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From page 44... ... The web is subject to regional transverse bending which results in tensile stresses on the local slab. Detailed local analysis models were used to evaluate the local stresses resulting from longitudinal tendons generating transverse forces on curved webs. Read the entire page →
From page 45... ... The top slab thickness at Las Lomas varied transversely and the 45 GLOBAL Girder Action LOCAL Slab Action REGIONAL Bean Action Figure 5-1. Types of actions considered. Read the entire page →
From page 46... ... At Las Lomas, the centerline distance between interior and exterior webs was 11 feet. This scaled to 3 ft 8 in. Read the entire page →
From page 47... ... A 5-ft curve was more than twice the clear height of the web and was thought to be sufficient to allow regional transverse bending. A 5-ft straight transition zone on each end insulated the curve from the complex stresses at anchorages. Read the entire page →
From page 48... ... Specimen 1.0DC follows the Texas State Department of Highway and Public Transportation design of the San Antonio "Y" project with an arrangement that maintained a clear spacing between ducts equal to the diameter of the duct. It is believed that this allows for better consolidation and, more importantly, eliminates the single large discontinuity found at Las Lomas. Read the entire page →
From page 49... ... Figure 5-8 compares tendon horizontal force versus deflections for the four different webs tested. Finite Element (FE) Read the entire page →
From page 50... ... can indicate concrete cracking, which occurs at strain of approximately 1.50E-4 to 50 Figure 5-9. Finite element model and boundary conditions. Read the entire page →
From page 51... ... Figure 5-12 shows similar strain contours, but in an end view at a lower displacement. Here the crack zones are also fully formed, but are easier to see in cross section. Read the entire page →
From page 52... ... the regional moment calculation in the sloping exterior webs. Though not studied in depth, there was no apparent effect on the behavior of vertical webs caused by super-elevation so it was not included in the single cell section that was studied. Read the entire page →
From page 53... ... The boundary conditions for the models were the same as for the UT Test simulation, which produced reasonable correlation between analysis and test. The model is a sector slice taken from a curve. Read the entire page →
From page 54... ... Web A B C D 13 k/ft 17 k/ft 17 k/ft 15 k/ft In order to establish a baseline for comparison with design calculations, as previously mentioned, Pc is defined as a "Capacity" calculated using conventional means, but removing safety factors, so as to make direct comparison to finite element analyses. For the interior (B or C webs) Read the entire page →
From page 55... ... 88.4% of that caused by a single point load at midheight. So the baseline Pc becomes Pc = [10.9/(h/4) Read the entire page →
From page 56... ... Figure 5-16. Example finite element mesh for multicell local analysis prototype. Read the entire page →
From page 57... ... The maximum principal strain contours illustrate the general level of damage to the concrete surrounding the tendon ducts (maximum tensile strain regardless of orientation) Read the entire page →
From page 58... ... total forces (sum of all tendon ducts in the web) applied when any part of the stirrup reaches yield, and when the web distortion reaches 0.06 inch. Read the entire page →
From page 59... ... than the vertical webs, but part of this difference was caused by being exterior webs rather than interior. Exterior webs have more flexible end conditions at their connection with the top and bottom slab, and this produces larger mid-height moments. Read the entire page →
From page 60... ... 60 Web A Web B Web C Web D Percent Mid Quarter Mid Quarter Mid Quarter Mid Quarter Model # Capacity 1m 75% 0.0290 0.0287 0.0360 0.0262 0.0271 0.0210 0.0199 0.0139 100% 0.0830 0.0686 0.0962 0.0555 0.0797 0.0420 0.0554 0.0225 125% 0.1851 0.1553 0.2249 0.1371 0.1981 0.1115 0.1390 0.0625 150% 0.4067 0.3567 0.5017 0.3382 0.4859 0.3083 0.3379 0.1867 2m 75% 0.0309 0.0340 0.0242 0.0262 0.0237 0.0259 0.0254 0.0216 100% 0.0872 0.0891 0.0702 0.0690 0.0673 0.0672 0.0673 0.0573 125% 0.1966 0.2026 0.1702 0.1629 0.1676 0.1623 0.1566 0.1366 150% 0.4455 0.4509 0.3821 0.3756 0.4080 0.3897 0.3477 0.3067 3m 75% 0.0554 0.0520 0.0411 0.0403 0.0225 0.0293 0.0309 0.0266 100% 0.1524 0.1395 0.1323 0.1191 0.0615 0.0792 0.0863 0.0751 125% 0.3711 0.3367 0.3314 0.2972 0.1571 0.1974 0.2103 0.1841 150% 2.2610 2.2670 1.6490 1.5490 0.9640 1.2280 0.9860 0.6550 4m 75% 0.2148 0.3214 0.2289 0.3171 0.1890 0.2885 0.2141 0.2803 100% 0.8136 1.2218 0.9112 1.2538 0.7589 1.1392 0.8323 1.0922 125% 2.3248 3.5099 2.7380 3.7348 2.2520 3.3725 2.4692 3.2460 150% 11.1900 16.3600 11.3300 15.5600 9.9500 15.1500 12.4100 14.2900 5m 75% 0.0251 0.0269 0.0190 0.0202 0.0172 0.0195 0.0179 0.0142 100% 0.0665 0.0687 0.0518 0.0539 0.0409 0.0481 0.0511 0.0415 125% 0.1385 0.1408 0.1103 0.1114 0.0938 0.0986 0.1082 0.0870 150% 0.2707 0.2731 0.2248 0.2240 0.1954 0.1983 0.2109 0.1726 6m 75% 0.0352 0.0386 0.0278 0.0304 0.0506 0.0385 0.0257 0.0231 100% 0.1240 0.1290 0.1051 0.1048 0.1610 0.1313 0.0887 0.0840 125% 0.3047 0.3182 0.2684 0.2603 0.3685 0.3123 0.2182 0.2071 150% 0.7176 0.7433 0.6550 0.6354 0.8475 0.7286 0.5231 0.4981 7m 75% 0.0279 0.0298 0.0220 0.0230 0.0207 0.0225 0.0206 0.0170 100% 0.0789 0.0799 0.0583 0.0606 0.0548 0.0587 0.0596 0.0486 125% 0.1674 0.1702 0.1295 0.1325 0.1283 0.1305 0.1332 0.1074 150% 0.2980 0.3033 0.2425 0.2393 0.2493 0.2427 0.2385 0.1935 8m 75% 0.0313 0.0337 0.0217 0.0253 0.0214 0.0253 0.0235 0.0202 100% 0.0922 0.0916 0.0545 0.0660 0.0621 0.0680 0.0671 0.0558 125% 0.2020 0.2030 0.1338 0.1560 0.1639 0.1630 0.1563 0.1285 150% 0.4180 0.4180 0.2815 0.3252 0.3478 0.3461 0.3340 0.2714 9m 75% 0.1442 0.1983 0.1270 0.1825 0.1067 0.1682 0.1481 0.1654 100% 0.5575 0.7819 0.5310 0.7502 0.4394 0.6840 0.5756 0.6430 125% 1.6680 2.3691 1.6878 2.3781 1.3931 2.1697 1.7823 1.9963 150% 9.7190 13.7340 8.8200 12.3520 7.6240 11.8020 11.0610 11.3050 10m 75% 0.0230 0.0254 0.0178 0.0197 0.0178 0.0195 0.0156 0.0122 100% 0.0591 0.0627 0.0397 0.0480 0.0390 0.0463 0.0427 0.0363 125% 0.1350 0.1428 0.0892 0.1096 0.0924 0.1098 0.0990 0.0847 150% 0.2458 0.2636 0.1778 0.2091 0.1755 0.2090 0.1939 0.1626 11m 75% 0.0388 0.0390 0.0253 0.0273 0.0183 0.0213 0.0195 0.0154 100% 0.1024 0.1019 0.0683 0.0765 0.0453 0.0566 0.0575 0.0491 125% 0.2601 0.2544 0.1764 0.1961 0.1160 0.1450 0.1534 0.1270 150% 1.1300 1.2390 0.7370 0.7760 0.6300 0.6890 0.5420 0.3130 12m 75% 0.0212 0.0236 0.0168 0.0181 0.0161 0.0180 0.0153 0.0113 100% 0.0493 0.0537 0.0355 0.0414 0.0343 0.0412 0.0407 0.0328 125% 0.1051 0.1118 0.0761 0.0864 0.0705 0.0860 0.0991 0.0748 150% 0.1949 0.2089 0.1515 0.1688 0.1332 0.1642 0.1939 0.1454 13m 75% 0.0190 0.0202 0.0161 0.0169 0.0162 0.0175 0.0154 0.0117 100% 0.0372 0.0392 0.0285 0.0319 0.0288 0.0327 0.0324 0.0256 125% 0.0750 0.0780 0.0533 0.0610 0.0541 0.0627 0.0630 0.0516 150% 0.1201 0.1258 0.0986 0.1089 0.1059 0.1164 0.1122 0.0903 Table 5-2. Deflections. Read the entire page →
From page 61... ... The results of the parameter study were influenced by the fact that when the cover is reduced, for the same overall web thickness, the moment arm for the stirrups is increased, and this is an off-setting influence on pullout resistance. As will be discussed further in the conclusions, it appears appropriate to check cover concrete thickness for resistance to initial cracking, but not to include cover concrete tensile strength in the calculation of regional transverse bending strength. Read the entire page →
From page 62... ... 62 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 1m 75% 0.0002 0.0003 0.0002 0.0002 0.0005 0.0004 0.0002 0.0004 0.0002 0.0002 0.0003 0.0002 100% 0.0007 0.0011 0.0005 0.0006 0.0017 0.0010 0.0005 0.0015 0.0006 0.0006 0.0011 0.0005 125% 0.0015 0.0023 0.0013 0.0012 0.0045 0.0016 0.0012 0.0033 0.0013 0.0013 0.0026 0.0013 150% 0.0026 0.0057 0.0018 0.0017 0.0104 0.0026 0.0020 0.0085 0.0026 0.0024 0.0071 0.0019 2m 75% 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0001 100% 0.0007 0.0003 0.0003 0.0003 0.0005 0.0008 0.0003 0.0012 0.0003 0.0006 0.0004 0.0003 125% 0.0013 0.0008 0.0006 0.0007 0.0013 0.0018 0.0008 0.0018 0.0008 0.0013 0.0019 0.0007 150% 0.0026 0.0015 0.0012 0.0018 0.0021 0.0039 0.0019 0.0083 0.0014 0.0024 0.0019 0.0012 3m 75% 0.0003 0.0003 0.0002 0.0003 0.0002 0.0003 0.0002 0.0001 0.0001 0.0003 0.0005 0.0001 100% 0.0009 0.0008 0.0005 0.0012 0.0008 0.0008 0.0004 0.0004 0.0003 0.0010 0.0012 0.0003 125% 0.0023 0.0019 0.0013 0.0027 0.0019 0.0018 0.0010 0.0009 0.0006 0.0018 0.0032 0.0009 150% 0.0209 0.0186 0.0207 0.0225 0.0153 0.0218 0.0178 0.0170 0.0172 0.0242 0.0244 0.0164 4m 75% 0.0011 0.0019 0.0007 0.0008 0.0013 0.0014 0.0009 0.0015 0.0010 0.0016 0.0013 0.0003 100% 0.0025 0.0029 0.0025 0.0019 0.0045 0.0080 0.0027 0.0068 0.0046 0.0056 0.0021 0.0011 125% 0.0093 0.0235 0.0090 0.0065 0.0153 0.0246 0.0107 0.0171 0.0158 0.0197 0.0048 0.0021 150% 0.0789 0.0978 0.0787 0.0793 0.0756 0.0994 0.0870 0.0796 0.0876 0.1241 0.0923 0.0653 5m 75% 0.0002 0.0002 0.0001 0.0002 0.0001 0.0002 0.0001 0.0001 0.0001 0.0003 0.0003 0.0001 100% 0.0007 0.0003 0.0003 0.0007 0.0004 0.0003 0.0003 0.0003 0.0002 0.0007 0.0012 0.0002 125% 0.0015 0.0009 0.0006 0.0016 0.0009 0.0006 0.0009 0.0008 0.0003 0.0014 0.0020 0.0005 150% 0.0029 0.0015 0.0012 0.0033 0.0015 0.0012 0.0019 0.0017 0.0007 0.0025 0.0040 0.0010 6m 75% 0.0003 0.0002 0.0002 0.0002 0.0002 0.0002 0.0007 0.0006 0.0004 0.0004 0.0004 0.0001 100% 0.0016 0.0009 0.0004 0.0007 0.0010 0.0004 0.0018 0.0016 0.0011 0.0014 0.0004 0.0003 125% 0.0041 0.0022 0.0015 0.0014 0.0027 0.0012 0.0042 0.0036 0.0023 0.0028 0.0026 0.0008 150% 0.0099 0.0065 0.0037 0.0027 0.0026 0.0031 0.0110 0.0029 0.0054 0.0081 0.0020 0.0017 7m 75% 0.0002 0.0002 0.0001 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0002 0.0001 100% 0.0006 0.0006 0.0003 0.0005 0.0005 0.0003 0.0005 0.0005 0.0003 0.0006 0.0006 0.0003 125% 0.0013 0.0012 0.0005 0.0010 0.0010 0.0007 0.0010 0.0010 0.0007 0.0013 0.0013 0.0007 150% 0.0026 0.0017 0.0010 0.0017 0.0019 0.0013 0.0017 0.0019 0.0013 0.0023 0.0019 0.0014 8m 75% 0.0002 0.0002 0.0002 0.0002 0.0001 0.0002 0.0001 0.0001 0.0001 0.0003 0.0003 0.0001 100% 0.0009 0.0008 0.0003 0.0003 0.0004 0.0003 0.0004 0.0004 0.0004 0.0008 0.0009 0.0003 125% 0.0019 0.0016 0.0005 0.0008 0.0010 0.0007 0.0012 0.0010 0.0008 0.0015 0.0019 0.0008 150% 0.0040 0.0035 0.0012 0.0015 0.0022 0.0017 0.0024 0.0020 0.0017 0.0024 0.0046 0.0018 9m 75% 0.0010 0.0005 0.0002 0.0007 0.0009 0.0006 0.0008 0.0008 0.0004 0.0013 0.0006 0.0001 100% 0.0042 0.0022 0.0010 0.0029 0.0042 0.0025 0.0027 0.0036 0.0022 0.0062 0.0013 0.0003 125% 0.0147 0.0083 0.0019 0.0101 0.0133 0.0105 0.0100 0.0118 0.0070 0.0203 0.0038 0.0012 150% 0.0747 0.0664 0.0559 0.0708 0.0742 0.0753 0.0721 0.0713 0.0688 0.1066 0.0592 0.0514 10m 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% 0.0004 0.0004 0.0003 0.0002 0.0002 0.0002 0.0002 0.0001 0.0002 0.0008 0.0003 0.0002 125% 0.0009 0.0009 0.0007 0.0003 0.0003 0.0005 0.0004 0.0003 0.0007 0.0016 0.0006 0.0004 150% 0.0016 0.0016 0.0011 0.0008 0.0007 0.0012 0.0008 0.0007 0.0013 0.0027 0.0014 0.0008 11m 75% 0.0002 0.0002 0.0002 0.0002 0.0001 0.0002 0.0001 0.0001 0.0001 0.0003 0.0001 0.0001 100% 0.0006 0.0005 0.0004 0.0003 0.0002 0.0005 0.0002 0.0001 0.0002 0.0008 0.0002 0.0002 125% 0.0016 0.0013 0.0011 0.0008 0.0005 0.0012 0.0004 0.0002 0.0005 0.0021 0.0006 0.0005 150% 0.0103 0.0091 0.0109 0.0108 0.0048 0.0117 0.0098 0.0042 0.0096 0.0154 0.0070 0.0086 Table 5-3. Stirrup strain (%) Read the entire page →
From page 63... ... mode is tending toward local duct pullout, stirrups are not a very effective deterrent against this failure mode. But if the duct layout and duct ties are properly detailed to eliminate the local pullout failure mode, the stirrup spacing does define the web "regional" beam strength. Read the entire page →
From page 64... ... 64 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 Table 5-4. Distortion (web thickness change) Read the entire page →
From page 65... ... Since there were only three ducts distributed vertically, the increase to capacity caused by load distribution was small, so no capacity increase was applied for this. So the baseline Pc became Pc = [52.6/(h/4) Read the entire page →
From page 66... ... 66 Total Force (in % of Pc and in K/ft) Model # Web AWeb A Web B Web B Web C Web C Web D Web D 1M 119.55% 9.93 107.36% 11.38 111.04% 11.77 122.41% 11.18 2M 141.66% 11.77 128.85% 13.66 128.67% 13.64 129.38% 11.82 3M 121.11% 10.06 118.77% 12.59 144.72% 15.34 134.24% 12.26 4M - 6.24 - 8.59 - 8.57 - 7.42 5M 134.96% 11.21 133.11% 14.11 150.47% 15.95 126.25% 11.53 6M 105.54% 8.77 118.54% 12.57 105.75% 11.21 117.92% 10.77 7M 140.98% 11.71 154.06% 16.33 153.87% 16.31 147.93% 13.51 8M 124.72% 10.36 148.49% 15.74 145.38% 15.41 129.86% 11.86 9M - 7.28 - 9.59 - 9.58 - 7.75 10M 157.23% 13.06 162.45% 17.22 161.60% 17.13 142.01% 12.97 11M 131.45% 10.92 141.51% 15.00 148.15% 15.70 126.77% 11.58 12M 160.55% 13.34 165.81% 17.58 165.58% 17.55 135.53% 12.38 13M 180.74% 15.01 184.97% 19.61 184.00% 19.50 166.09% 15.17 14M - 8.65 - 10.47 - 11.81 - 8.48 2MVert 151.05% 12.55 148.79% 15.77 145.06% 15.38 151.69% 13.85 11MVert 140.59% 11.68 152.49% 16.16 165.41% 17.53 167.19% 15.27 - Percentages not shown for cases other than ducts placed at midheight * Read the entire page →
From page 67... ... Effect of web thickness – thin webs. Read the entire page →
From page 68... ... 13.85 17% change with vertical web 11M-A vs. 11Mvert-A 10.92 vs. Read the entire page →
From page 69... ... Effect of different duct configurations – thin webs. Model-Web Force at stirrup yield (kips/ft) Read the entire page →
From page 70... ... 12M-A 15.01 vs. 13.34 -11% change with 33% less stirrup steel 13M-B vs. Read the entire page →
From page 71... ... 71 21'- 6"21'- 6" 10'- 0" 11'- 6" 5'-0" 9" 18 " 20" 16 " 9'- 0" 9'- 0" 3'-6" 12 ' 6" 10 " 9" Ty p 24 " @ Pi er ~3.5" 6" 6" 2" Cl 1.5" Cl Tendons assumed 6-31 F 0.6" 1 web Ducts 5"00 20" # 4 at 12" Typ # 7 at 12" Typ # 6 at 12" Figure 5-23. Tendon duct and local reinforcement for the local analysis prototype for a single-cell box. Read the entire page →
From page 72... ... For the single-cell example, with the 20-inch webs and double row of ducts, the finite element analysis showed capacities that were mostly lower than the hand-calculated regional transverse bending capacity (i.e., stirrup yield was reached at a range from 52% Pc up to 100% Pc) , but this is explained by the fact that, for the thicker web, failures were dominated by local lateral shearing. Read the entire page →
From page 73... ... 73 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 00097 00150 00150 00150 100% 0.00421 0.00222 00173 00310 00310 00310 125% 0.01851 0.01023 00275 01506 01506 01506 150% 0.04107 0.03204 01021 04032 04032 04032 2S 75% 0.01429 0.00345 00187 00680 00311 00188 100% 0.03765 0.01701 00450 02543 01638 00724 125% 0.07417 0.04288 01750 04969 03558 02096 150% 0.24986 0.15104 06873 21465 10079 05699 3S 75% 0.00152 0.00127 00090 00158 00097 00049 100% 0.00376 0.00218 00176 00326 00236 00164 125% 0.01529 0.00902 00279 01341 00712 00421 150% 0.04083 0.03034 00937 03334 02640 01838 4S 75% 0.00332 0.00190 00134 00165 00172 00175 100% 0.01269 0.00563 00244 00361 00580 00520 125% 0.03219 0.02447 00713 01271 02075 02036 150% 0.06683 0.05776 01953 03541 04853 04659 5S 75% 0.00126 0.00112 00076 00140 00141 00110 100% 0.00189 0.00177 00137 00244 00332 00187 125% 0.00942 0.00452 00200 01017 01499 00759 150% 0.02689 0.01755 00329 03406 03425 03028 6S 75% 0.00178 0.00137 00109 00150 00132 00113 100% 0.00642 0.00204 00190 00415 00284 00215 125% 0.02163 0.00915 00323 01628 01319 00910 150% 0.04799 0.02955 00911 03942 03223 02922 7S 75% 0.00159 0.00135 00092 00160 00140 00124 100% 0.00329 0.00215 00160 00525 00335 00259 125% 0.01451 0.01098 00257 01872 01541 00807 150% 0.03987 0.03238 00851 04636 04096 02690 8S 75% 0.00162 0.00149 00134 00154 00106 00059 100% 0.00387 0.00339 00277 00407 00243 00158 125% 0.01690 0.01528 01066 01612 00684 00332 150% 0.04019 0.03653 02766 04088 02560 01352 9S 75% 0.00129 0.00110 00072 00207 00174 00151 100% 0.00207 0.00178 00129 00841 00630 00387 125% 0.01140 0.00698 00196 02662 02184 01958 150% 0.03106 0.02321 00373 06473 05138 04844 10S 75% 0.01253 0.00783 00210 00703 00380 00184 100% 0.03730 0.02768 00920 02789 01708 00750 125% 0.07189 0.05973 02640 05278 03636 01851 150% 0.23078 0. Read the entire page →
From page 74... ... 74 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 Table 5-17. Distortion (web thickness changes – inches) Read the entire page →
From page 75... ... Regional transverse bending strength is directly tied to stirrup area, but it controls the design only when web/duct tie reinforcement is NOT used or when the websplitting/lateral shear-failure does not occur. In other words, if the failure mode is tending toward local duct breakout, stirrups are not a very effective deterrent against this failure mode. Read the entire page →
From page 76... ... 7S-2 23.78 vs. 26.64 21% increase with 50% more stirrup steel Model-Web Force at stirrup yield (kips) Read the entire page →
From page 77... ... Where Mn is defined by an allowable tensile stress for concrete of , and φ = 0.55. The allowable tensile stress should also be reduced by the tensile stress in the concrete at the critical point due to regional transverse bending. Read the entire page →
From page 78... ... Dimensional changes of 0.5 inch can make considerable difference in the stresses in the web concrete and reinforcing steel. The following is an example of how design and construction issues can affect conditions for lateral tendon breakout. Read the entire page →

From page 44...

... The web is subject to regional transverse bending which results in tensile stresses on the local slab. Detailed local analysis models were used to evaluate the local stresses resulting from longitudinal tendons generating transverse forces on curved webs.