## 5 Non-Uniform In-Depth Residual Stress Field of the Orthotropic Bridge Deck
### Residual Stress Distribution of the Orthotropic Steel Deck  
The residual stresses from the experimental measurements are implemented in a finite element model and the results are shown in Section 5.2. These residual stress results are more representative since the finite element model makes use of an elastic-plastic material model which is more realistic than the elastic behavior of the experimental setup. A general residual stress distribution is established in relation to the distance to the weld which can be compared with Figure 12. Also here, a distinction is made between compressive and tensile residual stress zones and both the longitudinal and transverse direction are considered. The residual stress values assigned to these zones are calculated by averaging the residual stresses of the strain gauge rosettes present in the considered zone. This residual stress distribution is shown in Figure 16a for the longitudinal direction and Figure 16b for the transverse direction. Figure 15: Comparison of residual stress distribution on the longitudinal stiffener between ASTM and the 3D model in the longitudinal (**a**) and transverse (**b**) directions. In the longitudinal direction, there is a tensile and a compressive residual stress zone present on top of the deck plate. The tensile zone has a value of 51% of the yield strength (\(\mathrm{f_{y}}\)) while the compressive zone reaches the yield strength. For the bottom of the deck plate, there is a tensile residual stress zone of 0.74 \(\times\)\(\mathrm{f_{y}}\) present in the longitudinal direction. On the stiffener, there is a small tensile yield stress zone present near the weld which is followed by a compressive and a tensile zone. For the transverse direction, two tensile zones and a compressive zone are recognized on the top of the deck plate. In between the two welded webs of the stiffener, an average tensile residual stress of 133 MPa exists, this corresponds to 56% of the yield strength. Near the weld location on the deck plate, there is a compressive zone with an average residual stress equal to 0.23 \(\times\)\(\mathrm{f_{y}}\). Another tensile residual stress zone with an average value of 53% of the yield strength exists at the right-hand side of the weld region on the deck plate. On the bottom side of the deck plate, an average tensile residual stress equal to 0.88 \(\times\)\(\mathrm{f_{y}}\) exists. For the longitudinal stiffener, there is a small tensile yield stress zone present near the weld which is followed by very small compressive residual stresses, close to zero. Further away from the weld, there is a tensile residual stress zone of 80% of the yield strength present. When the results of the finite element modeling (Figure 16) are compared with the residual stresses from the experimental measurements (Figure 12), a general residual stress distribution of the orthotropic steel deck can be established. The FEM results are more representative since it makes use of a more realistic material model. First the results of the longitudinal direction are discussed. There is a compressive zone present between the two welded webs of the stiffener on top of the deck  
Figure 16: Residual stress distribution of the orthotropic steel deck according FEM for the (**a**) longitudinal and (**b**) transverse directions. plate. This compressive zone is equal to half of the material's yield strength according to the FEM results. This is 10% smaller compared to the results from the experimental setup. Near the weld region on top of the deck plate, there are tensile yield residual stresses present. On the bottom side of the deck plate, there is a tensile zone of 74% of the yield strength present for the results from the finite element modeling. This is 24% larger than the value from the experimental results. For the stiffener, there is a small tensile yield zone present near the weld which is followed by a small compressive zone of 23% of the yield strength.