# Influence of Construction Joint and Bridge Geometry on Integral Abument Bridges
## 4 Bridge Response Results
### Girder Axial Force  
Girder axial force with respect to AB joint stiffness, backfill height, and bridge length is presented in Figure 11a,c. Both tensile and compressive axial forces of steel (STL) and PSC girders were significantly affected by the following factors, in order of importance: bridge length > AB joint stiffness > backfill height. Bridge length significantly influenced girder axial forces. Steel (STL) and PSC girders exhibited clear differences in response to the bridge length parameter, but showed similar responses for AB joint stiffness and backfill height. Bridge length influence on girder axial force exhibited a highly nonlinear trend. Bridge length and girder material determine the amount of bridge thermal movement. Thus, bridge length is highly correlated to the girder axial force. However, owing to the nonlinear boundaries provided by backfills and supporting piles, girder axial forces were not linearly proportional to bridge length, but tended to increase as bridge length increased. During bridge contraction, girder tensile axial forces of 61.0, 121.9, and 182.9 m PSC and steel IABs varied 7.5, 4.8, and 2.2 times higher and 1.2, 3.0, and 1.8 times higher than those of the 30.5 m bridge, respectively. During bridge expansion, girder compressive axial forces of 61.0, 121.9, and 182.9 m PSC and steel IABs varied 3.1, 2.8, and 1.3 times higher and 1.1, 2.0, and 1.7 times higher than those of the 30.5 m bridge, respectively. Once a bridge expands, the nonlinear boundaries may yield at a certain point, and then the bridge expands easily and girder axial forces decrease. Although a steel girder has a larger thermal expansion coefficient, PSC girder IABs, owing to time-dependent effects, exhibited earlier yielding at L = 61.0 m, while steel girder IABs yielded at L = 121.9 m. Both axial forces of steel and PSC girder IABs increased up to the yielding of soil boundaries and then decreased as bridge length increased. AB (abutment to backwall) joint stiffness significantly influenced compressive girder axial forces. Compressive girder axial forces showed a tendency to increase as AB joint stiffness increased. As AB joints and backfill height become stiffer and higher, the compressive girder axial forces increased. This is because stiffer AB joints induce the abutment to displace by longitudinal translation rather than rotation, which results in larger backfill  
Figure 12: Construction joint opening cases: (**a**) short abutment-short girder (expansion), (**b**) short abutment-long girder (expansion), (**c**) high abutment-long girder (expansion), (**d**) short abutment-short girder (contraction), (**e**) short abutment-long girder (contraction), and (**f**) high abutment-long girder (contraction). resistance. Abutment translation is resisted by the full backfill height, while abutment rotation is resisted by the top portion of the backfill. This trend was clear in steel girder IABs because PSC girders had time-dependent effects. However, tensile forces were not significantly influenced by AB joint stiffness because bridge contraction is mainly related to pile rotational stiffness, which is constant in this study. During bridge expansion, girder compressive axial forces of PSC and steel IABs with PA (Pennsylvanian) standard and rigid AB joint varied 1.2 and 1.3 times higher and 1.3 and 1.5 times higher than those of IABs with hinged AB joint, respectively. During bridge contraction, girder compressive axial forces of steel IABs with PA standard and rigid AB joint varied 1.1 and 1.3 times higher than those of IABs with hinged AB joint, respectively, while PSC IABs produced similar girder tensile forces regardless of AB joint stiffness. Backfill height influenced compressive axial forces as the AB joint became stiffer. All girder moments showed tendencies to increase as backfill height increased. This is because increasing backfill height increases backfill passive pressure.