# 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
By comparing the differential deflections between adjacent beams of the model with filled transverse post-tensioning ducts and the model with non-filled ones, it can be concluded that dowel action is the main shear force transmission mechanism when the concrete and reinforcements are not yielding, and that shear force transmission performance is not highly affected by variations in the amount of transverse post-tensioning. [PERSON] [30], [PERSON] [31], and [PERSON] [32] have all studied the LLDFs of ARHB bridges before and after external transverse prestressing. It can be concluded that the LLDFs of ARHB bridges with external transverse prestress applied are approximately equal to the LLDFs calculated by reducing the bending and torsional parameter \(\gamma\) of the bridge without external transverse prestress. [PERSON] [33] and [PERSON] [34] analyzed the influence of the installing end and intermediate diaphragms on the LLDFs of fabricated hollow-beam bridges. By comparing the LLDFs of the bridges with and without diaphragms, it can be seen that the LLDFs of the bridge with diaphragms are approximately equal to the ones calculated by reducing \(\gamma\) of the bridge without diaphragms. According to the analysis of the above research data, when no dowel action is provided by transverse prestressed ties, the effect of transverse prestress and diaphragms can be regarded as reducing \(\gamma\) to obtain more uniform LLDFs. For longitudinal prestressed concrete beams, the static flexural rigidity, \(EI\), increases with rising post-tensioning force magnitude [35]. Similarly, it is reasonable to deem that the torsional rigidity, \(GI_{T}\), of transversal prestressed adjacent rectangular hollow beams increases with rising transversal post-tensioning force magnitude. Furthermore, the bending and torsional parameter \(\gamma\) decreases with an increase in \(GI_{T}\). This assumption is verified by [31; 32; 33]. For most ARHB bridges, there is a high risk that the interfaces between shear keys and beams crack due to the load actions from temperature gradient and traffic, and instability workmanship quality. Cracked interfaces slip slightly under the action of shear force, and the resulting small deformation will cause dowel action to counteract the slip and shear force [36]. High concentrated forces are generated in the grouting where the crosswise reinforcements are placed, and considerable tensile stresses may appear in the rest area of the grouting around the crosswise reinforcements [28]. The grouting in the transverse post-tensioning ducts is more likely to fail by the concentrated forces and tensile stresses caused by the dowel action than the concrete in the beam. Therefore, when cracks and leakage occur at joints, it can be considered that the grouting in the transverse post-tensioning ducts yields at the joint interface. In this case, only when sufficient displacement occurs at the joint can sufficient dowel force be generated to transfer the shear force [36]. However, for small-to-medium-span bridges, the deflection caused by the live load is too small to generate sufficient dowel force [37]. Therefore, for ARHB bridges in service with cracks and leaks at joints, the dowel action caused by transverse prestressed reinforcements can be considered to have failed, and the lateral force transmission mechanism of the bridge will be similar to that of ARHB bridges without diaphragms and transverse prestressed ties. The effects of the joint damage degree on LLDFs can be analyzed by a modified hinge connected beam method to assess the degradation degree of ARHB bridge-bearing capacity.