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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
