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36 Table 4-2. Section properties for two-cell curved line (spine) bridge model. 200 ft. Single 100 ft. Single 200/300/200 150/200/150 75/100/75 ft. Span Span ft. Multi-Span ft. Multi-Span Multi-Span CG (ft) 4.53 2.24 5.46 4.06 2.01 Area (ft2) 81.73 66.73 87.73 78.73 65.23 Avy (ft2) 56.60 56.60 56.60 56.60 56.60 Avz (ft2) 30.00 15.00 36.00 27.00 13.50 Iyy (ft4) 1,326.25 256.23 2,028.29 1,037.00 197.80 Izz (ft4) 9,544.20 7,488.61 10,366.44 9,133.08 7283.05 Jxx (ft4) 1,559.82 365.08 2,213.30 1,267.24 286.74 Depth (ft) 10.0 5.0 12.0 9.0 4.5 Midspan Transverse Bending Moment at middle of center technique. An example of such graphs is shown in Fig- span; ures 4-14a and 4-14b. Midspan End Shear at first abutment in single span and at start of middle span in 3-span case; Summary of Results Midspan Normal Stress at bottom outside corner of cross section, at middle of center span; and Numerous scattergrams were plotted for each of the re- Midspan Normal Stress at bottom inside corner of cross sults listed in the previous section and bridge types shown in section, at middle of center span. Figures 4-4 through 4-10. Figure 4-14 shows the plots with the most divergent results (i.e., with values furthest away from The graphical review of results included scatter-grams of 1.00) between the spine and grillage models. As a result, the each response quantity from spine and grillage models. An outside web shear force and longitudinal stress are the main example of such graphs is shown in Figure 4-13. effects that need attention in design. To better quantify these The ratio of stresses and shear forces from the spine results and the effects of curvature on various bridge types, model to those of the grillage model were also obtained ratios of results for various bridge models were combined to review the effect of radius of curvature and modeling and plotted as shown in Figures 4-15 through 4-18. Average Table 4-3. Section properties for two-cell grillage bridge model. 200 ft. 100 ft. EXTERIOR Single Single 200/300/200 ft. 150/200/150 ft. 75/100/75 ft. GIRDER Span Span Multi-Span Multi-Span Multi-Span CG (ft) 4.23 2.06 5.13 3.78 1.85 Area (ft2) 25.03 20.03 27.03 24.03 19.53 Avy (ft2) 18.87 18.87 18.87 18.87 18.87 Avz (ft2) 10.00 5.00 12.00 9.00 4.50 Iyy (ft4) 386.50 73.28 594.75 301.19 56.45 Izz (ft4) 216.76 208.19 219.34 215.31 207.11 Jxx (ft4) 519.94 121.69 737.77 422.41 95.58 200 ft. 100 ft. INTERIOR Single Single 200/300/200 ft. 150/200/150 ft. 75/100/75 ft. GIRDER Span Span Multi-Span Multi-Span Multi-Span CG (ft) 5 2.50 6.00 4.50 2.25 Area (ft2) 31.67 26.67 33.67 30.67 26.17 Avy (ft2) 18.87 18.87 18.87 18.87 18.87 Avz (ft2) 10.00 5.00 12.00 9.00 4.50 Iyy (ft4) 541.74 106.59 823.13 425.04 82.44 Izz (ft4) 399.43 399.02 399.60 399.35 398.97 Jxx (ft4) 519.94 121.69 737.77 422.41 95.58 200 ft. 100 ft. Transverse Single Single 200/300/200 ft. 150/200/150 ft. 75/100/75 ft. Element Span Span Multi-Span Multi-Span Multi-Span CG (ft) 5 2.50 6.00 4.50 2.25 Area (ft2) 1.63 1.63 1.63 1.63 1.63 Avy (ft2) 0.01 0.01 0.01 0.01 0.01 Avz (ft2) 1.63 1.63 1.63 1.63 1.63 Iyy (ft4) 34.38 7.21 50.94 27.32 5.61 Izz (ft4) 0.14 0.14 0.14 0.14 0.14 Jxx (ft4) 68.58 14.25 101.69 54.47 11.05