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67 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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68 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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69 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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70 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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71 ~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