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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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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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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
