# Nonlinear Stiffness of Semi-Fixed Dowel Joints in Semi-Integral Bridges
## 4 Test Results
### Strain of Steel Dowel  
The measured strains on both sides of the steel dowel are basically closed in values. Therefore, only one side of the steel bar was analyzed for tensile strain gauge, as shown in Figure 9. From Figure 9 of the loading displacement-steel bar strain curve of B-R1, it can be seen that the strain of steel bar can be divided into two stages: elastic stage and plastic stage. After the loading displacements of 8 mm, 10 mm and 12 mm, respectively, the steel bar began to yield and entered into plastic deformation.  
By comparing the influences of different thicknesses of rubber sleeves in Figure 9a, it can be seen that the strain of steel bar increased with the decrease of the wall thickness of the rubber sleeve. The reason is that, the smaller the wall thickness of rubber sleeve, the larger the rotation angle and flexural-tensile strain of the steel bar. By comparing JD2 and JD4 with different thicknesses of rubber pads in Figure 9b, it can be seen that the two curves are almost the same, indicating that the thickness of the rubber pad has little influence on the stiffness of the steel bar within the range of test parameters, which can be ignored.  
Figure 10 shows the relationship of loaded displacement versus strains of B-R1, B-R2 and B-R3 on the steel dowel in specimen JD2, where strains of B-R4 are not presented due to too small values. The steel strains decreased from top to bottom, where the largest strains came from B-R1 at the location of the rubber pad, which were in the elastic range at the first loading stage, and then entered into the plastic range. However, the strains of B-R2 and B-R3 buried in the concrete block were always in the elastic stage.  
Figure 8: Loading displacement–rotation angle curve of semi-fixed dowel joint. (**a**) Thickness of rubber sleeve. (**b**) Thickness of rubber pad.  
Figure 9: Loading displacement–steel bar strain curve of B–R1. (**a**) Thickness of rubber sleeve. (**b**) Thickness of rubber pad.  
Figure 11 shows the relationship of loaded displacement versus strains of B-R2 and B-R3 on steel dowels in specimens of JD1, JD2 and JD3, respectively, to investigate the influence of the thickness of the rubber sleeve. For the same loaded displacement, the strains of both B-R2 and B-R3 from largest to smallest appeared in the specimens from JD1 to JD2 to JD3.  
In the whole loading process, the steel dowels can be divided into two stages. At the first stage, strains increased linearly with the load, and the main deformation of the steel dowel was bending. Then, the bending deformation concentrated on the gap (occupied by the rubber pad) between the upper and bottom blocks, and the steel dowel began to yield. The strains of the steel dowel embedded in the bottom concrete block were all in elasticity, and their values decreased with the deeper buried location.  
Based on the above analysis, the mechanical properties of dowel joints are significantly affected by the wall thickness of the rubber sleeve, but less affected by the thickness of the rubber pad. Therefore, if the deformation of 10 mm in the longitudinal direction caused by the maximum temperature effect of the beam is taken as the design allowable value, the wall thickness of the rubber sleeve should not be less than 40 mm to ensure that the dowel joint behaves in the linear elastic range for the case studied.