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From page 105... ... D-1 APPENDIX D: Evaluation of Shear Design Provisions In this appendix an evaluation of several shear design approaches is presented. In Section D.1, the relative strengths and weaknesses of six different codes of practice are assessed based on statistical values of strength ratios for the experimental test data of the shear database presented in Appendix C Read the entire page →
From page 106... ... D-2 (iii) The overall performances of the LRFD and CSA provisions are very similar, which is not surprising considering that they both are derived from the modified compression field theory. Read the entire page →
From page 107... ... D-3 (ii) The variations in the Means for the LRFD, CSA, and JSCE methods are reasonably low. Read the entire page →
From page 108... ... D-4 The following observations can be made from Table D-6: (i) The Mean for the ACI provisions is particularly low for large members that do not contain shear reinforcement and have small amounts of longitudinal reinforcement. Read the entire page →
From page 109... ... D-5 D.1.3 Remarks on Relationships between Statistical Values and Safety of Design Approach In the evaluation of the results, it is useful to consider the relationship between the Mean, the COV, and the Fractile value. For the development of codes of practice, the Fractile level refers to the percentage of members that, if designed by the provisions, would be expected to fail if the full factored load were applied to the test structure. Read the entire page →
From page 110... ... D-6 using the code relations. While this is not completely valid, it is probably the best possible way to proceed given the available information. Read the entire page →
From page 111... ... D-7 Information on the sectional shapes and loading geometries of the 85 selected PC members are shown in Table D-10. Most of them (79 of 85, or about 93 %) Read the entire page →
From page 112... ... D-8 ASBI methods follow in that order while their mean values are comparable (approximately 1.25) Read the entire page →
From page 113... ... D-9 Consideration of the influences of either concrete compressive strength or tensile strength is included for all the approaches presented here. Read the entire page →
From page 114... ... D-10 approach basically gives the same trends as the ACI approach and is also unconservative for members lightly reinforced against flexure as discussed in Section D.2.2.3. For PC members, the concrete contribution term in the ASBI method is somewhat similar to the web-shear cracking strength, Vcw, in the ACI method, but a little more conservative in most cases. Read the entire page →
From page 115... ... D-11 effect exists for any of the eight approaches when members contain at least minimum shear reinforcement D.2.2.3 Longitudinal Reinforcement Ratio ( lρ ) The longitudinal reinforcement ratio affects the amount of longitudinal strain and thereby affects crack width, interface shear transfer, dowel action, and thus the shear strength. Read the entire page →
From page 116... ... D-12 accounts for the influence of axial stress at the centroid of section in a similar manner to the ACI 318-02 Eq. 11-12 (web shear cracking strength) Read the entire page →
From page 117... ... D-13 members, the ACI, AASHTO LRFD, CSA, and R2k approaches all give good predictions over the full range of a/d ratios, while the TMwCF, ASBI, Frosch, and STD79 approaches give relatively large scatters. D.2.2.5 Shear Reinforcement Strength ( vyv fρ ) Read the entire page →
From page 118... ... D-14 larger scatter than the ACI approach and tends to be more conservative as the stirrup strength increases. The Frosch approach also gives predictions that are similar to the ACI and ASBI approaches for RC members. Read the entire page →
From page 119... ... D-15 3. The AASHTO LRFD and CSA approaches, which are both based on the modified compression field theory, give very similar results with good levels of accuracy for both RC and PC members. Read the entire page →
From page 120... ... D-16 Table D-1 Code Assessment for Broad Categories (RC and PC with and without Av) All RC RC RC PC PC PC Both No Av With Av Both No Av With Av count (#) Read the entire page →
From page 121... ... D-17 Table D-3 Reinforced Concrete Members with Shear Reinforcement f'c (KSI) Read the entire page →
From page 122... ... D-18 Table D-5 Prestressed Concrete Members with Shear Reinforcement f'c (KSI) Read the entire page →
From page 123... ... D-19 Table D-7 Comparison of Code Performance across Four Broad Categories Member Type All RC RC RC PC PC PC Largest Largest Lowest Highest With or without Av Both No Av With Av Both No Av With Av Variation Variation COV & COV & count (#) 1359 878 718 160 481 321 160 in Mean in COV Category Category ACI Mean 1.44 1.51 1.54 1.35 1.32 1.38 1.21 0.34 0.221 0.418 COV 0.371 0.404 0.418 0.277 0.248 0.247 0.221 0.20 PC with Av RC No Av LRFD Mean 1.38 1.37 1.39 1.27 1.40 1.44 1.32 0.17 0.154 0.290 COV 0.262 0.262 0.266 0.224 0.261 0.290 0.154 0.14 PC with Av PC No Av CSA Mean 1.31 1.25 1.27 1.19 1.41 1.46 1.31 0.27 0.147 0.287 COV 0.275 0.274 0.282 0.218 0.261 0.287 0.147 0.14 PC with Av PC No Av JSCE Mean 1.51 1.36 1.35 1.38 1.80 1.85 1.70 0.50 0.216 0.297 COV 0.321 0.280 0.293 0.216 0.292 0.297 0.272 0.08 RC with Av PC No Av EC2 Mean 1.85 1.74 1.75 1.70 2.06 2.13 1.91 0.43 0.328 0.687 COV 0.409 0.336 0.328 0.373 0.470 0.343 0.687 0.36 RC No Av PC with Av DIN Mean 2.05 1.95 2.10 1.25 2.25 2.59 1.58 1.34 0.267 0.357 COV 0.395 0.368 0.327 0.267 0.413 0.345 0.357 0.09 RC with Av PC with Av Table D-8 Relationship Between Selected Fractile Level and Required Mean ACI ( COV = 0.37) Read the entire page →
From page 124... ... D-20 Table D-11 Comparison of predictions by various approaches (64 RC members) Ratio of VTest / VTest / VTest / VTest / VTest / VTest / VTest / VTest / VTest/VPred VACI VLRFD VCSA VR2k VTMwCF VASBI VFrosch VSTD79 # of Beams 64 64 64 64 64 64 64 64 Mean 1.296 1.214 1.105 1.019 1.237 1.233 1.257 1.263 STDEV 0.431 0.217 0.172 0.110 0.236 0.329 0.324 0.308 COV 0.333 0.179 0.156 0.108 0.191 0.267 0.258 0.244 Distribution (%) Read the entire page →
From page 125... ... D-21 Table D-12 Comparison of predictions by various approaches (85 PC members) Ratio of VTest / VTest / VTest / VTest / VTest / VTest / VTest / VTest / VTest/VPred VACI VLRFD VCSA VR2k VTMwCF VASBI VFrosch VSTD79 # of Beams 85 85 85 85 85 85 85 85 Mean 1.318 1.243 1.261 1.107 1.328 1.515 1.455 1.090 STDEV 0.206 0.174 0.165 0.188 0.333 0.300 0.292 0.417 COV 0.156 0.140 0.131 0.170 0.251 0.198 0.200 0.383 Distribution (%) Read the entire page →
From page 126... ... D-22 0x 0.1 5328.0 37.0 44.1 0 = = = x COV σ 0.2045 1.441.0 Figure D-1 Distribution of Ratio Vtest/Vaci for All Test Data (Gaussian Distribution of Data Assumed) Read the entire page →
From page 127... ... D-23 Figure D-4 Strength ratio (VTest/VPred) versus concrete compressive strength (f'c) Read the entire page →
From page 128... ... D-24 Figure D-5 Strength ratio (VTest/VPred) versus concrete compressive strength (f'c) Read the entire page →
From page 129... ... D-25 Figure D-6 Strength ratio (VTest/VPred) versus member depth (d) Read the entire page →
From page 130... ... D-26 Figure D-7 Strength ratio (VTest/VPred) versus member depth (d) Read the entire page →
From page 131... ... D-27 Figure D-8 Strength ratio (VTest/VPred) versus longitudinal reinforcement ratio ( lρ ) Read the entire page →
From page 132... ... D-28 Figure D-9 Strength ratio (VTest/VPred) versus versus longitudinal reinforcement ratio ( lρ ) Read the entire page →
From page 133... ... D-29 Figure D-10 Strength ratio (VTest/VPred) versus shear span to depth ratio (a/d) Read the entire page →
From page 134... ... D-30 Figure D-11 Strength ratio (VTest/VPred) versus shear span to depth ratio (a/d) Read the entire page →
From page 135... ... D-31 Figure D-12 Strength ratio (VTest/VPred) versus shear reinforcement strength ( vyv fρ ) Read the entire page →
From page 136... ... D-32 Figure D-13 Strength ratio (VTest/VPred) versus shear reinforcement strength ( vyv fρ ) Read the entire page →

From page 105...

... D-1 APPENDIX D: Evaluation of Shear Design Provisions In this appendix an evaluation of several shear design approaches is presented. In Section D.1, the relative strengths and weaknesses of six different codes of practice are assessed based on statistical values of strength ratios for the experimental test data of the shear database presented in Appendix C