Effects of Partial Depth End Diaphragm on Elastic Shear Distribution

One end of the laboratory bridge was constructed with a partial depth end diaphragm placed simultaneously with the bridge deck and connected to the girder with dowels placed transversely to the girder through the top flange and web. Validation of an FE modeling technique considering an end diaphragm was discussed in Section 5.3.2.4 and data from laboratory testing corroborated well with FEM results. The impact of the end diaphragm on lateral shear distribution was studied in depth using the FEM of the laboratory bridge and results are presented in this section. Results in the following discussion were generated with the rigid diaphragm-to-girder connection as discussed in

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Section 5.3.2. This connectivity was selected to eliminate the concrete penetration that was allowed in the other FEM validation connectivity cases (free and pinned).

Previous research has been done to investigate the effects of end diaphragms and intermediate diaphragms on shear distribution. Bae and Oliva (2012) specifically considered the effect of end diaphragms on shear load distribution from overload trucks and reported that end diaphragms increased shear distribution factors by up to seven percent compared to bridges without an end diaphragm. Meaning, the most heavily loaded composite girder section (including the deck) may carry more shear and distribute less to adjacent girders. Furthermore, conflicting numerical analysis results were presented by Huo et al. (2003) and Puckett et al. (2007) in their studies of Bridge No. 24, which was a prestressed concrete girder bridge described by Huo et al. Results from Huo et al. (2003) indicated that abutment support diaphragms caused a decrease in the shear distribution factor in conflict with the study done by Puckett et al. (2007) that indicated abutment support diaphragms slightly increased the shear distribution factor.

To investigate the effect of the partial depth end diaphragm on shear distribution in this study, FEM results are compared for the end of the laboratory bridge with no end diaphragm (LBESE) and the end of the bridge with an end diaphragm (LBESW). The results were generated from two load cases at 4dv, utilizing either the north (N) actuator

over interior girder G3 or the south (S) actuator over exterior girder G4. Shear forces in the composite section (including shear in the deck) were collected at transverse cross sections corresponding to 0.5dv, 1dv, 2dv. Shear forces were obtained from the FEM nodal forces

using methods discussed in Section 3.3.2 and a composite deck width equal to the girder spacing as discussed in Section 5.2. The results shown in Table 5-28 from loading above both the interior and exterior composite girder indicated that the percent of applied shear would be larger if load was applied closer to the end of the bridge with the diaphragm compared to the end of the bridge without the diaphragm. Results indicated that approximately 4 percent more applied shear was carried in the exterior composite girder with an end diaphragm present and approximately 6 percent more applied shear was carried in the interior composite girder with an end diaphragm present. Each cross section along the length had similar percent increases. An increase of 4 to 6 percent applied shear is not

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significant, but it does indicate that the end diaphragm acts to keep shear in the loaded composite girder rather than distributing it to adjacent composite girders.

To further examine the effect of the end diaphragm, shear force results from the validated FEM were tabulated separately for each bridge girder (no deck) and the corresponding composite deck section (no girder). However, to amplify the effect of the diaphragm and study the upper bound, the FE model was rerun using the fixed partial depth end diaphragm after increasing the modulus of elasticity of the diaphragm by a factor of 10. This modification also increased the shear modulus by a factor of 10 because an isotropic material model was used for the diaphragm concrete. Results are presented in Table 5-29 for the laboratory bridge quadrant that contained no end diaphragm and in Table 5-30 and Table 5-31 for the quadrant that contained an end diaphragm. Results in Table 5-30 were generated using the fixed partial depth end diaphragm; Table 5-31 shows the results generated using the stiffened end diaphragm. The left set of tables shows the percent of applied shear generated for the girder cross section only and the right set of tables shows the percent of applied shear for the bridge deck only. Addition of the girder shear and deck shear in Table 5-29 yields results from LBESE (without an end diaphragm) in the left half of Table 5-28; addition of the girder shear and deck shear in Table 5-30 yields results from LBESW (with an end diaphragm) in the right side of Table 5-28.

Comparison of the percent of applied shear for the exterior girder with no end diaphragm, with the as-built end diaphragm, and with the stiffened end diaphragm (highlighted in green in the left side of Table 5-29 through Table 5-31) indicate that as the end diaphragm stiffness was increased, the percent of applied shear at 0.5dv near the end

of the span decreased from 69 to 68 percent while the percent of applied shear at 2dv near

the loading point increased from 71 to 79 percent. Furthermore, the opposite trend was evident in the percent of applied shear calculated for the exterior girder composite deck as the stiffness of the end diaphragm changed (highlighted in orange in right side of Table 5-29 through Table 5-31). As the end diaphragm stiffness increased, the percentage of shear that the bridge deck carried increased from 21 to 30 percent at the end of the girder near the support. The same trend was revealed in a comparison of the percent of applied shear for the interior girder (highlighted in blue in the left side of Table 5-29 through Table 5-31). Results indicated that as the end diaphragm stiffness was increased, the percent of applied

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shear carried by the girder at 0.5dv near the end of the span decreased from 51 to 50 percent

while the percent of applied shear carried by the girder at 2dv near the loading point

increased from 58 to 68 percent. Similar to the exterior girder, the opposite trend was evident in the percent of applied shear calculated for the interior girder composite deck (highlighted in gray in right side of Table 5-29 through Table 5-31). As the end diaphragm stiffness increased, the percentage of the applied shear carried by the bridge deck increased from 18 to 32 percent at the end of the girder near the support.

Results from the validated FEM indicated that the end diaphragm increased the amount of shear force in the girder near the point of applied load but slightly decreased the amount of shear force in the girder near the end of the span when load was applied over the girder. However, results in Table 5-28 indicated that the distribution of the percent of applied shear did not change significantly (6 percent or less) amongst composite girders; the amount of shear force carried in the deck and girder changed. For this length structure and loading scenario, the end diaphragm increased the amount of load carried to the end of the span through the bridge deck rather than through the girder. This behavior, observed with results from the upper bound, stiffened diaphragm case, indicated that more shear remained in the deck until the very end of the span, near the reaction, and transferred to the support through the end diaphragm or the girder web at the very end of the span. In this region, the girder has additional shear capacity because it experiences vertical compression due to the load and reaction. This conclusion assumed a fixed condition connecting the end diaphragm to the girder web and was also drawn from a single bridge with a specified length and an upper bound end diaphragm stiffness (10 times the measured Young’s modulus).

Cai et al. (2002) and Cai and Shahawy (2004) indicated that the as-built diaphragm stiffness in bridges is uncertain due to possible concrete cracking and weakness of the diaphragm-to-girder connection. Cracking at the end diaphragm-to-girder connection was seen in this project during field testing, shown in Figure 5-12, and during inelastic laboratory testing as discussed in Section 5.4. End diaphragm cracking was also observed during field visual inspection conducted by Dereli et al. (2010). These issues create many unknowns related to the effect of end diaphragms on load distribution of in-service bridges.

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In summary, the end diaphragm acted to increase the amount of shear carried to the end of the span via the deck rather than the girder; however, the shear force in the short shear span carried by the composite girder section increased by 4 to 6 percent when the end diaphragm was present. It was shown to be slightly inaccurate to ignore the effects of an end diaphragm when considering elastic bridge behavior in prestressed concrete girder structures, but neglecting the effects of an end diaphragm may still be warranted to increase the speed and ease of modeling a structure using FEM without sacrificing a significant amount of accuracy. Additional discussion related to the effects of an end diaphragm are presented in Section 5.4.3 related to testing of the laboratory bridge through the inelastic range.