fibre reinforced polymer (BFRP) was feasible to strengthen the beam behaviour [10]. Except using tendons to introduce compressive stress in concrete deck, some construction strategies are used. Temporary loads are sometimes applied to the sagging regions (the regions of positive moment) before the concrete cast in the hogging regions. In this way, the compressive stress is induced in the hogging regions after the hogging region concrete is hardened and the temporary loads are removed. [PERSON] et al. and [PERSON] et al. studied the behaviour of composite bridges considering different construction processes and they found that the construction sequence could affect the tension stress in concrete deck in the hogging regions [11; 12]. [PERSON] et al. analysed the jacking-up method to prestress the concrete deck and they found that jacking-up the interior support could efficiently introduce compressive stress in the concrete deck in the hogging regions to overcome the tensile stresses induced by shrinkage and live load [13]. Either prestressed tendons or construction strategies can introduce initial compressive stress in the concrete deck to avoid or reduce concrete cracking in the hogging regions. However, for the preconnected composite girder systems, the prestressed forces are applied to the whole composite section and mostly are applied to the steel section. [PERSON] et al. and [PERSON] et al. studied the behaviour of steel-concrete composite girders with prestressing tendons before concrete deck connected to steel girders [14; 15]. [PERSON] et al. studied the behaviour of a continuous composite box girder with prefabricated prestressed concrete slab in the hogging region [16]. [PERSON] et al. studied the long-term behaviour of the composite box girders with post connected prestressed concrete deck and the research shows the prestressed concrete deck before connected with steel box girders can improve concrete shrinkage [17]. In recent years, a significant amount of continuous twin-I girders with precast concrete deck are built in China. The cracks in the hogging regions are usually controlled by the crack width control [18; 19; 20]. However, crack width control is not an efficient way to improve the behaviour in the hogging regions. The way to arrange prestressed tendons in concrete deck in the hogging regions is used for twin-I girders with post connected prestressed concrete deck.