# Low-Cost Assessment Method for Existing Adjacent Beam Bridges
## 2 Influence of Damage Joints on LLDFs Based on the Modified Hinge Connected Beam Method
### Influence of Damaged Joints at Different Locations on the LLDF
The closer the joint is to the beam with the external load applied on, the greater the influencing extent \(\lambda_{i}\) is. Furthermore, after calculation and analysis of \(\lambda_{i}\) of ARHB bridges with different \(\gamma\) and different total number of beams, it can be concluded that the influencing extent \(\lambda_{i}\) of joint-\(i\) on the LLDF of beam-\(j\) decreases approximately exponentially with an increasing number of beams between joint-\(i\) and beam-\(j\);
2. When damages occur in joints, for the adjacent beams on both sides of the damaged joint, the LLDF of the beam closer to the external load will be larger;
3. When the external load \(p=1\) loads onto an interior beam-\(k\), for damaged joints with the same distance from beam-\(k\), the damaged joint on the side with more beams has the larger impact than the damaged joint on the side with fewer beams on \(\eta_{kk}\). For example, for an ARHB bridge with \(n=7\) beams, when the external load \(p=1\) loads onto beam-2 and all joints have the same damage degree, the influencing extent \(\lambda_{2}\) from large to small is \(\lambda_{2}>\lambda_{1}>\lambda_{3}>\lambda_{4}>\lambda_{5}>\lambda_{6}\). When the external load \(p=1\) is loaded onto beam-3, the influencing extent of each joint is \(\lambda_{3}>\lambda_{2}>\lambda_{4}>\lambda_{1}>\lambda_{5}>\lambda_{6}\);
4. For ARHB bridges with the same number of beams, it takes different bending and torsional parameter \(\gamma\) values to calculate the LLDFs. Under the same conditions of the external load position, the number of the adjacent rectangular hollow beams, and the damage degree of the joints, the joint with larger \(\gamma\) has smaller influencing extent \(\lambda_{i}\) on LLDFs. For example, consider two ARHB bridges A and B with \(n=7\) beams and beam-2 loaded, where the bending and torsional parameter \(\gamma\) of bridges A and B are \(\gamma_{A}=0.1\) and \(\gamma_{B}=0.05\). Then, the influencing extent \(\lambda_{i,A}\) of bridge A is smaller than the influencing extent \(\lambda_{i,B}\) of bridge B, i.e., \(\lambda_{i,A}<\lambda_{i,B}\). The calculation process will not be repeated. Feasibility of the Modified Hinged Connected Beam Method on ARHB Bridges with Diaphrags and Transverse Prestressed Ties  
In the United States, Japan, and South Korea, most ARHB bridges are equipped with diaphragms and transverse prestressed reinforcements. For such bridges with reliable transverse connections, accurate LLDFs cannot be obtained by the hinge connected beam method. However, when damage occurs in joints so that the transverse connections of the ARHB bridge become weak, it is feasible to utilize the hinge connected beam method to qualitatively analyze variations in the LLDFs to evaluate the degradation degree of bridge-bearing capacity. According to _FIB bulletin 43 Structural connections for precast concrete buildings_[28], there are three transmission mechanisms of shear force between adjacent rectangular hollow beams of ARHB bridges: (1) adhesion or friction at joint interfaces, (2) shear-key effect at indented joint faces, and (3) dowel action of transverse steel bars, pins, and bolt crossing joints. When joints are not cracked, shear force can be transferred by the adhesive bond at joints and the mechanical interlock of shear keys. When cracks arise in joints, the shear force can be transferred by the mechanical interlock of shear keys, dowel action, and the friction enhanced by the pullout resistance of tie bars placed across joints. In order to explore the contribution of different transmission mechanisms to shear-force transfer, [PERSON] [29] established a finite-element model with two adjacent rectangular hollow beams connected through a partial-depth shear key.