II. MARCO TEÓRICO
2.2 Marco conceptual
2.2.8 Las empresas más importantes del Perú: Sector alimenticio
Measured girder displacement, rotation, and bearing pad displacement were compared to FEM results in four quadrants at the 75 kip per actuator load level (except SMN load case which was 50 kip per actuator). Girder displacements were recorded at three locations along the span length (at 2dv on both the east and west ends of the span and
at midspan.). Girder rotations and bearing pad displacements were measured at the loaded end of the span. Bearing pad vertical displacement data were averaged from four values measured at each corner of the rectangular pad. Finite element models were linear elastic and did not contain bi-linear or nonlinear behavior for the neoprene bearing pad material. The bearing pad was assumed to have a Young’s modulus of 17.9 ksi, a Poisson’s ratio of 0.49995, and a density of 0.0813 lb /in.3 as discussed in Section 3.3.1.
Girder vertical displacement along the span length, rotation at the east or west end, and bearing pad vertical displacements are compared to FEM results in Table 5-10 through Table 5-21. The percent difference between measured laboratory data and FEM results are reported. Percent difference values may be exaggerated when comparing measured data that is the same order of magnitude as the noise or resolution of the signal. Other than the vertical displacement at G3_E_2d in Table 5-10, FEM results and laboratory data compared well for girder displacement, girder rotation, and bearing pad displacement. Percent differences of magnitude 20 to 30 percent may be attributed to comparing data that
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was the same order of magnitude as the noise or resolution of the signal. However, in the case of the LVDT measurements for girder or bearing pad vertical displacement, this may not explain the large percent differences. Data in Table 5-16 through Table 5-18 show that the fixity of the end diaphragm in the LBESW finite element results had a negligible effect on the corresponding tabulated behaviors.
5.3.2.3 Traffic Barrier
Barrier shear strains calculated using measured data from a single VWG box-type rosette (including the effects of torsion) from the north side of the traffic barrier were compared to FEM results for model validation in the LBENE_4d_N load case at 0.5dv, 1dv,
and 2dv as shown in Table 5-7. Large percent differences were noticeable, but the results
were within approximately 5 to 10 με. Exaggerated differences between FEM results and laboratory data were attributed to the flexural behavior of the barrier outlined in the following discussion.
Measured barrier longitudinal strains through the section due to flexure were compared to FEM results for model validation in the LBENE_4d_N load case at 0.5dv, 1dv,
and 2dv as shown in Table 5-22. This load case produced maximum longitudinal bending
in the traffic barrier. The differences between the measured strains and the FEM predicted strains were always within 8 με, which was close to the accuracy of the foil strain gages. Extrapolating the linear trendlines from FEM results to the y-axis intercept in Figure 5-8 indicates that the neutral axis of the traffic barrier was approximately 6 to 7.5 in. below the barrier-to-deck interface. Data recorded from the bottom (B) strain gage at 1dv and 2dv did
not follow the expected linear trend, shown in Figure 5-8, for use in finding the neutral axis of the composite barrier section. Due to these discrepencies, supplementary data were collected in the LBENW quadrant for barrier FEM validation.
Additional longitudinal VW gages were added to the exterior of the girder bottom flange, girder top flange, traffic barrier near the barrier-to-deck interface, and on the south side of the barrier at 2dv in quadrant LBENW as shown in Figure 5-9. These gages were in
addition to the longitudinal gages that made up the box-type rosette and the four longitudinal gages on the north side of the barrier (similar to those in Table 5-22). Data collected from the additional instrumentation was used to investigate the neutral axis (NA) because of the observed nonlinear relationship between longitudinal strain and height in
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the barrier shown in Figure 5-8. Loading after the installation of the additional gages was primarily over the exterior girder at 4dv in the LBENW_4d_N load case. This load case
produced the least amount of torsion in the exterior girder, as shown in Table 5-3, and the maximum amount of shear and bending in the barrier.
Longitudinal strains from the VWGs through the section depth are shown in Figure 5-9. A linear trendline from FEM results and the single point at which both the lab data and FEM results cross the y-axis were used to estimate the neutral axis location to be between 38 and 41 in. above the bottom of the composite cross section. This was equivalent to approximately 5 to 8 in. below the barrier-to-deck interface. Data from the barrier in the LBENE quadrant also indicated that the barrier neutral axis was approximately 6 to 7.5 in. below the barrier-to-deck interface.
Figure 5-9 shows that the laboratory longitudinal strains exhibited a nonlinear behavior with height through the cross section in the barrier, near the change in cross section width. The vibrating wire strain gages added to the south side of the barrier were used to double check the unusual behavior. As expected, FEM results predicted the strains to vary linearly through the depth of the cross section. To further investigate the nonlinear relation between strain and depth, additional load cases using combinations of actuators were investigated with the increased barrier instrumentation. Data from loading with the north and middle actuator (LBENW_4d_NM) and from loading with the south, middle, and north actuators (LBENW_4d_SMN) are shown in Figure 5-10 (data are from the same instruments used to generate Figure 5-9). The north and south barrier data indicated that the neutral axis was in approximately the same vertical location, 36 in. above the bottom of the composite section. However, the nonplanar behavior was still visible in the barrier cross section near the thickness change. The reason for the nonplanar behavior was not determined. This behavior was likely not due to the precense of the end diaphragm and was observed throughout the experimental portion of the project (lab data and field data).
Discussion related to the effects of the traffic barrier on shear distribution, beyond FEM validation, are presented in Section 5.3.3.