Simplified Shear Design of Structural Concrete Members: Appendixes (2005)

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H-1 Appendix H: Examination of Simplified Proposal Using Design Database H.1 Presentation of Design Database The proposal for simplified LRFD provisions is examined further in this Appendix using a Design Database intended to encompass the general loading and continuity conditions (e.g., distributed loads), section characteristics and design shear levels likely to be encountered in practice. The Design Database consists of concrete members having the typical bridge sections that the Experimental Shear Database could not cover; e.g., 36 inch-deep I shapes, 72 inch-deep T shapes, 78 inch-deep box shapes, and 36 inch-deep rectangular shapes. Included are composite and non-composite sections, precast and prestressed/post-tensioned and non-prestressed members, and simple and continuous designs. Fig. H-1 shows the sectional shapes and strand profiles of the sections in Design Database. Flexural Design of Members in Design Database The studies reported in this Appendix are aimed at determining how shear reinforcement amounts, determined using the proposed simplified provisions, differ from those determined using the AASHTO Standard, 2004 AASHTO LRFD, 2004 CSA, and R2K methods. Accordingly, significant effort was devoted to defining situations where the shear reinforcement amounts were not controlled by minimum shear requirements. Otherwise, in such cases, ratios of shear reinforcement requirements in accordance the different methods would be meaningless. First, the largest shear stress that could be applied to a given section was determined by reducing the span length and proportioning the strands or reinforcing bars, for prestressed members, so that the extreme fiber concrete stresses did not exceed the allowable stress limits specified in the 2004 AASHTO LRFD. Thereafter, the number of strands or reinforcing bars was reduced to 75%, 50%, or some other appropriate percentage of the maximum number of strands or bars determined in the first step. Then, the same approach was repeated for different span lengths. For prestressed members the number of strands and the span lengths required to keep the extreme fiber concrete stresses less than the allowable stress limits were not the only the major issues studied. Differences resulting from draping strands or placing top strands were also studied. The latter considerations resulted in large conservatisms for some members in the Design Database for some of the different design methods. This issue is discussed in Section H.2. Shear Design of the Members in Design Database Five or six different sections in each member were designed using four different shear design approaches: the proposed simplified method (Proposal); the AASHTO Standard method (Standard); the 2004 AASHTO LRFD (LRFD) method; and the 2004 Canadian Code (CSA)

H-2 method. The following assumptions were made for consistency: (1) The compressive strut angle was taken as 45 degrees whenever the design flexural moment was greater than the cracking moment at the section under consideration. (2) The applied moment at 90 percent of the flexural capacity of the member was used to determine the design forces. (3) The resistance or material factors specified for shear in the applicable codes are shown in Table H-1. Different codes use different load factors and different resistance or material factors to achieve their intended levels of safety and reliability. If the differing factors specified in each code are used to obtain values of design shear forces and nominal shear resistances for comparison purposes, then the relative performance of the different methods will depend directly on those factors. Thus, for this study the demand and resistance relationships were deliberately decoupled, and all resistance or material factors set equal to 0.9. (4) No less than the minimum shear reinforcement requirement was provided for any case. Minimum shear reinforcement requirements used were those specified in the applicable code. Values are shown in Table H-2. H.2 Comparison and Discussion of the Results The amount of shear reinforcement required, the strut angle, and the concrete component of the shear capacity were compared for the proposed simplified method, the other three shear design codes, and RESPONSE 2000, Reinforced Concrete Sectional Analysis Program using the Modified Compression Field Theory. . The minimum shear reinforcement requirements of the AASHTO LRFD were also enforced for analyses using RESPONSE 2000 (R2k). Table H-3 summarizes results for the members of the Design Database in terms of the relative ratios of the amounts of the required shear reinforcement for each approach to that of the R2K counterpart. Table H-3 contains six major columns. The first column lists the member type and the second lists the shear design procedure. The third column provides overall summary information on relative performance of the different design methods in terms of the number of cases studied for a particular beam type and the mean and coefficient of variation of those results for each of the four methods examined. The fourth through sixth columns provide a further breakdown of the information in column three. The governing relationship for assessing shear resistance is characterized as web-shear, transition, or flexure-shear for the information in columns four, five, and six, respectively. In a web-shear region Vcw is smaller than Vci and Mu is also smaller than Mcr, which means that in the proposed simplified method Vcw governs the shear strength of the member at the section considered and the angle of compression strut is smaller than 45 degrees. In the flexure-shear region Vci is smaller than Vcw, which means that in the

H-3 proposed simplified method Vci governs the shear strength of the member at the section considered and the angle of compression strut is 45 degrees. A transition region is a location that does not belong to either a web-shear region or a flexure-shear region. In a transition region Vcw governs the shear strength of the member at the section considered and the angle of compression strut is 45 degrees. It should be noted that the values in Table H-3 included non-minimum shear reinforcement cases only (i.e., design cases where the required shear reinforcement is less than or equal to minimum shear reinforcement are not shown in Table H-3). Non-minimum means all approaches required shear reinforcement amounts at a given section greater than the minimum amount shown in Table H-2. Tables H-4 through H-9 compare details for the concrete component of the shear capacity, the compressive strut (or crack) angle, and the amount of the required shear reinforcement for the five different design methods for each of the six design beams shown in Fig. H-1. All results, including minimum shear reinforcement cases, generated using the Design Database are shown. Figures H-2 through H-7 provide graphical comparisons of the amount of required shear reinforcement for the five different approaches for different positions along the length of the beam. The horizontal axis is the distance from the support and that axis terminates at mid span of the beam Figures H-8 through H-11 summarize comparison results for each of the six members of Fig. H-1 in terms of the ρvfy ratio required by each method to that required by the R2K results. The horizontal axis represents the amount of stirrup reinforcement required by the R2K method. The insert on each plot shows the mean, (m), and the standard deviation, (s), obtained from non- minimum cases. Also listed with each plot are the total number of cases included in the plot, including minimum cases, and the number of non-minimum cases. In the plots, the solid symbols represent non-minimum cases and the hollow symbols represent minimum cases. Comparisons The summary Table H-3, last row, shows that of the four methods the Proposal has the largest mean value (1.57) but the smallest coefficient of variation (0.23). The Proposal shows relatively large mean values for reinforced concrete members compared to the other approaches; e.g., R.C. rectangular single-span beams (1.78), R.C. T-shaped single-span beams (1.78), and R.C. rectangular continuous beams (1.35). Those mean values are slightly and consistently larger than those of the Standard (e.g., 1.50, 1.55, and 1.11), respectively, for the same members. This result is a reasonable since both provisions use similar equations - for R.C. members the Vc in the Proposal equals approximately 2√f’c and the compressive strut angle equals 45 degrees. However, the term, dv in the Proposal differs from that of d in the Standard and eventually produces a slightly larger required amount of shear reinforcement due to its reduced value in the

H-4 Vc term. For the prestressed members, I-Beams and Bulb T-Beams, in the Design Database, the LRFD and the CSA methods are slightly more conservative than the Standard method. This issue is discussed in depth in the next section. The Standard method shows the smallest mean value (1.26) and a modest coefficient of variations, 0.31. However, the Standard method is also non conservative for some members in the Design Database, especially in transition zone sections. The mean value for the Standard method in the transition zone is 0.90. This matter is also discussed in the next section. Discussion of the Results The LRFD and the CSA methods were conservative in the amount of required shear reinforcement, for specific cases, for members containing top strands. This conservatism is due to the code-based methods for taking account of top strands during evaluations of effective shear depth and longitudinal strain. The CSA method provides the following simplified equation for longitudinal strain: )A2(E 5.0/ ss pp popfpfvf x AE fANVVdM + −+−+=ε (CSA Eq. 11-13) where Mf, Vf, and Nf are design forces and Ap is defined as the area of tendons on the flexural tension side of the member, i.e., the area of tendons in the bottom-half of the section. For this definition the strain increases or remains the same when top strands are provided since Ap is constant and Mf or Vf increases or remains the same. This result directly increases the strut angle θ, decreases the multiplier β, and hence requires more stirrups. However, intuitively, additional top strands should reduce the required amount of stirrups because they reduce the longitudinal strain in the member. Second, a small conservatism may also result from the conservatively-drawn definition for the evaluation of “effective shear depth”. The LRFD method requires that the effective shear depth be taken as the distance, measured perpendicular to the neutral axis, between the resultants of the tensile and compressive forces due to flexure; it need not be taken to be less than the greater of 0.9de or 0.72h (AASHTO LRFD Art. 5.8.2.7). The quantity de is in turn defined as the effective depth from extreme compression fiber to the centroid of the tensile force in the tensile reinforcement. A similar definition for effective shear depth is used in the CSA method and proposed in the Proposal. With this definition the effective shear depth is reduced if a large number of prestressing strands are provided at top of the section, the neutral axis lies above them and, hence, those strands are considered as tensile reinforcement. This situation commonly occurs in practice when top strands are provided to control flexural cracks at transfer and at

H-5 service loads in a short member where only a small number of bottom strands are required for flexural strength. The resultant shortened shear depth reduces Vc proportionally. This definition causes a slightly excessive reduction in Vc for members containing top strands that represent a significant fraction of the total number prestressing strands in the beam. Consider for example a 43.5 in.-deep composite I-Beam containing 6 bottom strands and 2 top strands. This beam is the first member appearing in the Design Database of I-Beams, Table H-4. In this example, the neutral axis lies within the slab and therefore above the top strands. Hence the top strands should be considered as tensile steel according to the CSA or LRFD methods. Consequently, the calculated effective shear depth, dv is 31.3 in., (see Table H-4), rather than the value of 37.4 in. for the same beam without top strands. The value of longitudinal strain, εx is equal to 0.0022 for dv of 31.3 in.,(all other data not included in the Table H-4 are provided in the Process 12-50 digital format, see Appendix I). By contrast the same strain equals 0.0018 if the top strands are not considered and hence the design moment and design shear force would have been smaller, (561 k ft and 163 kips, respectively). Finally, the amount of required shear reinforcement is equal to 882 psi, whereas that amount would have been only 523 psi if the top strands were omitted. The latter value is 125% of the RESPONSE 2000 result where top strands are considered. Another observation is that the Standard method appears to be unconservative for some members in the Design Database, especially in transition region sections; the mean values of the relative ratios of the transverse reinforcement amounts required by the Standard and R2k methods for Bulb T-beams and Box girders are 0.85 and 0.80, respectively. A closer examination revealed that in most of the non conservative cases Mu was greater than Mcr and Vcw governed, which implies that the Standard method does not incorporate moment effects explicitly in its equations while the LRFD and CSA methods do; e.g., the longitudinal strain increases as the moment increases in the LRFD and CSA methods. In the Proposal the additional criterion that θ equals 45 degrees if Mu exceeds Mcr implicitly precludes such unconservatism. By contrast, for the Proposal, mean values of the relative ratios for Bulb T-beams and Box girders were 1.68 and 1.35, respectively. This situation commonly occurs in a high-shear and high-moment region such as occurs over an interior support in a continuous beam. As an alternative, the ASBI provisions provide a higher level of assurance against web cracking by limiting the shear capacity to '2 cf over interior supports of continuous beams. Closing Remarks This Design Database study disclosed intrinsic code conservatisms or unconservatisms that the use of a limited experimental database could not have disclosed. However, any user of this

H-6 document should be careful before making any judgments based on this Design Database study. The Design Database does not reflect the actual probability distributions of bridges that are currently being built or that already exist even though considerable effort was spent in trying to achieve a database representative of a comprehensive range of practical design cases. Additional information is provided in the Process 12-50 digital format so that a user can readily reproduce outputs and compare them with the results given by this Design Database study.

H-7 Figure H-1 Sectional Shapes and Strand Profile Section (unit: in.) Profile PC RC

H-8 Table H-1 Resistance Factors or Material Factors Proposal AASHTO Standard AASHTO LRFD CSA 0.90 RC: 0.85 PC: 0.90 0.90 Concrete - 0.65 Steel - 0.85 Prestress - 0.90 Table H-2 Minimum Shear Reinforcement, Av,min (unit: in.2) Proposal AASHTO Standard AASHTO LRFD CSA y w c f sbf ' y w f sb 50 y w c f sbf ' y w c f sbf ' * f’c and fy are in psi.

H-9 Table H-3 Relative Ratios of Amount of Required Shear Reinforcement to R2K Amount Total Web-Shear Transition Flexure-Shear Member Approach* no. mean c.o.v. no. mean c.o.v. no. mean c.o.v. no. mean c.o.v. std 1.36 0.28 1.43 0.22 1.12 0.45 0 0 lrfd 1.98 0.33 1.76 0.32 2.69 0.11 0 0 p 1.83 0.20 1.68 0.14 2.31 0.13 0 0 I Beam (Single Span) csa 38 2.10 0.42 29 1.77 0.38 9 3.16 0.19 0 0 0 std 1.14 0.29 1.21 0.25 0.85 0.34 0 0 lrfd 1.48 0.30 1.34 0.27 2.08 0.13 0 0 p 1.38 0.18 1.30 0.15 1.68 0.10 0 0 Bulb T (Single Span) csa 82 1.43 0.45 66 1.24 0.46 16 2.22 0.10 0 0 0 std 1.5 0.24 lrfd 1.23 0.24 p 1.78 0.22 RC Rect** (Single Span) csa 25 1.24 0.20 std 1.55 0.15 lrfd 1.21 0.12 p 1.78 0.16 RC T-Shape (Single Span) csa 35 1.18 0.12 std 0.77 0.26 0.66 0.38 0.8 0.20 0.08 0 lrfd 1.06 0.14 1.13 0.09 1.04 0.15 0.85 0 p 1.33 0.08 1.35 0.06 1.35 0.07 1.07 0 Box (Cont**) csa 18 0.88 0.25 6 0.72 0.14 11 0.97 0.24 1 0.85 0 std 1.11 0.22 lrfd 0.85 0.24 p 1.35 0.21 RC (Cont**) csa 15 0.9 0.19 std 1.26 0.31 1.24 0.28 0.90 0.38 0.08 0 lrfd 1.42 0.37 1.45 0.32 1.91 0.36 0.85 0 p 1.57 0.23 1.41 0.19 1.74 0.24 1.07 0 All csa 213 1.40 0.48 101 1.36 0.48 36 2.07 0.44 1 0.85 0 * std – AASHTO Standard, lrfd – AASHTO LRFD, p – Proposal, csa – Canadian Code approach ** Rect - Rectangular, Cont - Continuous Span *** All values are based on non-minimum cases, where non-minimum means all of the approaches required the shear reinforcement greater than the minimum requirements (see Table H-2) for a given section.

H-10 Table H-4 Summary of Results – Simply-Supported I Beam aashto standard aashto lrfd proposal csa r2k loca- tion dv Vu vu Mcr Mu Vci Vcw yv fρ Vc yv fρ θ Vc yv fρ θ Vc yv fρ θ Vcr yv fρbeam no. no. of bottom strands ft in kips ksi k ft k ft kips kips psi kips psi deg kips psi deg kips psi deg kips psi 1 6 2.9 31.3 171 0.911 920 612 274 87 492 27 804 43 52 537 36 17 882 44 83 320 - - - - - - - - - - - - - - - - - - - - - 6 3.6 31.3 151 0.804 915 725 209 88 382 28 699 43 52 446 36 15 840 46 63 260 6 5.4 31.3 101 0.538 900 951 110 89 113 28 431 44 53 228 36 13 613 50 (80) 160 6 7.2 31.3 50 0.266 895 1087 55 89 50 28 141 44 53 89 35 13 258 50 (42) 89 2 6 2.9 31.3 129 0.687 765 430 253 97 220 37 351 37 63 349 39 44 253 32 84 220 - - - - - - - - - - - - - - - - - - - - - 6 5 33 101 0.51 810 672 142 94 81 39 203 36 58 243 42 28 236 37 84 200 6 7.5 35.2 67 0.317 875 881 85 89 50 37 89 41 52 113 46 26 104 39 (62) 89 6 10 37.4 34 0.152 945 1007 48 81 50 39 89 41 43 89 52 30 89 38 (27) 89 3 6 2.9 31.3 74 0.394 661 229 252 98 50 63 89 22 62 89 36 78 89 29 91 89 6 5 31.3 67 0.357 626 378 146 97 50 63 89 22 61 89 36 75 89 29 87 89 6 10 33 50 0.253 581 672 73 99 50 42 89 34 61 89 37 42 89 33 (32) 89 6 15 35.2 34 0.161 571 881 46 99 50 42 89 36 (46) 89 45 31 89 37 (32) 89 6 20 37.4 17 0.076 596 1007 38 95 50 39 89 41 (38) 89 45 32 89 37 (15) 89 4 8 2.9 31.8 222 1.164 1184 797 348 82 777 26 1047 42 47 828 38 19 1092 43 85 460 - - - - - - - - - - - - - - - - - - - - - 8 3.6 31.8 197 1.032 1179 944 264 83 642 27 929 43 47 705 38 17 1043 45 95 380 8 5.4 31.8 131 0.687 1164 1239 139 83 293 29 572 43 48 398 38 15 754 48 80 200 8 7.2 31.8 66 0.346 1159 1416 67 84 50 28 226 44 48 101 38 14 335 48 (49) 89 5 8 2.9 31.8 181 0.949 1169 605 374 83 555 40 529 32 48 624 38 33 595 35 90 340 - - - - - - - - - - - - - - - - - - - - - 8 5 31.8 142 0.744 1139 944 191 85 345 28 636 43 49 436 37 21 613 41 91 220 8 7.5 31.8 94 0.493 1119 1239 103 86 87 28 383 44 50 214 37 16 459 45 (80) 120 8 10 31.8 47 0.246 1104 1416 51 87 50 28 120 44 (51) 89 45 15 197 47 (35) 89 * The values in parentheses represent the cases where the flexural shear cracking force governs for Vc.

H-11 Table H-4 Summary of Results – Simply-Supported I Beam (continued) aashto standard aashto lrfd proposal csa r2k loca- tion dv Vu vu Mcr Mu Vci Vcw yv fρ Vc yv fρ θ Vc yv fρ θ Vc yv fρ θ Vcr yv fρbeam no. no. of bottom strands ft in kips ksi k ft k ft kips kips psi kips psi deg kips psi deg kips psi deg kips psi 6 8 2.9 31.8 99 0.519 925 305 338 93 82 64 89 22 57 216 38 81 89 29 82 120 8 5 32.5 89 0.456 890 503 194 94 50 65 89 22 57 167 38 79 89 29 89 100 8 10 34.1 67 0.327 845 893 94 95 50 44 89 34 57 89 39 47 89 32 76 89 8 15 35.7 45 0.21 835 1173 57 93 50 43 89 36 54 89 41 33 89 36 (38) 89 8 20 37.4 22 0.098 860 1340 38 88 50 39 89 41 (38) 89 45 32 89 37 (19) 89 7 8 2.9 31.5 69 0.365 855 208 336 95 50 69 89 21 59 89 36 84 89 28 80 89 8 7.5 32.5 60 0.308 676 503 128 104 50 65 89 22 66 89 34 80 89 29 78 89 8 15 34.1 45 0.22 457 893 62 115 50 47 89 31 (62) 89 45 57 89 31 (51) 89 8 22.5 35.7 30 0.14 327 1173 39 122 50 43 89 36 (39) 89 45 35 89 35 (25) 89 8 30 37.4 15 0.067 282 1340 38 124 50 39 89 41 (38) 89 45 32 89 37 (13) 89 8 10 2.9 32.4 269 1.384 1428 967 416 81 1011 26 1253 42 45 1079 40 21 1246 41 85 640 - - - - - - - - - - - - - - - - - - - - - 10 3.6 32.4 239 1.229 1423 1145 315 81 853 27 1114 42 45 927 39 18 1188 43 95 520 10 5.4 32.4 159 0.818 1408 1503 165 82 439 29 713 43 46 546 39 16 855 46 97 280 10 7.2 32.4 80 0.412 1403 1718 79 82 50 29 296 44 46 180 39 16 384 46 (64) 120 9 10 2.9 32.4 220 1.132 1413 734 447 82 753 40 676 33 46 828 39 38 693 34 89 460 - - - - - - - - - - - - - - - - - - - - - 10 5 32.4 172 0.885 1383 1145 228 83 500 29 783 43 47 591 39 23 702 40 92 300 10 7.5 32.4 115 0.592 1363 1503 121 84 201 29 474 43 48 321 38 18 532 44 (93) 160 10 10 32.4 57 0.293 1348 1718 60 85 50 29 170 44 49 89 38 17 229 45 (46) 89 10 10 2.9 32.5 121 0.621 1169 374 417 91 199 57 138 21 55 330 39 85 89 28 83 160 10 5 33.1 110 0.554 1134 617 237 92 136 67 94 22 55 275 39 82 89 29 90 140 10 10 34.4 82 0.397 1084 1096 112 92 50 48 98 31 54 153 41 51 89 32 88 100 10 15 35.7 55 0.257 1074 1439 66 89 50 43 89 36 51 89 43 34 89 36 (50) 89 10 20 37 27 0.122 1104 1644 38 83 50 39 89 41 (38) 89 45 32 89 37 (21) 89 * The values in parentheses represent the cases where the flexural shear cracking force governs for Vc.

H-12 Table H-4 Summary of Results – Simply-Supported I Beam (continued) aashto standard aashto lrfd proposal csa r2k loca- tion dv Vu vu Mcr Mu Vci Vcw yv fρ Vc yv fρ θ Vc yv fρ θ Vc yv fρ θ Vcr yv fρbeam no. no. of bottom strands ft in kips ksi k ft k ft kips kips psi kips psi deg kips psi deg kips psi deg kips psi 11 10 2.9 32.3 84 0.433 1094 255 415 93 50 71 89 21 56 144 37 90 89 28 101 89 10 7.5 33.1 73 0.368 920 617 157 102 50 67 89 22 64 89 35 84 89 29 95 89 10 15 34.4 55 0.266 696 1096 74 112 50 54 89 27 72 89 33 63 89 30 (59) 89 10 22.5 35.7 37 0.173 566 1439 45 118 50 43 89 36 (45) 89 45 36 89 35 (33) 89 10 30 37 18 0.081 526 1644 37 119 50 39 89 41 (38) 89 45 32 89 37 (14) 89 12 12 2.9 32.9 319 1.616 1667 1143 483 78 1260 25 1473 41 42 1364 41 22 1430 41 107 820 - - - - - - - - - - - - - - - - - - - - - 12 3.6 32.9 282 1.429 1662 1354 365 78 1073 26 1297 42 42 1184 41 20 1350 42 96 700 12 5.4 32.9 188 0.952 1647 1777 190 79 593 28 847 43 43 719 41 17 972 45 96 340 12 7.2 32.9 94 0.476 1642 2030 90 80 113 29 365 44 44 261 40 17 436 45 (71) 160 13 12 2.9 32.9 260 1.317 1652 868 519 79 958 38 820 33 43 1065 41 41 801 33 92 618 - - - - - - - - - - - - - - - - - - - - - 12 5 32.9 203 1.028 1622 1354 264 81 660 37 729 37 45 762 40 25 804 39 90 412 12 7.5 32.9 135 0.684 1602 1777 140 82 309 30 570 43 46 431 39 19 603 43 93 206 12 10 32.9 68 0.344 1587 2030 68 83 50 29 225 44 47 119 39 18 271 44 (51) 89 14 12 2.9 32.9 150 0.76 1597 462 556 82 385 52 244 23 46 500 39 86 194 28 99 240 12 5 32.9 135 0.684 1528 761 307 86 291 55 198 23 49 396 38 81 168 29 82 220 12 10 32.9 102 0.517 1393 1354 134 94 87 39 276 36 57 203 35 37 246 34 92 140 12 15 32.9 68 0.344 1298 1777 73 100 50 34 180 41 62 89 34 23 208 40 (58) 89 12 20 32.9 34 0.172 1239 2030 38 103 50 29 89 44 (38) 89 45 20 89 42 (26) 89 15 12 2.9 32.8 100 0.508 1333 303 495 91 92 84 89 20 54 228 38 94 89 28 107 120 12 7.5 33.5 87 0.433 1159 733 185 99 50 74 89 21 61 128 36 86 89 29 97 89 12 15 34.6 65 0.313 935 1303 86 109 50 55 89 27 69 89 34 67 89 30 74 89 12 22.5 35.7 43 0.201 810 1711 51 115 50 43 89 36 (51) 89 45 37 89 35 (37) 89 12 30 36.7 22 0.1 765 1955 37 114 50 38 89 41 (37) 89 45 32 89 37 (18) 89 * The values in parentheses represent the cases where the flexural shear cracking force governs for Vc.

H-13 Table H-4 Summary of Results – Simply-Supported I Beam (continued) aashto standard aashto lrfd proposal csa r2k loca- tion dv Vu vu Mcr Mu Vci Vcw yv fρ Vc yv fρ θ Vc yv fρ θ Vc yv fρ θ Vcr yv fρbeam no. no. of bottom strands ft in kips ksi k ft k ft kips kips psi kips psi deg kips psi deg kips psi deg kips psi 16 12 2.9 32.8 82 0.417 1294 245 494 92 50 84 89 20 56 138 37 98 89 28 97 89 12 9 33.5 70 0.348 985 707 153 108 50 74 89 21 69 89 33 88 89 28 96 89 12 18 34.6 52 0.25 631 1257 72 127 50 60 89 24 (72) 89 45 81 89 29 (62) 89 12 27 35.7 35 0.163 407 1650 43 139 50 46 89 34 (43) 89 45 42 89 33 (31) 89 12 36 36.7 17 0.077 307 1885 37 143 50 44 89 36 (37) 89 45 36 89 35 (14) 89 17 14 2.9 31.3 171 0.911 1543 529 537 121 331 49 294 23 83 320 29 84 250 28 108 280 14 5 31.3 155 0.825 1508 872 303 120 249 48 269 24 82 270 29 77 225 29 118 240 14 10 31.6 116 0.612 1463 1551 139 118 52 37 325 37 80 150 30 36 285 34 113 140 14 15 32.4 78 0.401 1453 2035 79 115 50 34 194 41 77 89 32 24 213 39 (68) 89 14 20 33.2 39 0.196 1478 2326 43 110 50 30 89 44 (42) 89 45 22 89 41 (29) 89 18 14 2.9 33.2 116 0.582 1577 351 576 89 182 60 117 20 52 319 40 100 89 28 108 160 14 7.5 33.8 101 0.498 1398 850 214 97 69 74 89 21 59 200 37 89 89 28 97 120 14 15 34.7 76 0.365 1179 1511 98 106 50 55 89 27 66 89 35 69 89 30 83 89 14 22.5 35.6 50 0.234 1049 1984 57 110 50 45 89 34 (57) 89 45 38 89 35 (46) 89 14 30 36.6 25 0.114 1005 2267 37 109 50 38 89 41 (37) 89 45 32 89 37 (20) 89 19 14 2.9 33.2 98 0.492 1538 295 575 90 85 85 89 20 53 223 39 103 89 28 107 120 14 9 33.8 84 0.414 1224 850 177 106 50 74 89 21 67 89 34 90 89 28 96 89 14 18 34.7 63 0.303 875 1511 82 124 50 55 89 27 (82) 89 45 76 89 29 69 89 14 27 35.6 42 0.197 646 1984 48 135 50 45 89 34 (48) 89 45 39 89 34 (38) 89 14 36 36.6 21 0.096 546 2267 37 138 50 38 89 41 (37) 89 45 33 89 36 (16) 89 20 16 2.9 31.3 131 0.698 1548 397 565 119 129 57 153 20 81 201 30 97 89 28 114 180 16 7.5 31.9 114 0.596 1418 961 216 121 50 55 123 21 83 133 30 85 89 28 103 140 16 15 33.4 85 0.424 1269 1709 102 124 50 53 89 27 84 89 31 62 89 30 (89) 89 16 22.5 34.9 57 0.272 1214 2243 61 121 50 42 89 36 (61) 89 45 36 89 35 (47) 89 16 30 36.5 28 0.128 1249 2563 37 111 50 38 89 41 (37) 89 45 33 89 36 (22) 89 * The values in parentheses represent the cases where the flexural shear cracking force governs for Vc.

H-14 Table H-4 Summary of Results – Simply-Supported I Beam (continued) aashto standard aashto lrfd proposal csa r2k loca- tion dv Vu vu Mcr Mu Vci Vcw yv fρ Vc yv fρ θ Vc yv fρ θ Vc yv fρ θ Vcr yv fρbeam no. no. of bottom strands ft in kips ksi k ft k ft kips kips psi kips psi deg kips psi deg kips psi deg kips psi 21 16 2.9 31.3 111 0.591 1503 333 563 120 50 57 113 20 82 125 30 101 89 28 111 140 16 9 31.9 95 0.496 1244 961 178 129 50 70 89 21 90 89 29 86 89 28 115 89 16 18 33.4 71 0.354 965 1709 85 140 50 53 89 27 (85) 89 45 67 89 30 (73) 89 16 27 34.9 47 0.224 810 2243 52 143 50 45 89 34 (51) 89 45 37 89 34 (41) 89 16 36 36.5 24 0.11 790 2563 37 139 50 44 89 36 (37) 89 45 33 89 36 (19) 89 22 18 2.9 31.3 123 0.655 1722 370 636 119 83 57 139 20 81 168 30 104 89 28 112 160 18 9 32.1 106 0.55 1463 1069 200 130 50 71 89 21 90 89 29 89 89 28 117 120 18 18 33.5 79 0.393 1184 1900 94 140 50 53 89 27 (94) 89 45 72 89 29 (87) 89 18 27 34.8 53 0.254 1029 2493 56 143 50 44 89 34 (56) 89 45 38 89 34 (46) 89 18 36 36.2 26 0.12 1005 2849 37 137 50 43 89 36 (37) 89 45 34 89 36 (20) 89 * The values in parentheses represent the cases where the flexural shear cracking force governs for Vc.

H-15 Table H-5 Summary of Results – Simply-Supported Bulb-T aashto standard aashto lrfd proposal csa r2k loca- tion dv Vu vu Mcr Mu Vci Vcw yv fρ Vc yv fρ θ Vc yv fρ θ Vc yv fρ θ Vcr yv fρbeam no. no. of bottom strands ft in kips ksi k ft k ft kips kips psi kips psi deg kips psi deg kips psi deg kips psi 1 18 5.3 63.2 525 1.384 4670 3810 679 179 961 50 1253 42 106 903 36 33 1441 45 166 800 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 18 7.5 63.2 365 0.963 4638 4789 384 179 539 55 857 43 106 789 45 32 1004 46 184 460 18 10.0 63.2 182 0.480 4621 5473 181 180 53 57 369 44 108 250 45 35 419 44 (138) 160 2 18 5.3 65.0 442 1.133 4391 2834 730 203 664 77 690 35 130 703 37 65 707 35 176 500 - - - - - - - - - - - - - - - - - - - - - 18 7.2 65.9 376 0.951 4408 3612 501 204 486 75 598 37 130 557 37 55 634 37 176 390 18 10.8 67.5 251 0.620 4473 4741 273 204 166 70 385 41 129 371 45 49 396 39 (205) 200 18 14.4 69.1 125 0.301 4572 5418 137 204 50 72 89 41 127 89 45 53 98 38 (104) 89 3 18 5.3 64.4 356 0.921 4244 2139 761 197 462 95 352 26 124 520 37 150 300 29 179 360 - - - - - - - - - - - - - - - - - - - - - 18 10.0 65.9 271 0.685 4227 3612 366 200 230 82 339 34 126 332 37 71 347 34 199 230 18 15.0 67.5 181 0.447 4244 4741 202 202 50 71 234 41 126 186 45 56 222 37 (166) 120 18 20.0 69.1 90 0.217 4293 5418 104 202 50 72 89 41 (104) 89 45 57 89 38 (75) 89 4 18 5.3 63.8 258 0.674 4080 1483 787 193 221 108 179 23 120 315 36 160 136 29 180 190 18 7.5 64.3 241 0.625 3998 2032 546 195 169 108 157 23 122 271 36 156 115 29 184 170 18 15.0 65.9 181 0.458 3752 3612 248 203 50 84 174 34 127 133 35 97 125 32 181 120 18 22.5 67.5 120 0.296 3620 4741 141 207 50 81 89 36 130 89 45 65 89 36 (110) 89 18 30.0 69.1 60 0.145 3588 5418 77 210 50 72 89 41 (76) 89 45 60 89 37 (51) 89 5 18 5.3 69.1 202 0.487 4391 1133 880 180 96 152 89 21 103 230 38 181 89 28 129 144 18 10.0 69.1 181 0.437 4014 2032 448 187 50 139 89 22 109 167 37 172 89 29 172 120 18 20.0 69.1 135 0.326 3341 3612 199 202 50 109 89 27 123 89 45 139 89 30 (163) 89 18 30.0 69.1 90 0.217 2882 4741 113 212 50 83 89 36 (112) 89 45 74 89 34 (83) 89 18 40.0 69.1 45 0.109 2587 5418 70 218 50 72 89 41 (70) 89 45 60 89 37 (36) 89 * The values in parentheses represent the cases where the flexural shear cracking force governs for Vc.

H-16 Table H-5 Summary of Results – Simply-Supported Bulb-T (continued) aashto standard aashto lrfd proposal csa r2k loca- tion dv Vu vu Mcr Mu Vci Vcw yv fρ Vc yv fρ θ Vc yv fρ θ Vc yv fρ θ Vcr yv fρbeam no. no. of bottom strands ft in kips ksi k ft k ft kips kips psi kips psi deg kips psi deg kips psi deg kips psi 6 20 5.3 63.6 583 1.528 5097 4229 738 182 1097 47 1387 41 109 998 35 34 1592 45 167 940 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 20 7.5 63.6 405 1.061 5064 5316 417 184 628 55 959 43 111 890 45 32 1109 46 184 560 20 10.0 63.6 203 0.532 5048 6076 195 184 99 57 425 44 111 301 45 35 472 44 (163) 190 7 20 5.3 63.6 496 1.300 5048 3178 832 184 866 66 873 35 111 811 35 55 960 37 151 660 - - - - - - - - - - - - - - - - - - - - - 20 7.2 63.6 422 1.106 4998 4050 561 185 669 53 989 42 112 652 35 46 898 39 152 520 20 10.8 63.6 281 0.736 4933 5316 296 186 297 57 628 43 113 522 45 39 638 42 204 280 20 14.4 63.6 141 0.369 4900 6076 142 186 50 57 251 44 113 115 45 38 271 42 (122) 100 8 20 5.3 64.7 395 1.018 4687 2378 835 201 552 90 429 27 127 586 36 150 359 29 180 400 - - - - - - - - - - - - - - - - - - - - - 20 10.0 66.1 301 0.759 4654 4015 398 204 297 82 394 34 128 382 36 71 404 34 200 270 20 15.0 67.6 201 0.496 4687 5269 219 205 50 71 281 41 128 234 45 56 265 37 166 140 20 20.0 69.0 100 0.242 4736 6022 112 205 50 72 89 41 (111) 89 45 56 89 38 (88) 89 9 20 5.3 64.2 287 0.745 4523 1648 865 196 286 108 212 23 123 363 35 162 177 29 181 220 20 7.5 64.6 268 0.691 4424 2258 597 199 229 109 187 23 125 316 35 158 154 29 185 200 20 15.0 66.1 201 0.507 4178 4015 270 206 50 84 211 34 130 164 35 97 159 32 182 140 20 22.5 67.6 134 0.330 4063 5269 152 211 50 81 99 36 134 89 45 65 112 36 123 89 20 30.0 69.0 67 0.162 4030 6022 81 213 50 72 89 41 (81) 89 45 59 89 37 (56) 89 10 20 5.3 64.0 224 0.583 4359 1259 872 196 123 111 130 21 123 229 35 170 89 28 182 152 20 10.0 64.6 201 0.519 4047 2258 449 203 50 130 89 22 128 166 34 161 89 29 182 126 20 20.0 66.1 151 0.381 3505 4015 204 216 50 92 98 31 138 89 45 118 89 30 (173) 89 20 30.0 67.6 100 0.247 3194 5269 118 226 50 81 89 36 (118) 89 45 70 89 35 (91) 89 20 40.0 69.0 50 0.121 3030 6022 70 232 50 72 89 41 (70) 89 45 61 89 37 (41) 89 * The values in parentheses represent the cases where the flexural shear cracking force governs for Vc.

H-17 Table H-5 Summary of Results – Simply-Supported Bulb-T (continued) aashto standard aashto lrfd proposal csa r2k loca- tion dv Vu vu Mcr Mu Vci Vcw yv fρ Vc yv fρ θ Vc yv fρ θ Vc yv fρ θ Vcr yv fρbeam no. no. of bottom strands ft in kips ksi k ft k ft kips kips psi kips psi deg kips psi deg kips psi deg kips psi 11 22 5.3 64.0 639 1.664 5540 4632 799 187 1225 44 1518 41 114 1075 35 34 1726 45 168 1120 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 22 7.5 64.0 444 1.156 5507 5823 450 187 717 53 1040 42 114 989 45 33 1203 45 183 640 22 10.0 64.0 222 0.578 5491 6655 210 187 139 58 460 43 114 347 45 36 513 44 (162) 220 12 22 5.3 64.0 543 1.414 5491 3481 901 189 972 67 961 35 115 874 34 57 1044 37 152 760 - - - - - - - - - - - - - - - - - - - - - 22 7.2 64.0 462 1.203 5441 4436 608 189 761 53 1087 42 115 713 34 47 976 39 205 580 22 10.8 64.0 308 0.802 5376 5823 319 190 357 57 697 43 116 589 45 40 695 42 152 320 22 14.4 64.0 154 0.401 5343 6655 153 191 50 57 285 44 117 141 45 39 297 42 (123) 116 12 22 5.3 64.0 437 1.138 5409 2628 954 190 693 74 757 35 116 656 34 128 510 30 162 500 - - - - - - - - - - - - - - - - - - - - - 22 10.0 64.0 333 0.867 5261 4436 442 192 416 65 690 41 118 441 34 61 568 36 182 320 22 15.0 64.0 222 0.578 5146 5823 235 195 121 66 405 41 120 329 45 45 423 40 (186) 190 22 20.0 64.0 111 0.289 5064 6655 115 196 50 57 165 44 (115) 89 45 42 172 41 (89) 89 14 22 5.3 64.6 316 0.815 4949 1812 939 201 348 99 270 24 127 403 35 164 218 29 182 250 22 7.5 64.9 294 0.755 4851 2484 647 203 287 100 240 24 128 356 35 159 192 29 185 230 22 15.0 66.3 221 0.556 4621 4416 292 210 80 85 247 34 134 192 34 97 192 32 206 170 22 22.5 67.6 147 0.362 4490 5795 163 214 50 81 125 36 136 89 45 64 139 36 (135) 89 22 30.0 68.9 74 0.179 4457 6623 86 217 50 72 89 41 (85) 89 45 59 89 37 (62) 89 15 22 5.3 64.3 247 0.640 4802 1385 951 200 174 112 155 21 125 265 34 173 101 28 183 180 22 10.0 64.9 221 0.568 4473 2484 487 207 89 109 134 23 131 196 34 163 89 29 183 150 22 20.0 66.3 166 0.417 3948 4416 221 220 50 92 122 31 142 106 45 119 89 30 (173) 110 22 30.0 67.6 110 0.271 3620 5795 126 228 50 81 89 36 (126) 89 45 70 89 35 (102) 89 22 40.0 68.9 55 0.133 3456 6623 70 234 50 72 89 41 (70) 89 45 61 89 37 (44) 89 * The values in parentheses represent the cases where the flexural shear cracking force governs for Vc.

H-18 Table H-5 Summary of Results – Simply-Supported Bulb-T (continued) aashto standard aashto lrfd proposal csa r2k loca- tion dv Vu vu Mcr Mu Vci Vcw yv fρ Vc yv fρ θ Vc yv fρ θ Vc yv fρ θ Vcr yv fρbeam no. no. of bottom strands ft in kips ksi k ft k ft kips kips psi kips psi deg kips psi deg kips psi deg kips psi 16 22 5.3 64.2 202 0.524 4654 1121 956 201 54 141 89 21 127 171 34 179 89 28 182 134 22 12.5 64.9 177 0.455 3998 2484 390 215 50 131 89 22 139 94 32 166 89 29 181 110 22 25.0 66.3 132 0.332 3095 4416 179 235 50 105 89 27 156 89 45 137 89 30 (152) 89 22 37.5 67.6 88 0.217 2488 5795 103 251 50 86 89 34 (103) 89 45 73 89 34 (82) 89 22 50.0 68.9 44 0.106 2177 6623 70 260 50 72 89 41 (70) 89 45 62 89 36 (34) 89 17 24 5.3 64.3 693 1.796 5966 5025 858 191 1352 45 1646 41 116 1155 34 35 1845 44 169 1260 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 24 7.5 64.3 481 1.247 5934 6317 483 191 802 53 1131 42 116 1084 45 34 1284 45 186 700 24 10.0 64.3 241 0.625 5917 7220 224 192 177 58 508 43 118 389 45 37 553 43 -179 230 18 24 5.3 64.3 590 1.529 5917 3777 968 192 1082 60 1042 34 118 944 34 58 1126 36 153 840 - - - - - - - - - - - - - - - - - - - - - 24 7.2 64.3 501 1.299 5868 4813 652 193 848 51 1168 42 119 763 34 48 1047 39 153 660 24 10.8 64.3 334 0.866 5802 6317 342 193 415 58 763 43 119 654 45 41 746 41 207 340 24 14.4 64.3 167 0.433 5770 7220 163 195 54 58 319 44 120 170 45 41 322 41 (136) 130 19 24 5.3 64.3 474 1.229 5835 2851 1025 193 778 74 828 35 119 711 34 135 553 30 163 600 - - - - - - - - - - - - - - - - - - - - - 24 10.0 64.3 361 0.936 5688 4813 475 196 479 76 587 35 121 481 34 62 613 35 184 380 24 15.0 64.3 241 0.625 5573 6317 251 198 162 67 450 41 123 374 45 47 458 39 186 210 24 20.0 64.3 120 0.311 5491 7220 122 200 50 67 148 41 (122) 89 45 43 188 40 (97) 89 20 24 5.3 64.8 344 0.885 5376 1973 1013 205 411 100 303 24 130 446 34 166 257 29 183 290 24 7.5 65.2 320 0.818 5294 2704 700 207 342 100 271 24 132 390 34 161 228 29 173 290 24 15.0 66.4 240 0.602 5048 4807 313 213 120 83 288 34 136 220 34 99 221 32 207 180 24 22.5 67.6 160 0.394 4916 6310 174 217 50 81 151 36 138 97 45 65 163 36 (136) 100 24 30.0 68.9 80 0.194 4900 7211 91 219 50 72 89 41 (90) 89 45 59 89 37 (64) 89 * The values in parentheses represent the cases where the flexural shear cracking force governs for Vc.

H-19 Table H-5 Summary of Results – Simply-Supported Bulb-T (continued) aashto standard aashto lrfd proposal csa r2k loca- tion dv Vu vu Mcr Mu Vci Vcw yv fρ Vc yv fρ θ Vc yv fρ θ Vc yv fρ θ Vcr yv fρbeam no. no. of bottom strands ft in kips ksi k ft k ft kips kips psi kips psi deg kips psi deg kips psi deg kips psi 21 24 5.3 64.6 269 0.694 5228 1508 1027 205 219 112 178 21 130 294 34 176 129 28 184 200 24 10.0 65.2 240 0.613 4916 2704 526 211 127 110 155 23 135 219 33 166 101 29 183 170 24 20.0 66.4 180 0.452 4375 4807 237 223 50 105 107 27 145 139 45 121 89 30 (192) 120 24 30.0 67.6 120 0.296 4047 6310 134 232 50 81 89 36 (134) 89 45 70 89 35 (111) 89 24 40.0 68.9 60 0.145 3899 7211 73 237 50 72 89 41 (72) 89 45 61 89 37 (47) 89 22 24 5.3 64.5 220 0.568 5080 1220 1033 205 92 117 115 20 130 197 34 183 89 28 183 150 24 12.5 65.2 192 0.491 4441 2704 421 218 50 143 89 21 141 114 32 168 89 29 216 89 24 25.0 66.4 144 0.361 3522 4807 191 238 50 105 89 27 158 89 45 140 89 29 171 89 24 37.5 67.6 96 0.237 2915 6310 110 253 50 86 89 34 (109) 89 45 74 89 34 (97) 89 24 50.0 68.9 48 0.116 2620 7211 70 262 50 72 89 41 (70) 89 45 62 89 36 (46) 89 23 26 5.3 61.3 512 1.392 5852 3080 1027 222 847 64 906 35 149 697 31 125 632 30 182 600 - - - - - - - - - - - - - - - - - - - - - 26 10.0 62.3 390 1.043 5835 5200 485 224 503 74 633 35 150 466 32 60 665 36 203 400 26 15.0 63.4 260 0.683 5852 6824 262 225 151 66 460 41 150 365 45 46 464 39 205 200 26 20.0 64.4 130 0.336 5901 7799 129 225 50 67 126 41 (129) 89 45 45 160 40 (101) 89 24 26 5.3 64.9 370 0.950 5802 2120 1088 209 466 95 363 25 133 479 34 168 293 29 184 330 26 7.5 65.3 344 0.878 5704 2905 748 211 393 101 300 24 135 420 34 162 263 29 186 290 26 15.0 66.4 258 0.648 5458 5164 334 217 157 89 275 31 140 243 33 101 246 31 208 220 26 22.5 67.5 172 0.425 5343 6778 185 221 50 81 176 36 142 121 45 66 184 35 (149) 110 26 30.0 68.6 86 0.209 5310 7746 96 223 50 72 89 41 (95) 89 45 59 89 37 (68) 89 25 26 5.3 64.7 289 0.744 5638 1620 1100 207 264 112 200 21 132 323 34 179 154 28 185 220 26 10.0 65.3 258 0.658 5327 2905 563 214 166 110 176 23 138 245 33 167 126 29 184 190 26 20.0 66.4 194 0.487 4785 5164 252 227 50 105 126 27 148 169 45 124 98 30 194 130 26 30.0 67.5 129 0.319 4473 6778 142 235 50 81 95 36 (142) 89 45 71 92 35 (112) 89 26 40.0 68.6 65 0.158 4309 7746 76 240 50 72 89 41 (76) 89 45 61 89 36 (51) 89 * The values in parentheses represent the cases where the flexural shear cracking force governs for Vc.

H-20 Table H-5 Summary of Results – Simply-Supported Bulb-T (continued) aashto standard aashto lrfd proposal csa r2k loca- tion dv Vu vu Mcr Mu Vci Vcw yv fρ Vc yv fρ θ Vc yv fρ θ Vc yv fρ θ Vcr yv fρbeam no. no. of bottom strands ft in kips ksi k ft k ft kips kips psi kips psi deg kips psi deg kips psi deg kips psi 26 26 5.3 64.6 236 0.609 5491 1310 1107 209 124 117 131 20 133 216 33 187 89 28 184 170 26 12.5 65.3 207 0.528 4851 2905 450 223 50 144 89 21 145 132 31 170 89 28 182 140 26 25.0 66.4 155 0.389 3932 5164 204 242 50 105 89 27 162 89 45 144 89 29 (169) 89 26 37.5 67.5 103 0.254 3341 6778 116 257 50 86 89 34 (116) 89 45 75 89 34 (97) 89 26 50.0 68.6 52 0.126 3030 7746 70 265 50 82 89 36 (70) 89 45 62 89 36 (49) 89 27 28 5.3 61.4 309 0.839 5622 1734 1096 226 287 97 259 23 152 311 31 172 192 28 193 240 28 10.0 62.4 276 0.737 5359 3109 565 232 179 105 201 23 158 234 30 161 158 29 192 200 28 20.0 64.4 207 0.536 4949 5527 258 243 50 90 184 31 165 167 45 115 124 30 201 140 28 30.0 66.4 138 0.346 4752 7254 147 250 50 79 100 36 (147) 89 45 70 97 35 (117) 89 28 40.0 68.5 69 0.168 4720 8290 80 253 50 82 89 36 (79) 89 45 63 89 36 (76) 89 28 28 5.3 61.2 253 0.689 5458 1402 1100 224 139 111 156 20 151 209 30 180 94 28 192 180 28 12.5 62.4 221 0.590 4884 3109 452 237 50 108 127 21 161 127 29 164 89 28 224 140 28 25.0 64.4 166 0.430 4096 5527 208 256 50 102 89 27 177 89 45 132 89 30 (177) 100 28 37.5 66.4 111 0.279 3620 7254 120 269 50 85 89 34 (119) 89 45 73 89 34 (113) 89 28 50.0 68.5 55 0.134 3440 8290 69 277 50 82 89 36 (70) 89 45 64 89 36 (61) 89 29 28 5.3 64.7 214 0.551 5786 1177 1189 214 55 165 89 20 138 161 32 198 89 28 183 150 28 15.0 65.3 184 0.470 4687 3109 400 237 50 144 89 21 158 89 30 175 89 28 209 89 28 30.0 66.4 138 0.346 3325 5527 181 266 50 115 89 24 (181) 89 45 155 89 29 (164) 89 28 45.0 67.4 92 0.227 2390 7254 103 288 50 86 89 34 (103) 89 45 79 89 34 (79) 89 28 60.0 68.5 46 0.112 1881 8290 69 300 50 82 89 36 (70) 89 45 64 89 36 (44) 89 30 30 5.3 58.5 330 0.940 5934 1855 1151 239 327 92 305 23 167 316 29 165 249 28 194 260 30 10.0 59.3 296 0.832 5671 3327 591 246 211 91 269 24 172 245 29 152 215 29 194 220 30 20.0 61.1 222 0.606 5261 5914 268 256 50 82 236 31 180 182 45 92 208 32 222 150 30 30.0 62.9 148 0.392 5064 7763 152 263 50 75 135 36 (152) 89 45 58 156 36 (131) 89 30 40.0 64.6 74 0.191 5031 8872 81 266 50 68 89 41 (80) 89 45 52 89 38 (76) 89 * The values in parentheses represent the cases where the flexural shear cracking force governs for Vc.

H-21 Table H-5 Summary of Results – Simply-Supported Bulb-T (continued) aashto standard aashto lrfd proposal csa r2k loca- tion dv Vu vu Mcr Mu Vci Vcw yv fρ Vc yv fρ θ Vc yv fρ θ Vc yv fρ θ Vcr yv fρbeam no. no. of bottom strands ft in kips ksi k ft k ft kips kips psi kips psi deg kips psi deg kips psi deg kips psi 31 30 5.3 61.6 271 0.733 5884 1502 1177 229 175 112 175 20 155 228 30 185 115 28 196 190 30 12.5 62.6 237 0.631 5310 3328 482 242 52 109 145 21 165 145 29 166 91 28 228 150 30 25.0 64.5 178 0.460 4523 5917 221 260 50 102 104 27 180 89 45 132 89 30 (182) 100 30 37.5 66.4 118 0.296 4047 7766 126 273 50 85 89 34 (126) 89 45 73 89 34 (122) 89 30 50.0 68.3 59 0.144 3866 8876 71 279 50 82 89 36 (70) 89 45 63 89 36 (64) 89 32 30 5.3 61.4 229 0.622 5737 1261 1179 228 63 111 131 20 154 155 30 191 89 28 191 150 30 15.0 62.6 197 0.524 4720 3328 401 250 50 138 89 21 173 89 29 168 89 28 217 120 30 30.0 64.5 148 0.382 3489 5917 184 278 50 112 89 24 (184) 89 45 146 89 29 (160) 89 30 45.0 66.4 99 0.248 2685 7766 107 298 50 85 89 34 (106) 89 45 75 89 34 (99) 89 30 60.0 68.3 49 0.120 2308 8876 69 310 50 82 89 36 (70) 89 45 64 89 36 (53) 89 33 32 5.3 59.0 287 0.811 5868 1594 1173 244 191 95 228 22 171 232 29 180 144 28 200 210 32 12.5 60.5 251 0.691 5359 3533 485 257 54 105 163 21 182 149 29 161 115 28 231 160 32 25.0 63.0 188 0.497 4703 6281 226 273 50 99 115 27 194 89 45 123 89 30 (198) 120 32 37.5 65.6 126 0.320 4342 8244 131 285 50 84 89 34 (130) 89 45 71 89 34 (105) 89 32 50.0 68.2 63 0.154 4277 9422 74 290 50 82 89 36 (73) 89 45 64 89 36 (69) 89 34 32 5.3 58.8 243 0.689 5720 1338 1175 243 69 107 152 20 170 157 29 187 89 28 189 160 32 15.0 60.5 209 0.576 4769 3533 403 264 50 133 89 21 188 89 29 163 89 28 220 120 32 30.0 63.0 157 0.415 3670 6281 188 289 50 99 89 27 (188) 89 45 135 89 29 (164) 89 32 45.0 65.6 105 0.267 2980 8244 110 308 50 84 89 34 (110) 89 45 73 89 34 (104) 89 32 60.0 68.2 52 0.127 2718 9422 69 318 50 82 89 36 (69) 89 45 65 89 36 (57) 89 35 34 5.3 57.2 257 0.749 6032 1415 1231 260 67 104 176 20 187 160 29 185 93 28 196 180 34 15.0 57.9 221 0.636 5080 3736 421 277 50 101 142 21 201 89 29 156 89 28 252 89 34 30.0 60.2 166 0.460 3965 6642 195 301 50 95 97 27 (195) 89 45 110 89 30 (190) 89 34 45.0 62.5 111 0.296 3292 8718 113 320 50 75 89 36 (113) 89 45 62 89 35 (108) 89 34 60.0 64.8 55 0.141 3030 9964 66 331 50 68 89 41 (66) 89 45 55 89 37 (61) 89 * The values in parentheses represent the cases where the flexural shear cracking force governs for Vc.

H-22 Table H-6 Summary of Results – Continuous Box Girder aashto standard aashto lrfd proposal csa r2k loca- tion dv Vu vu Mcr Mu Vci Vcw yv fρ Vc yv fρ θ Vc yv fρ θ Vc yv fρ θ yv fρbeam no. no. of strands ft in kips ksi k ft k ft kips kips psi kips psi deg kips psi deg kips psi deg psi 1 172 5.2 56.16 1733 0.643 17781 11086 2918 1859 50 677 118 21 1160 158 29 1047 77 28 203 172 22 56.16 967 0.359 22655 34428 776 1715 100 541 77 31 (778) 110 45 566 77 32 99 172 44 58.14 66 0.024 25520 46136 406 1563 50 482 77 36 (410) 77 45 377 77 36 77 172 66 56.9 1098 0.402 23494 35124 875 1645 115 548 99 31 (879) 125 45 522 100 33 117 172 88 56.16 2131 0.791 12787 1392 19714 2059 103 614 175 23 1361 207 29 1081 106 28 151 172 104.61 58.17 2897 1.037 35733 38276 2844 1755 487 463 586 35 1190 726 45 410 583 35 495 2 172 5.2 56.16 1406 0.522 17322 8838 2896 1774 50 706 77 20 1076 100 29 1084 77 28 77 172 28 56.16 760 0.282 22655 34428 639 1653 68 541 77 31 (640) 77 45 599 77 31 77 172 56 58.14 52 0.018 25520 46136 406 1542 50 482 77 36 (410) 77 45 377 77 36 77 172 84 56.9 863 0.316 23494 35124 717 1600 80 548 77 31 (719) 88 45 559 77 32 77 172 112 56.16 1674 0.621 12787 1392 15519 1923 50 706 90 20 1225 131 29 1116 77 28 109 172 134.54 58.98 2321 0.82 36288 41745 2160 1611 317 456 498 37 1033 546 45 403 466 35 417 3 172 5.2 56.16 1122 0.416 16939 6955 2873 1702 50 992 77 20 1004 77 29 1118 77 28 77 172 36 56.16 591 0.219 22655 34428 528 1602 50 541 77 31 (527) 77 45 629 77 31 77 172 72 58.14 40 0.014 25520 46136 406 1525 50 482 77 36 (410) 77 45 376 77 36 77 172 108 56.9 671 0.246 23494 35124 589 1563 52 548 77 31 (589) 77 45 593 77 32 77 172 144 56.16 1302 0.483 12787 1392 12101 1813 50 992 77 20 1114 77 29 1147 77 28 77 172 174.49 59.5 1834 0.642 36655 44622 1650 1517 169 471 370 37 933 387 45 398 358 36 313 4 240 5.2 56.16 2189 0.812 21847 13302 3734 2207 75 624 189 22 1266 240 29 1146 122 28 198 240 22 56.16 1215 0.451 27948 42900 931 2026 140 677 77 24 (933) 155 45 837 77 29 135 240 44 56.16 81 0.03 31441 57296 394 1787 50 497 77 34 (396) 77 45 444 77 34 77 240 66 56.16 1377 0.511 28903 43187 1060 1924 157 574 133 27 984 203 45 739 97 30 154 240 88 56.16 2672 0.991 15801 575 73601 2439 177 583 258 23 1498 303 29 1188 172 28 219 240 104.8 56.16 3646 1.353 44180 50239 3346 2022 678 361 796 34 1237 1044 45 421 779 34 781 * The values in parentheses represent the cases where the flexural shear cracking force governs for Vc.

H-23 Table H-6 Summary of Results – Continuous Box Girder (Continued) aashto standard aashto lrfd proposal csa r2k loca- tion dv Vu vu Mcr Mu Vci Vcw yv fρ Vc yv fρ θ Vc yv fρ θ Vc yv fρ θ yv fρbeam no. no. of strands ft in kips ksi k ft k ft kips kips psi kips psi deg kips psi deg kips psi deg psi 5 240 5.2 56.16 1774 0.658 21303 10600 3704 2101 50 706 115 20 1161 167 29 1200 77 28 125 240 28 56.16 954 0.354 27948 42900 761 1949 100 677 77 24 (761) 111 45 902 77 29 99 240 56 56.16 64 0.024 31441 57296 394 1761 50 497 77 34 (396) 77 45 443 77 34 77 240 84 56.16 1082 0.401 28903 43187 863 1869 113 677 77 24 (864) 125 45 809 77 30 104 240 112 56.16 2100 0.779 15801 575 57860 2273 50 624 164 22 1333 206 29 1240 77 28 150 240 134.76 56.61 2919 1.074 44808 54442 2542 1827 473 408 637 35 1047 808 45 410 630 35 583 6 240 5.2 56.16 1414 0.525 20848 8338 3675 2011 50 706 77 20 1070 103 29 1250 77 28 83 240 36 56.16 742 0.275 27948 42900 623 1887 67 783 77 22 (622) 77 45 908 77 29 77 240 72 56.16 49 0.018 31441 57296 394 1740 50 497 77 34 (396) 77 45 443 77 34 77 240 108 56.16 841 0.312 28903 43187 702 1824 78 677 77 24 (702) 86 45 876 77 29 77 240 144 56.16 1633 0.606 15801 575 45033 2138 50 706 88 20 1198 127 29 1287 77 28 104 240 174.72 57.03 2305 0.842 45225 57926 1939 1702 287 469 485 35 928 596 45 404 490 35 417 7 288 5.2 56.16 2451 0.909 24575 14391 4324 2427 99 583 248 23 1316 290 29 1233 149 28 219 288 22 56.16 1355 0.503 31243 47496 1031 2229 159 783 77 22 (1033) 175 45 927 77 29 167 288 44 56.16 90 0.033 34989 63200 394 1968 50 541 77 31 (396) 77 45 564 77 32 77 288 66 56.16 1535 0.569 32198 47112 1188 2113 173 656 119 23 1001 261 45 919 84 29 171 288 88 56.16 2980 1.106 32402 768 125914 2477 279 555 329 25 1552 363 29 1176 232 28 260 288 104.8 56.16 4076 1.512 49147 58273 3577 2183 783 330 928 34 1258 1213 45 458 858 34 979 8 288 5.2 56.16 1985 0.736 23999 11464 4294 2311 50 624 165 22 1200 207 29 1289 77 28 135 288 28 56.16 1065 0.395 31243 47496 840 2145 115 783 77 22 (840) 127 45 935 77 29 113 288 56 56.16 71 0.026 34989 63200 394 1940 50 541 77 31 (396) 77 45 563 77 32 77 288 84 56.16 1206 0.447 32198 47112 964 2054 126 783 77 22 943 148 45 929 77 29 125 288 112 56.16 2342 0.869 32402 768 98962 2300 101 624 198 22 1375 253 29 1221 116 28 177 288 134.8 56.16 3261 1.21 49792 62867 2722 1980 549 361 734 34 1055 953 45 438 701 34 760 * The values in parentheses represent the cases where the flexural shear cracking force governs for Vc.

H-24 Table H-6 Summary of Results – Continuous Box Girder (Continued) aashto standard aashto lrfd proposal csa r2k loca- tion dv Vu vu Mcr Mu Vci Vcw yv fρ Vc yv fρ θ Vc yv fρ θ Vc yv fρ θ yv fρbeam no. no. of strands ft in kips ksi k ft k ft kips kips psi kips psi deg kips psi deg kips psi deg psi 9 288 5.2 56.16 1581 0.586 23518 9015 4263 2213 50 791 77 18 1101 135 29 1289 77 28 89 288 36 56.16 828 0.307 31243 47496 684 2077 79 783 77 22 (683) 88 45 942 77 29 77 288 72 56.16 55 0.02 34989 63200 394 1917 50 541 77 31 (396) 77 45 562 77 32 77 288 108 56.16 938 0.348 32198 47112 780 2006 87 783 77 22 (780) 97 45 938 77 29 77 288 144 56.16 1821 0.676 32402 768 77001 2156 50 706 112 20 1231 163 29 1261 77 28 120 288 174.8 56.16 2574 0.955 50221 66673 2078 1850 337 447 579 35 925 718 45 426 552 34 536 * The values in parentheses represent the cases where the flexural shear cracking force governs for Vc.

H-25 Table H-7 Summary of Results – Simply-Supported RC Rectangular Beam aashto standard aashto lrfd proposal csa r2k loca- tion dv Vu vu Mu Vc yv fρ Vc yv fρ θ Vc yv fρ Vc yv fρ θ yv fρbeam no. no. of bottom bars ft in kips ksi k ft kips psi kips psi deg kips psi kips psi deg psi 1 8 2.4 29.3 167 0.475 535 60.4 321 59 268 37 52 381 44 290 37 270 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 8 3.6 29.3 111 0.316 702 60.4 161 61 131 36 52 204 43 161 37 200 8 4.8 29.3 56 0.159 803 60.4 50 53 77 41 52 77 44 77 37 97 2 8 2.4 29.3 152 0.432 450 60.4 278 59 232 37 52 333 48 237 36 200 - - - - - - - - - - - - - - - - - 8 3 29.3 134 0.381 535 60.4 227 61 185 36 52 276 47 201 36 180 8 4.5 29.3 89 0.253 702 60.4 99 61 80 36 52 134 45 104 37 130 8 6 29.3 45 0.128 803 60.4 50 61 77 36 52 77 45 77 37 77 3 8 2.4 29.3 94 0.267 246 60.4 113 71 77 31 52 150 64 77 33 100 8 3 29.3 89 0.253 301 60.4 99 65 77 34 52 134 61 77 33 85 8 6 29.3 67 0.191 535 60.4 50 65 77 34 52 77 53 77 35 77 8 9 29.3 45 0.128 702 60.4 50 61 77 36 52 77 48 77 36 77 8 12 29.3 22 0.063 803 60.4 50 61 77 36 52 77 47 77 36 77 4 12 2.4 28.4 229 0.672 733 58.6 518 56 438 37 50 600 45 440 36 330 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 12 3.6 28.4 153 0.449 962 58.6 295 58 246 37 50 352 44 264 37 230 12 4.8 28.4 76 0.223 1100 58.6 68 59 77 36 50 101 45 77 36 83 5 12 2.4 28.4 208 0.61 616 58.6 456 56 387 37 50 531 49 368 35 280 - - - - - - - - - - - - - - - - - 12 3 28.4 183 0.537 733 58.6 383 58 319 37 50 450 47 317 36 235 12 4.5 28.4 122 0.358 962 58.6 204 59 166 36 50 251 45 182 36 145 12 6 28.4 61 0.179 1100 58.6 50 59 77 36 50 77 45 77 36 77

H-26 Table H-7 Summary of Results – Simply-Supported RC Rectangular Beam (Continued) aashto standard aashto lrfd proposal csa r2k loca- tion dv Vu vu Mu Vc yv fρ Vc yv fρ θ Vc yv fρ Vc yv fρ θ yv fρbeam no. no. of bottom bars ft in kips ksi k ft kips psi kips psi deg kips psi kips psi deg psi 6 12 2.4 28.4 128 0.376 337 58.6 221 68 128 31 50 270 64 133 33 155 12 3 28.4 122 0.358 412 58.6 204 63 142 34 50 251 62 128 33 125 12 6 28.4 92 0.27 733 58.6 116 63 77 34 50 153 53 87 34 90 12 9 28.4 61 0.179 962 58.6 50 59 77 36 50 77 49 77 35 77 12 12 28.4 31 0.091 1100 58.6 50 59 77 36 50 77 47 77 36 77 7 16 2.4 27.4 300 0.912 959 56.7 756 50 645 37 48 867 45 618 36 530 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 16 3.6 27.4 200 0.608 1259 56.7 452 54 385 37 48 529 44 382 36 325 16 4.8 27.4 100 0.304 1439 56.7 149 57 122 36 48 191 45 134 36 140 8 16 2.4 27.4 272 0.827 806 56.7 671 50 574 37 48 772 49 524 35 400 - - - - - - - - - - - - - - - - - 16 3 27.4 240 0.73 959 56.7 574 53 495 37 48 664 48 457 35 340 16 4.5 27.4 160 0.487 1259 56.7 331 56 277 37 48 394 46 277 36 225 16 6 27.4 80 0.243 1439 56.7 88 57 77 36 48 123 46 83 36 90 9 16 2.4 27.4 168 0.511 441 56.7 355 64 223 31 48 421 64 223 32 180 16 3 27.4 160 0.487 540 56.7 331 59 243 34 48 394 62 214 33 190 16 6 27.4 120 0.365 959 56.7 209 61 147 34 48 259 53 153 34 132 16 9 27.4 80 0.243 1259 56.7 88 57 77 36 48 123 49 77 35 80 16 12 27.4 40 0.122 1439 56.7 50 57 77 36 48 77 47 77 35 77

H-27 Table H-8 Summary of Results – Simply-Supported RC T-shape Beam aashto standard aashto lrfd proposal csa r2k loca- tion dv Vu vu Mu Vc yv fρ Vc yv fρ θ Vc yv fρ Vc yv fρ θ yv fρbeam no. no. of bottom bars ft in kips ksi k ft kips psi kips psi deg kips psi kips psi deg psi 1 20 2.9 33.3 378 0.946 1356 68.8 791 55 665 36 59 904 56 640 36 520 - - - - - - - - - - - - - - - - - - 3.6 33.3 334 0.836 1605 68.8 681 61 581 37 59 782 54 563 36 450 20 5.4 33.3 223 0.558 2107 68.8 403 66 343 37 -59 473 52 351 36 280 20 7.2 33.3 111 0.278 2408 68.8 123 60 136 41 -59 162 52 121 36 150 2 20 2.9 33.3 312 0.781 1043 68.8 626 68 486 35 59 721 63 470 34 365 - - - - - - - - - - - - - - - - - 20 5 33.3 244 0.611 1627 68.8 456 66 387 37 -59 531 57 367 35 262 20 7.5 33.3 163 0.408 2136 68.8 253 67 212 37 -59 306 53 222 36 155 20 10 33.3 81 0.203 2441 68.8 50 60 77 41 -59 78 52 77 36 77 3 20 2.9 33.3 181 0.453 561 68.8 298 77 185 31 59 356 83 170 32 150 20 5 33.3 164 0.41 924 68.8 255 72 186 34 59 309 74 161 33 135 20 10 33.3 123 0.308 1642 68.8 153 74 105 34 -59 195 62 116 34 95 20 15 33.3 82 0.205 2155 68.8 50 69 77 36 -59 81 56 77 35 77 20 20 33.3 41 0.103 2463 68.8 50 69 77 36 -59 77 53 77 36 77 4 28 2.9 31.5 489 1.294 1754 65.1 1139 44 953 36 56 1290 54 908 35 850 - - - - - - - - - - - - - - - - - - 3.6 31.5 433 1.146 2076 65.1 991 48 823 36 56 1126 52 805 36 720 28 5.4 31.5 288 0.762 2725 65.1 607 61 522 37 -56 700 49 515 36 430 28 7.2 31.5 144 0.381 3114 65.1 226 57 235 41 -56 276 49 204 36 165 5 28 2.9 31.5 407 1.077 1358 65.1 922 57 719 35 56 1049 61 689 34 600 - - - - - - - - - - - - - - - - - 28 5 31.5 318 0.841 2119 65.1 686 57 586 37 56 788 54 546 35 420 28 7.5 31.5 212 0.561 2781 65.1 406 62 345 37 -56 476 51 344 36 265 28 10 31.5 106 0.28 3179 65.1 126 65 102 36 -56 165 50 121 36 100

H-28 Table H-8 Summary of Results – Simply-Supported RC T-shape Beam (Continued) aashto standard aashto lrfd proposal csa r2k loca- tion dv Vu vu Mu Vc yv fρ Vc yv fρ θ Vc yv fρ Vc yv fρ θ yv fρbeam no. no. of bottom bars ft in kips ksi k ft kips psi kips psi deg kips psi kips psi deg psi 6 28 2.9 31.5 237 0.627 734 65.1 472 71 311 31 56 550 79 289 32 245 28 5 31.5 215 0.569 1208 65.1 414 71 271 31 56 485 71 273 33 220 28 10 31.5 161 0.426 2148 65.1 271 68 198 34 -56 326 59 205 34 150 28 15 31.5 107 0.283 2820 65.1 128 65 105 36 -56 168 53 113 35 95 28 20 31.5 54 0.143 3223 65.1 50 65 77 36 -56 77 50 77 36 77 7 36 2.9 31.3 576 1.534 2069 61.3 1461 44 1145 36 55 1557 55 1074 35 1190 - - - - - - - - - - - - - - - - - - 3.6 31.3 510 1.358 2449 61.3 1276 44 1004 36 55 1362 54 954 35 990 36 5.4 31.3 340 0.905 3215 61.3 799 57 639 37 -55 859 51 616 36 620 36 7.2 31.3 170 0.453 3674 61.3 322 63 249 37 -55 356 51 254 36 200 8 36 2.9 31.3 484 1.289 1615 61.3 1203 46 893 34 55 1285 62 834 34 830 - - - - - - - - - - - - - - - - - 36 5 31.3 378 1.006 2520 61.3 906 52 714 36 55 971 56 662 35 580 36 7.5 31.3 252 0.671 3308 61.3 552 62 437 37 -55 599 52 422 36 380 36 10 31.3 126 0.335 3780 61.3 199 65 147 36 -55 226 51 160 36 140 9 36 2.9 31.3 284 0.756 877 61.3 642 69 412 32 55 693 80 372 32 340 36 5 31.3 257 0.684 1445 61.3 566 69 362 32 55 613 72 349 32 295 36 10 31.3 193 0.514 2569 61.3 387 67 264 34 -55 424 60 266 34 200 36 15 31.3 128 0.341 3371 61.3 204 65 152 36 -55 232 54 153 35 130 36 20 31.3 64 0.17 3853 61.3 50 65 77 36 -55 77 52 77 36 77

H-29 Table H-9 Summary of Results – Continuous RC Rectangular Beam aashto standard aashto lrfd proposal csa r2k As loca- tion dv Vu vu Mu Vc yv fρ Vc yv fρ θ Vc yv fρ Vc yv fρ θ yv fρbeam no. in.2 ft in kips ksi k ft kips psi kips psi deg kips psi kips psi deg psi 1 2.9 2.7 28.8 70 0.203 249 60 50 60 77 36 51 79 45 77 36 104 2.9 3.6 28.8 54 0.157 307 60 50 60 77 36 51 77 44 77 37 77 2.9 7.2 28.8 8 0.022 391 60 50 60 77 36 51 77 46 77 36 77 2.9 10.8 28.8 70 0.202 251 60 50 60 77 36 51 77 45 77 36 104 2.9 14.4 28.8 132 0.381 112 60 226 60 185 36 51 277 50 184 35 233 5.3 15.3 28.8 148 0.428 242 60 273 60 223 36 51 328 47 234 36 333 2 2.9 2.7 28.8 47 0.135 140 60 50 64 77 34 51 77 60 77 33 77 2.9 7.2 28.8 27 0.078 307 60 50 60 77 36 51 77 49 77 35 77 2.9 14.4 28.8 4 0.011 391 60 50 60 77 36 51 77 47 77 36 77 2.9 21.6 28.8 35 0.101 251 60 50 60 77 36 51 77 52 77 35 77 2.9 28.8 28.8 66 0.191 112 60 50 69 77 31 51 77 70 77 32 77 5.3 33.3 28.8 85 0.247 454 60 92 60 77 36 51 128 49 83 35 96 3 2.9 2.7 28.8 34 0.097 97 60 50 69 77 31 51 77 70 77 32 77 2.9 10.8 28.8 18 0.052 307 60 50 60 77 36 51 77 50 77 35 77 2.9 21.6 28.8 3 0.007 391 60 50 60 77 36 51 77 47 77 36 77 2.9 32.4 28.8 23 0.067 251 60 50 64 77 34 51 77 54 77 34 77 2.9 43.2 28.8 44 0.127 112 60 50 69 77 31 51 77 80 77 31 77 5.3 51.3 28.8 59 0.172 532 60 50 60 77 36 51 77 48 77 35 77 4 4.2 2.7 28.8 101 0.293 358 60 138 60 112 36 51 178 46 131 36 158 4.2 3.6 28.8 78 0.226 441 60 71 60 77 36 51 104 44 80 37 138 4.2 7.2 28.8 11 0.032 562 60 50 60 77 36 51 77 46 77 36 77 4.2 10.8 28.8 100 0.29 361 60 135 60 110 36 51 176 45 129 36 158 4.2 14.4 28.8 189 0.548 161 60 393 61 297 34 51 462 51 309 35 333 7.9 15.3 28.8 213 0.615 348 60 460 57 391 37 51 537 48 377 36 396

H-30 Table H-9 Summary of Results – Continuous RC Rectangular Beam (Continued) aashto standard aashto lrfd proposal csa r2k As loca- tion dv Vu vu Mu Vc yv fρ Vc yv fρ θ Vc yv fρ Vc yv fρ θ yv fρbeam no. in.2 ft in kips ksi k ft kips psi kips psi deg kips psi kips psi deg psi 5 4.2 2.7 28.8 67 0.194 201 60 50 64 77 34 51 77 60 77 33 77 4.2 7.2 28.8 39 0.113 441 60 50 60 77 36 51 77 49 77 35 77 4.2 14.4 28.8 6 0.016 562 60 50 60 77 36 51 77 47 77 36 77 4.2 21.6 28.8 50 0.145 361 60 50 60 77 36 51 77 52 77 35 77 4.2 28.8 28.8 95 0.274 161 60 119 69 77 31 51 158 71 77 32 108 7.9 33.3 28.8 123 0.355 654 60 200 60 164 36 51 248 50 164 35 133 6 4.2 2.7 28.8 48 0.14 139 60 50 69 77 31 51 77 70 77 32 77 4.2 10.8 28.8 26 0.075 441 60 50 60 77 36 51 77 50 77 35 77 4.2 21.6 28.8 4 0.011 562 60 50 60 77 36 51 77 47 77 36 77 4.2 32.4 28.8 33 0.097 361 60 50 64 77 34 51 77 54 77 34 77 4.2 43.2 28.8 63 0.183 161 60 50 69 77 31 51 77 81 77 31 77 7.9 51.3 28.8 86 0.248 765 60 93 60 77 36 51 128 50 82 35 88 7 5.5 2.7 28.8 129 0.374 457 60 219 60 179 36 51 269 46 195 36 213 5.5 3.6 28.8 100 0.289 564 60 134 60 109 36 51 174 45 130 36 183 5.5 7.2 28.8 14 0.041 718 60 50 60 77 36 51 77 47 77 36 77 5.5 10.8 28.8 128 0.371 462 60 216 60 177 36 51 265 46 193 36 208 5.5 14.4 28.8 242 0.701 205 60 546 59 424 35 51 632 53 420 35 479 10.5 15.3 28.8 272 0.786 445 60 631 56 543 37 51 727 49 505 35 521 8 5.5 2.7 28.8 86 0.248 257 60 93 64 77 34 51 129 60 77 33 99 5.5 7.2 28.8 50 0.144 564 60 50 60 77 36 51 77 49 77 35 77 5.5 14.4 28.8 7 0.021 718 60 50 60 77 36 51 77 47 77 36 77 5.5 21.6 28.8 64 0.185 462 60 50 60 77 36 51 77 52 77 35 77 5.5 28.8 28.8 121 0.35 205 60 195 69 111 31 51 242 72 97 32 150 10.5 33.3 28.8 157 0.454 835 60 299 58 250 37 51 358 51 236 35 196

H-31 Table H-9 Summary of Results – Continuous RC Rectangular Beam (Continued) aashto standard aashto lrfd proposal csa r2k As loca- tion dv Vu vu Mu Vc yv fρ Vc yv fρ θ Vc yv fρ Vc yv fρ θ yv fρbeam no. in.2 ft in kips ksi k ft kips psi kips psi deg kips psi kips psi deg psi 9 5.5 2.7 28.8 62 0.179 177 60 50 69 77 31 51 77 70 77 32 77 5.5 10.8 28.8 33 0.096 564 60 50 60 77 36 51 77 51 77 35 77 5.5 21.6 28.8 5 0.014 718 60 50 60 77 36 51 77 47 77 36 77 5.5 32.4 28.8 43 0.124 462 60 50 64 77 34 51 77 55 77 34 77 5.5 43.2 28.8 81 0.234 205 60 79 69 77 31 51 113 82 77 31 79 10.5 51.3 28.8 109 0.316 978 60 161 60 132 36 51 205 51 131 35 125

H-32 Figure H-2 Comparisons of Required Shear Reinforcement (Simply-Supported I Beam) Beam Number 1 2 3 4 5 6 7 8 9

H-33 Figure H-2 Comparisons of Required Shear Reinforcement (Simply-Supported I Beam) -continued Beam Number 10 11 12 13 14 15 16 17 18

H-34 Figure H-2 Comparisons of Required Shear Reinforcement (Simply-Supported I Beam) -continued Beam Number 19 20 21 22

H-35 Figure H-3 Comparisons of Required Shear Reinforcement (Simply-Supported Bulb-T) Beam Number 1 2 3 4 5 6 7 8 9

H-36 Figure H-3 Comparisons of Required Shear Reinforcement (Simply-Supported Bulb-T) -continued Beam Number 10 11 12 13 14 15 16 17 18

H-37 Figure H-3 Comparisons of Required Shear Reinforcement (Simply-Supported Bulb-T) -continued Beam Number 19 20 21 22 23 24 25 26 27

H-38 Figure H-3 Comparisons of Required Shear Reinforcement (Simply-Supported Bulb-T) –continued Beam Number 28 29 30 31 32 33 34 35

H-39 Figure H-4 Comparisons of Required Shear Reinforcement (Continuous Box Beam) Beam Number 1 2 3 4 5 6 7 8 9

H-40 Figure H-5 Comparisons of Required Shear Reinforcement (Simply-Supported RC Rectangular Beam) Beam Number 1 2 3 4 5 6 7 8 9

H-41 Figure H-6 Comparisons of Required Shear Reinforcement (Simply-Supported RC T-shape Beam) Beam Number 1 2 3 4 5 6 7 8 9

H-42 Figure H-7 Comparisons of Required Shear Reinforcement Amounts (Continuous RC Rectangular Beam) Beam Number 1 2 3 4 5 6 7 8 9

H-43 Figure H-8 I-Beams

H-44 Figure H-9 Bulb-T Girders

H-45 Figure H-10 Box Girders

H-46 Figure H-11 RC Beams