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63 Table 5-3. (Continued). Web A Web B Web C Web D Percent Duct 1 Duct 3 Duct 5 Duct 1 Duct 3 Duct 5 Duct 1 Duct 3 Duct 5 Duct 1 Duct 3 Duct 5 Model # Capacity 12m 75% 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0002 0.0001 0.0001 100% 0.0002 0.0003 0.0003 0.0002 0.0002 0.0002 0.0002 0.0001 0.0002 0.0008 0.0002 0.0002 125% 0.0005 0.0008 0.0007 0.0004 0.0004 0.0005 0.0004 0.0003 0.0005 0.0017 0.0007 0.0006 150% 0.0009 0.0013 0.0014 0.0009 0.0008 0.0010 0.0008 0.0005 0.0009 0.0034 0.0013 0.0011 13m 75% 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0002 0.0001 0.0001 100% 0.0002 0.0002 0.0003 0.0002 0.0001 0.0002 0.0001 0.0001 0.0002 0.0006 0.0002 0.0002 125% 0.0006 0.0005 0.0006 0.0003 0.0002 0.0004 0.0002 0.0002 0.0003 0.0011 0.0004 0.0003 150% 0.0009 0.0008 0.0009 0.0006 0.0005 0.0007 0.0005 0.0005 0.0007 0.0017 0.0007 0.0005 14m 75% 0.0005 0.0005 0.0002 0.0001 0.0001 0.0004 0.0002 0.0001 0.0003 0.0011 0.0002 0.0001 100% 0.0017 0.0015 0.0009 0.0004 0.0007 0.0021 0.0010 0.0004 0.0013 0.0034 0.0008 0.0002 125% 0.0045 0.0048 0.0019 0.0011 0.0013 0.0063 0.0032 0.0014 0.0032 0.0111 0.0011 0.0004 150% 0.0125 0.0143 0.0046 0.0017 0.0022 0.0182 0.0113 0.0036 0.0081 0.0273 0.0018 0.0012 2MV ert 75% 0.0001 0.0001 0.0001 0.0002 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 100% 0.0003 0.0003 0.0002 0.0005 0.0004 0.0003 0.0004 0.0004 0.0003 0.0003 0.0003 0.0002 125% 0.0010 0.0009 0.0006 0.0009 0.0010 0.0008 0.0011 0.0010 0.0006 0.0008 0.0010 0.0007 150% 0.0019 0.0017 0.0011 0.0019 0.0021 0.0016 0.0023 0.0020 0.0015 0.0020 0.0021 0.0016 11MV ert 75% 0.0002 0.0001 0.0002 0.0002 0.0001 0.0002 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 100% 0.0006 0.0002 0.0007 0.0002 0.0002 0.0006 0.0002 0.0002 0.0002 0.0002 0.0002 0.0003 125% 0.0013 0.0007 0.0014 0.0006 0.0005 0.0011 0.0003 0.0003 0.0004 0.0005 0.0005 0.0006 150% 0.0024 0.0015 0.0026 0.0013 0.0011 0.0019 0.0006 0.0006 0.0008 0.0011 0.0011 0.0012 mode is tending toward local duct pullout, stirrups are not a Local Analysis of Single-Cell very effective deterrent against this failure mode. But if the Box Girders duct layout and duct ties are properly detailed to eliminate the local pullout failure mode, the stirrup spacing does define Model Prototype: Single-Cell CIP Box Girder the web "regional" beam strength. A single-cell box configuration was used as shown in Fig- ure 5-23, with the tendon duct arrangements and local rein- forcements shown in Figure 5-16 and further illustrated in Concrete Material Properties, Especially Assumed Figure 5-23. The duct and tie configurations are referred to as Tensile Strength #6 and #6a, to differentiate from the configurations of the This was evaluated by comparing Model-Webs 5M-C to multi-cell. The only difference between these is that #6 has no 2M-C, 6M-C to 2M-C, 12M-D to 11M-D, and 12M-C to duct ties, and #6a has the two rebar ties as shown. The basic 12M-B. This comparison is shown in Table 5-13. model uses 3D elements and a slice, with out-of-page thick- So the web section strength tends to be significantly influ- ness equal to one stirrup spacing. The stirrups (and other enced by the concrete strength only when the section is prone rebar) are modeled explicitly (unlike in 2D, where the stirrup to web-splitting/local-lateral shear-failures, i.e., when vul- is smeared). This allows introduction of the out-of-page nerable duct placement is used or web/duct tie reinforcement compression due to prestress. Using this model framework, is NOT used. When web/duct tie reinforcement is used, con- geometry variabilities were introduced directly into the mod- crete tensile strength has little effect on the section strength. els--e.g., one web can have one thickness and another have a This tends to further underscore the importance of providing different thickness. Webs 1 and 2 demonstrate the differences web/duct tie reinforcement; because of the various parame- related to web sloping away from the radius of curvature ver- ters involved in reinforced concrete design, concrete tensile sus sloping toward the radius of curvature. strength has wide variability, and low reliability. Thus de- Web 1 - left, Web 2 - right. (Duct/Tie configuration "6". signers should be directed toward design rules that will ensure "6a" would include horizontal crossties.) good performance regardless of variabilities in concrete Similar to the multi-cell analysis series, in order to estab- tensile strength. lish a baseline for comparison with design calculations, Pc was

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64 Table 5-4. Distortion (web thickness change) across the mid-height of ducts (Duct 1 bottom, Duct 3 middle, Duct 5 top). Web A Web B Web C Web D Percent Duct1 Duct 3 Duct 5 Duct1 Duct 3 Duct 5 Duct1 Duct 3 Duct 5 Duct1 Duct 3 Duct 5 Model # Capacity 1m 75% 0.0020 0.0029 0.0016 0.0029 0.0088 0.0020 0.0020 0.0078 0.0010 0.0020 0.0116 0.0016 100% 0.0033 0.0092 0.0041 0.0368 0.0283 0.0039 0.0039 0.0303 0.0029 0.0041 0.0251 0.0035 125% 0.0075 0.0209 0.0078 0.0254 0.0693 0.0107 0.0078 0.0732 0.0078 0.0062 0.0251 0.0073 150% 0.0101 0.0409 0.0150 0.0508 0.1387 0.0234 0.0156 0.1621 0.0244 0.0089 0.0591 0.0133 2m 75% 0.0016 0.0012 0.0014 0.0010 0.0049 0.0020 0.0010 0.0039 0.0020 0.0034 0.0032 0.0014 100% 0.0026 0.0035 0.0018 0.0020 0.0146 0.0029 0.0020 0.0137 0.0039 0.0067 0.0098 0.0019 125% 0.0051 0.0943 0.0044 0.0010 0.0342 0.0059 0.0068 0.0332 0.0059 0.0158 0.0221 0.0053 150% 0.0113 0.1010 0.0087 0.0029 0.0742 0.0146 0.0293 0.0791 0.0117 0.0443 0.0488 0.0089 3m 75% 0.0019 0.0013 0.0010 0.0029 0.0029 0.0020 0.0020 0.0049 0.0020 0.0024 0.0033 0.0011 100% 0.0023 0.0031 0.0032 0.0098 0.0117 0.0020 0.0039 0.0107 0.0039 0.0064 0.0087 0.0017 125% 0.0052 0.0055 0.0087 0.0244 0.0342 0.0059 0.0078 0.0264 0.0107 0.0112 0.0242 0.0052 150% 0.1803 0.1789 0.1843 0.1748 0.3154 0.1875 0.2803 0.4268 0.2910 0.2535 0.3563 0.2105 4m 75% 0.0019 0.0170 0.0021 0.0078 0.0127 0.0049 0.0078 0.0137 0.0059 0.0104 0.0110 0.0022 100% 0.0048 0.0133 0.0042 0.0293 0.0596 0.0039 0.0264 0.0459 0.0068 0.0380 0.0437 0.0083 125% 0.0249 0.0081 0.0074 0.0947 0.2266 0.0010 0.0752 0.1211 0.0117 0.0918 0.1244 0.0292 150% 0.9973 0.8594 0.8428 1.1494 1.7051 0.9990 1.1553 1.5244 1.1211 1.0413 1.2327 0.9574 5m 75% 0.0014 0.0013 0.0021 0.0020 0.0029 0.0020 0.0010 0.0029 0.0020 0.0034 0.0024 0.0006 100% 0.0013 0.0025 0.0026 0.0068 0.0059 0.0029 0.0020 0.0059 0.0029 0.0065 0.0037 0.0016 125% 0.0042 0.0045 0.0056 0.0186 0.0146 0.0049 0.0049 0.0176 0.0049 0.0133 0.0059 0.0029 150% 0.0065 0.0088 0.0093 0.0361 0.0312 0.0107 0.0117 0.0371 0.0098 0.0253 0.0130 0.0046 6m 75% 0.0016 0.0019 0.0013 0.0029 0.0039 0.0020 0.0059 0.0117 0.0039 0.0026 0.0032 0.0014 100% 0.0044 0.0149 0.0020 0.0068 0.0186 0.0029 0.0225 0.0381 0.0107 0.0075 0.0117 0.0028 125% 0.0080 0.0174 0.0046 0.0146 0.0479 0.0098 0.0547 0.0801 0.0234 0.1099 0.0321 0.0105 150% 0.0193 0.0282 0.0110 0.0391 0.1055 0.0186 0.1113 0.1660 0.0537 0.0447 0.0764 0.0140 7m 75% 0.0021 0.0007 0.0014 0.0020 0.0039 0.0010 0.0029 0.0049 0.0020 0.0027 0.0040 0.0014 100% 0.0021 0.0036 0.0034 0.0059 0.0088 0.0029 0.0049 0.0098 0.0049 0.0082 0.0073 0.0025 125% 0.0035 0.0064 0.0046 0.0117 0.0195 0.0068 0.0156 0.0244 0.0088 0.0184 0.0169 0.0052 150% 0.0068 0.0130 0.0093 0.0283 0.0391 0.0146 0.0303 0.0498 0.0195 0.0358 0.0369 0.0109 8m 75% 0.0014 0.0014 0.0011 0.0020 0.0020 0.0020 0.0029 0.0010 0.0010 0.0040 0.0037 0.0012 100% 0.0010 0.0049 0.0029 0.0029 0.0049 0.0029 0.0029 0.0098 0.0029 0.0083 0.0057 0.0022 125% 0.0039 0.0077 0.0056 0.0078 0.0137 0.0049 0.0244 0.0303 0.0068 0.0197 0.0174 0.0047 150% 0.0075 0.0167 0.0103 0.0156 0.0321 0.0107 0.0527 0.0625 0.0176 0.0478 0.0438 0.0084 9m 75% -0.0001 0.0014 0.0013 0.0049 0.0117 0.0039 0.0029 0.0098 0.0029 0.0031 0.0032 0.0011 100% 0.0012 0.0015 0.0031 0.0215 0.0361 0.0078 0.0078 0.0352 0.0059 -0.0040 0.0089 0.0035 125% -0.0140 -0.0261 0.0055 0.0801 0.1162 0.0059 0.0352 0.1143 0.0146 -0.0002 0.0296 0.0111 150% 0.7518 0.6562 0.6789 0.9424 1.1504 0.7197 0.7256 1.1426 0.8164 0.7270 0.9038 1.8598

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65 Table 5-4. (Continued). Web A Web B Web C Web D Percent Duct1 Duct 3 Duct 5 Duct1 Duct 3 Duct 5 Duct1 Duct 3 Duct 5 Duct1 Duct 3 Duct 5 Model # Capacity 10m 75% 0.0014 0.0019 0.0013 0.0010 0.0020 0.0020 0.0010 0.0029 0.0010 0.0021 0.0013 0.0016 100% 0.0026 0.0035 0.0013 0.0020 0.0039 0.0020 0.0010 0.0039 0.0029 0.0035 0.0025 0.0024 125% 0.0041 0.0046 8.0000 0.0049 0.0088 0.0049 0.0020 0.0117 0.0049 0.0061 0.0062 0.0031 150% 0.0060 0.0095 9.0000 0.0127 0.0176 0.0078 0.0059 0.0225 0.0088 0.0082 0.0146 0.0064 11m 75% 0.0015 0.0010 0.0015 0.0020 0.0020 0.0010 0.0010 0.0020 0.0010 0.0019 0.0016 0.0008 100% 0.0560 0.0010 0.0021 0.0029 0.0029 0.0010 0.0010 0.0039 0.0020 0.0033 0.0021 0.0024 125% 0.0036 0.0033 0.0032 0.0049 0.0078 0.0029 0.0029 0.0107 0.0049 -0.0090 0.0086 0.0049 150% 0.0809 0.0963 0.0978 0.0977 0.1387 0.0781 0.1211 0.1963 0.1328 0.0939 0.1518 0.1160 12m 75% 0.0014 0.0014 0.0014 0.0008 0.0008 0.0008 0.0020 0.0020 0.0020 0.0018 0.0018 0.0018 100% 0.0020 0.0020 0.0020 0.0016 0.0016 0.0016 0.0039 0.0039 0.0039 0.0030 0.0030 0.0030 125% 0.0041 0.0041 0.0041 0.0041 0.0041 0.0041 0.0078 0.0078 0.0078 0.0038 0.0038 0.0038 150% 0.0078 0.0078 0.0078 0.0093 0.0093 0.0093 0.0127 0.0127 0.0127 0.0071 0.0071 0.0071 13m 75% 0.0015 0.0017 0.0008 0.0010 0.0020 0.0020 0.0000 0.0020 0.0020 0.0014 0.0014 0.0017 100% 0.0023 0.0026 0.0021 0.0020 0.0029 0.0020 0.0000 0.0029 0.0020 0.0026 0.0027 0.0017 125% 0.0022 0.0027 0.0021 0.0039 0.0068 0.0029 0.0000 0.0068 0.0039 0.0041 0.0058 0.0028 150% 0.0047 0.0045 0.0021 0.0078 0.0137 0.0059 0.0000 0.0117 0.0059 0.0059 0.0117 0.0017 14m 75% 0.0018 0.0018 0.0012 0.0010 0.0022 0.0004 0.0010 0.0020 0.0020 0.0016 0.0022 0.0011 100% 0.0030 0.0029 0.0015 0.0042 0.0043 0.0065 0.0010 0.0049 0.0059 0.0013 0.0053 0.0019 125% 0.0072 -0.0008 0.0017 0.0097 0.0109 0.0086 -0.0010 0.0059 0.0117 0.0060 0.0104 0.0047 150% 0.0228 -0.0302 0.0064 0.0268 0.0279 -0.0193 -0.0195 0.0146 0.0098 -0.0168 0.0364 0.0140 2MVert 75% 0.0015 0.0028 0.0020 0.0020 0.0029 0.0010 0.0010 0.0029 0.0020 0.0021 0.0029 0.0020 100% 0.0021 0.0057 0.0020 0.0059 0.0088 0.0020 0.0010 0.0088 0.0029 -0.0017 0.0050 -0.0233 125% 0.0065 0.0204 0.0059 0.0000 0.0000 0.0039 0.0049 0.0264 0.0000 0.0046 0.0175 0.0074 150% 0.0132 0.0397 0.0109 0.0332 0.0488 0.0068 0.0117 0.0557 0.0117 0.0074 0.0371 0.0163 11MVert 75% 0.0010 0.0010 0.0010 0.0010 0.0020 0.0010 0.0020 0.0020 0.0010 0.0022 0.0010 0.0019 100% 0.0000 0.0020 0.0000 0.0020 0.0029 0.0010 0.0039 0.0039 0.0029 0.0024 0.0030 0.0019 125% 0.0000 0.0039 0.0010 0.0039 0.0049 -0.0013 0.0059 0.0068 0.0049 0.0050 0.0069 0.0038 150% 0.0000 0.0107 0.0020 0.0068 0.0146 0.0000 0.0127 0.0107 0.0088 0.0091 0.0148 0.0068 defined as a "Capacity" calculated using conventional means, Applying an over-strength factor for rebar strain harden- but removing resistance factors. This provided the best direct ing (which is included in the FE analysis), comparison to finite element analyses. For the webs of the single-cell geometry prototype, Pc was calculated as follows: Mo = Mn 1.125 = 52.6 k-ft/ft As described earlier, moment-fixity effects were approxi- h = 9.67 feet mately 0.6 for interior webs and 0.7 for exterior webs. Since Mn = 42.1 k-ft/ft there were only three ducts distributed vertically, the increase to capacity caused by load distribution was small, so no ca- Removing the safety factor = 0.9, pacity increase was applied for this. So the baseline Pc became Mn = 46.8 k-ft/ft Pc = [52.6/(h/4)]/0.7 = 31.1 k/ft