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Table 5-7. Effect of web thickness thin webs.
Model-Web Force at stirrup yield (kips/ft) Difference
2M-A vs. 3M-A 11.77 vs. 10.06 -15% change between 12" vs. 10"
2M-B vs. 3M-B 13.66 vs. 12.59 -8% change between 12" vs. 10"
2M-C vs. 3M-C 13.64 vs. 15.34 12% change between 12" vs. 14"
12M-A vs. 11M-A 13.34 vs. 10.92 -18% change between 12" vs. 10"
12M-B vs. 11M-B 17.58 vs. 15.00 -15% change between 12" vs. 10"
Model-Web Force at web delam. (kips/ft) Difference
2M-B vs. 3M-B 15.17 vs. 12.81 -16% change between 12" vs. 10"
12M-A* vs. 11M-A 16.61 vs. 12.06 -27% change between 12" vs. 10"
12M-B* vs. 11M-B 21.20 vs. 14.62 -31% change between 12" vs. 10"
* Never reached delamination limit
· Maximum Principal Strain Contours in Concrete at 75%, Discussion of Results
100%, 125%, and 150% Pc
Analyses of these models showed similar trends as the multi-
· Strains in stirrup rebar at 3 locations along duct bank at
cell model analyses, and there were no surprises as to the per-
75%, 100%, 125%, and 150% Pc
formance of the sections. As expected, the sections with duct
· Distortions (change in web width) 3 locations along duct
ties performed better than those without. Having the double
bank 75%, 100%, 125%, and 150% Pc
row of tendons was found to concentrate the local damage area
within the web, but having the 20-inch web thickness with local
Detailed results are included in Appendix F-a. reinforcement was quite adequate to accommodate this.
16
14
12
10
Fr (Kips/Ft)
8
6
4
2
0
0.00E+00 5.00E-02 1.00E-01 1.50E-01 2.00E-01 2.50E-01 3.00E-01 3.50E-01 4.00E-01
Defl (in)
Model 2M Web A Model 2M Web D Model 2MVert Web A Model 2MVert Web D
Figure 5-22a. Model 2M and 2MVert force vs. deflection comparison for Webs A and D (quarter height).
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20
18
16
14
12
Fr (Kips/Ft)
10
8
6
4
2
0
0.00E+00 5.00E-02 1.00E-01 1.50E-01 2.00E-01 2.50E-01 3.00E-01 3.50E-01 4.00E-01
Defl (in)
Model 11M Web A Model 11M Web D Model 11MVert Web A Model 11MVert Web D
Figure 5-22b. Model 11M and 11MVert force vs. deflection comparison for Webs A and D (mid height).
Table 5-8. Effect of web slope thin webs.
Model-Web Force at stirrup yield (kips/ft) Difference
2M-A vs. 2Mvert-A 11.77 vs. 12.55 7% change with vertical web
2M-D vs. 2Mvert-D 11.82 vs. 13.85 17% change with vertical web
11M-A vs. 11Mvert-A 10.92 vs. 11.68 7% change with vertical web
11M-D vs. 11Mvert-D 11.58 vs. 15.27 32% change with vertical web
Model-Web Force at web delam. (kips/ft) Difference
2M-A vs. 2Mvert-A 10.83 vs. 13.82 28% change with vertical web
2M-D vs. 2Mvert-D 14.56 vs. 15.67 8% change with vertical web
11M-A vs. 11Mvert-A* 12.06 vs. 16.61 38% change with vertical web
11M-D vs. 11Mvert-D* 12.84 vs. 18.27 42% change with vertical web
* Never reached delamination limit
Table 5-9. Effect of cover thickness thin webs.
Model-Web Force at stirrup yield (kips/ft) Difference
8M-A vs. 2M-A 10.36 vs. 11.77 14% change between 2" vs. 3"
8M-C vs. 2M-C 15.41 vs. 13.64 -11% change between 4" vs. 3"
8M-D vs. 2M-D 11.86 vs. 11.82 -0.3% change between 2" vs. 3"
Model-Web Force at web delam. (kips/ft) Difference
8M-C vs. 2M-C 15.08 vs. 15.06 -0.2% change between 4" vs. 3"
8M-D vs. 2M-D 15.34 vs. 14.56 -5% change between 2" vs. 3"
Qualitative evidence can also be obtained by examining the strain plots in the Appendixes for the models where cover
thickness was varied.
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Table 5-10. Effect of different duct configurations thin webs.
Model-Web Force at stirrup yield (kips/ft) Difference
1M-A vs. 2M-A 9.93 vs. 11.77 19% change - Config. 1 vs. 2A
1M-B vs. 2M-B 11.38 vs. 13.66 20% change - Config. 1 vs. 2A
1M-C vs. 2M-C 11.77 vs. 13.64 16% change - Config. 1 vs. 2A
3M-D vs. 2M-D 12.26 vs. 11.82 -4% change - Config. 2B vs. 2A
5M-B vs. 2M-B 14.11 vs. 13.66 -3% change - Config. 2B vs. 2A
10M-C vs. 7M-C 17.13 vs. 16.31 -5% change - Config. 3A vs. 2A
Model-Web Force at web delam. (kips/ft) Difference
1M-B vs. 2M-B 12.83 vs. 15.17 18% change - Config. 1 vs. 2A
1M-C vs. 2M-C 12.60 vs. 15.06 19% change - Config. 1 vs. 2A
5M-B vs. 2M-B 19.60 vs. 15.17 -23% change - Config. 2B vs. 2A
10M-C* vs. 7M-C 21.20 vs. 17.11 * change - Config. 3A vs. 2A
* Never reached delamination limit
Similar to the multi-cell studies, the analysis results can be section) of 0.3%. For sections with web ties, this means
used to compare the web design parameters. For purposes of the web ties have yielded; for sections without web ties, the
interpreting the 3D finite element analysis results, the follow- section is at a web splitting or a cover concrete spalling
ing damage limit criteria are suggested: condition.
· Stirrup rebar strain exceeding yield (i.e., 0.2% strain for One of the criteria, Stirrup Yield, has been summarized
Grade 60 steel); for Load Factor Design, concrete rein- in Table 5-18. These are the total forces (sum of all tendon
forcement is designed to yield; yield should be considered ducts in the web) applied when any part of the stirrup reaches
an upper bound criteria for unfactored loads. yield.
· Visible concrete cracking occurs at strains of approxi- Using these criteria, and examining the results tables and
mately 0.016%, but this is not necessarily web failure; plots resulted in the following observations.
concrete with maximum principal strains of 0.3% can be
considered to be heavily cracked. Concrete with strains in
Web Slope
excess of 1.0% will generally show wide-open cracks and
potential spalling from the section. Similar to the multi-cell series, the inside radius web, slop-
· Significant distortion or delamination (change of width ing toward the center of the curve, was found to be roughly
of the webs) also represents an upper limit on capacity 10% stronger than the outside radius web, sloping away from
for webs; the delamination is evidence of a local split- the center of the curve. Further study indicated a possible rea-
ting or lateral shear failure within the web; it was again son for this was that loading the inside radius web (Web 2)
assumed that an upper bound on crack width of 1/16" is created positive transverse moment in the top slab adjacent
an indicator of such a failure. For 20" webs, this repre- to the web (tension on the bottom of the slab), whereas load-
sents a distortion ratio (average strain through the ing Web 1 created negative moment. The slab resistance to
Table 5-11. Effect of duct tie arrangements thin webs.
Model-Web Force at stirrup yield (kips/ft) Difference
10M-B vs. 12M-B 17.22 vs. 17.58 2% change - Config. 3A vs. 4A
10M-C vs. 12M-C 17.13 vs. 17.55 2% change - Config. 3A vs. 4B
10M-A vs. 13M-A 13.06 vs. 15.01 15% change - Config. 3A vs. 4A
10M-B vs. 13M-B 17.22 vs. 19.61 14% change - Config. 3A vs. 4A
10M-C vs. 13M-C 17.13 vs. 19.50 14% change - Config. 3A vs. 4A
10M-D vs. 13M-D 12.97 vs. 15.17 17% change - Config. 3A vs. 4A
12M-B vs. 12M-C 17.58 vs. 17.55 -0.2% change - Config. 4A vs. 4B
9M-B vs. 14M-B 9.59 vs. 10.47 9% change - Config. 2A vs. 4B
Model-Web Force at web delam. (kips/ft) Difference
9M-B vs. 14M-B 10.94 vs. 20.19 85% change - Config. 2A vs. 4B
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Table 5-12. Effect of stirrup spacing thin webs.
Model-Web Force at stirrup yield (kips/ft) Difference
6M-A vs. 2M-A 8.77 vs. 11.77 34% change with 50% more stirrup steel
6M-B vs. 2M-B 12.57 vs. 13.66 9% change with 50% more stirrup steel
6M-D vs. 2M-D 10.77 vs. 11.82 10% change with 50% more stirrup steel
7M-B vs. 2M-B 16.33 vs. 13.66 -16% change with 33% less stirrup steel
7M-D vs. 2M-D 13.51 vs. 11.82 -13% change with 33% less stirrup steel
13M-A vs. 12M-A 15.01 vs. 13.34 -11% change with 33% less stirrup steel
13M-B vs. 12M-B 19.61 vs. 17.58 -10% change with 33% less stirrup steel
13M-D vs. 12M-D 15.17 vs. 12.38 -18% change with 33% less stirrup steel
Model-Web Force at web delam.(kips/ft) Difference
6M-B vs. 2M-B 13.92 vs. 15.17 9% change with 50% more stirrup steel
6M-D vs. 2M-D 13.04 vs. 14.56 12% change with 50% more stirrup steel
7M-B vs. 2M-B 18.36 vs. 15.17 -17% change with 33% less stirrup steel
7M-D vs. 2M-D 16.37 vs. 14.56 -11% change with 33% less stirrup steel
these moments was stronger (about 2 times stronger, based and 10S). The number and relative position of the ducts to
on typical deck reinforcing) in positive moment than in each other was held constant. But it was again observed that,
negative moment, and this translated to more strength in the when the ducts occurred near the bottom of the web (either
associated web. "quarter-height" or "bottom" as tested in Configurations 4M
and 14M), the force at "failure" was substantially lower than
when the ducts were placed at the mid-height, i.e., on average
Cover Thickness
as much as 25% to 40% lower when comparing these cases to
Cover thickness was varied in Model 6S, where increases for similar cases. The reason for this was a tendency toward
Webs 1 and 2 were by 50% and 75%, respectively. Table 5-19 lateral shear failure of the overall web, and a tendency toward
summarizes the relevant strength comparisons. flexural damage in the top slab, thus weakening the whole
The local concrete damage was less severe with thicker system. When the ducts were located at the mid-height, the
cover, but the comparisons for stirrup yield were incon- lateral shear was divided equally between the top and bottom
clusive because (1) for 2-inch cover and above, cover fail- of the web. But when the ducts moved down, the bottom of
ure did not control the failure mode, and (2) when the the web carried most of the lateral shear. This is a different
cover was less, the "moment arm" between the stirrups mechanism than the failure modes observed for tendon ducts
was more, and this increased capacity rather than decreas- at mid-height, but one that still warrants consideration in
ing it. design.
Number and Configuration of Tendon Ducts Number and Configuration of Duct Ties
The only variation studied in the single-cell case was the This was evaluated by comparing duct tie Configuration 6a,
positioning of the duct group (studied in Configurations 2S which had duct ties, to Configuration 6, which had no duct
Table 5-13. Effect of concrete strengths thin webs.
Model-Web Force at stirrup yield (kips/ft) Difference
2M-C vs. 5M-C 13.64 vs. 15.95 17% change with 50% larger concr. strength
2M-C vs. 6M-C 13.64 vs. 11.21 -18% change with 50% smaller concr. strength
12M-B vs. 12M-C 17.58 vs. 17.55 -0.2% change with 50% larger concr. strength
Model-Web Force at web delam. (kips/ft) Difference
2M-C vs. 5M-C 15.06 vs. 18.30 22% change with 50% larger concr. strength
2M-C vs. 6M-C 15.06 vs. 12.15 -19% change with 50% smaller concr. strength
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~3.5"
21'- 6" 21'- 6"
10'- 0" 11'- 6"
5'-0"
18"
10"
9"
6"
Tendons assumed
6-31 F 0.6" 1 web
12' -6"
20"
6"
Ducts 5"00
24"@Pier
9" Typ
# 4 at 12" Typ
16"
# 7 at 12" Typ
3'-6"
# 6 at 12"
9'- 0" 9'- 0"
2" Cl 1.5" Cl
20"
Figure 5-23. Tendon duct and local reinforcement for the local analysis prototype
for a single-cell box.
ties. Table 5-20 compares Model/Webs 7S to 1S, 8S to 3S, and Stirrups
9S-1 to 5S-1.
These comparisons show that, for the wider web (20 inches) Stirrup spacing was evaluated by comparing Model-Webs
and double row of tendon ducts, the ties do not make a 4S-1 to 1S-1, 5S-1 to 1S-1, and 9S-1, 2 to 7S-1, 2. The results
significant difference in the force to cause stirrup yield, but are shown in Table 5-21.
they make a large difference in the delamination-damage that The web section strength tends to be significantly influ-
can occur within the web. Delaminations (width changes in enced by the stirrup spacing for this geometry also, perhaps
the web) are reduced by 24 to 31% with duct ties as compared even more so than for the multi-cell geometry. Again, stirrup
to without duct ties. spacing is a driver of web "regional" beam strength.
Table 5-14. Single-cell box variations/parameter study.
Concr.
Tens.
Web Web- Web Duct/Tie Bundle Stirrup Cover Str.
Analysis # Model Type # ties Thickness Config.* Vert. Pos. Spacing(in.) Thickness (xfc`)
1S Single-cell 1 N 20 6 midheight 12 1.5"/2"
4
"baseline" 2 N 20 6 midheight 12 1.5"/2"
4
2S Single-cell 1 N 20 6 1/4 height 12 1.5"/2" 4
2 N 20 6 bottom 12 1.5"/2" 4
3S Single-cell 1 N 20 6 midheight 12 1.5"/2" 4
2 N 20 6 midheight 12 1.5"/2" 6
4S Single-cell 1 N 20 6 midheight 8 1.5"/2" 4
2 N 20 6 midheight 12 1.5"/2" 2
5S Single-cell 1 N 20 6 midheight 18 1.5"/2"
4
2 N 20 6 midheight 12 1.5"/2"
4
6S Single-cell 1 N 20 6 midheight 12 2.5"/3"
4
2 N 20 6 midheight 12 3:/3.5"
4
7S Single-cell 1 Y 20 6a midheight 12 1.5"/2"
4
2 Y 20 6a midheight 12 1.5"/2"
4
8S Single-cell 1 Y 20 6a midheight 12 1.5"/2"
2
2 Y 20 6a midheight 12 1.5"/2"
6
9S Single-cell 1 Y 20 6a midheight 18 1.5"/2"
4
2 Y 20 6a midheight 8 1.5"/2"
4
10S Single-cell 1 Y 20 6a 1/4 height 12 1.5"/2"
4
2 N 20 6a bottom 12 1.5"/2"
4
