## 1 Introduction  
Box girder cracking and mid-span deflection are common problems of prestressed concrete (PSC) continuous box girder bridges (CBGBs) around the world [1; 2; 3; 4; 5]. Traditionally, these problems have been effectively treated by pasting carbon fiber cloth, applying steel plate, increasing sectional size and adding prestressing tendons. However, the traditional methods vary greatly in enhancement effect, when the PSC-CBGB has a long span and serious problems [6]. The cable-stayed system (CSS) is a novel active reinforcement method that improves the shear capacity and mid-span height of the girder [7; 8]: on each side of the pile foundation, a steel joist is added in the tower laterally to the lower part of the girder, the steel joist is joined to the girder by a connection in the anchorage zone at the bottom of the girder and stay cables are anchored from the tower to the steel joist. In this way, cable forces are transmitted from the girder via the joist and the connection. The steel joist and the girder are generally connected tightly with both bolts and welds or with high-strength bolts [9; 10; 11; 12; 13]. The bolted-welded connection faces two defects: on the one hand, the connection is difficult to construct or dismantle, and poor in reliability. Although a welded connection is stronger than bolted connections, the quality of it is unreliable, especially when it is not factory-made. Compared with a welded connection, a bolt connection has a quick construction speed and requires fewer skilled workers. From an economic and performance perspective, all of these give bolted connections a distinct advantage over a welded connection [9]; on the other hand, each connection has a unique stiffness and ductility, and complex mechanical properties [14]. The effects of these demands are often compounded by the sensitivity to fracture typical welded connection details. Even if the welds are properly executed, these strain demands will lead to tearing of the base metal in proximity of the weld access hole. This results in low rotational ductility and poor connection performance under large cyclic load reversals [15]. These defects are made up of a high-strength bolted (HSB) connection, which has been widely applied in bridges and other steel structures [16; 17]. Based on the load transfer mode, the HSB connections can be divided into the bearing type and the friction type. For the bearing type HSB (BHSB) connection, the shear force is transmitted by the wall pressure and the screw shear. Despite its high ultimate bearing capacity, the BHSB connection is not applicable under dynamic load or fatigue load. For the friction type HSB (FHSB) connection, the shear force is transmitted by the friction between the contact surfaces. Compared with a BHSB connection, high tensile strength in flexure and tensile behaviors, high performance in fatigue loading due to the reduced stress range, avoidance of bolt loosening to vibration, etc. [18; 19]. The FHSB connection has been extensively adopted for the connections in bridges [20; 21]. As shown in Figure 1, FHSB connections have been employed for the CSS enhancement of Dongming Yellow River Highway Bridge. In engineering practice, many bolts are implanted to provide the connection with required shear capacity according to the _Standard for Design of Steel Structures_ (GB 50017-2017) [22]. However, the relevant design specification and research results do not involve the design method of the anti-slip bearing capacity for FHSB connections under combined shear and compression. The friction load of such a connection depends heavily on the pressure from the cable force and the friction between the contact surfaces induced by the axial force of the bolt. In our previous research, a scaled model test was carried out on the connections in the anchorage zone of the Dongming Yellow River Highway Bridge. The results show a positive correlation between cable force, the pressure on the contract surfaces and the loss of shear force and the clamping force of the bolt.