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72 Table 5-15. Deflections (inches) measured by the concrete strength, and mostly this influence occurs at mid-height of webs on backside. when web/duct tie reinforcement is NOT used. When web/ duct tie reinforcement is used, concrete tensile strength has less Web 1 Web 2 effect on the section strength. Of the various parameters in- Percent Mid Quarter Mid Quarter volved in reinforced concrete design, concrete tensile strength Model # Capacity has wide variability, and low reliability, so designers should use 1S 75% 0.176 0.174 0.179 0.158 design rules that will ensure good performance, regardless of 100% 0.404 0.402 0.418 0.360 variabilities in concrete tensile strength. 125% 1.076 1.090 1.208 0.978 150% 2.496 2.499 2.903 2.224 2S 75% 0.888 1.251 0.724 1.068 Conclusions from Local Analyses 100% 2.340 3.365 1.924 2.852 125% 4.521 6.484 3.647 5.410 General Observations on Capacity 150% 26.702 36.174 22.345 31.707 Using the capacity definitions described in this section 3S 75% 0.156 0.152 0.135 0.131 100% 0.366 0.357 0.338 0.307 (Pc, developed based on regional transverse bending consid- 125% 0.918 0.906 0.871 0.778 erations), it was found that all of the multi-cell box-girders 150% 2.239 2.161 2.246 1.868 achieved this target capacity. The baseline (Model 1M) inte- rior webs achieved it marginally (i.e., stirrup yield was reached 4S 75% 0.272 0.274 0.314 0.256 100% 0.678 0.681 0.764 0.609 at 107% of Pc), while stronger details that use spreading apart 125% 1.805 1.775 2.050 1.570 the ducts, adding duct ties, or moving the ducts toward the 150% 4.030 3.904 4.542 3.445 curve-outside-face of the web reached as high as 185% of Pc. 5S 75% 0.140 0.140 0.159 0.137 The variations in force to cause local duct bank breakout 100% 0.295 0.298 0.351 0.293 (either local shearing or web delamination) were even larger, 125% 0.685 0.701 0.961 0.722 depending on the detailing used, so the detailing significantly 150% 1.728 1.815 2.526 1.835 influences resistance to lateral pullout. For the single-cell 6S 75% 0.195 0.190 0.192 0.170 example, with the 20-inch webs and double row of ducts, the 100% 0.462 0.457 0.463 0.405 finite element analysis showed capacities that were mostly 125% 1.212 1.204 1.288 1.066 lower than the hand-calculated regional transverse bending 150% 2.805 2.691 2.974 2.362 capacity (i.e., stirrup yield was reached at a range from 52% Pc 7S 75% 0.168 0.168 0.174 0.154 up to 100% Pc), but this is explained by the fact that, for the 100% 0.372 0.377 0.400 0.355 thicker web, failures were dominated by local lateral shearing. 125% 0.953 0.987 1.056 0.923 150% 2.286 2.335 2.600 2.169 Summary of Influences 8S 75% 0.205 0.192 0.155 0.154 from Detailing Parameters 100% 0.435 0.420 0.357 0.341 125% 1.095 1.046 0.866 0.846 150% 2.588 2.447 2.127 1.996 Web Depth can be adequately accounted for by consider- 9S 75% 0.146 0.148 0.182 0.151 ing and designing for web moments. 100% 0.320 0.335 0.472 0.365 Web Thickness significantly influences resistance to re- 125% 0.849 0.915 1.409 1.011 gional transverse bending and tendon pullout. For stirrup 150% 2.102 2.292 3.413 2.463 yield, capacity formulae based on regional flexure consid- 10S 75% 0.808 1.131 0.659 0.972 erations appear to be appropriate for design. 100% 2.301 3.242 1.877 2.785 Web Slope. Sloped webs were found to be significantly 125% 4.462 6.274 3.493 5.187 weaker (roughly 30%) than the vertical webs, but much 150% 23.358 31.548 19.232 27.371 of this difference is caused because these are exterior webs rather than interior ones. Exterior webs have more Concrete Material Properties, Especially Assumed flexible end conditions at their connection with the Tensile Strength top and bottom slab, and this produces larger mid-height The effect of concrete strength was evaluated by compar- moments. Comparison of Webs A to D for the inclined ing Model-Webs 3S-2 to 1S-2, 4S-2 to 1S-2, and 8S-1, 2 to webs show that Web A is generally weaker than D by 7S-1, 2. The results are shown in Table 5-22. about 10%. It is believed this is due to the difference in So, repeating the trend observed in the multi-cell analysis, positive bending versus negative bending strength of the the web section strength tends to be only marginally influenced top slab. Lateral force for Web D applies positive moment

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73 Table 5-16. Stirrup strain (%) on curve inside - face. Web 1 Web 2 Percent Duct 2 Duct 4 Duct 6 Duct 2 Duct 4 Duct 6 Model # Capacity 1S 75% 0.00166 0.00137 0.00097 0.00150 0.00150 0.00150 100% 0.00421 0.00222 0.00173 0.00310 0.00310 0.00310 125% 0.01851 0.01023 0.00275 0.01506 0.01506 0.01506 150% 0.04107 0.03204 0.01021 0.04032 0.04032 0.04032 2S 75% 0.01429 0.00345 0.00187 0.00680 0.00311 0.00188 100% 0.03765 0.01701 0.00450 0.02543 0.01638 0.00724 125% 0.07417 0.04288 0.01750 0.04969 0.03558 0.02096 150% 0.24986 0.15104 0.06873 0.21465 0.10079 0.05699 3S 75% 0.00152 0.00127 0.00090 0.00158 0.00097 0.00049 100% 0.00376 0.00218 0.00176 0.00326 0.00236 0.00164 125% 0.01529 0.00902 0.00279 0.01341 0.00712 0.00421 150% 0.04083 0.03034 0.00937 0.03334 0.02640 0.01838 4S 75% 0.00332 0.00190 0.00134 0.00165 0.00172 0.00175 100% 0.01269 0.00563 0.00244 0.00361 0.00580 0.00520 125% 0.03219 0.02447 0.00713 0.01271 0.02075 0.02036 150% 0.06683 0.05776 0.01953 0.03541 0.04853 0.04659 5S 75% 0.00126 0.00112 0.00076 0.00140 0.00141 0.00110 100% 0.00189 0.00177 0.00137 0.00244 0.00332 0.00187 125% 0.00942 0.00452 0.00200 0.01017 0.01499 0.00759 150% 0.02689 0.01755 0.00329 0.03406 0.03425 0.03028 6S 75% 0.00178 0.00137 0.00109 0.00150 0.00132 0.00113 100% 0.00642 0.00204 0.00190 0.00415 0.00284 0.00215 125% 0.02163 0.00915 0.00323 0.01628 0.01319 0.00910 150% 0.04799 0.02955 0.00911 0.03942 0.03223 0.02922 7S 75% 0.00159 0.00135 0.00092 0.00160 0.00140 0.00124 100% 0.00329 0.00215 0.00160 0.00525 0.00335 0.00259 125% 0.01451 0.01098 0.00257 0.01872 0.01541 0.00807 150% 0.03987 0.03238 0.00851 0.04636 0.04096 0.02690 8S 75% 0.00162 0.00149 0.00134 0.00154 0.00106 0.00059 100% 0.00387 0.00339 0.00277 0.00407 0.00243 0.00158 125% 0.01690 0.01528 0.01066 0.01612 0.00684 0.00332 150% 0.04019 0.03653 0.02766 0.04088 0.02560 0.01352 9S 75% 0.00129 0.00110 0.00072 0.00207 0.00174 0.00151 100% 0.00207 0.00178 0.00129 0.00841 0.00630 0.00387 125% 0.01140 0.00698 0.00196 0.02662 0.02184 0.01958 150% 0.03106 0.02321 0.00373 0.06473 0.05138 0.04844 10S 75% 0.01253 0.00783 0.00210 0.00703 0.00380 0.00184 100% 0.03730 0.02768 0.00920 0.02789 0.01708 0.00750 125% 0.07189 0.05973 0.02640 0.05278 0.03636 0.01851 150% 0.23078 0.19175 0.09182 0.19842 0.09676 0.04984

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74 Table 5-17. Distortion (web thickness changes inches) at mid-height of ducts. Web A Web B Percent Duct 2 Duct 4 Duct 6 Duct 2 Duct 4 Duct 6 Model # Capacity 1S 75% 0.0126 0.0104 0.0026 0.0128 0.0247 0.0095 100% 0.0351 0.0297 0.0053 0.0442 0.0630 0.0316 125% 0.0732 0.0666 0.0179 0.0987 0.1464 0.0876 150% 0.1398 0.1446 0.0673 0.1702 0.3469 0.2093 2S 75% 0.0169 0.0278 0.0064 0.0472 0.0849 0.0226 100% 0.0635 0.0779 0.0303 0.1207 0.2037 0.0671 125% 0.1959 0.2289 0.1114 0.2546 0.4035 0.1122 150% 0.4625 0.4472 0.2166 0.4946 0.7850 0.2093 3S 75% 0.0165 0.0084 0.0031 0.0051 0.0108 0.0034 100% 0.0348 0.0277 0.0092 0.0176 0.0455 0.0137 125% 0.0658 0.0512 0.0196 0.0374 0.0875 0.0412 150% 0.1347 0.1356 0.0813 0.1102 0.2152 0.1084 4S 75% 0.0245 0.0141 0.0039 0.0339 0.0496 0.0332 100% 0.0569 0.0392 0.0132 0.0928 0.1219 0.0903 125% 0.1079 0.0971 0.0463 0.1995 0.2876 0.2064 150% 0.2377 0.2341 0.1441 0.4056 0.5930 0.4169 5S 75% 0.0077 0.0094 0.0031 0.0112 0.0223 0.0087 100% 0.0247 0.0212 0.0058 0.0356 0.0521 0.0250 125% 0.0459 0.0462 0.0133 0.0862 0.1145 0.0600 150% 0.0734 0.0898 0.0346 0.1594 0.3204 0.1824 6S 75% 0.0158 0.0129 0.0021 0.0106 0.0235 0.0048 100% 0.0366 0.0328 0.0077 0.0406 0.0632 0.0175 125% 0.0935 0.0748 0.0302 0.0965 0.1555 0.0424 150% 0.1985 0.2021 0.1147 0.2057 0.3781 0.1055 7S 75% 0.0106 0.0093 0.0026 0.0104 0.0217 0.0075 100% 0.0213 0.0237 0.0053 0.0274 0.0479 0.0153 125% 0.0425 0.0405 0.0085 0.0573 0.0939 0.0261 150% 0.0567 0.0824 0.0253 0.1254 0.2166 0.0563 8S 75% 0.0936 0.0157 0.0069 0.0106 0.0173 0.0052 100% 0.0207 0.0273 0.0164 0.0246 0.0503 0.0127 125% 0.0413 0.0574 0.0461 0.0442 0.0872 0.0250 150% 0.0735 0.1541 0.0933 0.0922 0.1443 0.2584 9S 75% 0.0057 0.0095 0.0032 0.0390 0.0227 -0.0218 100% 0.0189 0.0190 0.0062 0.0298 0.0480 0.0126 125% 0.0345 0.0361 0.0139 0.0630 0.1241 0.0217 150% 0.0386 0.0645 0.0274 0.1379 0.3115 0.0543 10S 75% 0.0132 0.0250 0.0064 0.0399 0.0661 0.0072 100% 0.0124 0.0600 0.0154 0.0800 0.1449 0.0163 125% 0.0751 0.1321 0.0279 0.1604 0.2918 0.0202 150% 0.1939 0.2563 0.0306 0.2885 0.5176 0.0376