Below are the first 10 and last 10 pages of uncorrected machine-read text (when available) of this chapter, followed by the top 30 algorithmically extracted key phrases from the chapter as a whole.
Intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text on the opening pages of each chapter.
Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.
Do not use for reproduction, copying, pasting, or reading; exclusively for search engines.
OCR for page 32
32
Figure 4-1. Finite element model of the bridge used
for model verification.
Figure 4-2. Grillage model of the bridge used
The typical cross sections are shown in Figures 4-3, 4-5, 4-7, for model verification.
and 4-9. The section geometry remains the same for various
bridge span lengths, with the exception of the overall section pier stiffness. The stiffer columns were 6 ft by 8 ft which can
depth. Also, in order to simplify the analysis cases and automate also be considered similar in behavior to a multi-column pier.
the model generation, without jeopardizing the global behavior The softer columns are 6 ft by 6 ft, 7 ft by 7 ft, and 8 ft by 8 ft
of the bridge, the cross section was idealized as shown in Fig- for the short, medium, and long bridges respectively. All
ures 4-4, 4-6, 4-8, and 4-10. The cross-section properties used column heights were assumed to be 50 ft to the point of fixity
for the analytical models are shown in Tables 4-2 through 4-5 at the base. It was assumed that the pier and abutment
For each cross-section type, five typical bridge models were diaphragms were relatively stiff, i.e., they had a moment of in-
considered: ertia of 5000 ft4.
· Single Span 200 ft long; Each of the above 32 bridges was configured as a straight
· Single Span 100 ft long; bridge and as curved bridges with radii of 200, 400, 600, 800,
· Three Span 200, 300, and 200 ft long; and 1000 feet, resulting in 192 bridge configurations.
· Three Span 150, 200, and 150 ft long; and
· Three Span 75, 100, and 75 ft long. Structural Analysis
Each of the three-span bridges was analyzed with two types Each bridge configuration was modeled as a spine model
of piers to identify the effect of softer versus stiffer transverse (in which one line of elements was used for superstructure,
Table 4-1. Comparison of results, grillage vs. FEM two cell box.
Action Location DL LL2C
Grillage FEM Grillage/FEM Grillage FEM Grillage/FEM
Midspan Span 2 Deflections Left -4.40 -4.31 1.02 -0.23 -0.26 0.91
(inches)
Right -3.87 -3.80 1.02 -0.25 -0.23 1.10
Gross 52103 53523 0.97 3791 3829 0.99
Midspan Span 2 Moments Left Girder 14016 16290 0.86 1197 1190 1.01
(ft. kips)
Center Girder 21523 21735 0.99 1566 1504 1.04
Right Girder 16565 15499 1.07 1028 1135 0.91
Gross -91261 -94623 0.96 -3095 -3235 0.96
Negative Bent 3 Moments Left Girder -27469 -27309 1.01 -1007 -845 1.19
(ft. kips)
Center Girder -38265 -39494 0.97 -1342 -1526 0.88
Right Girder -25528 -27820 0.92 -746 -864 0.86
OCR for page 33
33
Figure 4-3. Typical single-cell cast-in-place cross section.
located along the centerline of the bridge), and also as a The section properties for the grillage model included a set
grillage analogy (grid) model (where each web line was of properties for the exterior girder, a set of properties for the
modeled as a line of elements along its centerline and trans- interior girder, and a set of properties for the transverse ele-
verse elements along radial lines were used to connect them ment. Furthermore, the transverse element shear area was
in the transverse direction). Typical spine and grillage calculated via a special formula to account for the warping on
modeling techniques are shown in Figures 4-11 and 4-12. the cells. An example of these properties for the two-cell sec-
Each model uses several elements per span in the longitu- tion is shown in Table 4-3. The transverse element properties
dinal direction of the bridge. Each span element is limited may be different for each element based on its width and
to a central angle of 3.5 degrees as recommended in therefore is shown here for a unit width. The members on the
Appendix C. outside of the curve were longer than the ones on the inside.
The section properties for the spine model were based on Likewise, the widths of transverse members along the outside
the entire section. An example of these for the two-cell cross of the curve were larger than those of the members along the
section is shown in Table 4-2. inside. The actual member property used in analysis was
Figure 4-4. Idealized single-cell cast-in-place cross section.
