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D APPENDIX D â CALIBRATION OF SERVICE III LIMIT STATE D-1
Table of Contents D.1 Calibration Process .................................................................................. D-21 D.2 Simulated Bridge databases, Bridge characteristics ................................. D-22 D.2.1 I Girder Bridges .................................................................................. D-22 D.2.2 Adjacent Box Girder Bridges .............................................................. D-46 D.2.3 Spread Box Girder Bridges ................................................................ D-54 D.2.4 PCI ASBI Box Girder Bridge ............................................................... D-66 D.3 Application of the Calibration Process to I-Girders and Bulb-Tees ........... D-67 D.3.1 Effect of changing design specifications (old losses, new losses) ...... D-67 D.3.2 Reliability indices of existing and redesigned bridges ......................... D-71 D.3.2.1 Evaluation of Existing Bridges (NCHRP 12-78 Bridge Database) ............................................................................... D-71 D.3.2.2 Evaluation of redesigned bridges using new loss provisions and tensile stress limit of 3âðâ²ð39T ..................................................... D-75 D.3.2.3 Evaluation of redesigned bridges using new losses provisions and tensile stress limit of 6âðâ²ð39T ..................................................... D-76 D.3.2.4 Evaluation of redesigned bridges using new losses provisions and tensile stress limit of 0.253âðâ²ð39T .............................................. D-77 D.3.3 Selection of Target Reliability indices ................................................. D-78 D.3.4 Reliability indices of girders designed for various design criteria (I Girders) ........................................................................................... D-80 D.3.4.1 Calibration for ADTT=1000 ..................................................... D-80 D.3.4.1.1 Bridges Designed for Maximum Concrete Tensile Stress of 0.0948t cf f â²= ................................................................. D-80 D.3.4.1.2 Bridges Designed for Maximum Concrete Tensile Stress of 0.158t cf f â²= .................................................................. D-85 D.3.4.1.3 Bridges Designed for Maximum Concrete Tensile Stress of 0.19t cf f â²= ..................................................................... D-91 D.3.4.1.4 Bridges Designed for Maximum Concrete Tensile Stress of 0.253t cf f â²= .................................................................. D-97 D.3.4.2 Calibration for ADTT=2500 ................................................... D-103 D.3.4.2.1 Bridges Designed for Maximum Concrete Tensile Stress of 0.0948t cf f â²= ............................................................... D-103 D-2
D.3.4.2.2 Bridges Designed for Maximum Concrete Tensile Stress of 0.158t cf f â²= ................................................................ D-107 D.3.4.2.3 Bridges Designed for Maximum Concrete Tensile Stress of 0.19t cf f â²= ................................................................... D-111 D.3.4.2.4 Bridges Designed for Maximum Concrete Tensile Stress of 0.253t cf f â²= ................................................................ D-115 D.3.4.3 Calibration Procedure for ADTT=5000 .................................. D-119 D.3.4.3.1 Bridges Designed for Maximum Concrete Tensile Stress of 0.0948t cf f â²= ............................................................... D-119 D.3.4.3.2 Bridges Designed for Maximum Concrete Tensile Stress of 0.158t cf f â²= ................................................................ D-123 D.3.4.3.3 Bridges Designed for Maximum Concrete Tensile Stress of 0.19t cf f â²= ................................................................... D-127 D.3.4.3.4 Bridges Designed for Maximum Concrete Tensile Stress of 0.253t cf f â²= ................................................................ D-131 D.3.4.4 Calibration Procedure for ADTT=10000 ................................ D-135 D.3.4.4.1 Bridges Designed for Maximum Concrete Tensile Stress of 0.0948t cf f â²= ............................................................... D-135 D.3.4.4.2 C6.4.2 Bridges Designed for Maximum Concrete Tensile Stress of 0.158t cf f â²= .................................................. D-139 D.3.4.4.3 Bridges Designed for Maximum Concrete Tensile Stress of 0.19t cf f â²= ................................................................... D-143 D.3.4.4.4 Bridges Designed for Maximum Concrete Tensile Stress of 0.253t cf f â²= ................................................................ D-147 D.4 Calibration for Other Types of Girders .................................................... D-151 D.4.1 Reliability indices of girders designed for various design criteria (Adjacent Box Girders) ..................................................................................... D-151 D.4.1.1 Bridges Designed for Maximum Concrete Tensile Stress of 0.0948âðâ²ð39T ........................................................................... D-151 D.4.1.2 C7.2 Bridges Designed for Maximum Concrete Tensile Stress of 0.158âðâ²ð39T ............................................................................. D-156 D.4.1.3 Bridges Designed for Maximum Concrete Tensile Stress of 0.19âðâ²ð39T ............................................................................... D-160 D.4.1.4 Bridges Designed for Maximum Concrete Tensile Stress of 0.253âðâ²ð39T ............................................................................. D-165 D-3
D.4.2 Reliability indices of girders designed for various design criteria (Spread Box Girders) ..................................................................................... D-169 D.4.2.1 Bridges Designed for Maximum Concrete Tensile Stress of 0.0948âðâ²ð39T ........................................................................... D-169 D.4.2.2 Bridges Designed for Maximum Concrete Tensile Stress of 0.158âðâ²ð39T ............................................................................. D-175 D.4.2.3 Bridges Designed for Maximum Concrete Tensile Stress of 0.19âðâ²ð39T ............................................................................... D-180 D.4.2.4 Bridges Designed for Maximum Concrete Tensile Stress of 0.253âðâ²ð39T ............................................................................. D-185 D.4.3 Reliability indices of girders designed for various design criteria (ASBI Box Girder Bridges) .......................................................................... D-190 D.4.3.1 C9.1 Bridges Designed for Maximum Concrete Tensile Stress of 0.0948âðâ²ð39T ........................................................................... D-190 D.4.3.2 Bridges Designed for Maximum Concrete Tensile Stress of 0.158âðâ²ð39T ............................................................................. D-194 D.4.3.3 Bridges Designed for Maximum Concrete Tensile Stress of 0.19âðâ²ð39T ............................................................................... D-198 D.4.3.4 Bridges Designed for Maximum Concrete Tensile Stress of 0.253âðâ²ð39T ............................................................................. D-202 D.5 Selection of load and resistance factors for use in the AASHTO LRFD .. D-207 D-4
List of Tables Table D-1- Design Outcomes of I Girder Bridges Designed with Compressive Strength of 6ksi, Live Load Factor of 0.8 and Tensile Stress Limit of ð.ððððâðâ²ð. ................................... D-22 Table D-2- Design Outcomes of I Girder Bridges Designed with Compressive Strength of 6ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.158âðâ²ð. ..................................... D-23 Table D-3- Design Outcomes of I Girder Bridges Designed with Compressive Strength of 6ksi, Live Load Factor of 0.8 and Tensile Stress Limit of ð.ððâðâ²ð. ....................................... D-24 Table D-4- Design Outcomes of I Girder Bridges Designed with Compressive Strength of 6ksi, Live Load Factor of 0.8 and Tensile Stress Limit of ð.ðððâðâ²ð. .................................... D-25 Table D-5- Design Outcomes of I Girder Bridges Designed with Compressive Strength of 6ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.0948âðâ²ð. ................................... D-26 Table D-6- Design Outcomes of I Girder Bridges Designed with Compressive Strength of 6ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.158âðâ²ð. ..................................... D-27 Table D-7- Design Outcomes of I Girder Bridges Designed with Compressive Strength of 6ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.19âðâ²ð. ....................................... D-28 Table D-8- Design Outcomes of I Girder Bridges Designed with Compressive Strength of 6ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.253âðâ²ð. ..................................... D-29 Table D-9- Design Outcomes of I Girder Bridges Designed with Compressive Strength of 8ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.0948âðâ²ð. ................................... D-30 Table D-10- Design Outcomes of I Girder Bridges Designed with Compressive Strength of 8ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.158âðâ²ð. ..................................... D-31 Table D-11- Design Outcomes of I Girder Bridges Designed with Compressive Strength of 8ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.19âðâ²ð. ....................................... D-32 Table D-12- Design Outcomes of I Girder Bridges Designed with Compressive Strength of 8ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.253âðâ²ð. ..................................... D-33 Table D-13- Design Outcomes of I Girder Bridges Designed with Compressive Strength of 8ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.0948âðâ²ð. ................................... D-34 Table D-14- Design Outcomes of I Girder Bridges Designed with Compressive Strength of 8ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.158âðâ²ð. ..................................... D-35 Table D-15- Design Outcomes of I Girder Bridges Designed with Compressive Strength of 8ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.19âðâ²ð. ....................................... D-36 Table D-16- Design Outcomes of I Girder Bridges Designed with Compressive Strength of 8ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.253âðâ²ð. ..................................... D-37 Table D-17- Design Outcomes of I Girder Bridges Designed with Compressive Strength of 10 ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.0948âðâ²ð. ............................. D-38 Table D-18- Design Outcomes of I Girder Bridges Designed with Compressive Strength of 10 ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.158âðâ²ð. ............................... D-39 Table D-19- Design Outcomes of I Girder Bridges Designed with Compressive Strength of 10 ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.19âðâ²ð. ................................. D-40 Table D-20- Design Outcomes of I Girder Bridges Designed with Compressive Strength of 10 ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.253âðâ²ð. ............................... D-41 Table D-21- Design Outcomes of I Girder Bridges Designed with Compressive Strength of 10 ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.0948âðâ²ð. ............................. D-42 D-5
Table D-22- Design Outcomes of I Girder Bridges Designed with Compressive Strength of 10 ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.158âðâ²ð. ............................... D-43 Table D-23- Design Outcomes of I Girder Bridges Designed with Compressive Strength of 10 ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.19âðâ²ð. ................................. D-44 Table D-24- Design Outcomes of I Girder Bridges Designed with Compressive Strength of 10 ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.253âðâ²ð. ............................... D-45 Table D-25- Design Outcomes of Adjacent Box Girder Bridges Designed with Compressive Strength of 6 ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.0948âðâ²ð. ........ D-46 Table D-26- Design Outcomes of Adjacent Box Girder Bridges Designed with Compressive Strength of 6 ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.158âðâ²ð. .......... D-46 Table D-27- Design Outcomes of Adjacent Box Girder Bridges Designed with Compressive Strength of 6 ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.19âðâ²ð. ............ D-47 Table D-28- Design Outcomes of Adjacent Box Girder Bridges Designed with Compressive Strength of 6 ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.253âðâ²ð. .......... D-47 Table D-29- Design Outcomes of Adjacent Box Girder Bridges Designed with Compressive Strength of 6 ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.0948âðâ²ð. ........ D-48 Table D-30- Design Outcomes of Adjacent Box Girder Bridges Designed with Compressive Strength of 6 ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.158âðâ²ð. .......... D-48 Table D-31- Design Outcomes of Adjacent Box Girder Bridges Designed with Compressive Strength of 6 ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.19âðâ²ð. ............ D-49 Table D-32- Design Outcomes of Adjacent Box Girder Bridges Designed with Compressive Strength of 6 ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.253âðâ²ð. .......... D-49 Table D-33- Design Outcomes of Adjacent Box Girder Bridges Designed with Compressive Strength of 8 ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.0948âðâ²ð. ........ D-50 Table D-34- Design Outcomes of Adjacent Box Girder Bridges Designed with Compressive Strength of 8 ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.158âðâ²ð. .......... D-50 Table D-35- Design Outcomes of Adjacent Box Girder Bridges Designed with Compressive Strength of 8 ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.19âðâ²ð. ............ D-51 Table D-36- Design Outcomes of Adjacent Box Girder Bridges Designed with Compressive Strength of 8 ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.253âðâ²ð. .......... D-51 Table D-37- Design Outcomes of Adjacent Box Girder Bridges Designed with Compressive Strength of 8 ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.0948âðâ²ð. ........ D-52 Table D-38- Design Outcomes of Adjacent Box Girder Bridges Designed with Compressive Strength of 8 ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.158âðâ²ð. .......... D-52 Table D-39- Design Outcomes of Adjacent Box Girder Bridges Designed with Compressive Strength of 8 ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.19âðâ²ð. ............ D-53 Table D-40- Design Outcomes of Adjacent Box Girder Bridges Designed with Compressive Strength of 8 ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.253âðâ²ð. .......... D-53 Table D-41- Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 6ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.0948âðâ²ð. ......... D-54 Table D-42- Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 6ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.158âðâ²ð. ........... D-54 Table D-43- Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 6ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.19âðâ²ð. ............. D-55 D-6
Table D-44- Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 6ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.253âðâ²ð. ........... D-55 Table D-45- Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 6ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.0948âðâ²ð. ......... D-56 Table D-46- Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 6ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.158âðâ²ð. ........... D-56 Table D-47- Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 6ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.19âðâ²ð. ............. D-57 Table D-48- Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 6ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.253âðâ²ð. ........... D-57 Table D-49- Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 8ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.0948âðâ²ð. ......... D-58 Table D-50- Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 8ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.158âðâ²ð. ........... D-58 Table D-51- Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 8ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.19âðâ²ð. ............. D-59 Table D-52- Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 8ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.253âðâ²ð. ........... D-59 Table D-53- Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 8ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.0948âðâ²ð. ......... D-60 Table D-54- Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 8ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.158âðâ²ð. ........... D-60 Table D-55- Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 8ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.19âðâ²ð. ............. D-61 Table D-56- Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 8ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.253âðâ²ð. ........... D-61 Table D-57- Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 10ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.0948âðâ²ð. ....... D-62 Table D-58- Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 10ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.158âðâ²ð. ......... D-62 Table D-59- Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 10ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.19âðâ²ð. ........... D-63 Table D-60- Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 10ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.253âðâ²ð. ......... D-63 Table D-61- Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 10ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.0948âðâ²ð. ....... D-64 Table D-62- Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 10ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.158âðâ²ð. ......... D-64 Table D-63- Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 10ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.19âðâ²ð. ........... D-65 Table D-64- Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 10ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.253âðâ²ð. ......... D-65 Table D-65- Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 8ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.0948âðâ²ð. ......... D-66 D-7
Table D-66- Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 8ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.158âðâ²ð. ........... D-66 Table D-67- Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 8ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.19âðâ²ð. ............. D-66 Table D-68- Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 8ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.253âðâ²ð. ........... D-67 Table D-69 Summary Information of Bridges Designed using AASHTO I-Girders with ADTT 5000 and 0.0948t cf f â²= .............................................................................................. D-69 Table D-70 - Summary Information of Bridges Designed using AASHTO I-Girders with ADTT 5000 and 0.19t cf f â²= ................................................................................................... D-70 Table D-71- Summary of NCHRP 12-78 I-Girder Bridge ....................................................... D-72 Table D-72- Summary of NCHRP 12-78 Spread Box Girder Bridge ...................................... D-73 Table D-73- Summary of NCHRP 12-78 Adjacent Box Girder Bridge .................................... D-74 Table D-74- Summary of Reliability Indices for Existing Bridges ........................................... D-75 Table D-75- Summary of Probability of Exceedance for Existing Bridges .............................. D-75 Table D-76- Summary of Reliability Indices for redesigned bridges using new losses provisions and tensile stress limit of 0.0948âðâ²ð39T ............................................................................ D-76 Table D-77- Summary of Probability of Exceedance for redesigned bridges using new losses provisions and tensile stress limit of 0.0948âðâ²ð39T ........................................................... D-76 Table D-78- Summary of Reliability Indices for redesigned bridges using new losses provisions and tensile stress limit of 0.19âðâ²ð39T ................................................................................ D-77 Table D-79- Summary of Probability of Exceedance for redesigned bridges using new losses provisions and tensile stress limit of 0.19âðâ²ð39T ............................................................... D-77 Table D-80- Summary of Reliability Indices for redesigned bridges using new losses provisions and tensile stress limit of 0.253âðâ²ð39T .............................................................................. D-78 Table D-81- Summary of Probability of Exceedance for redesigned bridges using new losses provisions and tensile stress limit of 0.253âðâ²ð39T ............................................................. D-78 Table D-82- Reliability Indices for Existing Bridges (Return Period of 1 Year) with One Lane Loaded (ADTT 5000) ..................................................................................................... D-79 Table D-83- Summary Information of Bridges Designed with γLL=0.8 ( 0.0948t cf f â²= ) ...... D-80 Table D-84- Summary Information of Bridges Designed with γLL=1.0 ( 0.0948t cf f â²= ) ...... D-83 Table D-85- Summary Information of Bridges Designed with γLL=0.8 ( 0.158t cf f â²= ) ........ D-86 Table D-86- Summary Information of Bridges Designed with γLL=1.0 ( 0.158t cf f â²= ) ........ D-89 Table D-87- Summary Information of Bridges Designed with γLL=0.8 ( 0.19t cf f â²= ) .......... D-92 Table D-88- Summary Information of Bridges Designed with γLL=1.0 ( 0.19t cf f â²= ) .......... D-95 Table D-89- Summary Information of Bridges Designed with γLL=0.8 ( 0.253t cf f â²= ) ........ D-98 Table D-90- Summary Information of Bridges Designed with γLL=1.0 ( 0.253t cf f â²= ) ...... D-101 Table D-91- Summary Information of Bridges Designed with γLL=0.8 ( 0.0948t cf f â²= ) .... D-152 Table D-92- Summary Information of Bridges Designed with γLL=1.0 ( 0.0948t cf f â²= ) .... D-154 D-8
Table D-93- Summary Information of Bridges Designed with γLL=0.8 ( 0.158t cf f â²= ) ...... D-156 Table D-94- Summary Information of Bridges Designed with γLL=1.0 ( 0.158t cf f â²= ) ...... D-158 Table D-95- Summary Information of Bridges Designed with γLL=0.8 ( 0.19t cf f â²= ) ........ D-160 Table D-96- Summary Information of Bridges Designed with γLL=1.0 ( 0.19t cf f â²= ) ........ D-163 Table D-97- Summary Information of Bridges Designed with γLL=0.8 ( 0.253t cf f â²= ) ...... D-165 Table D-98- Summary Information of Bridges Designed with γLL=1.0 ( 0.253t cf f â²= ) ...... D-167 Table D-99- Summary Information of Bridges Designed with γLL=0.8 ( 0.0948t cf f â²= ) .... D-170 Table D-100- Summary Information of Bridges Designed with γLL=1.0 ( 0.0948t cf f â²= ) .. D-173 Table D-101- Summary Information of Bridges Designed with γLL=0.8 ( 0.158t cf f â²= ) .... D-175 Table D-102- Summary Information of Bridges Designed with γLL=1.0 ( 0.158t cf f â²= ) .... D-178 Table D-103- Summary Information of Bridges Designed with γLL=0.8 ( 0.19t cf f â²= ) ...... D-180 Table D-104- Summary Information of Bridges Designed with γLL=1.0 ( 0.19t cf f â²= ) ...... D-183 Table D-105- Summary Information of Bridges Designed with γLL=0.8 ( 0.253t cf f â²= ) .... D-185 Table D-106- Summary Information of Bridges Designed with γLL=1.0 ( 0.253t cf f â²= ) .... D-188 Table D-107- Summary Information of Bridges Designed with γLL=0.8 ( 0.0948t cf f â²= ) .. D-190 Table D-108- Summary Information of Bridges Designed with γLL=1.0 ( 0.0948t cf f â²= ) .. D-192 Table D-109- Summary Information of Bridges Designed with γLL=0.8 ( 0.158t cf f â²= ) .... D-194 Table D-110- Summary Information of Bridges Designed with γLL=1.0 ( 0.158t cf f â²= ) .... D-196 Table D-111- Summary Information of Bridges Designed with γLL=0.8 ( 0.19t cf f â²= ) ...... D-198 Table D-112- Summary Information of Bridges Designed with γLL=1.0 ( 0.19t cf f â²= ) ...... D-200 Table D-113- Summary Information of Bridges Designed with γLL=0.8 ( 0.253t cf f â²= ) .... D-202 Table D-114- Summary Information of Bridges Designed with γLL=1.0 ( 0.253t cf f â²= ) .... D-205 D-9
List of Figures Figure D-1- Calibration process for Service III limit state ........................................... D-21 Figure D-2- Reliability Indices for Bridges at Decompression Limit State (ADTT=1000), γLL=0.8 ( 0.0948t cf f â²= ) ................................................................................. D-81 Figure D-3- Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=1000), γLL=0.8 ( 0.0948t cf f â²= ) ................................................ D-82 Figure D-4- Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=1000), γLL=0.8 ( 0.0948t cf f â²= ) ......................................................... D-82 Figure D-5- Reliability Indices for Bridges at Decompression Limit State (ADTT=1000), γLL=1.0 ( 0.0948t cf f â²= ) ................................................................................. D-84 Figure D-6- Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=1000), γLL=1.0 ( 0.0948t cf f â²= ) ......................................................... D-84 Figure D-7- Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=1000), γLL=1.0 ( 0.0948t cf f â²= ) ......................................................... D-85 Figure D-8- Reliability Indices for Bridges at Decompression Limit State (ADTT=1000), γLL=0.8 ( 0.158t cf f â²= ) ................................................................................... D-87 Figure D-9- Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=1000), γLL=0.8 ( 0.158t cf f â²= ) .................................................. D-87 Figure D-10- Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=1000), γLL=0.8 ( 0.158t cf f â²= ) .................................................. D-88 Figure D-11- Reliability Indices for Bridges at Decompression Limit State (ADTT=1000) , γLL=1.0 ( 0.158t cf f â²= ) ................................................................................... D-90 Figure D-12- Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=1000), γLL=1.0 ( 0.158t cf f â²= ) ........................................................... D-90 Figure D-13- Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=1000), γLL=1.0 ( 0.158t cf f â²= ) ........................................................... D-91 Figure D-14- Reliability Indices for Bridges at Decompression Limit State (ADTT=1000), γLL=0.8 ( 0.19t cf f â²= ) ..................................................................................... D-93 Figure D-15- Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=1000), γLL=0.8 ( 0.19t cf f â²= ) .................................................... D-93 Figure D-16- Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=1000), γLL=0.8 ( 0.19t cf f â²= ) .................................................... D-94 D-10
Figure D-17- Reliability Indices for Bridges at Decompression Limit State (ADTT=1000) , γLL=1.0 ( 0.19t cf f â²= ) ..................................................................................... D-96 Figure D-18- Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=1000), γLL=1.0 ( 0.19t cf f â²= ) .............................................................. D-96 Figure D-19- Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=1000), γLL=1.0 ( 0.19t cf f â²= ) .............................................................. D-97 Figure D-20- Reliability Indices for Bridges at Decompression Limit State (ADTT=1000), γLL=0.8 ( 0.253t cf f â²= ) ................................................................................... D-99 Figure D-21- Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=1000), γLL=0.8 ( 0.253t cf f â²= ) .................................................. D-99 Figure D-22- Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=1000), γLL=0.8 ( 0.253t cf f â²= ) ................................................ D-100 Figure D-23- Reliability Indices for Bridges at Decompression Limit State (ADTT=1000), γLL=1.0 ( 0.253t cf f â²= ) ................................................................................. D-102 Figure D-24- Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=1000), γLL=1.0 ( 0.253t cf f â²= ) ................................................ D-102 Figure D-25- Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=1000), γLL=1.0 ( 0.253t cf f â²= ) ................................................ D-103 Figure D-26- Reliability Indices for Bridges at Decompression Limit State (ADTT=2500), γLL=0.8 ( 0.0948t cf f â²= ) ............................................................................... D-104 Figure D-27- Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=2500), γLL=0.8 ( 0.0948t cf f â²= ) .............................................. D-104 Figure D-28- Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=2500), γLL=0.8 ( 0.0948t cf f â²= ) .............................................. D-105 Figure D-29- Reliability Indices for Bridges at Decompression Limit State (ADTT=2500), γLL=1.0 ( 0.0948t cf f â²= ) ............................................................................... D-106 Figure D-30- Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=2500), γLL=1.0 ( 0.0948t cf f â²= ) ....................................................... D-106 Figure D-31- Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=2500), γLL=1.0 ( 0.0948t cf f â²= ) ....................................................... D-107 Figure D-32- Reliability Indices for Bridges at Decompression Limit State (ADTT=2500), γLL=0.8 ( 0.158t cf f â²= ) ................................................................................. D-108 D-11
Figure D-33- Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=2500), γLL=0.8 ( 0.158t cf f â²= ) ................................................ D-108 Figure D-34- Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=2500), γLL=0.8 ( 0.158t cf f â²= ) ................................................ D-109 Figure D-35- Reliability Indices for Bridges at Decompression Limit State (ADTT=2500) , γLL=1.0 ( 0.158t cf f â²= ) ................................................................................. D-110 Figure D-36- Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=2500), γLL=1.0 ( 0.158t cf f â²= ) ......................................................... D-110 Figure D-37- Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=2500), γLL=1.0 ( 0.158t cf f â²= ) ......................................................... D-111 Figure D-38- Reliability Indices for Bridges at Decompression Limit State (ADTT=2500), γLL=0.8 ( 0.19t cf f â²= ) ................................................................................... D-112 Figure D-39- Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=2500), γLL=0.8 ( 0.19t cf f â²= ) .................................................. D-112 Figure D-40- Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=2500), γLL=0.8 ( 0.19t cf f â²= ) .................................................. D-113 Figure D-41- Reliability Indices for Bridges at Decompression Limit State (ADTT=2500) , γLL=1.0 ( 0.19t cf f â²= ) ................................................................................... D-114 Figure D-42- Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=2500), γLL=1.0 ( 0.19t cf f â²= ) ............................................................ D-114 Figure D-43- Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=2500), γLL=1.0 ( 0.19t cf f â²= ) ............................................................ D-115 Figure D-44- Reliability Indices for Bridges at Decompression Limit State (ADTT=2500), γLL=0.8 ( 0.253t cf f â²= ) ................................................................................. D-116 Figure D-45- Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=2500), γLL=0.8 ( 0.253t cf f â²= ) ................................................ D-116 Figure D-46- Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=2500), γLL=0.8 ( 0.253t cf f â²= ) ................................................ D-117 Figure D-47- Reliability Indices for Bridges at Decompression Limit State (ADTT=2500) , γLL=1.0 ( 0.253t cf f â²= ) ................................................................................. D-118 Figure D-48- Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=2500), γLL=1.0 ( 0.253t cf f â²= ) ......................................................... D-118 D-12
Figure D-49- Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=2500), γLL=1.0 ( 0.253t cf f â²= ) ......................................................... D-119 Figure D-50- Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=0.8 ( 0.0948t cf f â²= ) ............................................................................... D-120 Figure D-51- Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=5000), γLL=0.8 ( 0.0948t cf f â²= ) .............................................. D-120 Figure D-52- Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=5000), γLL=0.8 ( 0.0948t cf f â²= ) .............................................. D-121 Figure D-53- Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=1.0 ( 0.0948t cf f â²= ) ............................................................................... D-122 Figure D-54- Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=5000), γLL=1.0 ( 0.0948t cf f â²= ) ....................................................... D-122 Figure D-55- Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=5000), γLL=1.0 ( 0.0948t cf f â²= ) ....................................................... D-123 Figure D-56- Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=0.8 ( 0.158t cf f â²= ) ................................................................................. D-124 Figure D-57- Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=5000), γLL=0.8 ( 0.158t cf f â²= ) ................................................ D-124 Figure D-58- Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=5000), γLL=0.8 ( 0.158t cf f â²= ) ................................................ D-125 Figure D-59- Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=1.0 ( 0.158t cf f â²= ) ................................................................................. D-126 Figure D-60- Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=5000), γLL=1.0 ( 0.158t cf f â²= ) ......................................................... D-126 Figure D-61- Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=5000), γLL=1.0 ( 0.158t cf f â²= ) ......................................................... D-127 Figure D-62- Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=0.8 ( 0.19t cf f â²= ) ................................................................................... D-128 Figure D-63- Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=5000), γLL=0.8 ( 0.19t cf f â²= ) .................................................. D-128 Figure D-64- Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=5000), γLL=0.8 ( 0.19t cf f â²= ) .................................................. D-129 D-13
Figure D-65- Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=1.0 ( 0.19t cf f â²= ) ................................................................................... D-130 Figure D-66- Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=5000), γLL=1.0 ( 0.19t cf f â²= ) ............................................................ D-130 Figure D-67- Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=5000), γLL=1.0 ( 0.19t cf f â²= ) ............................................................ D-131 Figure D-68- Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=0.8 ( 0.253t cf f â²= ) ................................................................................. D-132 Figure D-69- Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=5000), γLL=0.8 ( 0.253t cf f â²= ) ................................................ D-132 Figure D-70- Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=5000), γLL=0.8 ( 0.253t cf f â²= ) ................................................ D-133 Figure D-71- Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=1.0 ( 0.253t cf f â²= ) ................................................................................. D-134 Figure D-72- Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=5000), γLL=1.0 ( 0.253t cf f â²= ) ......................................................... D-134 Figure D-73- Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=5000), γLL=1.0 ( 0.253t cf f â²= ) ......................................................... D-135 Figure D-74- Reliability Indices for Bridges at Decompression Limit State (ADTT=10000), γLL=0.8 ( 0.0948t cf f â²= ) ............................................................................... D-136 Figure D-75- Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=10000), γLL=0.8 ( 0.0948t cf f â²= ) ............................................ D-136 Figure D-76- Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=10000), γLL=0.8 ( 0.0948t cf f â²= ) ............................................ D-137 Figure D-77- Reliability Indices for Bridges at Decompression Limit State (ADTT=10000), γLL=1.0 ( 0.0948t cf f â²= ) ............................................................................... D-138 Figure D-78- Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=10000), γLL=1.0 ( 0.0948t cf f â²= ) ..................................................... D-138 Figure D-79- Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=10000), γLL=1.0 ( 0.0948t cf f â²= ) ..................................................... D-139 Figure D-80- Reliability Indices for Bridges at Decompression Limit State (ADTT=10000), γLL=0.8 ( 0.158t cf f â²= ) ................................................................................. D-140 D-14
Figure D-81- Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=10000), γLL=0.8 ( 0.158t cf f â²= ) .............................................. D-140 Figure D-82- Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=10000), γLL=0.8 ( 0.158t cf f â²= ) .............................................. D-141 Figure D-83- Reliability Indices for Bridges at Decompression Limit State (ADTT=10000), γLL=1.0 ( 0.158t cf f â²= ) ................................................................................. D-142 Figure D-84- Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=10000), γLL=1.0 ( 0.158t cf f â²= ) ....................................................... D-142 Figure D-85- Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=10000), γLL=1.0 ( 0.158t cf f â²= ) ....................................................... D-143 Figure D-86- Reliability Indices for Bridges at Decompression Limit State (ADTT=10000), γLL=0.8 ( 0.19t cf f â²= ) ................................................................................... D-144 Figure D-87- Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=10000), γLL=0.8 ( 0.19t cf f â²= )................................................. D-144 Figure D-88- Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=10000), γLL=0.8 ( 0.19t cf f â²= )................................................. D-145 Figure D-89- Reliability Indices for Bridges at Decompression Limit State (ADTT=10000), γLL=1.0 ( 0.19t cf f â²= ) ................................................................................... D-146 Figure D-90- Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=10000), γLL=1.0 ( 0.19t cf f â²= ) .......................................................... D-146 Figure D-91- Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=10000), γLL=1.0 ( 0.19t cf f â²= ) .......................................................... D-147 Figure D-92- Reliability Indices for Bridges at Decompression Limit State (ADTT=10000), γLL=0.8 ( 0.253t cf f â²= ) ................................................................................. D-148 Figure D-93- Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=10000), γLL=0.8 ( 0.253t cf f â²= ) .............................................. D-148 Figure D-94- Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=10000), γLL=0.8 ( 0.253t cf f â²= ) .............................................. D-149 Figure D-95- Reliability Indices for Bridges at Decompression Limit State (ADTT=10000), γLL=1.0 ( 0.253t cf f â²= ) ................................................................................. D-150 Figure D-96- Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=10000), γLL=1.0 ( 0.253t cf f â²= ) ....................................................... D-150 D-15
Figure D-97- Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=10000), γLL=1.0 ( 0.253t cf f â²= ) ....................................................... D-151 Figure D-98- Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=0.8 ( 0.0948t cf f â²= ) ............................................................................... D-152 Figure D-99- Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=5000), γLL=0.8 ( 0.0948t cf f â²= ) .............................................. D-153 Figure D-100- Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=5000), γLL=0.8 ( 0.0948t cf f â²= ) .............................................. D-153 Figure D-101- Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=1.0 ( 0.0948t cf f â²= ) ............................................................................... D-154 Figure D-102- Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=5000), γLL=1.0 ( 0.0948t cf f â²= ) ....................................................... D-155 Figure D-103- Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=5000), γLL=1.0 ( 0.0948t cf f â²= ) ....................................................... D-155 Figure D-104- Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=0.8 ( 0.158t cf f â²= ) ................................................................................. D-157 Figure D-105- Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=5000), γLL=0.8 ( 0.158t cf f â²= ) ................................................ D-157 Figure D-106- Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=5000), γLL=0.8 ( 0.158t cf f â²= ) ................................................ D-158 Figure D-107- Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=1.0 ( 0.158t cf f â²= ) ................................................................................. D-159 Figure D-108- Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=5000), γLL=1.0 ( 0.158t cf f â²= ) ......................................................... D-159 Figure D-109- Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=5000), γLL=1.0 ( 0.158t cf f â²= ) ......................................................... D-160 Figure D-110- Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=0.8 ( 0.19t cf f â²= ) ................................................................................... D-161 Figure D-111- Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=5000), γLL=0.8 ( 0.19t cf f â²= ) .................................................. D-162 Figure D-112- Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=5000), γLL=0.8 ( 0.19t cf f â²= ) .................................................. D-162 D-16
Figure D-113- Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=1.0 ( 0.19t cf f â²= ) ................................................................................... D-163 Figure D-114- Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=5000), γLL=1.0 ( 0.19t cf f â²= ) ............................................................ D-164 Figure D-115- Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=5000), γLL=1.0 ( 0.19t cf f â²= ) ............................................................ D-164 Figure D-116- Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=0.8 ( 0.253t cf f â²= ) ................................................................................. D-166 Figure D-117- Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=5000), γLL=0.8 ( 0.253t cf f â²= ) ................................................ D-166 Figure D-118- Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=5000), γLL=0.8 ( 0.253t cf f â²= ) ................................................ D-167 Figure D-119- Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=1.0 ( 0.253t cf f â²= ) ................................................................................. D-168 Figure D-120- Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=5000), γLL=1.0 ( 0.253t cf f â²= ) ................................................ D-168 Figure D-121- Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=5000), γLL=1.0 ( 0.253t cf f â²= ) ................................................ D-169 Figure D-122- Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=0.8 ( 0.0948t cf f â²= ) ............................................................................... D-171 Figure D-123- Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=5000), γLL=0.8 ( 0.0948t cf f â²= ) .............................................. D-171 Figure D-124- Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=5000), γLL=0.8 ( 0.0948t cf f â²= ) .............................................. D-172 Figure D-125- Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=1.0 ( 0.0948t cf f â²= ) ............................................................................... D-173 Figure D-126- Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=5000), γLL=1.0 ( 0.0948t cf f â²= ) ....................................................... D-174 Figure D-127- Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=5000), γLL=1.0 ( 0.0948t cf f â²= ) ....................................................... D-174 Figure D-128- Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=0.8 ( 0.158t cf f â²= ) ................................................................................. D-176 D-17
Figure D-129- Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=5000), γLL=0.8 ( 0.158t cf f â²= ) ................................................ D-176 Figure D-130- Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=5000), γLL=0.8 ( 0.158t cf f â²= ) ................................................ D-177 Figure D-131- Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=1.0 ( 0.158t cf f â²= ) ................................................................................. D-178 Figure D-132- Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=5000), γLL=1.0 ( 0.158t cf f â²= ) ......................................................... D-179 Figure D-133- Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=5000), γLL=1.0 ( 0.158t cf f â²= ) ......................................................... D-179 Figure D-134- Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=0.8 ( 0.19t cf f â²= ) ................................................................................... D-181 Figure D-135- Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=5000), γLL=0.8 ( 0.19t cf f â²= ) .................................................. D-181 Figure D-136- Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=5000), γLL=0.8 ( 0.19t cf f â²= ) .................................................. D-182 Figure D-137- Reliability Indices for Bridges at Decompression Limit State (ADTT=5000) γLL=1.0 ( 0.19t cf f â²= ) ................................................................................... D-183 Figure D-138- Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=5000), γLL=1.0 ( 0.19t cf f â²= ) ............................................................ D-184 Figure D-139- Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=5000), γLL=1.0 ( 0.19t cf f â²= ) ............................................................ D-184 Figure D-140- Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=0.8 ( 0.253t cf f â²= ) ................................................................................. D-186 Figure D-141- Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=5000), γLL=0.8 ( 0.253t cf f â²= ) ................................................ D-186 Figure D-142- Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=5000), γLL=0.8 ( 0.253t cf f â²= ) ................................................ D-187 Figure D-143- Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=1.0 ( 0.253t cf f â²= ) ................................................................................. D-188 Figure D-144- Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=5000), γLL=1.0 ( 0.253t cf f â²= ) ................................................ D-189 D-18
Figure D-145- Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=5000), γLL=1.0 ( 0.253t cf f â²= ) ................................................ D-189 Figure D-146- Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=0.8 ( 0.0948t cf f â²= ) ............................................................................... D-191 Figure D-147- Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=5000), γLL=0.8 ( 0.0948t cf f â²= ) .............................................. D-191 Figure D-148- Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=5000), γLL=0.8 ( 0.0948t cf f â²= ) .............................................. D-192 Figure D-149- Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=1.0 ( 0.0948t cf f â²= ) ............................................................................... D-193 Figure D-150- Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=5000), γLL=1.0 ( 0.0948t cf f â²= ) ....................................................... D-193 Figure D-151- Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=5000), γLL=1.0 ( 0.0948t cf f â²= ) ....................................................... D-194 Figure D-152- Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=0.8 ( 0.158t cf f â²= ) ................................................................................. D-195 Figure D-153- Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=5000), γLL=0.8 ( 0.158t cf f â²= ) ................................................ D-195 Figure D-154- Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=5000), γLL=0.8 ( 0.158t cf f â²= ) ................................................ D-196 Figure D-155- Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=1.0 ( 0.158t cf f â²= ) ................................................................................. D-197 Figure D-156- Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=5000), γLL=1.0 ( 0.158t cf f â²= ) ......................................................... D-197 Figure D-157- Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=5000), γLL=1.0 ( 0.158t cf f â²= ) ......................................................... D-198 Figure D-158- Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=0.8 ( 0.19t cf f â²= ) ................................................................................... D-199 Figure D-159- Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=5000), γLL=0.8 ( 0.19t cf f â²= ) .................................................. D-199 Figure D-160- Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=5000), γLL=0.8 ( 0.19t cf f â²= ) .................................................. D-200 D-19
Figure D-161- Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=1.0 ( 0.19t cf f â²= ) ................................................................................... D-201 Figure D-162- Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=5000), γLL=1.0 ( 0.19t cf f â²= ) ............................................................ D-201 Figure D-163- Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=5000), γLL=1.0 ( 0.19t cf f â²= ) ............................................................ D-202 Figure D-164- Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=0.8 ( 0.253t cf f â²= ) ................................................................................. D-203 Figure D-165- Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=5000), γLL=0.8 ( 0.253t cf f â²= ) ................................................ D-204 Figure D-166- Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=5000), γLL=0.8 ( 0.253t cf f â²= ) ................................................ D-204 Figure D-167- Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=1.0 ( 0.253t cf f â²= ) ................................................................................. D-205 Figure D-168- Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=5000), γLL=1.0 ( 0.253t cf f â²= ) ................................................ D-206 Figure D-169- Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=5000), γLL=1.0 ( 0.253t cf f â²= ) ................................................ D-206 D-20
D.1 Calibration Process This section summarized the calibration procedure utilized in this study. The RT proposed the following general procedure for the calibration of Service III limit state. 1) Formulate the limit state function and identify basic variables. 2) Identify and select representative structural types and design cases. 3) Determine load and resistance parameters for the selected design cases. 4) Develop models for load and resistance. 5) Calculate the reliability indices for current design code and current practice. 6) Review the results and select the target reliability index βT. 7) Select new potential load and resistance factors or Revise the provisions. 8) Calculate reliability index. In order to achieve a specified and uniform target reliability index for each limit state, a detailed calibration process will be performed. Figure D-1 shows the flowchart of the calibration process. Figure D-1- Calibration process for Service III limit state Original Bridge Database Check Reliability Index, βave> βT Load and Resistance Models No Yes New Load & Resistance Factors Check Uniformity Redesign with New Live Load Factor No Redesign with New Tandem Model, Dead Load or Resistance Factor Yes D-21
D.2 Simulated Bridge databases, Bridge characteristics The following sections summarized the bridge databases developed by the research team that used in the calibration and investigation in this study. The majority of the girder section types, includes I girder, adjacent box girder, and spread box girder was included in the bridge databases with the span lengths ranging from 30 ft. to 160 ft. Furthermore, compressive strength of 6ksi, 8ksi, and 10ksi was employed in the design to represent the low, medium and high compressive strength that might be observed in current designs. In addition, live load factor of 0.8 and 1.0 were used in the design. D.2.1 I Girder Bridges Table D-1 Design Outcomes of I Girder Bridges Designed with Compressive Strength of 6ksi, Live Load Factor of 0.8 and Tensile Stress Limit of ð.ððððâðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 AASHTO I 30 6 1.224 8 2 AASHTO I 30 8 1.53 10 3 AASHTO I 30 10 1.836 12 4 AASHTO I 30 12 2.142 14 5 AASHTO II 60 6 2.754 18 6 AASHTO III 60 8 2.754 18 7 AASHTO III 60 10 3.366 22 8 AASHTO III 60 12 3.672 24 9 AASHTO III 80 6 3.978 26 10 AASHTO III 80 8 4.896 32 11 AASHTO IV 80 10 4.59 30 12 AASHTO IV 80 12 5.508 36 13 AASHTO IV 100 6 5.508 36 14 AASHTO IV 100 8 6.426 42 15 AASHTO V 100 10 6.426 42 16 AASHTO V 100 12 7.344 48 17 AASHTO V 120 6 7.038 46 18 AASHTO V 120 8 8.262 54 19 AASHTO VI 120 10 8.262 54 20 AASHTO VI 120 12 9.486 62 21 AASHTO VI 140 6 8.568 56 22 AASHTO VI 140 8 10.098 66 23 AASHTO VI 140 10 - - 24 F.I.B.-96 160 6 8.246 38 25 F.I.B.-96 160 8 9.548 44 26 F.I.B.-96 160 10 10.85 50 D-22
Table D-2 Design Outcomes of I Girder Bridges Designed with Compressive Strength of 6ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.158âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 AASHTO I 30 6 1.224 8 2 AASHTO I 30 8 1.53 10 3 AASHTO I 30 10 1.53 10 4 AASHTO I 30 12 1.836 12 5 AASHTO II 60 6 2.448 16 6 AASHTO III 60 8 2.448 16 7 AASHTO III 60 10 3.06 20 8 AASHTO III 60 12 3.366 22 9 AASHTO III 80 6 3.672 24 10 AASHTO IV 80 8 3.978 26 11 AASHTO IV 80 10 4.284 28 12 AASHTO IV 80 12 4.896 32 13 AASHTO IV 100 6 5.202 34 14 AASHTO IV 100 8 6.12 40 15 AASHTO V 100 10 5.814 38 16 AASHTO V 100 12 6.732 44 17 AASHTO V 120 6 6.426 42 18 AASHTO V 120 8 7.65 50 19 AASHTO VI 120 10 7.65 50 20 AASHTO VI 120 12 8.874 58 21 AASHTO VI 140 6 7.956 52 22 AASHTO VI 140 8 9.792 64 23 AASHTO VI 140 10 - - 24 F.I.B.-96 160 6 7.378 34 25 F.I.B.-96 160 8 8.68 40 26 F.I.B.-96 160 10 10.416 48 D-23
Table D-3 Design Outcomes of I Girder Bridges Designed with Compressive Strength of 6ksi, Live Load Factor of 0.8 and Tensile Stress Limit of ð.ððâðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 AASHTO I 30 6 1.224 8 2 AASHTO I 30 8 1.53 10 3 AASHTO I 30 10 1.836 12 4 AASHTO I 30 12 2.142 14 5 AASHTO II 60 6 2.448 16 6 AASHTO III 60 8 2.142 14 7 AASHTO III 60 10 2.754 18 8 AASHTO III 60 12 3.366 22 9 AASHTO III 80 6 3.366 22 10 AASHTO III 80 8 4.59 30 11 AASHTO IV 80 10 4.284 28 12 AASHTO IV 80 12 4.896 32 13 AASHTO IV 100 6 4.896 32 14 AASHTO IV 100 8 6.12 40 15 AASHTO V 100 10 5.814 38 16 AASHTO V 100 12 6.732 44 17 AASHTO V 120 6 6.12 40 18 AASHTO V 120 8 7.65 50 19 AASHTO VI 120 10 7.344 48 20 AASHTO VI 120 12 8.568 56 21 AASHTO VI 140 6 7.65 50 22 AASHTO VI 140 8 9.18 60 23 AASHTO VI 140 10 - - 24 F.I.B.-96 160 6 7.378 34 25 F.I.B.-96 160 8 8.68 40 26 F.I.B.-96 160 10 9.982 46 D-24
Table D-4 Design Outcomes of I Girder Bridges Designed with Compressive Strength of 6ksi, Live Load Factor of 0.8 and Tensile Stress Limit of ð.ðððâðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 AASHTO I 30 6 1.224 8 2 AASHTO I 30 8 1.224 8 3 AASHTO I 30 10 1.53 10 4 AASHTO I 30 12 1.836 12 5 AASHTO II 60 6 2.142 14 6 AASHTO III 60 8 2.142 14 7 AASHTO III 60 10 2.448 16 8 AASHTO III 60 12 3.06 20 9 AASHTO III 80 6 3.366 22 10 AASHTO IV 80 8 3.366 22 11 AASHTO IV 80 10 3.978 26 12 AASHTO IV 80 12 4.59 30 13 AASHTO IV 100 6 4.59 30 14 AASHTO IV 100 8 5.814 38 15 AASHTO V 100 10 5.202 34 16 AASHTO V 100 12 6.12 40 17 AASHTO V 120 6 5.814 38 18 AASHTO V 120 8 7.038 46 19 AASHTO VI 120 10 7.038 46 20 AASHTO VI 120 12 7.956 52 21 AASHTO VI 140 6 7.344 48 22 AASHTO VI 140 8 8.874 58 23 AASHTO VI 140 10 10.404 68 24 F.I.B.-96 160 6 6.944 32 25 F.I.B.-96 160 8 7.812 36 26 F.I.B.-96 160 10 9.114 42 D-25
Table D-5 Design Outcomes of I Girder Bridges Designed with Compressive Strength of 6ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.0948âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 AASHTO I 30 6 1.224 8 2 AASHTO I 30 8 1.53 10 3 AASHTO I 30 10 1.836 12 4 AASHTO I 30 12 2.142 14 5 AASHTO II 60 6 3.06 20 6 AASHTO III 60 8 3.06 20 7 AASHTO III 60 10 3.672 24 8 AASHTO III 60 12 4.284 28 9 AASHTO III 80 6 4.284 28 10 AASHTO IV 80 8 4.59 30 11 AASHTO IV 80 10 5.202 34 12 AASHTO IV 80 12 6.12 40 13 AASHTO IV 100 6 6.12 40 14 AASHTO V 100 8 6.12 40 15 AASHTO V 100 10 7.038 46 16 AASHTO V 100 12 7.956 52 17 AASHTO V 120 6 7.65 50 18 AASHTO VI 120 8 7.65 50 19 AASHTO VI 120 10 8.874 58 20 AASHTO VI 120 12 - - 21 AASHTO VI 140 6 9.18 60 22 AASHTO VI 140 8 - - 23 AASHTO VI 140 10 - - 24 F.I.B.-96 160 6 8.68 40 25 F.I.B.-96 160 8 10.416 48 26 F.I.B.-96 160 10 11.718 54 D-26
Table D-6 Design Outcomes of I Girder Bridges Designed with Compressive Strength of 6ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.158âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 AASHTO I 30 6 1.224 8 2 AASHTO I 30 8 1.53 10 3 AASHTO I 30 10 1.836 12 4 AASHTO I 30 12 2.448 16 5 AASHTO II 60 6 2.754 18 6 AASHTO III 60 8 2.754 18 7 AASHTO III 60 10 3.366 22 8 AASHTO III 60 12 3.978 26 9 AASHTO III 80 6 3.978 26 10 AASHTO IV 80 8 4.284 28 11 AASHTO IV 80 10 4.896 32 12 AASHTO IV 80 12 5.814 38 13 AASHTO IV 100 6 5.508 36 14 AASHTO IV 100 8 7.038 46 15 AASHTO V 100 10 6.732 44 16 AASHTO V 100 12 7.65 50 17 AASHTO V 120 6 7.038 46 18 AASHTO V 120 8 8.568 56 19 AASHTO VI 120 10 8.568 56 20 AASHTO VI 120 12 - - 21 AASHTO VI 140 6 8.874 58 22 AASHTO VI 140 8 - - 23 AASHTO VI 140 10 - - 24 F.I.B.-96 160 6 8.246 38 25 F.I.B.-96 160 8 9.548 44 26 F.I.B.-96 160 10 11.284 52 D-27
Table D-7 Design Outcomes of I Girder Bridges Designed with Compressive Strength of 6ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.19âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 AASHTO I 30 6 1.224 8 2 AASHTO I 30 8 1.53 10 3 AASHTO I 30 10 1.836 12 4 AASHTO I 30 12 2.448 16 5 AASHTO II 60 6 2.754 18 6 AASHTO III 60 8 2.448 16 7 AASHTO III 60 10 3.366 22 8 AASHTO III 60 12 3.978 26 9 AASHTO III 80 6 3.978 26 10 AASHTO IV 80 8 3.978 26 11 AASHTO IV 80 10 4.59 30 12 AASHTO IV 80 12 5.508 36 13 AASHTO IV 100 6 5.508 36 14 AASHTO IV 100 8 6.732 44 15 AASHTO V 100 10 6.426 42 16 AASHTO V 100 12 7.344 48 17 AASHTO V 120 6 6.732 44 18 AASHTO V 120 8 8.262 54 19 AASHTO VI 120 10 8.262 54 20 AASHTO VI 120 12 9.486 62 21 AASHTO VI 140 6 8.568 56 22 AASHTO VI 140 8 10.404 68 23 AASHTO VI 140 10 - - 24 F.I.B.-96 160 6 7.812 36 25 F.I.B.-96 160 8 9.548 44 26 F.I.B.-96 160 10 10.85 50 D-28
Table D-8 Design Outcomes of I Girder Bridges Designed with Compressive Strength of 6ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.253âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 AASHTO I 30 6 1.224 8 2 AASHTO I 30 8 1.224 8 3 AASHTO I 30 10 1.53 10 4 AASHTO I 30 12 1.836 12 5 AASHTO II 60 6 2.448 16 6 AASHTO III 60 8 2.448 16 7 AASHTO III 60 10 3.06 20 8 AASHTO III 60 12 3.672 24 9 AASHTO III 80 6 3.672 24 10 AASHTO IV 80 8 3.672 24 11 AASHTO IV 80 10 4.284 28 12 AASHTO IV 80 12 5.202 34 13 AASHTO IV 100 6 5.202 34 14 AASHTO IV 100 8 6.426 42 15 AASHTO V 100 10 5.814 38 16 AASHTO V 100 12 7.038 46 17 AASHTO V 120 6 6.426 42 18 AASHTO V 120 8 7.956 52 19 AASHTO VI 120 10 7.65 50 20 AASHTO VI 120 12 8.874 58 21 AASHTO VI 140 6 7.956 52 22 AASHTO VI 140 8 9.792 64 23 AASHTO VI 140 10 - - 24 F.I.B.-96 160 6 7.378 34 25 F.I.B.-96 160 8 8.68 40 26 F.I.B.-96 160 10 10.416 48 D-29
Table D-9 Design Outcomes of I Girder Bridges Designed with Compressive Strength of 8ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.0948âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 AASHTO I 30 6 1.224 8 2 AASHTO I 30 8 1.53 10 3 AASHTO I 30 10 1.836 12 4 AASHTO I 30 12 1.836 12 5 AASHTO II 60 6 2.448 16 6 AASHTO II 60 8 3.366 22 7 AASHTO III 60 10 3.06 20 8 AASHTO III 60 12 3.672 24 9 AASHTO III 80 6 3.672 24 10 AASHTO III 80 8 4.59 30 11 AASHTO III 80 10 5.508 36 12 AASHTO IV 80 12 5.202 34 13 AASHTO III 100 6 6.12 40 14 AASHTO IV 100 8 6.426 42 15 AASHTO IV 100 10 7.344 48 16 AASHTO V 100 12 7.038 46 17 AASHTO IV 120 6 7.956 52 18 AASHTO V 120 8 7.956 52 19 AASHTO V 120 10 9.18 60 20 AASHTO VI 120 12 8.874 58 21 AASHTO VI 140 6 8.262 54 22 AASHTO VI 140 8 9.792 64 23 AASHTO VI 140 10 11.322 74 24 F.I.B.-96 160 6 7.812 36 25 F.I.B.-96 160 8 9.114 42 26 F.I.B.-96 160 10 10.416 48 D-30
Table D-10 Design Outcomes of I Girder Bridges Designed with Compressive Strength of 8ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.158âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 AASHTO I 30 6 1.224 8 2 AASHTO I 30 8 1.53 10 3 AASHTO I 30 10 1.836 12 4 AASHTO I 30 12 2.295 15 5 AASHTO II 60 6 2.448 16 6 AASHTO II 60 8 3.672 24 7 AASHTO III 60 10 3.06 20 8 AASHTO III 60 12 3.672 24 9 AASHTO III 80 6 3.366 22 10 AASHTO III 80 8 4.284 28 11 AASHTO III 80 10 5.202 34 12 AASHTO IV 80 12 4.896 32 13 AASHTO III 100 6 5.814 38 14 AASHTO IV 100 8 5.814 38 15 AASHTO IV 100 10 7.038 46 16 AASHTO V 100 12 6.426 42 17 AASHTO IV 120 6 7.344 48 18 AASHTO V 120 8 7.344 48 19 AASHTO V 120 10 8.568 56 20 AASHTO VI 120 12 8.262 54 21 AASHTO VI 140 6 7.65 50 22 AASHTO VI 140 8 9.18 60 23 AASHTO VI 140 10 10.71 70 24 F.I.B.-96 160 6 7.378 34 25 F.I.B.-96 160 8 8.68 40 26 F.I.B.-96 160 10 9.548 44 D-31
Table D-11 Design Outcomes of I Girder Bridges Designed with Compressive Strength of 8ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.19âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 AASHTO I 30 6 1.224 8 2 AASHTO I 30 8 1.53 10 3 AASHTO I 30 10 1.836 12 4 AASHTO I 30 12 2.295 15 5 AASHTO II 60 6 2.448 16 6 AASHTO II 60 8 3.06 20 7 AASHTO III 60 10 3.06 20 8 AASHTO III 60 12 3.672 24 9 AASHTO III 80 6 3.366 22 10 AASHTO III 80 8 4.284 28 11 AASHTO III 80 10 4.896 32 12 AASHTO IV 80 12 4.896 32 13 AASHTO III 100 6 5.814 38 14 AASHTO IV 100 8 5.814 38 15 AASHTO IV 100 10 6.732 44 16 AASHTO V 100 12 6.426 42 17 AASHTO IV 120 6 7.344 48 18 AASHTO V 120 8 7.344 48 19 AASHTO V 120 10 8.262 54 20 AASHTO VI 120 12 8.262 54 21 AASHTO VI 140 6 7.344 48 22 AASHTO VI 140 8 8.874 58 23 AASHTO VI 140 10 10.404 68 24 F.I.B.-96 160 6 6.944 32 25 F.I.B.-96 160 8 8.246 38 26 F.I.B.-96 160 10 9.548 44 D-32
Table D-12 Design Outcomes of I Girder Bridges Designed with Compressive Strength of 8ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.253âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 AASHTO I 30 6 1.224 8 2 AASHTO I 30 8 1.53 10 3 AASHTO I 30 10 1.836 12 4 AASHTO I 30 12 2.142 14 5 AASHTO II 60 6 2.142 14 6 AASHTO II 60 8 2.754 18 7 AASHTO III 60 10 2.448 16 8 AASHTO III 60 12 3.06 20 9 AASHTO III 80 6 3.06 20 10 AASHTO III 80 8 3.978 26 11 AASHTO III 80 10 4.59 30 12 AASHTO IV 80 12 4.284 28 13 AASHTO III 100 6 5.202 34 14 AASHTO IV 100 8 5.202 34 15 AASHTO IV 100 10 6.426 42 16 AASHTO V 100 12 5.814 38 17 AASHTO IV 120 6 6.732 44 18 AASHTO V 120 8 6.732 44 19 AASHTO V 120 10 7.956 52 20 AASHTO VI 120 12 7.65 50 21 AASHTO VI 140 6 6.732 44 22 AASHTO VI 140 8 8.262 54 23 AASHTO VI 140 10 9.792 64 24 F.I.B.-96 160 6 6.51 30 25 F.I.B.-96 160 8 7.378 34 26 F.I.B.-96 160 10 8.68 40 D-33
Table D-13 Design Outcomes of I Girder Bridges Designed with Compressive Strength of 8ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.0948âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 AASHTO I 30 6 1.224 8 2 AASHTO I 30 8 1.53 10 3 AASHTO I 30 10 1.836 12 4 AASHTO I 30 12 2.295 15 5 AASHTO II 60 6 3.06 20 6 AASHTO II 60 8 3.978 26 7 AASHTO III 60 10 3.366 22 8 AASHTO III 60 12 4.284 28 9 AASHTO III 80 6 4.284 28 10 AASHTO III 80 8 5.202 34 11 AASHTO III 80 10 6.12 40 12 AASHTO IV 80 12 5.814 38 13 AASHTO III 100 6 7.038 46 14 AASHTO IV 100 8 7.038 46 15 AASHTO IV 100 10 8.262 54 16 AASHTO V 100 12 7.65 50 17 AASHTO IV 120 6 8.874 58 18 AASHTO V 120 8 8.874 58 19 AASHTO V 120 10 10.404 68 20 AASHTO VI 120 12 9.792 64 21 AASHTO VI 140 6 8.874 58 22 AASHTO VI 140 8 10.71 70 23 AASHTO VI 140 10 12.852 84 24 F.I.B.-96 160 6 8.246 38 25 F.I.B.-96 160 8 10.199 47 26 F.I.B.-96 160 10 11.284 52 D-34
Table D-14 Design Outcomes of I Girder Bridges Designed with Compressive Strength of 8ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.158âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 AASHTO I 30 6 1.224 8 2 AASHTO I 30 8 1.53 10 3 AASHTO I 30 10 1.836 12 4 AASHTO I 30 12 2.295 15 5 AASHTO II 60 6 2.754 18 6 AASHTO II 60 8 3.672 24 7 AASHTO III 60 10 3.06 20 8 AASHTO III 60 12 3.672 24 9 AASHTO III 80 6 3.978 26 10 AASHTO III 80 8 4.896 32 11 AASHTO III 80 10 5.814 38 12 AASHTO IV 80 12 5.508 36 13 AASHTO III 100 6 6.732 44 14 AASHTO IV 100 8 6.426 42 15 AASHTO IV 100 10 7.65 50 16 AASHTO V 100 12 7.344 48 17 AASHTO IV 120 6 8.262 54 18 AASHTO V 120 8 8.262 54 19 AASHTO V 120 10 9.486 62 20 AASHTO VI 120 12 9.18 60 21 AASHTO VI 140 6 8.262 54 22 AASHTO VI 140 8 10.098 66 23 AASHTO VI 140 10 11.628 76 24 F.I.B.-96 160 6 7.812 36 25 F.I.B.-96 160 8 9.114 42 26 F.I.B.-96 160 10 10.416 48 D-35
Table D-15 Design Outcomes of I Girder Bridges Designed with Compressive Strength of 8ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.19âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 AASHTO I 30 6 1.224 8 2 AASHTO I 30 8 1.53 10 3 AASHTO I 30 10 1.836 12 4 AASHTO I 30 12 2.295 15 5 AASHTO II 60 6 2.448 16 6 AASHTO II 60 8 3.366 22 7 AASHTO III 60 10 3.06 20 8 AASHTO III 60 12 3.672 24 9 AASHTO III 80 6 3.672 24 10 AASHTO III 80 8 4.59 30 11 AASHTO III 80 10 5.814 38 12 AASHTO IV 80 12 5.202 34 13 AASHTO III 100 6 6.426 42 14 AASHTO IV 100 8 6.426 42 15 AASHTO IV 100 10 7.65 50 16 AASHTO V 100 12 7.038 46 17 AASHTO IV 120 6 7.956 52 18 AASHTO V 120 8 7.956 52 19 AASHTO V 120 10 9.18 60 20 AASHTO VI 120 12 8.874 58 21 AASHTO VI 140 6 7.956 52 22 AASHTO VI 140 8 9.792 64 23 AASHTO VI 140 10 11.322 74 24 F.I.B.-96 160 6 7.378 34 25 F.I.B.-96 160 8 8.68 40 26 F.I.B.-96 160 10 10.416 48 D-36
Table D-16 Design Outcomes of I Girder Bridges Designed with Compressive Strength of 8ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.253âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 AASHTO I 30 6 1.224 8 2 AASHTO I 30 8 1.53 10 3 AASHTO I 30 10 1.836 12 4 AASHTO I 30 12 2.295 15 5 AASHTO II 60 6 2.448 16 6 AASHTO II 60 8 3.366 22 7 AASHTO III 60 10 3.06 20 8 AASHTO III 60 12 3.672 24 9 AASHTO III 80 6 3.366 22 10 AASHTO III 80 8 4.284 28 11 AASHTO III 80 10 5.202 34 12 AASHTO IV 80 12 4.896 32 13 AASHTO III 100 6 6.12 40 14 AASHTO IV 100 8 5.814 38 15 AASHTO IV 100 10 7.038 46 16 AASHTO V 100 12 6.426 42 17 AASHTO IV 120 6 7.65 50 18 AASHTO V 120 8 7.344 48 19 AASHTO V 120 10 8.874 58 20 AASHTO VI 120 12 8.568 56 21 AASHTO VI 140 6 7.344 48 22 AASHTO VI 140 8 9.18 60 23 AASHTO VI 140 10 10.71 70 24 F.I.B.-96 160 6 6.944 32 25 F.I.B.-96 160 8 8.246 38 26 F.I.B.-96 160 10 9.548 44 D-37
Table D-17 Design Outcomes of I Girder Bridges Designed with Compressive Strength of 10 ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.0948âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 AASHTO I 30 6 1.224 8 2 AASHTO I 30 8 1.53 10 3 AASHTO I 30 10 1.53 10 4 AASHTO I 30 12 1.836 12 5 AASHTO II 60 6 2.448 16 6 AASHTO II 60 8 3.366 22 7 AASHTO III 60 10 3.06 20 8 AASHTO III 60 12 3.672 24 9 AASHTO III 80 6 3.672 24 10 AASHTO III 80 8 4.59 30 11 AASHTO III 80 10 5.202 34 12 AASHTO IV 80 12 5.202 34 13 AASHTO III 100 6 6.12 40 14 AASHTO IV 100 8 6.12 40 15 AASHTO IV 100 10 7.038 46 16 AASHTO V 100 12 6.732 44 17 AASHTO IV 120 6 7.65 50 18 AASHTO V 120 8 7.65 50 19 AASHTO V 120 10 8.874 58 20 AASHTO VI 120 12 8.568 56 21 AASHTO VI 140 6 7.956 52 22 AASHTO VI 140 8 9.486 62 23 AASHTO VI 140 10 11.016 72 24 F.I.B.-96 160 6 7.812 36 25 F.I.B.-96 160 8 8.68 40 26 F.I.B.-96 160 10 9.982 46 D-38
Table D-18 Design Outcomes of I Girder Bridges Designed with Compressive Strength of 10 ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.158âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 AASHTO I 30 6 0.918 6 2 AASHTO I 30 8 1.224 8 3 AASHTO I 30 10 1.224 8 4 AASHTO I 30 12 1.53 10 5 AASHTO II 60 6 2.142 14 6 AASHTO II 60 8 3.06 20 7 AASHTO III 60 10 2.754 18 8 AASHTO III 60 12 3.366 22 9 AASHTO III 80 6 3.366 22 10 AASHTO III 80 8 4.284 28 11 AASHTO III 80 10 4.896 32 12 AASHTO IV 80 12 4.59 30 13 AASHTO III 100 6 5.508 36 14 AASHTO IV 100 8 5.814 38 15 AASHTO IV 100 10 6.732 44 16 AASHTO V 100 12 6.426 42 17 AASHTO IV 120 6 7.344 48 18 AASHTO V 120 8 7.038 46 19 AASHTO V 120 10 8.262 54 20 AASHTO VI 120 12 8.262 54 21 AASHTO VI 140 6 7.344 48 22 AASHTO VI 140 8 8.874 58 23 AASHTO VI 140 10 10.098 66 24 F.I.B.-96 160 6 6.944 32 25 F.I.B.-96 160 8 8.246 38 26 F.I.B.-96 160 10 9.548 44 D-39
Table D-19 Design Outcomes of I Girder Bridges Designed with Compressive Strength of 10 ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.19âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 AASHTO I 30 6 1.224 8 2 AASHTO I 30 8 1.53 10 3 AASHTO I 30 10 1.836 12 4 AASHTO I 30 12 2.142 14 5 AASHTO II 60 6 2.142 14 6 AASHTO II 60 8 2.754 18 7 AASHTO III 60 10 2.448 16 8 AASHTO III 60 12 3.06 20 9 AASHTO III 80 6 3.366 22 10 AASHTO III 80 8 3.978 26 11 AASHTO III 80 10 4.896 32 12 AASHTO IV 80 12 4.59 30 13 AASHTO III 100 6 5.508 36 14 AASHTO IV 100 8 5.508 36 15 AASHTO IV 100 10 6.426 42 16 AASHTO V 100 12 6.12 40 17 AASHTO IV 120 6 7.038 46 18 AASHTO V 120 8 7.038 46 19 AASHTO V 120 10 7.956 52 20 AASHTO VI 120 12 7.956 52 21 AASHTO VI 140 6 7.038 46 22 AASHTO VI 140 8 8.568 56 23 AASHTO VI 140 10 9.792 64 24 F.I.B.-96 160 6 6.944 32 25 F.I.B.-96 160 8 8.246 38 26 F.I.B.-96 160 10 9.114 42 D-40
Table D-20 Design Outcomes of I Girder Bridges Designed with Compressive Strength of 10 ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.253âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 AASHTO I 30 6 0.918 6 2 AASHTO I 30 8 1.224 8 3 AASHTO I 30 10 1.224 8 4 AASHTO I 30 12 1.836 12 5 AASHTO II 60 6 2.142 14 6 AASHTO II 60 8 2.754 18 7 AASHTO III 60 10 2.142 14 8 AASHTO III 60 12 2.754 18 9 AASHTO III 80 6 3.06 20 10 AASHTO III 80 8 3.672 24 11 AASHTO III 80 10 4.59 30 12 AASHTO IV 80 12 3.978 26 13 AASHTO III 100 6 5.202 34 14 AASHTO IV 100 8 5.202 34 15 AASHTO IV 100 10 6.12 40 16 AASHTO V 100 12 5.508 36 17 AASHTO IV 120 6 6.426 42 18 AASHTO V 120 8 6.426 42 19 AASHTO V 120 10 7.65 50 20 AASHTO VI 120 12 7.344 48 21 AASHTO VI 140 6 6.426 42 22 AASHTO VI 140 8 7.956 52 23 AASHTO VI 140 10 9.18 60 24 F.I.B.-96 160 6 6.076 28 25 F.I.B.-96 160 8 7.378 34 26 F.I.B.-96 160 10 8.246 38 D-41
Table D-21 Design Outcomes of I Girder Bridges Designed with Compressive Strength of 10 ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.0948âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 AASHTO I 30 6 1.224 8 2 AASHTO I 30 8 1.53 10 3 AASHTO I 30 10 1.836 12 4 AASHTO I 30 12 2.142 14 5 AASHTO II 60 6 3.06 20 6 AASHTO II 60 8 3.978 26 7 AASHTO III 60 10 3.366 22 8 AASHTO III 60 12 3.978 26 9 AASHTO III 80 6 3.978 26 10 AASHTO III 80 8 4.896 32 11 AASHTO III 80 10 6.12 40 12 AASHTO IV 80 12 5.814 38 13 AASHTO III 100 6 6.732 44 14 AASHTO IV 100 8 6.732 44 15 AASHTO IV 100 10 7.956 52 16 AASHTO V 100 12 7.65 50 17 AASHTO IV 120 6 8.568 56 18 AASHTO V 120 8 8.568 56 19 AASHTO V 120 10 10.098 66 20 AASHTO VI 120 12 9.486 62 21 AASHTO VI 140 6 8.568 56 22 AASHTO VI 140 8 10.404 68 23 AASHTO VI 140 10 11.934 78 24 F.I.B.-96 160 6 8.246 38 25 F.I.B.-96 160 8 9.548 44 26 F.I.B.-96 160 10 10.85 50 D-42
Table D-22 Design Outcomes of I Girder Bridges Designed with Compressive Strength of 10 ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.158âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 AASHTO I 30 6 1.224 8 2 AASHTO I 30 8 1.53 10 3 AASHTO I 30 10 1.53 10 4 AASHTO I 30 12 2.142 14 5 AASHTO II 60 6 2.754 18 6 AASHTO II 60 8 3.672 24 7 AASHTO III 60 10 3.06 20 8 AASHTO III 60 12 3.672 24 9 AASHTO III 80 6 3.672 24 10 AASHTO III 80 8 4.59 30 11 AASHTO III 80 10 5.508 36 12 AASHTO IV 80 12 5.202 34 13 AASHTO III 100 6 6.426 42 14 AASHTO IV 100 8 6.426 42 15 AASHTO IV 100 10 7.65 50 16 AASHTO V 100 12 7.038 46 17 AASHTO IV 120 6 7.956 52 18 AASHTO V 120 8 7.956 52 19 AASHTO V 120 10 9.18 60 20 AASHTO VI 120 12 8.874 58 21 AASHTO VI 140 6 7.956 52 22 AASHTO VI 140 8 9.486 62 23 AASHTO VI 140 10 11.322 74 24 F.I.B.-96 160 6 7.812 36 25 F.I.B.-96 160 8 9.114 42 26 F.I.B.-96 160 10 10.416 48 D-43
Table D-23 Design Outcomes of I Girder Bridges Designed with Compressive Strength of 10 ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.19âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 AASHTO I 30 6 1.224 8 2 AASHTO I 30 8 1.53 10 3 AASHTO I 30 10 1.53 10 4 AASHTO I 30 12 1.836 12 5 AASHTO II 60 6 2.448 16 6 AASHTO II 60 8 3.366 22 7 AASHTO III 60 10 2.754 18 8 AASHTO III 60 12 3.672 24 9 AASHTO III 80 6 3.672 24 10 AASHTO III 80 8 4.59 30 11 AASHTO III 80 10 5.508 36 12 AASHTO IV 80 12 5.202 34 13 AASHTO III 100 6 6.12 40 14 AASHTO IV 100 8 6.12 40 15 AASHTO IV 100 10 7.344 48 16 AASHTO V 100 12 6.732 44 17 AASHTO IV 120 6 7.65 50 18 AASHTO V 120 8 7.65 50 19 AASHTO V 120 10 8.874 58 20 AASHTO VI 120 12 8.568 56 21 AASHTO VI 140 6 7.65 50 22 AASHTO VI 140 8 9.18 60 23 AASHTO VI 140 10 11.016 72 24 F.I.B.-96 160 6 7.378 34 25 F.I.B.-96 160 8 8.68 40 26 F.I.B.-96 160 10 9.982 46 D-44
Table D-24 Design Outcomes of I Girder Bridges Designed with Compressive Strength of 10 ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.253âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 AASHTO I 30 6 1.224 8 2 AASHTO I 30 8 1.53 10 3 AASHTO I 30 10 1.53 10 4 AASHTO I 30 12 1.836 12 5 AASHTO II 60 6 2.448 16 6 AASHTO II 60 8 3.06 20 7 AASHTO III 60 10 2.754 18 8 AASHTO III 60 12 3.366 22 9 AASHTO III 80 6 3.366 22 10 AASHTO III 80 8 4.284 28 11 AASHTO III 80 10 5.202 34 12 AASHTO IV 80 12 4.59 30 13 AASHTO III 100 6 5.814 38 14 AASHTO IV 100 8 5.814 38 15 AASHTO IV 100 10 6.732 44 16 AASHTO V 100 12 6.426 42 17 AASHTO IV 120 6 7.344 48 18 AASHTO V 120 8 7.038 46 19 AASHTO V 120 10 8.262 54 20 AASHTO VI 120 12 8.262 54 21 AASHTO VI 140 6 7.038 46 22 AASHTO VI 140 8 8.874 58 23 AASHTO VI 140 10 10.404 68 24 F.I.B.-96 160 6 6.51 30 25 F.I.B.-96 160 8 8.246 38 26 F.I.B.-96 160 10 9.114 42 D-45
D.2.2 Adjacent Box Girder Bridges Table D-25 Design Outcomes of Adjacent Box Girder Bridges Designed with Compressive Strength of 6 ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.0948âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 3 1.224 8 2 BI-48 30 4 1.224 8 3 BI-36 60 3 2.754 18 4 BI-48 60 4 3.366 22 5 BII-36 80 3 3.672 24 6 BI-48 80 4 5.508 36 7 BIII-36 100 3 4.896 32 8 BII-48 100 4 7.038 46 9 BIV-36 120 3 6.732 44 10 BIII-48 120 4 8.874 58 Table D-26 Design Outcomes of Adjacent Box Girder Bridges Designed with Compressive Strength of 6 ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.158âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 3 0.918 6 2 BI-48 30 4 0.918 6 3 BI-36 60 3 2.448 16 4 BI-48 60 4 3.06 20 5 BII-36 80 3 3.366 22 6 BI-48 80 4 5.202 34 7 BIII-36 100 3 4.59 30 8 BII-48 100 4 6.426 42 9 BIV-36 120 3 6.12 40 10 BIII-48 120 4 8.262 54 D-46
Table D-27 Design Outcomes of Adjacent Box Girder Bridges Designed with Compressive Strength of 6 ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.19âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 3 0.918 6 2 BI-48 30 4 0.918 6 3 BI-36 60 3 2.448 16 4 BI-48 60 4 2.754 18 5 BII-36 80 3 3.366 22 6 BI-48 80 4 5.508 36 7 BIII-36 100 3 4.284 28 8 BII-48 100 4 6.426 42 9 BIV-36 120 3 6.12 40 10 BIII-48 120 4 7.956 52 Table D-28 Design Outcomes of Adjacent Box Girder Bridges Designed with Compressive Strength of 6 ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.253âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 3 0.612 4 2 BI-48 30 4 0.612 4 3 BI-36 60 3 2.142 14 4 BI-48 60 4 2.754 18 5 BII-36 80 3 3.06 20 6 BI-48 80 4 4.896 32 7 BIII-36 100 3 3.978 26 8 BII-48 100 4 6.12 40 9 BIV-36 120 3 5.814 38 10 BIII-48 120 4 7.344 48 D-47
Table D-29 Design Outcomes of Adjacent Box Girder Bridges Designed with Compressive Strength of 6 ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.0948âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 3 1.224 8 2 BI-48 30 4 1.224 8 3 BI-36 60 3 2.754 18 4 BI-48 60 4 3.366 22 5 BII-36 80 3 3.978 26 6 BI-48 80 4 5.814 38 7 BIII-36 100 3 4.896 32 8 BII-48 100 4 7.344 48 9 BIV-36 120 3 7.344 48 10 BIII-48 120 4 - - Table D-30 Design Outcomes of Adjacent Box Girder Bridges Designed with Compressive Strength of 6 ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.158âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 3 0.918 6 2 BI-48 30 4 1.224 8 3 BI-36 60 3 2.754 18 4 BI-48 60 4 3.06 20 5 BII-36 80 3 3.672 24 6 BI-48 80 4 5.508 36 7 BIII-36 100 3 4.896 32 8 BII-48 100 4 7.038 46 9 BIV-36 120 3 6.732 44 10 BIII-48 120 4 8.874 58 D-48
Table D-31 Design Outcomes of Adjacent Box Girder Bridges Designed with Compressive Strength of 6 ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.19âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 3 0.918 6 2 BI-48 30 4 0.918 6 3 BI-36 60 3 2.448 16 4 BI-48 60 4 3.06 20 5 BII-36 80 3 3.366 22 6 BI-48 80 4 5.508 36 7 BIII-36 100 3 4.59 30 8 BII-48 100 4 6.732 44 9 BIV-36 120 3 6.426 42 10 BIII-48 120 4 8.568 56 Table D-32 Design Outcomes of Adjacent Box Girder Bridges Designed with Compressive Strength of 6 ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.253âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 3 0.918 6 2 BI-48 30 4 0.612 4 3 BI-36 60 3 2.448 16 4 BI-48 60 4 2.754 18 5 BII-36 80 3 3.366 22 6 BI-48 80 4 5.202 34 7 BIII-36 100 3 4.284 28 8 BII-48 100 4 6.426 42 9 BIV-36 120 3 6.12 40 10 BIII-48 120 4 7.956 52 D-49
Table D-33 Design Outcomes of Adjacent Box Girder Bridges Designed with Compressive Strength of 8 ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.0948âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 3 1.224 8 2 BI-48 30 4 1.224 8 3 BI-36 60 3 2.754 18 4 BI-48 60 4 3.06 20 5 BII-36 80 3 3.672 24 6 BI-48 80 4 5.202 34 7 BIII-36 100 3 4.59 30 8 BII-48 100 4 6.732 44 9 BIV-36 120 3 6.426 42 10 BIII-48 120 4 8.262 54 Table D-34 Design Outcomes of Adjacent Box Girder Bridges Designed with Compressive Strength of 8 ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.158âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 3 0.918 6 2 BI-48 30 4 0.918 6 3 BI-36 60 3 2.448 16 4 BI-48 60 4 2.754 18 5 BII-36 80 3 3.366 22 6 BI-48 80 4 4.896 32 7 BIII-36 100 3 4.284 28 8 BII-48 100 4 6.12 40 9 BIV-36 120 3 5.814 38 10 BIII-48 120 4 7.65 50 D-50
Table D-35 Design Outcomes of Adjacent Box Girder Bridges Designed with Compressive Strength of 8 ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.19âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 3 0.918 6 2 BI-48 30 4 0.918 6 3 BI-36 60 3 2.448 16 4 BI-48 60 4 2.754 18 5 BII-36 80 3 3.06 20 6 BI-48 80 4 4.896 32 7 BIII-36 100 3 4.284 28 8 BII-48 100 4 6.12 40 9 BIV-36 120 3 5.814 38 10 BIII-48 120 4 7.344 48 Table D-36 Design Outcomes of Adjacent Box Girder Bridges Designed with Compressive Strength of 8 ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.253âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 3 0.612 4 2 BI-48 30 4 0.612 4 3 BI-36 60 3 2.142 14 4 BI-48 60 4 2.448 16 5 BII-36 80 3 3.06 20 6 BI-48 80 4 4.59 30 7 BIII-36 100 3 3.978 26 8 BII-48 100 4 5.814 38 9 BIV-36 120 3 5.508 36 10 BIII-48 120 4 7.038 46 D-51
Table D-37 Design Outcomes of Adjacent Box Girder Bridges Designed with Compressive Strength of 8 ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.0948âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 3 1.224 8 2 BI-48 30 4 1.53 10 3 BI-36 60 3 2.754 18 4 BI-48 60 4 3.366 22 5 BII-36 80 3 3.672 24 6 BI-48 80 4 5.814 38 7 BIII-36 100 3 4.896 32 8 BII-48 100 4 7.038 46 9 BIV-36 120 3 6.732 44 10 BIII-48 120 4 8.874 58 Table D-38 Design Outcomes of Adjacent Box Girder Bridges Designed with Compressive Strength of 8 ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.158âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 3 0.918 6 2 BI-48 30 4 0.918 6 3 BI-36 60 3 2.448 16 4 BI-48 60 4 3.06 20 5 BII-36 80 3 3.366 22 6 BI-48 80 4 5.508 36 7 BIII-36 100 3 4.59 30 8 BII-48 100 4 6.732 44 9 BIV-36 120 3 6.12 40 10 BIII-48 120 4 8.262 54 D-52
Table D-39 Design Outcomes of Adjacent Box Girder Bridges Designed with Compressive Strength of 8 ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.19âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 3 0.918 6 2 BI-48 30 4 0.918 6 3 BI-36 60 3 2.448 16 4 BI-48 60 4 3.06 20 5 BII-36 80 3 3.366 22 6 BI-48 80 4 5.202 34 7 BIII-36 100 3 4.284 28 8 BII-48 100 4 6.426 42 9 BIV-36 120 3 6.12 40 10 BIII-48 120 4 7.956 52 Table D-40 Design Outcomes of Adjacent Box Girder Bridges Designed with Compressive Strength of 8 ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.253âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 3 0.612 4 2 BI-48 30 4 0.612 4 3 BI-36 60 3 2.142 14 4 BI-48 60 4 2.754 18 5 BII-36 80 3 3.06 20 6 BI-48 80 4 4.896 32 7 BIII-36 100 3 3.978 26 8 BII-48 100 4 6.12 40 9 BIV-36 120 3 5.814 38 10 BIII-48 120 4 7.344 48 D-53
D.2.3 Spread Box Girder Bridges Table D-41 Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 6ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.0948âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in 2) # of Strands 1 BI-36 30 6 1.53 10 2 BI-36 30 8 1.836 12 3 BI-36 30 10 1.836 12 4 BI-36 30 12 2.142 14 5 BI-36 60 6 4.284 28 6 BI-36 60 8 4.896 32 7 BI-36 60 10 4.59 30 8 BI-48 60 12 5.202 34 9 BI-48 80 6 5.814 38 10 BII-48 80 8 5.814 38 11 BII-48 80 10 6.426 42 12 BIII-48 80 12 7.038 46 13 BIII-48 100 6 7.344 48 14 BIII-48 100 8 - - 15 BIV-48 100 10 - - Table D-42 Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 6ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.158âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in 2) # of Strands 1 BI-36 30 6 1.224 8 2 BI-36 30 8 1.53 10 3 BI-36 30 10 1.836 12 4 BI-36 30 12 1.836 12 5 BI-36 60 6 3.978 26 6 BI-36 60 8 4.896 32 7 BI-36 60 10 4.284 28 8 BI-48 60 12 4.896 32 9 BI-48 80 6 5.508 36 10 BII-48 80 8 5.508 36 11 BII-48 80 10 6.12 40 12 BIII-48 80 12 6.426 42 13 BIII-48 100 6 7.038 46 14 BIII-48 100 8 - - 15 BIV-48 100 10 - - D-54
Table D-43 Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 6ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.19âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in 2) # of Strands 1 BI-36 30 6 1.224 8 2 BI-36 30 8 1.53 10 3 BI-36 30 10 1.53 10 4 BI-36 30 12 1.836 12 5 BI-36 60 6 3.672 24 6 BI-36 60 8 4.59 30 7 BI-36 60 10 3.978 26 8 BI-48 60 12 4.59 30 9 BI-48 80 6 5.202 34 10 BII-48 80 8 5.202 34 11 BII-48 80 10 6.12 40 12 BIII-48 80 12 6.426 42 13 BIII-48 100 6 7.038 46 14 BIII-48 100 8 - - 15 BIV-48 100 10 - - Table D-44 Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 6ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.253âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in 2) # of Strands 1 BI-36 30 6 1.224 8 2 BI-36 30 8 1.224 8 3 BI-36 30 10 1.53 10 4 BI-36 30 12 1.53 10 5 BI-36 60 6 3.672 24 6 BI-36 60 8 4.284 28 7 BII-36 60 10 3.978 26 8 BII-48 60 12 4.284 28 9 BII-48 80 6 4.896 32 10 BIII-48 80 8 4.896 32 11 BIII-48 80 10 5.814 38 12 BIV-48 80 12 5.814 38 13 BIII-48 100 6 6.426 42 14 BIII-48 100 8 - - 15 BIV-48 100 10 - - D-55
Table D-45 Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 6ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.0948âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in 2) # of Strands 1 BI-36 30 6 1.53 10 2 BI-36 30 8 1.836 12 3 BI-36 30 10 2.142 14 4 BI-36 30 12 2.448 16 5 BI-36 60 6 4.59 30 6 BII-36 60 8 4.284 28 7 BII-36 60 10 4.896 32 8 BII-48 60 12 5.814 38 9 BII-48 80 6 6.12 40 10 BIII-48 80 8 6.12 40 11 BIV-48 80 10 6.732 44 12 BIV-48 80 12 7.65 50 13 BIV-48 100 6 7.344 48 14 BIII-48 100 8 - - 15 BIV-48 100 10 - - Table D-46 Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 6ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.158âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in 2) # of Strands 1 BI-36 30 6 1.53 10 2 BI-36 30 8 1.836 12 3 BI-36 30 10 1.836 12 4 BI-36 30 12 2.142 14 5 BI-36 60 6 4.284 28 6 BII-36 60 8 3.978 26 7 BII-36 60 10 4.59 30 8 BII-48 60 12 5.508 36 9 BII-48 80 6 5.814 38 10 BIII-48 80 8 5.814 38 11 BIII-48 80 10 6.732 44 12 BIV-48 80 12 7.038 46 13 BIII-48 100 6 7.65 50 14 BIII-48 100 8 - - 15 BIV-48 100 10 - - D-56
Table D-47 Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 6ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.19âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in 2) # of Strands 1 BI-36 30 6 1.53 10 2 BI-36 30 8 1.53 10 3 BI-36 30 10 1.836 12 4 BI-36 30 12 2.142 14 5 BI-36 60 6 4.284 28 6 BI-36 60 8 5.202 34 7 BII-36 60 10 4.59 30 8 BII-48 60 12 5.202 34 9 BII-48 80 6 5.814 38 10 BIII-48 80 8 5.814 38 11 BIII-48 80 10 6.732 44 12 BIV-48 80 12 7.038 46 13 BIII-48 100 6 7.65 50 14 BIII-48 100 8 - - 15 BIV-48 100 10 - - Table D-48 Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 6ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.253âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in 2) # of Strands 1 BI-36 30 6 1.224 8 2 BI-36 30 8 1.53 10 3 BI-36 30 10 1.53 10 4 BI-36 30 12 1.836 12 5 BI-36 60 6 3.978 26 6 BI-36 60 8 4.896 32 7 BII-36 60 10 4.284 28 8 BII-48 60 12 4.896 32 9 BII-48 80 6 5.508 36 10 BIII-48 80 8 5.508 36 11 BIII-48 80 10 6.426 42 12 BIV-48 80 12 7.038 46 13 BIII-48 100 6 7.038 46 14 BIII-48 100 8 - - 15 BIV-48 100 10 - - D-57
Table D-49 Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 8ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.0948âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in 2) # of Strands 1 BI-36 30 6 1.53 10 2 BI-36 30 8 1.836 12 3 BI-36 30 10 1.836 12 4 BI-36 30 12 2.142 14 5 BI-36 60 6 3.978 26 6 BI-36 60 8 4.896 32 7 BI-36 60 10 5.508 36 8 BI-48 60 12 6.426 42 9 BI-48 80 6 7.038 46 10 BII-48 80 8 6.732 44 11 BII-48 80 10 7.65 50 12 BIII-48 80 12 7.038 46 13 BIII-48 100 6 7.344 48 14 BIII-48 100 8 9.18 60 15 BIV-48 100 10 10.404 68 Table D-50 Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 8ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.158âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 6 1.224 8 2 BI-36 30 8 1.53 10 3 BI-36 30 10 1.836 12 4 BI-36 30 12 1.836 12 5 BI-36 60 6 3.672 24 6 BI-36 60 8 4.59 30 7 BI-36 60 10 5.202 34 8 BI-48 60 12 5.814 38 9 BI-48 80 6 6.732 44 10 BII-48 80 8 6.12 40 11 BII-48 80 10 7.344 48 12 BIII-48 80 12 6.732 44 13 BIII-48 100 6 7.038 46 14 BIII-48 100 8 8.262 54 15 BIV-48 100 10 9.18 60 D-58
Table D-51 Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 8ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.19âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 6 1.224 8 2 BI-36 30 8 1.53 10 3 BI-36 30 10 1.53 10 4 BI-36 30 12 1.836 12 5 BI-36 60 6 3.672 24 6 BI-36 60 8 4.284 28 7 BI-36 60 10 5.202 34 8 BI-48 60 12 5.814 38 9 BI-48 80 6 6.426 42 10 BII-48 80 8 6.12 40 11 BII-48 80 10 7.038 46 12 BIII-48 80 12 6.732 44 13 BIII-48 100 6 6.732 44 14 BIII-48 100 8 7.956 52 15 BIV-48 100 10 8.568 56 Table D-52 Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 8ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.253âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 6 0.918 6 2 BI-36 30 8 1.224 8 3 BI-36 30 10 1.53 10 4 BI-36 30 12 1.53 10 5 BI-36 60 6 3.366 22 6 BI-36 60 8 4.284 28 7 BI-36 60 10 4.896 32 8 BI-48 60 12 5.508 36 9 BI-48 80 6 6.12 40 10 BII-48 80 8 5.814 38 11 BII-48 80 10 6.732 44 12 BIII-48 80 12 6.12 40 13 BIII-48 100 6 6.426 42 14 BIII-48 100 8 7.65 50 15 BIV-48 100 10 7.956 52 D-59
Table D-53 Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 8ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.0948âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 6 1.53 10 2 BI-36 30 8 1.836 12 3 BI-36 30 10 2.142 14 4 BI-36 30 12 2.142 14 5 BI-36 60 6 4.284 28 6 BI-36 60 8 5.202 34 7 BI-36 60 10 6.426 42 8 BI-48 60 12 7.038 46 9 BI-48 80 6 7.65 50 10 BII-48 80 8 7.344 48 11 BII-48 80 10 8.874 58 12 BIII-48 80 12 7.956 52 13 BIII-48 100 6 7.956 52 14 BIII-48 100 8 - - 15 BIV-48 100 10 - - Table D-54 Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 8ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.158âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 6 1.53 10 2 BI-36 30 8 1.53 10 3 BI-36 30 10 1.836 12 4 BI-36 30 12 2.142 14 5 BI-36 60 6 4.284 28 6 BI-36 60 8 4.896 32 7 BI-36 60 10 5.814 38 8 BI-48 60 12 6.732 44 9 BI-48 80 6 7.344 48 10 BII-48 80 8 6.732 44 11 BII-48 80 10 7.956 52 12 BIII-48 80 12 7.344 48 13 BIII-48 100 6 7.344 48 14 BIII-48 100 8 9.792 64 15 BIV-48 100 10 - - D-60
Table D-55 Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 8ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.19âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 6 1.224 8 2 BI-36 30 8 1.53 10 3 BI-36 30 10 1.836 12 4 BI-36 30 12 1.836 12 5 BI-36 60 6 3.978 26 6 BI-36 60 8 4.896 32 7 BI-36 60 10 5.814 38 8 BI-48 60 12 6.426 42 9 BI-48 80 6 7.038 46 10 BII-48 80 8 6.732 44 11 BII-48 80 10 7.956 52 12 BIII-48 80 12 7.344 48 13 BIII-48 100 6 7.038 46 14 BIII-48 100 8 9.18 60 15 BIV-48 100 10 - - Table D-56 Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 8ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.253âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 6 1.224 8 2 BI-36 30 8 1.224 8 3 BI-36 30 10 1.53 10 4 BI-36 30 12 1.836 12 5 BI-36 60 6 3.672 24 6 BI-36 60 8 4.59 30 7 BI-36 60 10 5.508 36 8 BI-48 60 12 6.12 40 9 BI-48 80 6 6.732 44 10 BII-48 80 8 6.426 42 11 BII-48 80 10 7.344 48 12 BIII-48 80 12 6.732 44 13 BIII-48 100 6 6.732 44 14 BIII-48 100 8 8.568 56 15 BIV-48 100 10 8.874 58 D-61
Table D-57 Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 10ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.0948âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 6 1.53 10 2 BI-36 30 8 1.53 10 3 BI-36 30 10 1.836 12 4 BI-36 30 12 2.142 14 5 BI-36 60 6 3.978 26 6 BI-36 60 8 4.59 30 7 BI-36 60 10 5.508 36 8 BI-48 60 12 6.12 40 9 BI-48 80 6 6.732 44 10 BII-48 80 8 6.426 42 11 BII-48 80 10 7.344 48 12 BIII-48 80 12 7.038 46 13 BIII-48 100 6 7.038 46 14 BIII-48 100 8 8.568 56 15 BIV-48 100 10 9.486 62 Table D-58 Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 10ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.158âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 6 1.224 8 2 BI-36 30 8 1.53 10 3 BI-36 30 10 1.53 10 4 BI-36 30 12 1.836 12 5 BI-36 60 6 3.672 24 6 BI-36 60 8 4.284 28 7 BI-36 60 10 5.202 34 8 BI-48 60 12 5.814 38 9 BI-48 80 6 6.426 42 10 BII-48 80 8 6.12 40 11 BII-48 80 10 7.038 46 12 BIII-48 80 12 6.426 42 13 BIII-48 100 6 6.732 44 14 BIII-48 100 8 7.956 52 15 BIV-48 100 10 8.568 56 D-62
Table D-59 Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 10ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.19âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 6 1.224 8 2 BI-36 30 8 1.224 8 3 BI-36 30 10 1.53 10 4 BI-36 30 12 1.836 12 5 BI-36 60 6 3.672 24 6 BI-36 60 8 4.284 28 7 BI-36 60 10 4.896 32 8 BI-48 60 12 5.508 36 9 BI-48 80 6 6.426 42 10 BII-48 80 8 5.814 38 11 BII-48 80 10 6.732 44 12 BIII-48 80 12 6.426 42 13 BIII-48 100 6 6.732 44 14 BIII-48 100 8 7.65 50 15 BIV-48 100 10 8.262 54 Table D-60 Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 10ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.253âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 6 0.918 6 2 BI-36 30 8 1.224 8 3 BI-36 30 10 1.224 8 4 BI-36 30 12 1.53 10 5 BI-36 60 6 3.366 22 6 BI-36 60 8 3.978 26 7 BI-36 60 10 4.59 30 8 BI-48 60 12 5.202 34 9 BI-48 80 6 5.814 38 10 BII-48 80 8 5.508 36 11 BII-48 80 10 6.426 42 12 BIII-48 80 12 5.814 38 13 BIII-48 100 6 6.12 40 14 BIII-48 100 8 7.344 48 15 BIV-48 100 10 7.65 50 D-63
Table D-61 Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 10ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.0948âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 6 1.53 10 2 BI-36 30 8 1.836 12 3 BI-36 30 10 2.142 14 4 BI-36 30 12 2.142 14 5 BI-36 60 6 4.284 28 6 BI-36 60 8 5.202 34 7 BI-36 60 10 6.12 40 8 BI-48 60 12 6.732 44 9 BI-48 80 6 7.344 48 10 BII-48 80 8 7.038 46 11 BII-48 80 10 8.262 54 12 BIII-48 80 12 7.65 50 13 BIII-48 100 6 7.65 50 14 BIII-48 100 8 - - 15 BIV-48 100 10 - - Table D-62 Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 10ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.158âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 6 1.53 10 2 BI-36 30 8 1.53 10 3 BI-36 30 10 1.836 12 4 BI-36 30 12 2.142 14 5 BI-36 60 6 3.978 26 6 BI-36 60 8 4.896 32 7 BI-36 60 10 5.814 38 8 BI-48 60 12 6.426 42 9 BI-48 80 6 7.038 46 10 BII-48 80 8 6.732 44 11 BII-48 80 10 7.65 50 12 BIII-48 80 12 7.344 48 13 BIII-48 100 6 7.344 48 14 BIII-48 100 8 8.874 58 15 BIV-48 100 10 10.098 66 D-64
Table D-63 Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 10ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.19âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 6 1.224 8 2 BI-36 30 8 1.53 10 3 BI-36 30 10 1.836 12 4 BI-36 30 12 1.836 12 5 BI-36 60 6 3.978 26 6 BI-36 60 8 4.59 30 7 BI-36 60 10 5.508 36 8 BI-48 60 12 6.12 40 9 BI-48 80 6 6.732 44 10 BII-48 80 8 6.426 42 11 BII-48 80 10 7.65 50 12 BIII-48 80 12 7.038 46 13 BIII-48 100 6 7.038 46 14 BIII-48 100 8 8.568 56 15 BIV-48 100 10 9.486 62 Table D-64 Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 10ksi, Live Load Factor of 1.0 and Tensile Stress Limit of 0.253âðâ²ð. Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 6 0.918 6 2 BI-36 30 8 1.224 8 3 BI-36 30 10 1.53 10 4 BI-36 30 12 1.53 10 5 BI-36 60 6 3.672 24 6 BI-36 60 8 4.59 30 7 BI-36 60 10 5.202 34 8 BI-48 60 12 5.814 38 9 BI-48 80 6 6.426 42 10 BII-48 80 8 6.12 40 11 BII-48 80 10 7.038 46 12 BIII-48 80 12 6.426 42 13 BIII-48 100 6 6.732 44 14 BIII-48 100 8 7.956 52 15 BIV-48 100 10 8.568 56 D-65
D.2.4 PCI ASBI Box Girder Bridge Table D-65 Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 8ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.0948âðâ²ð. Cases Section Type Span Length (ft.) Aps (in2) # of Strands 1 1800-2 100 7.344 48 2 1800-2 120 10.71 70 3 1800-2 140 14.076 92 4 2100-2 160 21.266 98 5 2400-2 180 22.568 104 6 2400-2 200 27.342 126 Table D-66 Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 8ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.158âðâ²ð. Cases Section Type Span Length (ft.) Aps (in2) # of Strands 1 1800-2 100 5.814 38 2 1800-2 120 9.18 60 3 1800-2 140 12.546 82 4 2100-2 160 19.096 88 5 2400-2 180 20.398 94 6 2400-2 200 25.172 116 Table D-67 Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 8ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.19âðâ²ð. Cases Section Type Span Length (ft.) Aps (in2) # of Strands 1 1800-2 100 5.202 34 2 1800-2 120 8.568 56 3 1800-2 140 11.934 78 4 2100-2 160 17.794 82 5 2400-2 180 19.096 88 6 2400-2 200 24.304 112 D-66
Table D-68 Design Outcomes of Spread Box Girder Bridges Designed with Compressive Strength of 8ksi, Live Load Factor of 0.8 and Tensile Stress Limit of 0.253âðâ²ð. Cases Section Type Span Length (ft.) Aps (in2) # of Strands 1 1800-2 100 3.978 26 2 1800-2 120 7.344 48 3 1800-2 140 10.404 68 4 2100-2 160 16.058 74 5 2400-2 180 16.926 78 6 2400-2 200 22.134 102 D.3 Application of the Calibration Process to I-Girders and Bulb-Tees D.3.1 Effect of changing design specifications (old losses, new losses) Depending on the environmental exposure conditions, both the AASHTO Standard Specifications and the AASHTO LRFD Specifications allow designing prestressed components for maximum concrete tensile stress of 0.0948t cf f â²= or 0.19t cf f â²= . When either specifications are applied without ownerâs exceptions, most bridges are designed for 0.19t cf f â²= with a small number of bridges in coastal areas designed for 0.0948t cf f â²= . This makes it likely that the reliability indices calculated for existing bridges are for bridges designed for maximum concrete tensile stress of 0.19t cf f â²= . As indicated earlier, based on the dates of construction, it is likely that all bridges considered were designed using the prestressing loss provisions method that existed in both the AASHTO Standard Specifications and in the pre-2005 AASHTO LRFD. To study the effect of the maximum concrete tensile stress ( 0.0948t cf f â²= or 0.19t cf f â²= ) and the method of calculating the prestressing losses on the reliability index, a group of simulated I-girder bridges was designed for four cases: Case 1: AASHTO LRFD with maximum concrete tensile stress of 0.0948t cf f â²= and pre-2005 prestress loss method Case 2: AASHTO LRFD with maximum concrete tensile stress of 0.0948t cf f â²= and current (2012) prestress loss method Case 3: AASHTO LRFD with maximum concrete tensile stress of 0.19t cf f â²= and pre- 2005 prestress loss method Case 4: AASHTO LRFD with maximum concrete tensile stress of 0.19t cf f â²= and current (2012) prestress loss method D-67
The smallest possible AASHTO girder size was used for each simulated bridge. Comparing Case 1 to Case 2 and Case 3 to Case 4 shows the effect of changing the prestressing loss method. Results from Case 1 generally indicate the inherent reliability of existing bridges designed for severe environmental conditions ( 0.0948t cf f â²= ) and results from Case 3 indicate the inherent reliability of existing bridges designed for normal environmental conditions ( 0.19t cf f â²= ). Table D-69 and Table D-70 show the results for I-girder bridges designed for Maximum concrete tensile stress 0.0948t cf f â²= (Case 1 and Case 2) and 0.19t cf f â²= (Case 3 and Case 4) for I âgirder bridges for ADTT 5000. D-68
Table D-69 Summary Information of Bridges Designed using AASHTO I-Girders with ADTT 5000 and 0.0948t cf f â²= Case 1 Case 2 Cases Section Type Span Length (ft.) Spacin g (ft.) Designed Using Old Loss Method Designed Using New Loss Method Decomp. Max. Tensile Max. Crack Decomp. Max. Tensile Max. Crack 1 AASHTO I 30 6 1.05 1.49 2.92 1.03 1.51 2.55 2 AASHTO I 30 8 0.9 0.94 2.41 0.93 1 2.32 3 AASHTO I 30 10 1.16 1.68 2.87 1.28 1.67 2.82 4 AASHTO I 30 12 1.28 1.67 2.91 0.63 0.97 2.29 Average for 30 ft. Span 1.10 1.45 2.78 0.97 1.29 2.50 5 AASHTO II 60 6 0.66 1.01 3.35 0.23 0.61 2.47 6 AASHTO II 60 8 â â â 0.73 1.04 2.42 7 AASHTO III 60 10 1.22 1.62 3.01 0.43 0.76 1.97 8 AASHTO III 60 12 1.57 1.96 3.68 0.73 0.99 2.51 Average for 60 ft. Span 1.15 1.53 3.35 0.53 0.85 2.34 9 AASHTO III 80 6 1.35 1.66 4.1 0.61 0.92 3.07 10 AASHTO III 80 8 1.8 2.14 5.23 0.82 1.13 3.64 11 AASHTO III 80 10 â â â 0.90 1.19 2.93 12 AASHTO IV 80 12 2.2 2.49 5.11 0.83 1.17 3.32 Average for 80 ft. Span 1.78 2.10 4.81 0.79 1.10 3.24 13 AASHTO III 100 6 â â â 1.45 1.85 3.51 14 AASHTO IV 100 8 1.86 2 3.86 1.33 1.43 3.44 15 AASHTO IV 100 10 â â â 1.33 1.65 3.37 16 AASHTO V 100 12 1.68 1.99 4.08 0.93 1.24 3.33 Average for 100 ft. Span 1.77 2.00 3.97 1.26 1.54 3.41 17 AASHTO IV 120 6 â â â 1.32 1.76 3.81 18 AASHTO V 120 8 1.54 2.05 3.65 0.92 1.4 3.14 19 AASHTO V 120 10 â â â 0.95 1.46 3.02 20 AASHTO VI 120 12 1.82 2.26 3.88 0.9 1.35 3.38 Average for 120 ft. Span 1.68 2.16 3.77 1.02 1.49 3.34 21 AASHTO VI 140 6 1.48 1.99 3.91 0.86 1.36 2.32 22 AASHTO VI 140 8 â â â 0.99 1.47 2.79 23 AASHTO VI 140 10 â â â 1.05 1.53 3.22 24 â 140 12 â â â â â â Average for 140 ft. Span 1.48 1.99 3.91 0.97 1.45 2.78 Average for All Spans 1.44 1.80 3.66 0.92 1.28 2.94 D-69
Table D-70 Summary Information of Bridges Designed using AASHTO I-Girders with ADTT 5000 and 0.19t cf f â²= Case 3 Case 4 Cases Section Type Span Length (ft.) Spacing (ft.) Designed Using Old Loss Method Designed Using New Loss Method Decomp. Max. Tensile Max. Crack Decomp. Max. Tensile Max. Crack 1 AASHTO I 30 6 1 1.55 2.39 0.97 1.55 2.46 2 AASHTO I 30 8 0.94 0.92 2.35 0.91 1.00 2.16 3 AASHTO I 30 10 1.29 1.66 2.91 1.18 1.66 2.79 4 AASHTO I 30 12 1.3 1.72 3.02 1.26 1.70 2.91 Average for 30 ft. Span 1.13 1.46 2.67 1.08 1.48 2.58 5 AASHTO II 60 6 0.74 1.13 3.11 0.18 0.58 2.41 6 AASHTO II 60 8 1.04 1.39 2.82 0.28 0.66 1.91 7 AASHTO III 60 10 0.42 0.79 2.05 0.42 0.78 2.07 8 AASHTO III 60 12 0.66 1.00 2.5 0.68 0.96 2.53 Average for 60 ft. Span 0.72 1.08 2.62 0.39 0.75 2.23 9 AASHTO III 80 6 0.56 0.97 3.13 0.13 0.51 2.53 10 AASHTO III 80 8 1.06 1.46 3.43 0.42 0.78 3.2 11 AASHTO III 80 10 1.58 1.84 3.65 0.37 0.65 2.72 12 AASHTO IV 80 12 0.83 1.15 3.72 0.51 0.87 3.11 Average for 80 ft. Span 1.01 1.36 3.48 0.36 0.70 2.89 13 AASHTO III 100 6 â â â 0.82 1.23 3.44 14 AASHTO IV 100 8 1.31 1.42 3.6 0.69 0.76 2.76 15 AASHTO IV 100 10 1.8 1.98 3.67 0.75 1.04 3.12 16 AASHTO V 100 12 1.08 1.37 3.43 0.4 0.72 2.55 Average for 100 ft. Span 1.40 1.59 3.57 0.67 0.94 2.97 17 AASHTO IV 120 6 1.53 1.98 3.71 0.7 1.28 3.1 18 AASHTO V 120 8 0.9 1.30 3.31 0.46 0.85 2.55 19 AASHTO V 120 10 1.25 1.65 3.35 0.26 0.78 2.68 20 AASHTO VI 120 12 1.19 1.66 3.37 0.47 0.91 2.69 Average for 120 ft. Span 1.22 1.65 3.44 0.47 0.96 2.76 21 AASHTO VI 140 6 0.84 1.41 3.23 0.28 0.82 2.41 22 AASHTO VI 140 8 1.22 1.68 3.3 0.53 0.98 3.04 23 AASHTO VI 140 10 â â â 0.62 1.08 2.46 24 â 140 12 â â â â â â Average for 140 ft. Span 1.03 1.55 3.27 0.48 0.96 2.64 Average for All Spans 1.07 1.43 3.15 0.58 0.96 2.68 D-70
Using the current prestress loss method resulted in smaller number of strands than the old loss method. As shown in Table D-69 and Table D-70, this resulted in lower reliability index for bridges designed using the new (current) prestress loss method. With most bridges on the system designed using the old prestress loss method, the reliability indices corresponding to bridges designed using the old loss method (Case 1 and Case 3) are considered to better represent the inherent reliability of existing bridges designed for severe exposure conditions (Case 1) and normal exposure conditions (Case 3). D.3.2 Reliability indices of existing and redesigned bridges As specified in the AASHTO LRFD Bridge Design Specifications (2012), the service limit state is the limit state to restrict stress, deformation, and crack width under regular service conditions. The service III limit state is mainly related to the tension in prestressed concrete superstructures with the objective of crack control and to the principal tension in the webs of segmental concrete girders. According to the proposed calibration procedure, there are three limit states corresponding to the tension level at the bottom of the P/C girder that would need to be calibrated: (1) Decompression limit state, (2) Maximum allowable tensile stress limit state, and (3) Maximum allowable crack width limit state. In this section, following the proposed calibration procedure, the reliability indices of the following bridges databases were investigated: 1- Existing bridges from NCHRP 12-78 bridge database. 2- NCHRP 12-78 bridges redesigned using new losses provisions (AASHTO Specifications 2012) and tensile stress limit of 0.0948âðâ²ð. 3- NCHRP 12-78 bridges redesigned using new losses provisions (AASHTO Specifications 2012) and tensile stress limit of 0.19âðâ²ð. 4- NCHRP 12-78 bridges redesigned using new losses provisions (AASHTO Specifications 2012) and tensile stress limit of 0.253âðâ²ð. D.3.2.1 Evaluation of Existing Bridges (NCHRP 12-78 Bridge Database) Following the proposed calibration procedure, the RT evaluated the reliability levels of existing bridges. These existing bridges are taken from the NCHRP 12-78 bridge database, which include 30 I-girder bridges, 36 spread box girder bridges, and 31 adjacent box girder bridges. Among these existing bridges, Most of the bridges were designed before 2005, some of the bridges were designed over 70 years ago (e.g. Spread Box Girder Bridge #9349 was built on 1935). In Comparison with current design, the load distribution factors, impact factor, losses calculation, etc. might be different when the existing bridges have been designed, these differences might result in more conservative design. Table D-71 through Table D-73 shows a summary of the information for a total of these 97 existing bridges. D-71
Table D-71 Summary of NCHRP 12-78 I-Girder Bridge Bridge Name Section Type Girder Spacing (ft.) Span Length (ft.) Aps (in2) # of Strands 82 MN type 63 10.33 82.75 5.20 34 3107 36'' I BEAM 5.77 49.54 1.84 12 4794 BEAM Type 4 9.33 66.67 5.05 33 4827 BEAM Type 2 7.17 50.58 2.75 18 5624 BEAM Type 4 7.25 59.37 3.06 20 5794 BEAM Type 3 5.83 72.00 4.34 20 5840 BEAM Type 6 9.00 85.00 4.59 30 5884 BEAM Type 6 8.17 90.01 5.81 38 8330 BEAM Type 6 8.67 76.38 4.28 28 8783 AASHTO VI 7.75 143.15 9.98 46 8832 36'' I BEAM 10.00 43.26 3.06 20 8885 BT-63 10.58 90.01 5.51 36 8889 BT-63 10.58 90.85 5.51 36 8890 AASHTO VI 8.00 143.50 10.42 48 8891 BEAM Type 6 9.25 47.17 2.14 14 8957 BEAM Type 6 8.67 98.00 5.64 26 9378 Wisconsin Girder 10.42 101.83 6.12 40 10269 AASHTO III 6.67 78.00 4.28 28 10599 AASHTO II 6.75 62.83 4.28 28 10740 AASHTO III 7.00 78.55 4.90 32 10755 AASHTO II 7.00 52.50 3.67 24 10803 BT-72 6.00 138.25 7.68 46 11030 BT-72 6.38 136.00 7.65 50 11938 BT-63 7.31 116.52 7.68 46 12589 AASHTO IV 8.75 73.21 4.59 30 12596 AASHTO IV 11.15 96.79 10.85 50 12603 AASHTO II 11.48 37.73 3.04 14 12610 AASHTO IV 7.13 108.53 7.96 52 15620 Bulb-Tee 5.35 119.82 10.42 48 18067 AL BT-54 Mod. 5.29 131.02 10.85 50 D-72
Table D-72 Summary of NCHRP 12-78 Spread Box Girder Bridge Bridge Name Section Type Girder Spacing (ft.) Span Length (ft.) Aps (in2) # of Strands 1150 33" x 36" Box 8.50 70.58 5.97 39 3577 27"x36" IDOT 6.70 38.58 2.92 27 3754 33"x36" IDOT 6.36 53.61 3.24 30 8875 27"x48" P/S Box 11.25 38.00 3.52 23 9090 MDOT 33" Box 7.08 66.04 4.34 20 9091 MDOT 33" Box 7.08 66.20 4.34 20 9128 1525 Box 7.49 33.69 0.87 4 9192 21" x 36" Box 9.83 38.67 2.75 18 9217 17" Box 6.21 42.30 3.47 16 9219 MDOT 21" Box 5.25 53.17 3.47 16 9243 33in x 36in Box 6.17 73.33 4.56 21 9248 21 in Box Beam 8.00 37.75 3.91 18 9282 17" x 36" Box 7.83 36.30 2.45 16 9284 17" x 36" Box 6.66 31.56 1.95 9 9286 27" x 36" Box 8.04 50.67 4.34 20 9310 21" x 36" Box 5.97 51.97 4.34 20 9324 27" x 36" Box 10.50 42.33 3.06 20 9328 27" x 36" Box 6.92 57.27 3.98 26 9349 21" x 36" Box 7.00 48.67 3.37 22 9355 39" x 36" Box 7.92 75.20 5.64 26 9356 39" x 36" Box 7.92 75.20 5.64 26 9361 27" x 36" Box 6.00 65.79 4.59 30 9368 33" x 36" Box 7.38 71.25 4.59 30 9369 27" x 36" Box 6.50 51.32 3.04 14 9370 27" x 36" Box 6.42 51.32 3.04 14 9376 27" x 36" Box 7.38 53.35 3.26 15 9380 21" x 36" Box 9.10 32.09 1.84 12 9383 27" x 36" Box 10.58 46.82 3.47 16 9384 21" x 36" Box 6.60 44.13 3.04 14 9394 27x 48 in Box 7.50 66.91 5.20 34 12870 36" x 48" 6.50 77.50 4.59 30 14969 BIV-48 7.88 78.74 7.34 48 16293 1220 x 1220 box 8.86 57.27 5.64 26 16366 Beams B1-B6 6.58 60.38 5.81 38 17240 BII-48 8.00 51.50 3.67 24 17338 BII-48 8.00 49.00 2.75 18 D-73
Table D-73 Summary of NCHRP 12-78 Adjacent Box Girder Bridge Bridge Name Section Type Girder Spacing (ft.) Span Length (ft.) Aps (in2) # of Strands 3805 27"x36" IDOT 3.00 59.04 2.30 15 3819 33"x36" IDOT 3.00 74.88 2.60 17 5125 48"x33" P/S Box 4.00 66.00 3.98 26 5911 36"x27"P/S Box 3.00 59.42 2.14 14 9071 MDOT 840 x 915 Box 3.12 83.64 3.47 16 9103 MDOT 1220 x 1220 Box 4.13 111.21 5.43 25 9167 685mm x 1220mm Box 4.13 75.56 4.77 22 9180 MDOT 535 x 915 Box 3.13 44.70 2.82 13 9181 MDOT 535 x 915 Box 3.13 60.37 3.21 21 9191 27" x 36" Box 3.14 72.50 3.06 20 9228 1220mm x 1220 mm Box 4.23 110.44 5.21 24 9240 33in x 36in Box 3.13 97.92 4.28 28 9314 27" x 36" Box 3.13 83.67 4.77 22 12807 BII-48 4.04 84.00 5.20 34 12809 BII-48 4.04 82.00 5.20 34 12952 BIV-48 modified 3.79 79.96 6.43 42 13118- interior 915 AASHTO BI-915 3.35 69.23 3.87 18 13118-Interior 1220 AASHTO BI-1220 3.85 69.23 4.09 19 13788 BIV-48 4.04 83.00 4.90 32 13805 BI-48 4.06 52.50 3.67 24 14070 B 3' 45" 3.10 115.00 6.43 42 14246 BI-48 4.04 52.00 3.67 24 14987 BIV-48 4.06 73.00 5.20 34 15238 BII-48, 1.220 m Wide 4.04 73.82 5.20 34 16538 ps bx 4.06 101.71 5.81 38 16799 PS Shape 1-Interior 4.00 84.00 5.85 38 17008 AASHTO BII-1220 4.00 82.51 5.81 38 17042 4' PS Box 3.75 50.03 3.67 24 17075 BIV-48Modified 4.00 107.00 6.73 44 17143 BIII-48 3.75 70.00 4.59 30 17175 BII-48 3.75 88.75 6.73 44 The reliability analysis results for existing bridges are shown in Table D-74. Table D-75 shows the probability of exceedance for existing bridges for various conditions. D-74
Table D-74 Summary of Reliability Indices for Existing Bridges Performance Levels Existing Bridges (NCHRP 12-78) (Reliability Index β), 1 Year ADTT=1000 ADTT=2500 ADTT=5000 ADTT=10000 Decompression 0.95 0.85 0.74 0.61 Max.Tens ile Stress Limit 0.0948âðâ²ð 1.15 1.01 0.94 0.82 0.19âðâ²ð 1.24 1.14 1.05 0.95 0.253âðâ²ð 1.4 1.27 1.19 1.07 Maximum Crack Width .008 in 2.29 2.21 1.99 1.85 .012 in 2.65 2.6 2.37 2.22 .016 in 3.06 2.89 2.69 2.56 Table D-75 Summary of Probability of Exceedance for Existing Bridges Performance Levels Existing Bridges (NCHRP 12-78) (Reliability Index β), 1 Year ADTT=1000 ADTT=2500 ADTT=5000 ADTT=10000 Decompression 1539/10000 1814/10000 2119/10000 2546/10000 Max.Tens ile Stress Limit 0.0948âðâ²ð 1251/10000 1562/10000 1736/10000 2061/10000 0.19âðâ²ð 1075/10000 1271/10000 1469/10000 1711/10000 0.253âðâ²ð 808/10000 1020/10000 1170/10000 1423/10000 Maximum Crack Width .008 in 110/10000 136/10000 233/10000 322/10000 .012 in 40/10000 47/10000 89/10000 132/10000 .016 in 11/10000 19/10000 36/10000 52/10000 D.3.2.2 Evaluation of redesigned bridges using new loss provisions and tensile stress limit of 3âðâ²ð The reliability analysis results for existing bridges are shown in Table D-76. Table D-77 shows the probability of exceedance for existing bridges for various conditions. D-75
Table D-76 Summary of Reliability Indices for redesigned bridges using new losses provisions and tensile stress limit of 0.0948âðâ²ð Performance Levels Existing Bridges (NCHRP 12-78) (Reliability Index β), 1 Year ADTT=1000 ADTT=2500 ADTT=5000 ADTT=10000 Decompression 0.94 0.84 0.74 0.56 Max.Tensi le Stress Limit 0.0948âðâ²ð 1.18 1.03 0.88 0.74 0.19âðâ²ð 1.29 1.14 1 0.86 0.253âðâ²ð 1.36 1.2 1.05 0.9 Maximum Crack Width .008 in 2.33 2.18 2.04 1.89 .012 in 2.76 2.6 2.45 2.3 .016 in 3.14 2.99 2.84 2.69 Table D-77 Summary of Probability of Exceedance for redesigned bridges using new losses provisions and tensile stress limit of 0.0948âðâ²ð Performance Levels Existing Bridges (NCHRP 12-78) (Reliability Index β), 1 Year ADTT=1000 ADTT=2500 ADTT=5000 ADTT=10000 Decompression 1736/10000 2005/10000 2296/10000 2877/10000 Max.Tensi le Stress Limit 0.0948âðâ²ð 1190/10000 1515/10000 1894/10000 2296/10000 0.19âðâ²ð 985/10000 1271/10000 1587/10000 1949/10000 0.253âðâ²ð 869/10000 1151/10000 1469/10000 1841/10000 Maximum Crack Width .008 in 99/10000 146/10000 207/10000 294/10000 .012 in 29/10000 47/10000 71/10000 107/10000 .016 in 8/10000 14/10000 23/10000 36/10000 D.3.2.3 Evaluation of redesigned bridges using new losses provisions and tensile stress limit of 6âðâ²ð The reliability analysis results for existing bridges are shown in Table D-78. Table D-79 shows the probability of exceedance for existing bridges for various conditions. D-76
Table D-78 Summary of Reliability Indices for redesigned bridges using new losses provisions and tensile stress limit of 0.19âðâ²ð Performance Levels Existing Bridges (NCHRP 12-78) (Reliability Index β), 1 Year ADTT=1000 ADTT=2500 ADTT=5000 ADTT=10000 Decompression 0.86 0.75 0.64 0.45 Max.Tens ile Stress Limit 0.0948âðâ²ð 1.08 0.94 0.79 0.64 0.19âðâ²ð 1.19 1.04 0.9 0.75 0.253âðâ²ð 1.25 1.1 0.95 0.8 Maximum Crack Width .008 in 2.21 2.06 1.9 1.75 .012 in 2.62 2.47 2.32 2.17 .016 in 3.03 2.88 2.73 2.58 Table D-79 Summary of Probability of Exceedance for redesigned bridges using new losses provisions and tensile stress limit of 0.19âðâ²ð Performance Levels Existing Bridges (NCHRP 12-78) (Reliability Index β), 1 Year ADTT=1000 ADTT=2500 ADTT=5000 ADTT=10000 Decompression 1949/10000 2266/10000 2611/10000 3264/10000 Max.Tens ile Stress Limit 0.0948âðâ²ð 1401/10000 1736/10000 2148/10000 2611/10000 0.19âðâ²ð 1170/10000 1492/10000 1841/10000 2266/10000 0.253âðâ²ð 1056/10000 1357/10000 1711/10000 2119/10000 Maximum Crack Width .008 in 136/10000 197/10000 287/10000 401/10000 .012 in 44/10000 68/10000 102/10000 150/10000 .016 in 12/10000 20/10000 32/10000 49/10000 D.3.2.4 Evaluation of redesigned bridges using new losses provisions and tensile stress limit of 0.253âðâ²ð The reliability analysis results for existing bridges are shown in Table D-80. Table D-81 shows the probability of exceedance for existing bridges for various conditions. D-77
Table D-80 Summary of Reliability Indices for redesigned bridges using new losses provisions and tensile stress limit of 0.253âðâ²ð Performance Levels Existing Bridges (NCHRP 12-78) (Reliability Index β), 1 Year ADTT=1000 ADTT=2500 ADTT=5000 ADTT=10000 Decompression 0.82 0.73 0.62 0.44 Max.Tens ile Stress Limit 0.0948âðâ²ð 1.05 0.9 0.75 0.6 0.19âðâ²ð 1.16 1.01 0.86 0.71 0.253âðâ²ð 1.23 1.08 0.93 0.78 Maximum Crack Width .008 in 2.19 2.04 1.89 1.73 .012 in 2.61 2.46 2.3 2.15 .016 in 3 2.85 2.7 2.55 Table D-81 Summary of Probability of Exceedance for redesigned bridges using new losses provisions and tensile stress limit of 0.253âðâ²ð Performance Levels Existing Bridges (NCHRP 12-78) (Reliability Index β), 1 Year ADTT=1000 ADTT=2500 ADTT=5000 ADTT=10000 Decompression 2061/10000 2327/10000 2676/10000 3300/10000 Max.Tens ile Stress Limit 0.0948âðâ²ð 1469/10000 1841/10000 2266/10000 2743/10000 0.19âðâ²ð 1230/10000 1562/10000 1949/10000 2389/10000 0.253âðâ²ð 1093/10000 1401/10000 1762/10000 2177/10000 Maximum Crack Width .008 in 143/10000 207/10000 294/10000 418/10000 .012 in 45/10000 69/10000 107/10000 158/10000 .016 in 13/10000 22/10000 35/10000 54/10000 D.3.3 Selection of Target Reliability indices The target reliability indices for the serviceability limit states from various codes were discussed in the projectâs interim report. The European Code selected a target reliability index for irreversible service limit state equal to 2.9 and 1.5 for a 1-year and 50 years period, respectively, whereas the ISO 2394-1998 specified target reliability indices for reversible and irreversible limit states as 0 and 1.5 for life time duration, respectively. These are general values that do not take into account the specific nature of the limit state being considered, the limiting criteria, the inherent reliability of existing structures or the load used for calibration relative to the load used for design. For example, for prestressed concrete members the limiting criteria may be decompression, a calculated concrete tensile stress of a certain magnitude, or, a crack opening to a certain width. For a given girder, the reliability index will vary depending on the criteria and the limiting D-78
value. Limited contacts with individuals, who contributed to the development of the European Code indicate that the reliability indices listed for service limit states were not supported by research, rather they were based on general consensus. The proposed target reliability indices used herein were selected based on the calculated average values of the reliability levels of existing bridges and previous practices with some consideration given to experiences from other Codes (European Code and ISO 2394 Document). Return period of 1 year was selected due to the fact that the live load statistics were developed based on 1 year of reliable WIM data from various WIM sites. Furthermore, since only 3 out of 32 WIM sites have the ADTT larger than 5000 and only 1 out of 32 WIM sites have the ADTT larger than 8000, the average reliability indices for ADTT equals to 5000 were used to represent the reliability levels of existing bridges. Table D-82 shows the target reliability indices selected in this study. For example, the European Code specified target reliability indices for irreversible limit states as 2.9 for 1-year reference period. For ADTT of 5000, the reliability index of existing bridges, simulated bridges designed for severe environments, and simulated bridges designed for normal environments, at the Maximum Crack Width performance level is around 2.69, 3.55 and 3.15, respectively (See Table D-82). Therefore, a target reliability index of 3.30 and 3.10 was selected for Maximum Crack Width performance level for bridges designed for severe environments and bridges designed for normal environments, respectively. The reliability index of 3.0 means that 13 out of 10000 bridges will have a crack width at the bottom of the girder exceeding 0.016 inch in one year. Table D-82 Reliability Indices for Existing Bridges (Return Period of 1 Year) with One Lane Loaded (ADTT 5000) Performance Level Reliability Index Average β for Existing Bridges in the NCHRP 12-78 β for Simulated bridges designed for 3t cf f â²= and old loss method β for Simulated bridges designed for 6t cf f â²= and old loss method Proposed Target β for bridges in severe environment Proposed Target β for bridges in normal or benign environment Decompression 0.74 1.44 1.07 1.20 1.00 Maximum Allowable Tensile Stress of 6t cf f â²= 1.05 1.82 1.43 1.50 1.25 Maximum Allowable Crack Width of 0.016 in 2.69 3.55 3.15 3.30 3.10 D-79
D.3.4 Reliability indices of girders designed for various design criteria (I Girders) D.3.4.1 Calibration for ADTT=1000 D.3.4.1.1 Bridges Designed for Maximum Concrete Tensile Stress of 0.0948t cf f â²= In this section, the calibration process for a selected bridge database (shown in Table D-83) is performed for ADTT equal to 1000 and normal exposure condition. 0.6â diameter strands were used in the design for Florida I Beam (FIB) while 0.5â diameter strands were used in other designs. This rule is valid throughout this report. Please note that the allowable maximum crack width of 0.016 in is applied for maximum allowable crack width limit state and a compressive strength of concrete of 8 ksi is used for all the designed girders in this section and throughout the report. Table D-83 Summary Information of Bridges Designed with γLL=0.8 ( 0.0948t cf f â²= ) Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in 2) # of Strands 1 AASHTO I 30 6 1.224 8 2 AASHTO I 30 8 1.53 10 3 AASHTO I 30 10 1.836 12 4 AASHTO I 30 12 2.142 14 5 AASHTO II 60 6 2.448 16 6 AASHTO II 60 8 3.366 22 7 AASHTO III 60 10 3.06 20 8 AASHTO III 60 12 3.672 24 9 AASHTO III 80 6 3.672 24 10 AASHTO III 80 8 4.59 30 11 AASHTO III 80 10 5.508 36 12 AASHTO IV 80 12 5.202 34 13 AASHTO III 100 6 6.12 40 14 AASHTO IV 100 8 6.426 42 15 AASHTO IV 100 10 7.344 48 16 AASHTO V 100 12 7.038 46 17 AASHTO IV 120 6 7.956 52 18 AASHTO V 120 8 7.956 52 19 AASHTO V 120 10 9.18 60 20 AASHTO VI 120 12 8.874 58 21 AASHTO VI 140 6 8.262 54 22 AASHTO VI 140 8 9.792 64 23 AASHTO VI 140 10 11.322 74 24 AASHTO VI 140 12 - - 25 FIB-96 160 6 7.812 36 26 FIB-96 160 8 9.114 42 27 FIB-96 160 10 10.416 48 28 FIB-96 160 12 - - D-80
Step 1: Calculate the reliability level of designs according to AASHTO LRFD Specifications (2010) (Figure D-2~Figure D-4) Figure D-2 through Figure D-4 show the reliability indices for the bridges designed using AASHTO type girders according to AASHTO LRFD specifications (2010). It is observed that the average reliability index for decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 1.05, 1.41, and 3.16, respectively, which satisfy the proposed target reliability index of 1.0 for decompression limit state. However, a larger live load factor will be used to estimate the effect of changing live load factor on reliability level of structure. Figure D-2 Reliability Indices for Bridges at Decompression Limit State (ADTT=1000), γLL=0.8 ( 0.0948t cf f â²= ) D-81
Figure D-3 Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=1000), γLL=0.8 ( 0.0948t cf f â²= ) Figure D-4 Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=1000), γLL=0.8 ( 0.0948t cf f â²= ) Step 2: Redesign the bridges with live load factor of 1.0 (Figure D-5~Figure D-7) Since the reliability level of the original bridge database is below the target reliability level at decompression limit state and maximum allowable tensile stress limit state, the bridges have been redesigned using a live load factor of 1.0. Please note that only the live load factor of Service III limit state is increased from 0.8 to 1.0, dead load D-82
and resistance factors were kept the same during the redesign. Table D-84 shows the design outcomes of the redesigned bridges. Figure D-5 though Figure D-7 shows the reliability indices for the redesigned bridges using live load factor of 1.0. It is observed the average reliability index of decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 1.42, 1.79, and 3.36, respectively. Table D-84 Summary Information of Bridges Designed with γLL=1.0 ( 0.0948t cf f â²= ) Section Type Span Length (ft.) Spacing (ft.) Aps (in 2) # of Strands 1 AASHTO I 30 6 1.224 8 2 AASHTO I 30 8 1.53 10 3 AASHTO I 30 10 1.836 12 4 AASHTO I 30 12 2.142 14 5 AASHTO II 60 6 3.06 20 6 AASHTO II 60 8 3.978 26 7 AASHTO III 60 10 3.366 22 8 AASHTO III 60 12 4.284 28 9 AASHTO III 80 6 4.284 28 10 AASHTO III 80 8 5.202 34 11 AASHTO III 80 10 6.12 40 12 AASHTO IV 80 12 5.814 38 13 AASHTO III 100 6 7.038 46 14 AASHTO IV 100 8 7.038 46 15 AASHTO IV 100 10 8.262 54 16 AASHTO V 100 12 7.65 50 17 AASHTO IV 120 6 8.874 58 18 AASHTO V 120 8 8.874 58 19 AASHTO V 120 10 10.404 68 20 AASHTO VI 120 12 9.792 64 21 AASHTO VI 140 6 8.874 58 22 AASHTO VI 140 8 10.71 70 23 AASHTO VI 140 10 - - 24 AASHTO VI 140 12 - - 25 FIB-96 160 6 8.246 38 26 FIB-96 160 8 10.416 48 27 FIB-96 160 10 11.284 52 28 FIB-96 160 12 - - D-83
Figure D-5 Reliability Indices for Bridges at Decompression Limit State (ADTT=1000), γLL=1.0 ( 0.0948t cf f â²= ) Figure D-6 Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=1000), γLL=1.0 ( 0.0948t cf f â²= ) D-84
Figure D-7 Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=1000), γLL=1.0 ( 0.0948t cf f â²= ) Step 3: Propose new live load, dead load, and/or resistance factors Based on the calibration process shown in step 1 through step 3, it is observed that the uniform target reliability index can be achieved using a live load factor of 1.0. Therefore, for ADTT equal to 1000 and maximum concrete tensile stress of 0.0948t cf f â²= , a new live load factor of 1.0 is proposed. D.3.4.1.2 Bridges Designed for Maximum Concrete Tensile Stress of 0.158t cf f â²= In this section, the calibration process for a selected bridge database (shown in Table D-85) is performed for ADTT equal to 1000 and normal exposure condition. 0.6â diameter strands were used in the design for Florida I Beam (FIB) while 0.5â diameter strands were used in other designs. Please note that the allowable maximum crack width of 0.016 in is applied for maximum allowable crack width limit state and a compressive strength of concrete of 8 ksi is used for all the designed girders in this section and throughout the report. D-85
Table D-85 Summary Information of Bridges Designed with γLL=0.8 ( 0.158t cf f â²= ) Section Type Span Length (ft.) Spacing (ft.) Aps (in 2) # of Strands 1 AASHTO I 30 6 1.224 8 2 AASHTO I 30 8 1.53 10 3 AASHTO I 30 10 1.836 12 4 AASHTO I 30 12 2.142 14 5 AASHTO II 60 6 2.448 16 6 AASHTO II 60 8 3.672 24 7 AASHTO III 60 10 3.06 20 8 AASHTO III 60 12 3.672 24 9 AASHTO III 80 6 3.366 22 10 AASHTO III 80 8 4.284 28 11 AASHTO III 80 10 5.202 34 12 AASHTO IV 80 12 4.896 32 13 AASHTO III 100 6 5.814 38 14 AASHTO IV 100 8 5.814 38 15 AASHTO IV 100 10 7.038 46 16 AASHTO V 100 12 6.426 42 17 AASHTO IV 120 6 7.344 48 18 AASHTO V 120 8 7.344 48 19 AASHTO V 120 10 8.568 56 20 AASHTO VI 120 12 8.262 54 21 AASHTO VI 140 6 7.65 50 22 AASHTO VI 140 8 9.18 60 23 AASHTO VI 140 10 10.71 70 24 AASHTO VI 140 12 - - 25 FIB-96 160 6 7.378 34 26 FIB-96 160 8 8.246 38 27 FIB-96 160 10 9.548 44 28 FIB-96 160 12 - - Step 1: Calculate the reliability level of designs according to AASHTO LRFD Specifications (2010) (Figure D-8~Figure D-10) Figure D-8 through Figure D-10 show the reliability indices for the bridges designed using AASHTO type girders according to AASHTO LRFD specifications (2010). It is observed that the average reliability index for decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 0.97, 1.31, and 2.99, respectively. Live load factor of 1.0 will be used in next step. D-86
Figure D-8 Reliability Indices for Bridges at Decompression Limit State (ADTT=1000), γLL=0.8 ( 0.158t cf f â²= ) Figure D-9 Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=1000), γLL=0.8 ( 0.158t cf f â²= ) D-87
Figure D-10 Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=1000), γLL=0.8 ( 0.158t cf f â²= ) Step 2: Redesign the bridges with live load factor of 1.0 (Figure D-11~Figure D-13) Since the reliability level of the original bridge database is below the target reliability level at decompression limit state and maximum allowable tensile stress limit state, the bridges have been redesigned using a live load factor of 1.0. Please note that only the live load factor of Service III limit state is increased from 0.8 to 1.0, dead load and resistance factors were kept the same during the redesign. Table D-86 shows the design outcomes of the redesigned bridges. Figure D-11 though Figure D-13 show the reliability indices for the redesigned bridges using live load factor of 1.0. It is observed that the average reliability index of decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 1.16, 1.55, and 3.32, respectively. D-88
Table D-86 Summary Information of Bridges Designed with γLL=1.0 ( 0.158t cf f â²= ) Section Type Span Length (ft.) Spacing (ft.) Aps (in 2) # of Strands 1 AASHTO I 30 6 1.224 8 2 AASHTO I 30 8 1.53 10 3 AASHTO I 30 10 1.836 12 4 AASHTO I 30 12 2.142 14 5 AASHTO II 60 6 2.754 18 6 AASHTO II 60 8 3.672 24 7 AASHTO III 60 10 3.06 20 8 AASHTO III 60 12 3.672 24 9 AASHTO III 80 6 3.978 26 10 AASHTO III 80 8 4.896 32 11 AASHTO III 80 10 5.814 38 12 AASHTO IV 80 12 5.508 36 13 AASHTO III 100 6 6.732 44 14 AASHTO IV 100 8 6.426 42 15 AASHTO IV 100 10 7.65 50 16 AASHTO V 100 12 7.344 48 17 AASHTO IV 120 6 8.262 54 18 AASHTO V 120 8 8.262 54 19 AASHTO V 120 10 9.486 62 20 AASHTO VI 120 12 9.18 60 21 AASHTO VI 140 6 8.262 54 22 AASHTO VI 140 8 10.098 66 23 AASHTO VI 140 10 - - 24 AASHTO VI 140 12 - - 25 FIB-96 160 6 7.812 36 26 FIB-96 160 8 9.114 42 27 FIB-96 160 10 10.416 48 28 FIB-96 160 12 - - D-89
Figure D-11 Reliability Indices for Bridges at Decompression Limit State (ADTT=1000) , γLL=1.0 ( 0.158t cf f â²= ) Figure D-12 Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=1000), γLL=1.0 ( 0.158t cf f â²= ) D-90
Figure D-13 Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=1000), γLL=1.0 ( 0.158t cf f â²= ) Step 3: Propose new live load, dead load, and/or resistance factors Based on the calibration process shown in step 1 through step 3, it is observed that the uniform target reliability index can be achieved using a live load factor of 1.0. Therefore, for ADTT equal to 1000 and maximum concrete tensile stress of 0.158t cf f â²= , a new live load factor of 1.0 is proposed. D.3.4.1.3 Bridges Designed for Maximum Concrete Tensile Stress of 0.19t cf f â²= In this section, the calibration process for a selected bridge database (shown in Table D-87) is performed for ADTT equal to 1000 and normal exposure condition. 0.6â diameter strands were used in the design for Florida I Beam (FIB) while 0.5â diameter were used in other designs. This rule is valid throughout this report. Please note that the allowable maximum crack width of 0.016 in is applied for maximum allowable crack width limit state and a compressive strength of concrete of 8 ksi is used for all the designed girders in this section and throughout the report. D-91
Table D-87 Summary Information of Bridges Designed with γLL=0.8 ( 0.19t cf f â²= ) Section Type Span Length (ft.) Spacing (ft.) Aps (in 2) # of Strands 1 AASHTO I 30 6 1.224 8 2 AASHTO I 30 8 1.53 10 3 AASHTO I 30 10 1.836 12 4 AASHTO I 30 12 2.142 14 5 AASHTO II 60 6 2.448 16 6 AASHTO II 60 8 3.06 20 7 AASHTO III 60 10 3.06 20 8 AASHTO III 60 12 3.672 24 9 AASHTO III 80 6 3.366 22 10 AASHTO III 80 8 4.284 28 11 AASHTO III 80 10 4.896 32 12 AASHTO IV 80 12 4.896 32 13 AASHTO III 100 6 5.814 38 14 AASHTO IV 100 8 5.814 38 15 AASHTO IV 100 10 6.732 44 16 AASHTO V 100 12 6.426 42 17 AASHTO IV 120 6 7.344 48 18 AASHTO V 120 8 7.344 48 19 AASHTO V 120 10 8.262 54 20 AASHTO VI 120 12 8.262 54 21 AASHTO VI 140 6 7.344 48 22 AASHTO VI 140 8 8.874 58 23 AASHTO VI 140 10 10.404 68 24 AASHTO VI 140 12 - - 25 FIB-96 160 6 6.944 32 26 FIB-96 160 8 8.246 38 27 FIB-96 160 10 9.548 44 28 FIB-96 160 12 - - Step 1: Calculate the reliability level of designs according to AASHTO LRFD Specifications (2010) (Figure D-14~Figure D-16) Figure D-14 through Figure D-16 show the reliability indices for the bridges designed using AASHTO type girders according to AASHTO LRFD specifications (2010). It is observed that the average reliability index for decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 0.84, 1.27, and 2.92, respectively. Since the reliability indices are lower than target reliability index, live load factor of 1.0 will be used in next step. D-92
Figure D-14 Reliability Indices for Bridges at Decompression Limit State (ADTT=1000), γLL=0.8 ( 0.19t cf f â²= ) Figure D-15 Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=1000), γLL=0.8 ( 0.19t cf f â²= ) D-93
Figure D-16 Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=1000), γLL=0.8 ( 0.19t cf f â²= ) Step 2: Redesign the bridges with live load factor of 1.0 (Figure D-17~Figure D-19) Since the reliability level of the original bridge database is below the target reliability level at decompression limit state and maximum allowable tensile stress limit state, the bridges have been redesigned using a live load factor of 1.0. Please note that only the live load factor of Service III limit state is increased from 0.8 to 1.0, dead load and resistance factors were kept the same during the redesign. Table D-88 shows the design outcomes of the redesigned bridges. Figure D-17 though Figure D-19 show the reliability indices for the redesigned bridges using live load factor of 1.0. It is observed that the average reliability index of decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 1.11, 1.53, and 3.25, respectively. D-94
Table D-88 Summary Information of Bridges Designed with γLL=1.0 ( 0.19t cf f â²= ) Section Type Span Length (ft.) Spacing (ft.) Aps (in 2) # of Strands 1 AASHTO I 30 6 1.224 8 2 AASHTO I 30 8 1.53 10 3 AASHTO I 30 10 1.836 12 4 AASHTO I 30 12 2.142 14 5 AASHTO II 60 6 2.448 16 6 AASHTO II 60 8 3.366 22 7 AASHTO III 60 10 3.06 20 8 AASHTO III 60 12 3.672 24 9 AASHTO III 80 6 3.672 24 10 AASHTO III 80 8 4.59 30 11 AASHTO III 80 10 5.814 38 12 AASHTO IV 80 12 5.202 34 13 AASHTO III 100 6 6.426 42 14 AASHTO IV 100 8 6.426 42 15 AASHTO IV 100 10 7.65 50 16 AASHTO V 100 12 7.038 46 17 AASHTO IV 120 6 7.956 52 18 AASHTO V 120 8 7.956 52 19 AASHTO V 120 10 9.18 60 20 AASHTO VI 120 12 8.874 58 21 AASHTO VI 140 6 7.956 52 22 AASHTO VI 140 8 9.792 64 23 AASHTO VI 140 10 11.322 74 24 AASHTO VI 140 12 - - 25 FIB-96 160 6 7.378 34 26 FIB-96 160 8 8.68 40 27 FIB-96 160 10 10.416 48 28 FIB-96 160 12 - - D-95
Figure D-17 Reliability Indices for Bridges at Decompression Limit State (ADTT=1000) , γLL=1.0 ( 0.19t cf f â²= ) Figure D-18 Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=1000), γLL=1.0 ( 0.19t cf f â²= ) D-96
Figure D-19 Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=1000), γLL=1.0 ( 0.19t cf f â²= ) Step 3: Propose new live load, dead load, and/or resistance factors Based on the calibration process shown in step 1 through step 3, it is observed that the uniform target reliability index can be achieved using a live load factor of 1.0. Therefore, for ADTT equal to 1000 and maximum concrete tensile stress of 0.19t cf f â²= , a new live load factor of 1.0 is proposed. D.3.4.1.4 Bridges Designed for Maximum Concrete Tensile Stress of 0.253t cf f â²= In this section, the calibration for a selected bridge database (shown in Table D-89) is performed for a scenario of ADTT equal to 1000 and severe exposure conditions. Please note that the maximum allowable crack width is specified as 0.016 in for maximum allowable crack width limit state. Step 1: Calculate the reliability level of designs according to AASHTO LRFD Specifications (2010) (Figure D-20~Figure D-22) Figure D-20 through Figure D-22 show the reliability indices for the bridges designed using AASHTO type girders according to AASHTO LRFD specifications (2010) under severe exposure conditions. It is observed that the average reliability index for decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 0.2, 0.55, and 2.83, respectively, which is higher than proposed target reliability index. However, live load factor of 1.0 will be used to estimate the effect of changing live load factor on reliability level. D-97
Table D-89 Summary Information of Bridges Designed with γLL=0.8 ( 0.253t cf f â²= ) Section Type Span Length (ft.) Spacing (ft.) Aps (in 2) # of Strands 1 AASHTO I 30 6 1.224 8 2 AASHTO I 30 8 1.53 10 3 AASHTO I 30 10 1.836 12 4 AASHTO I 30 12 2.142 14 5 AASHTO II 60 6 2.142 14 6 AASHTO II 60 8 2.754 18 7 AASHTO III 60 10 2.448 16 8 AASHTO III 60 12 3.06 20 9 AASHTO III 80 6 3.06 20 10 AASHTO III 80 8 3.978 26 11 AASHTO III 80 10 4.59 30 12 AASHTO IV 80 12 4.284 28 13 AASHTO III 100 6 5.202 34 14 AASHTO IV 100 8 5.202 34 15 AASHTO IV 100 10 6.426 42 16 AASHTO V 100 12 5.814 38 17 AASHTO IV 120 6 6.732 44 18 AASHTO V 120 8 6.732 44 19 AASHTO V 120 10 7.956 52 20 AASHTO VI 120 12 7.65 50 21 AASHTO VI 140 6 6.732 44 22 AASHTO VI 140 8 8.262 54 23 AASHTO VI 140 10 9.792 64 24 AASHTO VI 140 12 - - 25 FIB-96 160 6 6.51 30 26 FIB-96 160 8 7.378 34 27 FIB-96 160 10 8.68 40 28 FIB-96 160 12 - - D-98
Figure D-20 Reliability Indices for Bridges at Decompression Limit State (ADTT=1000), γLL=0.8 ( 0.253t cf f â²= ) Figure D-21 Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=1000), γLL=0.8 ( 0.253t cf f â²= ) D-99
Figure D-22 Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=1000), γLL=0.8 ( 0.253t cf f â²= ) Step 2: Redesign the bridges with live load factor of 1.0 (Figure D-23~Figure D-25) In this step, the bridges were redesigned using a live load factor of 1.0. Please note that only the live load factor of Service III limit state is increased from 0.8 to 1.0, dead load and resistance factors were kept the same during the redesign. Table D-90 shows the design outcomes of the redesigned bridges. Figure D-23 though Figure D-25 show the reliability indices for the redesigned bridges using a live load factor of 1.0. It is observed that the average reliability index for the decompression limit state, the maximum allowable tensile stress limit state and the maximum allowable crack width limit state is 0.93, 1.29, and 3.03, respectively. D-100
Table D-90 Summary Information of Bridges Designed with γLL=1.0 ( 0.253t cf f â²= ) Section Type Span Length (ft.) Spacing (ft.) Aps (in 2) # of Strands 1 AASHTO I 30 6 1.224 8 2 AASHTO I 30 8 1.53 10 3 AASHTO I 30 10 1.836 12 4 AASHTO I 30 12 2.142 14 5 AASHTO II 60 6 2.142 14 6 AASHTO II 60 8 2.754 18 7 AASHTO III 60 10 2.448 16 8 AASHTO III 60 12 3.06 20 9 AASHTO III 80 6 3.06 20 10 AASHTO III 80 8 3.978 26 11 AASHTO III 80 10 4.59 30 12 AASHTO IV 80 12 4.284 28 13 AASHTO III 100 6 5.202 34 14 AASHTO IV 100 8 5.202 34 15 AASHTO IV 100 10 6.426 42 16 AASHTO V 100 12 5.814 38 17 AASHTO IV 120 6 6.732 44 18 AASHTO V 120 8 6.732 44 19 AASHTO V 120 10 7.956 52 20 AASHTO VI 120 12 7.65 50 21 AASHTO VI 140 6 6.732 44 22 AASHTO VI 140 8 8.262 54 23 AASHTO VI 140 10 9.792 64 24 AASHTO VI 140 12 - - 25 FIB-96 160 6 6.51 30 26 FIB-96 160 8 7.378 34 27 FIB-96 160 10 8.68 40 28 FIB-96 160 12 - - D-101
Figure D-23 Reliability Indices for Bridges at Decompression Limit State (ADTT=1000), γLL=1.0 ( 0.253t cf f â²= ) Figure D-24 Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=1000), γLL=1.0 ( 0.253t cf f â²= ) D-102
Figure D-25 Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=1000), γLL=1.0 ( 0.253t cf f â²= ) Step 3: Propose new live load, dead load, and/or resistance factors Based on the calibration process shown in step 1 through step 3, it is observed that the uniform target reliability index can be achieved using a live load factor of 1.0. Therefore, for ADTT equal to 1000 and maximum concrete tensile stress of 0.253t cf f â²= , a new live load factor of 1.0 is proposed. D.3.4.2 Calibration for ADTT=2500 D.3.4.2.1 Bridges Designed for Maximum Concrete Tensile Stress of 0.0948t cf f â²= In this section, the calibration for a selected bridge database (shown in Table D-83) is performed for ADTT equal to 2500 and maximum concrete tensile stress of 0.0948t cf f â²= . Please note that the allowable maximum crack width of 0.016 in is applied for maximum allowable crack width limit state. Step 1: Calculate the reliability level of designs according to AASHTO LRFD Specifications (2010) (Figure D-26~Figure D-28) Figure D-26 through Figure D-28 show the reliability indices for the bridges designed using AASHTO type girders according to AASHTO LRFD specifications (2010). It is observed that the average reliability index for decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 1.01, 1.35, and 3.11, respectively. Live load factor of 1.0 will be used in next step. D-103
Figure D-26 Reliability Indices for Bridges at Decompression Limit State (ADTT=2500), γLL=0.8 ( 0.0948t cf f â²= ) Figure D-27 Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=2500), γLL=0.8 ( 0.0948t cf f â²= ) D-104
Figure D-28 Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=2500), γLL=0.8 ( 0.0948t cf f â²= ) Step 2: Redesign the bridges with live load factor of 1.0 (Figure D-29~Figure D-31) Since the reliability level of the original bridge database was below the target reliability level at decompression limit state and maximum allowable tensile stress limit state, the bridges were redesigned using a live load factor of 1.0. Please note that only the live load factor of Service III limit state is increased from 0.8 to 1.0, dead load and resistance factors were kept the same during the redesign. Table D-84 shows the design outcomes of the redesigned bridges. Figure D-29 through Figure D-31 show the reliability indices for the redesigned bridges using live load factor of 1.0. It is observed that the average reliability index of decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 1.38, 1.75, and 3.33, respectively. D-105
Figure D-29 Reliability Indices for Bridges at Decompression Limit State (ADTT=2500), γLL=1.0 ( 0.0948t cf f â²= ) Figure D-30 Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=2500), γLL=1.0 ( 0.0948t cf f â²= ) D-106
Figure D-31 Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=2500), γLL=1.0 ( 0.0948t cf f â²= ) Step 3: Propose new live load, dead load, and/or resistance factors Based on the calibration process shown in step 1 through step 3, it is observed that the uniform target reliability index can be achieved using a live load factor of 1.0. Therefore, for ADTT equal to 2500 and maximum concrete tensile stress of 0.0948t cf f â²= , a new live load factor of 1.0 is proposed. D.3.4.2.2 Bridges Designed for Maximum Concrete Tensile Stress of 0.158t cf f â²= In this section, the calibration for a selected bridge database (shown in Table D-85) is performed for ADTT equal to 2500 and maximum concrete tensile stress of 0.158t cf f â²= . Please note that the allowable maximum crack width of 0.016 in is applied for maximum allowable crack width limit state. Step 1: Calculate the reliability level of designs according to AASHTO LRFD Specifications (2010) (Figure D-32~Figure D-34) Figure D-32 through Figure D-34 show the reliability indices for the bridges designed using AASHTO type girders according to AASHTO LRFD specifications (2010). It is observed that the average reliability index for decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 0.83, 1.19, and 2.96, respectively, which does not satisfy the proposed target reliability index of 1.0 for decompression limit state. Therefore, a larger live load factor will be used to modify the original design in order to improve the reliability level of the bridges. D-107
Figure D-32 Reliability Indices for Bridges at Decompression Limit State (ADTT=2500), γLL=0.8 ( 0.158t cf f â²= ) Figure D-33 Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=2500), γLL=0.8 ( 0.158t cf f â²= ) D-108
Figure D-34 Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=2500), γLL=0.8 ( 0.158t cf f â²= ) Step 2: Redesign the bridges with live load factor of 1.0 (Figure D-35~Figure D-37) Since the reliability level of the original bridge database was below the target reliability level at decompression limit state and maximum allowable tensile stress limit state, the bridges were redesigned using a live load factor of 1.0. Please note that only the live load factor of Service III limit state is increased from 0.8 to 1.0, dead load and resistance factors were kept the same during the redesign. Table D-86 shows the design outcomes of the redesigned bridges. Figure D-35 through Figure D-37 show the reliability indices for the redesigned bridges using live load factor of 1.0. It is observed that the average reliability index of decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 1.12, 1.50, and 3.29, respectively. D-109
Figure D-35 Reliability Indices for Bridges at Decompression Limit State (ADTT=2500) , γLL=1.0 ( 0.158t cf f â²= ) Figure D-36 Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=2500), γLL=1.0 ( 0.158t cf f â²= ) D-110
Figure D-37 Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=2500), γLL=1.0 ( 0.158t cf f â²= ) Step 3: Propose new live load, dead load, and/or resistance factors Based on the calibration process shown in step 1 through step 3, it is observed that the uniform target reliability index can be achieved using a live load factor of 1.0. Therefore, for ADTT equal to 2500 and maximum concrete tensile stress of 0.158t cf f â²= , a new live load factor of 1.0 is proposed. D.3.4.2.3 Bridges Designed for Maximum Concrete Tensile Stress of 0.19t cf f â²= In this section, the calibration for a selected bridge database (shown in Table D-87) is performed for ADTT equal to 2500 and maximum concrete tensile stress of 0.19t cf f â²= . Please note that the allowable maximum crack width of 0.016 in is applied for maximum allowable crack width limit state. Step 1: Calculate the reliability level of designs according to AASHTO LRFD Specifications (2010) (Figure D-38~Figure D-40) Figure D-38 through Figure D-40 show the reliability indices for the bridges designed using AASHTO type girders according to AASHTO LRFD specifications (2010). It is observed that the average reliability index for decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 0.7, 1.15, and 2.87, respectively, which does not satisfy the proposed target reliability index of 1.0 for decompression limit state and 1.25 for maximum allowable tensile stress limit state. Therefore, a larger live load factor will be used to modify the original design in order to improve the reliability level of the bridges. D-111
Figure D-38 Reliability Indices for Bridges at Decompression Limit State (ADTT=2500), γLL=0.8 ( 0.19t cf f â²= ) Figure D-39 Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=2500), γLL=0.8 ( 0.19t cf f â²= ) D-112
Figure D-40 Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=2500), γLL=0.8 ( 0.19t cf f â²= ) Step 2: Redesign the bridges with live load factor of 1.0 (Figure D-41~Figure D-43) Since the reliability level of the original bridge database was below the target reliability level at decompression limit state and maximum allowable tensile stress limit state, the bridges were redesigned using a live load factor of 1.0. Please note that only the live load factor of Service III limit state is increased from 0.8 to 1.0, dead load and resistance factors were kept the same during the redesign. Table D-88 shows the design outcomes of the redesigned bridges. Figure D-41 through Figure D-43 show the reliability indices for the redesigned bridges using live load factor of 1.0. It is observed that the average reliability index of decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 1.04, 1.46, and 3.17, respectively. D-113
Figure D-41 Reliability Indices for Bridges at Decompression Limit State (ADTT=2500) , γLL=1.0 ( 0.19t cf f â²= ) Figure D-42 Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=2500), γLL=1.0 ( 0.19t cf f â²= ) D-114
Figure D-43 Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=2500), γLL=1.0 ( 0.19t cf f â²= ) Step 4: Propose new live load, dead load, and/or resistance factors Based on the calibration process shown in step 1 through step 3, it is observed that the uniform target reliability index can be achieved using a live load factor of 1.0. Therefore, for ADTT equal to 2500 and maximum concrete tensile stress of 0.19t cf f â²= , a new live load factor of 1.0 is proposed. D.3.4.2.4 Bridges Designed for Maximum Concrete Tensile Stress of 0.253t cf f â²= In this section, the calibration for a selected bridge database (shown in Table D-89) is performed for ADTT equal to 2500 and maximum concrete tensile stress of 0.253t cf f â²= . Please note that the allowable maximum crack width of 0.016 in is applied for maximum allowable crack width limit state. Step 1: Calculate the reliability level of designs according to AASHTO LRFD Specifications (2010) (Figure D-44~Figure D-46) Figure D-44 through Figure D-46 show the reliability indices for the bridges designed using AASHTO type girders according to AASHTO LRFD specifications (2010). It is observed that the average reliability index for decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 0.08, 0.49, and 2.77, respectively, which does not satisfy the proposed target reliability index of 1.0 for decompression limit state and 1.25 for maximum allowable tensile stress limit state. Therefore, a larger live load factor will be used to modify the original design in order to improve the reliability level of the bridges. D-115
Figure D-44 Reliability Indices for Bridges at Decompression Limit State (ADTT=2500), γLL=0.8 ( 0.253t cf f â²= ) Figure D-45 Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=2500), γLL=0.8 ( 0.253t cf f â²= ) D-116
Figure D-46 Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=2500), γLL=0.8 ( 0.253t cf f â²= ) Step 2: Redesign the bridges with live load factor of 1.0 (Figure D-47~Figure D-49) Since the reliability level of the original bridge database was below the target reliability level at decompression limit state and maximum allowable tensile stress limit state, the bridges were redesigned using a live load factor of 1.0. Please note that only the live load factor of Service III limit state is increased from 0.8 to 1.0, dead load and resistance factors were kept the same during the redesign. Table D-90 shows the design outcomes of the redesigned bridges. Figure D-47 through Figure D-49 show the reliability indices for the redesigned bridges using live load factor of 1.0. It is observed that the average reliability index of decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 0.89, 1.27, and 2.95, respectively. D-117
Figure D-47 Reliability Indices for Bridges at Decompression Limit State (ADTT=2500) , γLL=1.0 ( 0.253t cf f â²= ) Figure D-48 Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=2500), γLL=1.0 ( 0.253t cf f â²= ) D-118
Figure D-49 Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=2500), γLL=1.0 ( 0.253t cf f â²= ) Step 4: Propose new live load, dead load, and/or resistance factors Based on the calibration process shown in step 1 through step 3, it is observed that the uniform target reliability index can be achieved using a live load factor of 1.0. Therefore, for ADTT equal to 2500 and maximum concrete tensile stress of 0.253t cf f â²= , a new live load factor of 1.0 is proposed. D.3.4.3 Calibration Procedure for ADTT=5000 D.3.4.3.1 Bridges Designed for Maximum Concrete Tensile Stress of 0.0948t cf f â²= In this section, the calibration for a selected bridge database (shown in Table D-83) is performed for ADTT equal to 5000 and maximum concrete tensile stress of 0.0948t cf f â²= . Please note that the allowable maximum crack width of 0.016 in is applied for maximum allowable crack width limit state. Step 1: Calculate the reliability level of designs according to AASHTO LRFD Specifications (2010) (Figure D-50~Figure D-52) Figure D-50 through Figure D-52 show the reliability indices for the bridges designed using AASHTO type girders according to AASHTO LRFD specifications (2010). It is observed that the average reliability index for decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 0.97, 1.31, and 3.06, respectively. The live load factor of 1.0 will be used in the next step D-119
Figure D-50 Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=0.8 ( 0.0948t cf f â²= ) Figure D-51 Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=5000), γLL=0.8 ( 0.0948t cf f â²= ) D-120
Figure D-52 Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=5000), γLL=0.8 ( 0.0948t cf f â²= ) Step 2: Redesign the bridges with live load factor of 1.0 (Figure D-53~Figure D-55) Since the reliability level of the original bridge database was below the target reliability level at decompression limit state and maximum allowable tensile stress limit state, the bridges were redesigned using a live load factor of 1.0. Please note that only the live load factor of Service III limit state is increased from 0.8 to 1.0, dead load and resistance factors were kept the same during the redesign. Table D-84 shows the design outcomes of the redesigned bridges. Figure D-53 through Figure D-55 show the reliability indices for the redesigned bridges using live load factor of 1.0. It is observed that the average reliability index of decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 1.33, 1.7, and 3.32, respectively. D-121
Figure D-53 Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=1.0 ( 0.0948t cf f â²= ) Figure D-54 Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=5000), γLL=1.0 ( 0.0948t cf f â²= ) D-122
Figure D-55 Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=5000), γLL=1.0 ( 0.0948t cf f â²= ) Step 4: Propose new live load, dead load, and/or resistance factors Based on the calibration process shown in step 1 through step 3, it is observed that the uniform target reliability index can be achieved using a live load factor of 1.0. Therefore, for ADTT equal to 5000 and maximum concrete tensile stress of 0.0948t cf f â²= , a new live load factor of 1.0 is proposed. D.3.4.3.2 Bridges Designed for Maximum Concrete Tensile Stress of 0.158t cf f â²= In this section, the calibration for a selected bridge database (shown in Table D-85) is performed for ADTT equal to 5000 and maximum concrete tensile stress of 0.158t cf f â²= . Please note that the allowable maximum crack width of 0.016 in is applied for maximum allowable crack width limit state. Step 1: Calculate the reliability level of designs according to AASHTO LRFD Specifications (2010) (Figure D-56~Figure D-58) Figure D-56 through Figure D-58 show the reliability indices for the bridges designed using AASHTO type girders according to AASHTO LRFD specifications (2010). It is observed that the average reliability index for decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 0.80, 1.14, and 2.91, respectively, which does not satisfy the proposed target reliability index of 1.0 for decompression limit state and 1.25 for maximum allowable tensile stress limit state. Therefore, a larger live load factor will be used to modify the original design in order to improve the reliability level of the bridges. D-123
Figure D-56 Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=0.8 ( 0.158t cf f â²= ) Figure D-57 Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=5000), γLL=0.8 ( 0.158t cf f â²= ) D-124
Figure D-58 Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=5000), γLL=0.8 ( 0.158t cf f â²= ) Step 2: Redesign the bridges with live load factor of 1.0 (Figure D-59~Figure D-61) Since the reliability level of the original bridge database was below the target reliability level at decompression limit state and maximum allowable tensile stress limit state, the bridges were redesigned using a live load factor of 1.0. Please note that only the live load factor of Service III limit state is increased from 0.8 to 1.0, dead load and resistance factors were kept the same during the redesign. Table D-86 shows the design outcomes of the redesigned bridges. Figure D-59 through Figure D-61 show the reliability indices for the redesigned bridges using live load factor of 1.0. It is observed that the average reliability index of decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 1.07, 1.44, and 3.26, respectively. D-125
Figure D-59 Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=1.0 ( 0.158t cf f â²= ) Figure D-60 Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=5000), γLL=1.0 ( 0.158t cf f â²= ) D-126
Figure D-61 Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=5000), γLL=1.0 ( 0.158t cf f â²= ) Step 4: Propose new live load, dead load, and/or resistance factors Based on the calibration process shown in step 1 through step 3, it is observed that the uniform target reliability index can be achieved using a live load factor of 1.0. Therefore, for ADTT equal to 5000 and maximum concrete tensile stress of 0.158t cf f â²= , a new live load factor of 1.0 is proposed. D.3.4.3.3 Bridges Designed for Maximum Concrete Tensile Stress of 0.19t cf f â²= In this section, the calibration for a selected bridge database (shown in Table D-87) is performed for ADTT equal to 5000 and maximum concrete tensile stress of 0.19t cf f â²= . Please note that the allowable maximum crack width of 0.016 in is applied for maximum allowable crack width limit state. Step 1: Calculate the reliability level of designs according to AASHTO LRFD Specifications (2010) (Figure D-62~Figure D-64) Figure D-62 through Figure D-64 show the reliability indices for the bridges designed using AASHTO type girders according to AASHTO LRFD specifications (2010). It is observed that the average reliability index for decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 0.68, 1.1, and 2.82, respectively, which does not satisfy the proposed target reliability index of 1.0 for decompression limit state and 1.25 for maximum allowable tensile stress limit state. Therefore, a larger live load factor will be used to modify the original design in order to improve the reliability level of the bridges. D-127
Figure D-62 Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=0.8 ( 0.19t cf f â²= ) Figure D-63 Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=5000), γLL=0.8 ( 0.19t cf f â²= ) D-128
Figure D-64 Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=5000), γLL=0.8 ( 0.19t cf f â²= ) Step 2: Redesign the bridges with live load factor of 1.0 (Figure D-65~Figure D-67) Since the reliability level of the original bridge database was below the target reliability level at decompression limit state and maximum allowable tensile stress limit state, the bridges were redesigned using a live load factor of 1.0. Please note that only the live load factor of Service III limit state is increased from 0.8 to 1.0, dead load and resistance factors were kept the same during the redesign. Table D-88 shows the design outcomes of the redesigned bridges. Figure D-65 through Figure D-67 show the reliability indices for the redesigned bridges using live load factor of 1.0. It is observed that the average reliability index of decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 1.00, 1.41, and 3.14, respectively. D-129
Figure D-65 Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=1.0 ( 0.19t cf f â²= ) Figure D-66 Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=5000), γLL=1.0 ( 0.19t cf f â²= ) D-130
Figure D-67 Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=5000), γLL=1.0 ( 0.19t cf f â²= ) Step 4: Propose new live load, dead load, and/or resistance factors Based on the calibration process shown in step 1 through step 3, it is observed that the uniform target reliability index can be achieved using a live load factor of 1.0. Therefore, for ADTT equal to 5000 and maximum concrete tensile stress of 0.19t cf f â²= , a new live load factor of 1.0 is proposed. D.3.4.3.4 Bridges Designed for Maximum Concrete Tensile Stress of 0.253t cf f â²= In this section, the calibration for a selected bridge database (shown in Table D-89) is performed for ADTT equal to 5000 and maximum concrete tensile stress of 0.253t cf f â²= . Please note that the allowable maximum crack width of 0.016 in is applied for maximum allowable crack width limit state. Step 1: Calculate the reliability level of designs according to AASHTO LRFD Specifications (2010) (Figure D-68~Figure D-70) Figure D-68 through Figure D-70 show the reliability indices for the bridges designed using AASHTO type girders according to AASHTO LRFD specifications (2010). It is observed that the average reliability index for decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 0.06, 0.44, and 2.72, respectively, which does not satisfy the proposed target reliability index of 1.0 for decompression limit state and 1.25 for maximum allowable tensile stress limit state. Therefore, a larger live load factor will be used to modify the original design in order to improve the reliability level of the bridges. D-131
Figure D-68 Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=0.8 ( 0.253t cf f â²= ) Figure D-69 Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=5000), γLL=0.8 ( 0.253t cf f â²= ) D-132
Figure D-70 Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=5000), γLL=0.8 ( 0.253t cf f â²= ) Step 2: Redesign the bridges with live load factor of 1.0 (Figure D-71~Figure D-73) Since the reliability level of the original bridge database was below the target reliability level at decompression limit state and maximum allowable tensile stress limit state, the bridges were redesigned using a live load factor of 1.0. Please note that only the live load factor of Service III limit state is increased from 0.8 to 1.0, dead load and resistance factors were kept the same during the redesign. Table D-90 shows the design outcomes of the redesigned bridges. Figure D-71 through Figure D-73 show the reliability indices for the redesigned bridges using live load factor of 1.0. It is observed that the average reliability index of decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 0.85, 1.23, and 2.92, respectively. D-133
Figure D-71 Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=1.0 ( 0.253t cf f â²= ) Figure D-72 Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=5000), γLL=1.0 ( 0.253t cf f â²= ) D-134
Figure D-73 Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=5000), γLL=1.0 ( 0.253t cf f â²= ) Step 4: Propose new live load, dead load, and/or resistance factors Based on the calibration process shown in step 1 through step 3, it is observed that the uniform target reliability index can be achieved using a live load factor of 1.0. Therefore, for ADTT equal to 5000 and maximum concrete tensile stress of 0.253t cf f â²= , a new live load factor of 1.0 is proposed. D.3.4.4 Calibration Procedure for ADTT=10000 D.3.4.4.1 Bridges Designed for Maximum Concrete Tensile Stress of 0.0948t cf f â²= In this section, the calibration for a selected bridge database (shown in Table D-83) is performed for ADTT equal to 10000 and maximum concrete tensile stress of 0.0948t cf f â²= . Please note that the allowable maximum crack width of 0.016 in is applied for maximum allowable crack width limit state. Step 1: Calculate the reliability level of designs according to AASHTO LRFD Specifications (2010) (Figure D-74~Figure D-76) Figure D-74 through Figure D-76 show the reliability indices for the bridges designed using AASHTO type girders according to AASHTO LRFD specifications (2010). It is observed that the average reliability index for decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 0.94, 1.30, and 3.00, respectively. Live load factor of 1.0 will be used in the next step. D-135
Figure D-74 Reliability Indices for Bridges at Decompression Limit State (ADTT=10000), γLL=0.8 ( 0.0948t cf f â²= ) Figure D-75 Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=10000), γLL=0.8 ( 0.0948t cf f â²= ) D-136
Figure D-76 Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=10000), γLL=0.8 ( 0.0948t cf f â²= ) Step 2: Redesign the bridges with live load factor of 1.0 (Figure D-77~Figure D-79) Since the reliability level of the original bridge database was below the target reliability level at decompression limit state and maximum allowable tensile stress limit state, the bridges were redesigned using a live load factor of 1.0. Please note that only the live load factor of Service III limit state is increased from 0.8 to 1.0, dead load and resistance factors were kept the same during the redesign. Table D-84 shows the design outcomes of the redesigned bridges. Figure D-77 through Figure D-79 show the reliability indices for the redesigned bridges using live load factor of 1.0. It is observed that the average reliability index of decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 1.32, 1.66, and 3.28, respectively. D-137
Figure D-77 Reliability Indices for Bridges at Decompression Limit State (ADTT=10000), γLL=1.0 ( 0.0948t cf f â²= ) Figure D-78 Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=10000), γLL=1.0 ( 0.0948t cf f â²= ) D-138
Figure D-79 Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=10000), γLL=1.0 ( 0.0948t cf f â²= ) Step 4: Propose new live load, dead load, and/or resistance factors Based on the calibration process shown in step 1 through step 3, it is observed that the uniform target reliability index can be achieved using a live load factor of 1.0. Therefore, for ADTT equal to 10000 and maximum concrete tensile stress of 0.0948t cf f â²= , a new live load factor of 1.0 is proposed. D.3.4.4.2 C6.4.2 Bridges Designed for Maximum Concrete Tensile Stress of 0.158t cf f â²= In this section, the calibration for a selected bridge database (shown in Table D-85) is performed for ADTT equal to 10000 and maximum concrete tensile stress of 0.158t cf f â²= . Please note that the allowable maximum crack width of 0.016 in is applied for maximum allowable crack width limit state. Step 1: Calculate the reliability level of designs according to AASHTO LRFD Specifications (2010) (Figure D-80~Figure D-82) Figure D-80 through Figure D-82 show the reliability indices for the bridges designed using AASHTO type girders according to AASHTO LRFD specifications (2010). It is observed that the average reliability index for decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 0.76, 1.11, and 2.85, respectively, which does not satisfy the proposed target reliability index of 1.0 for decompression limit state and 1.25 for maximum allowable tensile stress limit state. Therefore, a larger live load factor D-139
will be used to modify the original design in order to improve the reliability level of the bridges. Figure D-80 Reliability Indices for Bridges at Decompression Limit State (ADTT=10000), γLL=0.8 ( 0.158t cf f â²= ) Figure D-81 Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=10000), γLL=0.8 ( 0.158t cf f â²= ) D-140
Figure D-82 Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=10000), γLL=0.8 ( 0.158t cf f â²= ) Step 2: Redesign the bridges with live load factor of 1.0 (Figure D-83~Figure D-85) Since the reliability level of the original bridge database was below the target reliability level at decompression limit state and maximum allowable tensile stress limit state, the bridges were redesigned using a live load factor of 1.0. Please note that only the live load factor of Service III limit state is increased from 0.8 to 1.0, dead load and resistance factors were kept the same during the redesign. Table D-86 shows the design outcomes of the redesigned bridges. Figure D-83 through Figure D-85 show the reliability indices for the redesigned bridges using live load factor of 1.0. It is observed that the average reliability index of decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 1.04, 1.40, and 3.22, respectively. D-141
Figure D-83 Reliability Indices for Bridges at Decompression Limit State (ADTT=10000), γLL=1.0 ( 0.158t cf f â²= ) Figure D-84 Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=10000), γLL=1.0 ( 0.158t cf f â²= ) D-142
Figure D-85 Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=10000), γLL=1.0 ( 0.158t cf f â²= ) Step 4: Propose new live load, dead load, and/or resistance factors Based on the calibration process shown in step 1 through step 3, it is observed that the uniform target reliability index can be achieved using a live load factor of 1.0. Therefore, for ADTT equal to 10000 and maximum concrete tensile stress of 5t cf f â²= , a new live load factor of 1.0 is proposed. D.3.4.4.3 Bridges Designed for Maximum Concrete Tensile Stress of 0.19t cf f â²= In this section, the calibration for a selected bridge database (shown in Table D-87) is performed for ADTT equal to 10000 and maximum concrete tensile stress of 0.19t cf f â²= . Please note that the allowable maximum crack width of 0.016 in is applied for maximum allowable crack width limit state. Step 1: Calculate the reliability level of designs according to AASHTO LRFD Specifications (2010) (Figure D-86~Figure D-88) Figure D-86 through Figure D-88 show the reliability indices for the bridges designed using AASHTO type girders according to AASHTO LRFD specifications (2010). It is observed that the average reliability index for decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 0.64, 1.07, and 2.78, respectively, which does not satisfy the proposed target reliability index of 1.0 for decompression limit state and 1.25 for maximum allowable tensile stress limit state. Therefore, a larger live load factor will be used to modify the original design in order to improve the reliability level of the bridges. D-143
Figure D-86 Reliability Indices for Bridges at Decompression Limit State (ADTT=10000), γLL=0.8 ( 0.19t cf f â²= ) Figure D-87 Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=10000), γLL=0.8 ( 0.19t cf f â²= ) D-144
Figure D-88 Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=10000), γLL=0.8 ( 0.19t cf f â²= ) Step 2: Redesign the bridges with live load factor of 1.0 (Figure D-89~Figure D-91) Since the reliability level of the original bridge database was below the target reliability level at decompression limit state and maximum allowable tensile stress limit state, the bridges were redesigned using a live load factor of 1.0. Please note that only the live load factor of Service III limit state is increased from 0.8 to 1.0, dead load and resistance factors were kept the same during the redesign. Table D-88 shows the design outcomes of the redesigned bridges. Figure D-89 through Figure D-91 show the reliability indices for the redesigned bridges using live load factor of 1.0. It is observed that the average reliability index of decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 0.98, 1.34, and 3.11, respectively. D-145
Figure D-89 Reliability Indices for Bridges at Decompression Limit State (ADTT=10000), γLL=1.0 ( 0.19t cf f â²= ) Figure D-90 Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=10000), γLL=1.0 ( 0.19t cf f â²= ) D-146
Figure D-91 Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=10000), γLL=1.0 ( 0.19t cf f â²= ) Step 4: Propose new live load, dead load, and/or resistance factors Based on the calibration process shown in step 1 through step 3, it is observed that the uniform target reliability index can be achieved using a live load factor of 1.0. Therefore, for the scenario of ADTT equal to 10000 and maximum concrete tensile stress of 0.19t cf f â²= , a new live load factor of 1.0 is proposed. D.3.4.4.4 Bridges Designed for Maximum Concrete Tensile Stress of 0.253t cf f â²= In this section, the calibration for a selected bridge database (shown in Table D-89) is performed for ADTT equal to 10000 and maximum concrete tensile stress of 0.253t cf f â²= . Please note that the allowable maximum crack width of 0.016 in is applied for maximum allowable crack width limit state. Step 1: Calculate the reliability level of designs according to AASHTO LRFD Specifications (2010) (Figure D-92~Figure D-94) Figure D-92 through Figure D-94 show the reliability indices for the bridges designed using AASHTO type girders according to AASHTO LRFD specifications (2010). It is observed that the average reliability index for decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 0.02, 0.41, and 2.66, respectively, which does not satisfy the proposed target reliability index of 1.0 for decompression limit state and 1.25 for maximum allowable tensile stress limit state. Therefore, a larger live load factor will be used to modify the original design in order to improve the reliability level of the bridges. D-147
Figure D-92 Reliability Indices for Bridges at Decompression Limit State (ADTT=10000), γLL=0.8 ( 0.253t cf f â²= ) Figure D-93 Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=10000), γLL=0.8 ( 0.253t cf f â²= ) D-148
Figure D-94 Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=10000), γLL=0.8 ( 0.253t cf f â²= ) Step 2: Redesign the bridges with live load factor of 1.0 (Figure D-95~Figure D-97) Since the reliability level of the original bridge database was below the target reliability level at decompression limit state and maximum allowable tensile stress limit state, the bridges were redesigned using a live load factor of 1.0. Please note that only the live load factor of Service III limit state is increased from 0.8 to 1.0, dead load and resistance factors were kept the same during the redesign. Table D-90 shows the design outcomes of the redesigned bridges. Figure D-95 through Figure D-97 show the reliability indices for the redesigned bridges using live load factor of 1.0. It is observed that the average reliability index of decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 0.82, 1.20, and 2.88, respectively. D-149
Figure D-95 Reliability Indices for Bridges at Decompression Limit State (ADTT=10000), γLL=1.0 ( 0.253t cf f â²= ) Figure D-96 Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=10000), γLL=1.0 ( 0.253t cf f â²= ) D-150
Figure D-97 Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=10000), γLL=1.0 ( 0.253t cf f â²= ) Step 4: Propose new live load, dead load, and/or resistance factors Based on the calibration process shown in step 1 through step 3, it is observed that the uniform target reliability index can be achieved using a live load factor of 1.0. Therefore, for the scenario of ADTT equal to 10000 and maximum concrete tensile stress of 0.253t cf f â²= , a new live load factor of 1.0 is proposed. D.4 Calibration for Other Types of Girders D.4.1 Reliability indices of girders designed for various design criteria (Adjacent Box Girders) In this section, the reliability analysis was performed for adjacent box girders that designed for various design criteria with compressive strength of 8000 psi. The scenario of ADTT equals to 5000 was considered in this section. D.4.1.1 Bridges Designed for Maximum Concrete Tensile Stress of 0.0948âðâ²ð In this section, the calibration process for a selected bridge database (shown in Table D-91) is performed. D-151
Table D-91 Summary Information of Bridges Designed with γLL=0.8 ( 0.0948t cf f â²= ) Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 3 1.224 8 2 BI-48 30 4 1.224 8 3 BI-36 60 3 2.754 18 4 BI-48 60 4 3.06 20 5 BII-36 80 3 3.672 24 6 BI-48 80 4 5.202 34 7 BIII-36 100 3 4.59 30 8 BII-48 100 4 6.732 44 9 BIV-36 120 3 6.426 42 10 BIII-48 120 4 8.262 54 Step 1: Calculate the reliability level of designs according to AASHTO LRFD Specifications (2010) (Figure D-98~Figure D-100) Figure D-98 through Figure D-100 show the reliability indices for the bridges designed using AASHTO type girders according to AASHTO LRFD specifications (2010). It is observed that the average reliability index for decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 1.66, 2.0, and 4.83, respectively. A larger live load factor will be used to estimate the effect of changing live load factor on reliability level of structure. Figure D-98 Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=0.8 ( 0.0948t cf f â²= ) D-152
Figure D-99 Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=5000), γLL=0.8 ( 0.0948t cf f â²= ) Figure D-100 Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=5000), γLL=0.8 ( 0.0948t cf f â²= ) Step 2: Redesign the bridges with live load factor of 1.0 (Figure D-101~Figure D-103) In this step, the bridges have been redesigned using a live load factor of 1.0. Please note that only the live load factor of Service III limit state is increased from 0.8 to 1.0, dead load and resistance factors were kept the same during the redesign. Table D-92 shows the design outcomes of the redesigned bridges. D-153
Figure D-101 through Figure D-103 shows the reliability indices for the redesigned bridges using live load factor of 1.0. It is observed the average reliability index of decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 1.85, 2.18, and 4.96, respectively. Table D-92 Summary Information of Bridges Designed with γLL=1.0 ( 0.0948t cf f â²= ) Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 3 1.224 8 2 BI-48 30 4 1.53 10 3 BI-36 60 3 2.754 18 4 BI-48 60 4 3.366 22 5 BII-36 80 3 3.672 24 6 BI-48 80 4 5.814 38 7 BIII-36 100 3 4.896 32 8 BII-48 100 4 7.038 46 9 BIV-36 120 3 6.732 44 10 BIII-48 120 4 8.874 58 Figure D-101 Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=1.0 ( 0.0948t cf f â²= ) D-154
Figure D-102 Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=5000), γLL=1.0 ( 0.0948t cf f â²= ) Figure D-103 Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=5000), γLL=1.0 ( 0.0948t cf f â²= ) Step 3: Propose new live load, dead load, and/or resistance factors Based on the calibration process shown in step 1 through step 3, it is observed that the uniform target reliability index can be achieved using a live load factor of 1.0. Therefore, for the scenario of ADTT equal to 5000 and maximum concrete tensile stress of 0.0948t cf f â²= , a new live load factor of 1.0 is proposed. D-155
D.4.1.2 C7.2 Bridges Designed for Maximum Concrete Tensile Stress of 0.158âðâ²ð In this section, the calibration process for a selected bridge database (shown in Table D-93) is performed. Table D-93 Summary Information of Bridges Designed with γLL=0.8 ( 0.158t cf f â²= ) Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 3 0.918 6 2 BI-48 30 4 0.918 6 3 BI-36 60 3 2.448 16 4 BI-48 60 4 2.754 18 5 BII-36 80 3 3.366 22 6 BI-48 80 4 4.896 32 7 BIII-36 100 3 4.284 28 8 BII-48 100 4 6.12 40 9 BIV-36 120 3 5.814 38 10 BIII-48 120 4 7.65 50 Step 1: Calculate the reliability level of designs according to AASHTO LRFD Specifications (2010) (Figure D-104~Figure D-106) Figure D-104 through Figure D-106 show the reliability indices for the bridges designed using AASHTO type girders according to AASHTO LRFD specifications (2010). It is observed that the average reliability index for decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 1.12, 1.45, and 4.41, respectively. Live load factor of 1.0 will be used in next step. D-156
Figure D-104 Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=0.8 ( 0.158t cf f â²= ) Figure D-105 Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=5000), γLL=0.8 ( 0.158t cf f â²= ) D-157
Figure D-106 Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=5000), γLL=0.8 ( 0.158t cf f â²= ) Step 2: Redesign the bridges with live load factor of 1.0 (Figure D-107~Figure D-109) The bridges have been redesigned using a live load factor of 1.0. Please note that only the live load factor of Service III limit state is increased from 0.8 to 1.0, dead load and resistance factors were kept the same during the redesign. Table D-94 shows the design outcomes of the redesigned bridges. Figure D-107 through Figure D-109 show the reliability indices for the redesigned bridges using live load factor of 1.0. It is observed that the average reliability index of decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 1.39, 1.75, and 4.62, respectively. Table D-94 Summary Information of Bridges Designed with γLL=1.0 ( 0.158t cf f â²= ) Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 3 0.918 6 2 BI-48 30 4 0.918 6 3 BI-36 60 3 2.448 16 4 BI-48 60 4 3.06 20 5 BII-36 80 3 3.366 22 6 BI-48 80 4 5.508 36 7 BIII-36 100 3 4.59 30 8 BII-48 100 4 6.732 44 9 BIV-36 120 3 6.12 40 10 BIII-48 120 4 8.262 54 D-158
Figure D-107 Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=1.0 ( 0.158t cf f â²= ) Figure D-108 Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=5000), γLL=1.0 ( 0.158t cf f â²= ) D-159
Figure D-109 Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=5000), γLL=1.0 ( 0.158t cf f â²= ) Step 3: Propose new live load, dead load, and/or resistance factors Based on the calibration process shown in step 1 through step 3, it is observed that the uniform target reliability index can be achieved using a live load factor of 1.0. Therefore, for the scenario of ADTT equal to 5000 and maximum concrete tensile stress of 0.158t cf f â²= , a new live load factor of 1.0 is proposed. D.4.1.3 Bridges Designed for Maximum Concrete Tensile Stress of 0.19âðâ²ð In this section, the calibration process for a selected bridge database (shown in Table D-95) is performed for the scenario of ADTT equal to 5000. Table D-95 Summary Information of Bridges Designed with γLL=0.8 ( 0.19t cf f â²= ) Cases Section Type Span Length(ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 3 0.918 6 2 BI-48 30 4 0.918 6 3 BI-36 60 3 2.448 16 4 BI-48 60 4 2.754 18 5 BII-36 80 3 3.06 20 6 BI-48 80 4 4.896 32 7 BIII-36 100 3 4.284 28 8 BII-48 100 4 6.12 40 9 BIV-36 120 3 5.814 38 10 BIII-48 120 4 7.344 48 D-160
Step 1: Calculate the reliability level of designs according to AASHTO LRFD Specifications (2010) (Figure D-110~Figure D-112) Figure D-110 through Figure D-112 show the reliability indices for the bridges designed using AASHTO type girders according to AASHTO LRFD specifications (2010). It is observed that the average reliability index for decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 1.06, 1.34, and 4.37, respectively. Since the reliability indices are lower than target reliability index, live load factor of 1.0 will be used in next step. Figure D-110 Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=0.8 ( 0.19t cf f â²= ) D-161
Figure D-111 Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=5000), γLL=0.8 ( 0.19t cf f â²= ) Figure D-112 Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=5000), γLL=0.8 ( 0.19t cf f â²= ) Step 2: Redesign the bridges with live load factor of 1.0 (Figure D-113~Figure D-115) The bridges have been redesigned using a live load factor of 1.0. Please note that only the live load factor of Service III limit state is increased from 0.8 to 1.0, dead load and resistance factors were kept the same during the redesign. Table D-96 shows the design outcomes of the redesigned bridges. D-162
Figure 116 through Figure 118 show the reliability indices for the redesigned bridges using live load factor of 1.0. It is observed that the average reliability index of decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 1.31, 1.55, and 4.56, respectively. Table D-96 Summary Information of Bridges Designed with γLL=1.0 ( 0.19t cf f â²= ) Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 3 0.918 6 2 BI-48 30 4 0.918 6 3 BI-36 60 3 2.448 16 4 BI-48 60 4 3.06 20 5 BII-36 80 3 3.366 22 6 BI-48 80 4 5.202 34 7 BIII-36 100 3 4.284 28 8 BII-48 100 4 6.426 42 9 BIV-36 120 3 6.12 40 10 BIII-48 120 4 7.956 52 Figure D-113 Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=1.0 ( 0.19t cf f â²= ) D-163
Figure D-114 Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=5000), γLL=1.0 ( 0.19t cf f â²= ) Figure D-115 Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=5000), γLL=1.0 ( 0.19t cf f â²= ) Step 3: Propose new live load, dead load, and/or resistance factors Based on the calibration process shown in step 1 through step 3, it is observed that the uniform target reliability index can be achieved using a live load factor of 1.0. Therefore, for the scenario of ADTT equal to 5000 and maximum concrete tensile stress of 0.19t cf f â²= , a new live load factor of 1.0 is proposed. D-164
D.4.1.4 Bridges Designed for Maximum Concrete Tensile Stress of 0.253âðâ²ð In this section, the calibration for a selected bridge database (shown in Table D-97) is performed for a scenario of ADTT equal to 5000. Please note that the maximum allowable crack width is specified as 0.016 in for maximum allowable crack width limit state. Step 1: Calculate the reliability level of designs according to AASHTO LRFD Specifications (2010) (Figure D-116~Figure D-118) Figure D-116 through Figure D-118 show the reliability indices for the bridges designed using AASHTO type girders according to AASHTO LRFD specifications (2010). It is observed that the average reliability index for decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 0.68, 0.86, and 4.14, respectively. Live load factor of 1.0 will be used to estimate the effect of changing live load factor on reliability level. Table D-97 Summary Information of Bridges Designed with γLL=0.8 ( 0.253t cf f â²= ) Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 3 0.612 4 2 BI-48 30 4 0.612 4 3 BI-36 60 3 2.142 14 4 BI-48 60 4 2.448 16 5 BII-36 80 3 3.06 20 6 BI-48 80 4 4.59 30 7 BIII-36 100 3 3.978 26 8 BII-48 100 4 5.814 38 9 BIV-36 120 3 5.508 36 10 BIII-48 120 4 7.038 46 D-165
Figure D-116 Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=0.8 ( 0.253t cf f â²= ) Figure D-117 Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=5000), γLL=0.8 ( 0.253t cf f â²= ) D-166
Figure D-118 Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=5000), γLL=0.8 ( 0.253t cf f â²= ) Step 2: Redesign the bridges with live load factor of 1.0 (Figure D-119~Figure D-121) In this step, the bridges were redesigned using a live load factor of 1.0. Please note that only the live load factor of Service III limit state is increased from 0.8 to 1.0, dead load and resistance factors were kept the same during the redesign. Table D-98 shows the design outcomes of the redesigned bridges. Figure D-119 through Figure D-121 show the reliability indices for the redesigned bridges using a live load factor of 1.0. It is observed that the average reliability index for the decompression limit state, the maximum allowable tensile stress limit state and the maximum allowable crack width limit state is 0.76, 1.17, and 4.18, respectively. Table D-98 Summary Information of Bridges Designed with γLL=1.0 ( 0.253t cf f â²= ) Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 3 0.612 4 2 BI-48 30 4 0.612 4 3 BI-36 60 3 2.142 14 4 BI-48 60 4 2.754 18 5 BII-36 80 3 3.06 20 6 BI-48 80 4 4.896 32 7 BIII-36 100 3 3.978 26 8 BII-48 100 4 6.12 40 9 BIV-36 120 3 5.814 38 10 BIII-48 120 4 7.344 48 D-167
Figure D-119 Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=1.0 ( 0.253t cf f â²= ) Figure D-120 Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=5000), γLL=1.0 ( 0.253t cf f â²= ) D-168
Figure D-121 Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=5000), γLL=1.0 ( 0.253t cf f â²= ) Step 3: Propose new live load, dead load, and/or resistance factors Based on the calibration process shown in step 1 through step 3, it is observed that the uniform target reliability index can be achieved using a live load factor of 1.0. Therefore, for the scenario of ADTT equal to 5000 and maximum concrete tensile stress of 0.253t cf f â²= , a new live load factor of 1.0 is proposed. D.4.2 Reliability indices of girders designed for various design criteria (Spread Box Girders) In this section, the reliability analysis was performed for spread box girders that designed for various design criteria with compressive strength of 8000 psi. The scenario of ADTT equals to 5000 was considered in this section. D.4.2.1 Bridges Designed for Maximum Concrete Tensile Stress of 0.0948âðâ²ð In this section, the calibration process for a selected bridge database (shown in Table D-99) is performed. D-169
Table D-99 Summary Information of Bridges Designed with γLL=0.8 ( 0.0948t cf f â²= ) Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in 2) # of Strands 1 BI-36 30 6 1.53 10 2 BI-36 30 8 1.836 12 3 BI-36 30 10 1.836 12 4 BI-36 30 12 2.142 14 5 BI-36 60 6 3.978 26 6 BI-36 60 8 4.896 32 7 BI-36 60 10 5.508 36 8 BI-48 60 12 6.426 42 9 BI-48 80 6 7.038 46 10 BII-48 80 8 6.732 44 11 BII-48 80 10 7.65 50 12 BIII-48 80 12 7.038 46 13 BIII-48 100 6 7.344 48 14 BIII-48 100 8 9.18 60 15 BIV-48 100 10 10.404 68 Step 1: Calculate the reliability level of designs according to AASHTO LRFD Specifications (2010) (Figure D-122~Figure D-124) Figure D-122 through Figure D-124 show the reliability indices for the bridges designed using AASHTO type girders according to AASHTO LRFD specifications (2010). It is observed that the average reliability index for decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 1.36, 1.70, and 4.53, respectively. A larger live load factor will be used to estimate the effect of changing live load factor on reliability level of structure. D-170
Figure D-122 Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=0.8 ( 0.0948t cf f â²= ) Figure D-123 Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=5000), γLL=0.8 ( 0.0948t cf f â²= ) D-171
Figure D-124 Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=5000), γLL=0.8 ( 0.0948t cf f â²= ) Step 2: Redesign the bridges with live load factor of 1.0 (Figure D-125~Figure D-127) In this step, the bridges have been redesigned using a live load factor of 1.0. Please note that only the live load factor of Service III limit state is increased from 0.8 to 1.0, dead load and resistance factors were kept the same during the redesign. Table D-100 shows the design outcomes of the redesigned bridges. Figure D-125 through Figure D-127 shows the reliability indices for the redesigned bridges using live load factor of 1.0. It is observed the average reliability index of decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 1.45, 1.78, and 4.66, respectively. D-172
Table D-100 Summary Information of Bridges Designed with γLL=1.0 ( 0.0948t cf f â²= ) Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 6 1.53 10 2 BI-36 30 8 1.836 12 3 BI-36 30 10 2.142 14 4 BI-36 30 12 2.142 14 5 BI-36 60 6 4.284 28 6 BI-36 60 8 5.202 34 7 BI-36 60 10 6.426 42 8 BI-48 60 12 7.038 46 9 BI-48 80 6 7.65 50 10 BII-48 80 8 7.344 48 11 BII-48 80 10 8.874 58 12 BIII-48 80 12 7.956 52 13 BIII-48 100 6 7.956 52 14 BIII-48 100 8 - - 15 BIV-48 100 10 - - Figure D-125 Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=1.0 ( 0.0948t cf f â²= ) D-173
Figure D-126 Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=5000), γLL=1.0 ( 0.0948t cf f â²= ) Figure D-127 Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=5000), γLL=1.0 ( 0.0948t cf f â²= ) Step 3: Propose new live load, dead load, and/or resistance factors Based on the calibration process shown in step 1 through step 3, it is observed that the uniform target reliability index can be achieved using a live load factor of 1.0. Therefore, for the scenario of ADTT equal to 5000 and maximum concrete tensile stress of 0.0948t cf f â²= , a new live load factor of 1.0 is proposed. D-174
D.4.2.2 Bridges Designed for Maximum Concrete Tensile Stress of 0.158âðâ²ð In this section, the calibration process for a selected bridge database (shown in Table D-101) is performed. Table D-101 Summary Information of Bridges Designed with γLL=0.8 ( 0.158t cf f â²= ) Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 6 1.224 8 2 BI-36 30 8 1.53 10 3 BI-36 30 10 1.836 12 4 BI-36 30 12 1.836 12 5 BI-36 60 6 3.672 24 6 BI-36 60 8 4.59 30 7 BI-36 60 10 5.202 34 8 BI-48 60 12 5.814 38 9 BI-48 80 6 6.732 44 10 BII-48 80 8 6.12 40 11 BII-48 80 10 7.344 48 12 BIII-48 80 12 6.732 44 13 BIII-48 100 6 7.038 46 14 BIII-48 100 8 8.262 54 15 BIV-48 100 10 9.18 60 Step 1: Calculate the reliability level of designs according to AASHTO LRFD Specifications (2010) (Figure D-128~Figure D-130) Figure D-128 through Figure D-130 show the reliability indices for the bridges designed using AASHTO type girders according to AASHTO LRFD specifications (2010). It is observed that the average reliability index for decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 0.82, 1.15, and 4.11, respectively. Live load factor of 1.0 will be used in next step. D-175
Figure D-128 Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=0.8 ( 0.158t cf f â²= ) Figure D-129 Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=5000), γLL=0.8 ( 0.158t cf f â²= ) D-176
Figure D-130 Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=5000), γLL=0.8 ( 0.158t cf f â²= ) Step 2: Redesign the bridges with live load factor of 1.0 (Figure D-131~Figure D-133) The bridges have been redesigned using a live load factor of 1.0. Please note that only the live load factor of Service III limit state is increased from 0.8 to 1.0, dead load and resistance factors were kept the same during the redesign. Table D-102 shows the design outcomes of the redesigned bridges. Figure D-131 through Figure D-133 show the reliability indices for the redesigned bridges using live load factor of 1.0. It is observed that the average reliability index of decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 1.09, 1.45, and 4.32, respectively. D-177
Table D-102 Summary Information of Bridges Designed with γLL=1.0 ( 0.158t cf f â²= ) Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 6 1.53 10 2 BI-36 30 8 1.53 10 3 BI-36 30 10 1.836 12 4 BI-36 30 12 2.142 14 5 BI-36 60 6 4.284 28 6 BI-36 60 8 4.896 32 7 BI-36 60 10 5.814 38 8 BI-48 60 12 6.732 44 9 BI-48 80 6 7.344 48 10 BII-48 80 8 6.732 44 11 BII-48 80 10 7.956 52 12 BIII-48 80 12 7.344 48 13 BIII-48 100 6 7.344 48 14 BIII-48 100 8 9.792 64 15 BIV-48 100 10 - - Figure D-131 Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=1.0 ( 0.158t cf f â²= ) D-178
Figure D-132 Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=5000), γLL=1.0 ( 0.158t cf f â²= ) Figure D-133 Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=5000), γLL=1.0 ( 0.158t cf f â²= ) Step 3: Propose new live load, dead load, and/or resistance factors Based on the calibration process shown in step 1 through step 3, it is observed that the uniform target reliability index can be achieved using a live load factor of 1.0. D-179
Therefore, for the scenario of ADTT equal to 5000 and maximum concrete tensile stress of 0.158t cf f â²= , a new live load factor of 1.0 is proposed. D.4.2.3 Bridges Designed for Maximum Concrete Tensile Stress of 0.19âðâ²ð In this section, the calibration process for a selected bridge database (shown in Table D-103) is performed for the scenario of ADTT equal to 5000. Table D-103 Summary Information of Bridges Designed with γLL=0.8 ( 0.19t cf f â²= ) Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 6 1.224 8 2 BI-36 30 8 1.53 10 3 BI-36 30 10 1.53 10 4 BI-36 30 12 1.836 12 5 BI-36 60 6 3.672 24 6 BI-36 60 8 4.284 28 7 BI-36 60 10 5.202 34 8 BI-48 60 12 5.814 38 9 BI-48 80 6 6.426 42 10 BII-48 80 8 6.12 40 11 BII-48 80 10 7.038 46 12 BIII-48 80 12 6.732 44 13 BIII-48 100 6 6.732 44 14 BIII-48 100 8 7.956 52 15 BIV-48 100 10 8.568 56 Step 1: Calculate the reliability level of designs according to AASHTO LRFD Specifications (2010) (Figure D-134~Figure D-136) Figure D-134 through Figure D-136 show the reliability indices for the bridges designed using AASHTO type girders according to AASHTO LRFD specifications (2010). It is observed that the average reliability index for decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 0.66, 0.94, and 4.01, respectively. Since the reliability indices are lower than target reliability index, live load factor of 1.0 will be used in next step. D-180
Figure D-134 Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=0.8 ( 0.19t cf f â²= ) Figure D-135 Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=5000), γLL=0.8 ( 0.19t cf f â²= ) D-181
Figure D-136 Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=5000), γLL=0.8 ( 0.19t cf f â²= ) Step 2: Redesign the bridges with live load factor of 1.0 (Figure D-137~Figure D-139) The bridges have been redesigned using a live load factor of 1.0. Please note that only the live load factor of Service III limit state is increased from 0.8 to 1.0, dead load and resistance factors were kept the same during the redesign. Table D-104 shows the design outcomes of the redesigned bridges. Figure D-137 through Figure D-139 show the reliability indices for the redesigned bridges using live load factor of 1.0. It is observed that the average reliability index of decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 1.01, 1.25, and 4.26, respectively. D-182
Table D-104 Summary Information of Bridges Designed with γLL=1.0 ( 0.19t cf f â²= ) Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 6 1.224 8 2 BI-36 30 8 1.53 10 3 BI-36 30 10 1.836 12 4 BI-36 30 12 1.836 12 5 BI-36 60 6 3.978 26 6 BI-36 60 8 4.896 32 7 BI-36 60 10 5.814 38 8 BI-48 60 12 6.426 42 9 BI-48 80 6 7.038 46 10 BII-48 80 8 6.732 44 11 BII-48 80 10 7.956 52 12 BIII-48 80 12 7.344 48 13 BIII-48 100 6 7.038 46 14 BIII-48 100 8 9.18 60 15 BIV-48 100 10 - - Figure D-137 Reliability Indices for Bridges at Decompression Limit State (ADTT=5000) γLL=1.0 ( 0.19t cf f â²= ) D-183
Figure D-138 Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=5000), γLL=1.0 ( 0.19t cf f â²= ) Figure D-139 Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=5000), γLL=1.0 ( 0.19t cf f â²= ) Step 3: Propose new live load, dead load, and/or resistance factors Based on the calibration process shown in step 1 through step 3, it is observed that the uniform target reliability index can be achieved using a live load factor of 1.0. Therefore, for the scenario of ADTT equal to 5000 and maximum concrete tensile stress of 0.19t cf f â²= , a new live load factor of 1.0 is proposed. D-184
D.4.2.4 Bridges Designed for Maximum Concrete Tensile Stress of 0.253âðâ²ð In this section, the calibration for a selected bridge database (shown in Table D-105) is performed for a scenario of ADTT equal to 5000. Please note that the maximum allowable crack width is specified as 0.016 in for maximum allowable crack width limit state. Step 1: Calculate the reliability level of designs according to AASHTO LRFD Specifications (2010) (Figure D-140~Figure D-142) Figure D-140 through Figure D-142 show the reliability indices for the bridges designed using AASHTO type girders according to AASHTO LRFD specifications (2010). It is observed that the average reliability index for decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 0.48, 0.66, and 3.94, respectively. Live load factor of 1.0 will be used to estimate the effect of changing live load factor on reliability level. Table D-105 Summary Information of Bridges Designed with γLL=0.8 ( 0.253t cf f â²= ) Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 6 0.918 6 2 BI-36 30 8 1.224 8 3 BI-36 30 10 1.53 10 4 BI-36 30 12 1.53 10 5 BI-36 60 6 3.366 22 6 BI-36 60 8 4.284 28 7 BI-36 60 10 4.896 32 8 BI-48 60 12 5.508 36 9 BI-48 80 6 6.12 40 10 BII-48 80 8 5.814 38 11 BII-48 80 10 6.732 44 12 BIII-48 80 12 6.12 40 13 BIII-48 100 6 6.426 42 14 BIII-48 100 8 7.65 50 15 BIV-48 100 10 7.956 52 D-185
Figure D-140 Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=0.8 ( 0.253t cf f â²= ) Figure D-141 Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=5000), γLL=0.8 ( 0.253t cf f â²= ) D-186
Figure D-142 Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=5000), γLL=0.8 ( 0.253t cf f â²= ) Step 2: Redesign the bridges with live load factor of 1.0 (Figure D-143~Figure D-145) In this step, the bridges were redesigned using a live load factor of 1.0. Please note that only the live load factor of Service III limit state is increased from 0.8 to 1.0, dead load and resistance factors were kept the same during the redesign. Table D-106 shows the design outcomes of the redesigned bridges. Figure D-143 through Figure D-145 show the reliability indices for the redesigned bridges using a live load factor of 1.0. It is observed that the average reliability index for the decompression limit state, the maximum allowable tensile stress limit state and the maximum allowable crack width limit state is 0.56, 0.87, and 4.08, respectively. D-187
Table D-106 Summary Information of Bridges Designed with γLL=1.0 ( 0.253t cf f â²= ) Cases Section Type Span Length (ft.) Spacing (ft.) Aps (in2) # of Strands 1 BI-36 30 6 1.224 8 2 BI-36 30 8 1.224 8 3 BI-36 30 10 1.53 10 4 BI-36 30 12 1.836 12 5 BI-36 60 6 3.672 24 6 BI-36 60 8 4.59 30 7 BI-36 60 10 5.508 36 8 BI-48 60 12 6.12 40 9 BI-48 80 6 6.732 44 10 BII-48 80 8 6.426 42 11 BII-48 80 10 7.344 48 12 BIII-48 80 12 6.732 44 13 BIII-48 100 6 6.732 44 14 BIII-48 100 8 8.568 56 15 BIV-48 100 10 8.874 58 Figure D-143 Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=1.0 ( 0.253t cf f â²= ) D-188
Figure D-144 Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=5000), γLL=1.0 ( 0.253t cf f â²= ) Figure D-145 Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=5000), γLL=1.0 ( 0.253t cf f â²= ) Step 3: Propose new live load, dead load, and/or resistance factors Based on the calibration process shown in step 1 through step 3, it is observed that the uniform target reliability index can be achieved using a live load factor of 1.0. Therefore, for the scenario of ADTT equal to 5000 and maximum concrete tensile stress of 0.253t cf f â²= , a new live load factor of 1.0 is proposed. D-189
D.4.3 Reliability indices of girders designed for various design criteria (ASBI Box Girder Bridges) In this section, the reliability analysis was performed for adjacent box girders that designed for various design criteria with compressive strength of 8000 psi. The scenario of ADTT equals to 5000 was considered in this section. D.4.3.1 C9.1 Bridges Designed for Maximum Concrete Tensile Stress of 0.0948âðâ²ð In this section, the calibration process for a selected bridge database (shown in Table D-107) is performed. Table D-107 Summary Information of Bridges Designed with γLL=0.8 ( 0.0948t cf f â²= ) Cases Section Type Span Length (ft.) Aps (in2) # of Strands 1 1800-2 100 7.344 48 2 1800-2 120 10.71 70 3 1800-2 140 14.076 92 4 2100-2 160 21.266 98 5 2400-2 180 22.568 104 6 2400-2 200 27.342 126 Step 1: Calculate the reliability level of designs according to AASHTO LRFD Specifications (2010) (Figure D-146~Figure D-148) Figure D-146 through Figure D-148 show the reliability indices for the bridges designed using AASHTO type girders according to AASHTO LRFD specifications (2010). It is observed that the average reliability index for decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 1.08, 1.42, and 3.22, respectively. A larger live load factor will be used to estimate the effect of changing live load factor on reliability level of structure. D-190
Figure D-146 Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=0.8 ( 0.0948t cf f â²= ) Figure D-147 Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=5000), γLL=0.8 ( 0.0948t cf f â²= ) D-191
Figure D-148 Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=5000), γLL=0.8 ( 0.0948t cf f â²= ) Step 2: Redesign the bridges with live load factor of 1.0 (Figure D-149~Figure D-151) In this step, the bridges have been redesigned using a live load factor of 1.0. Please note that only the live load factor of Service III limit state is increased from 0.8 to 1.0, dead load and resistance factors were kept the same during the redesign. Table D-108 shows the design outcomes of the redesigned bridges. Figure D-149 through Figure D-151 shows the reliability indices for the redesigned bridges using live load factor of 1.0. It is observed the average reliability index of decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 1.41, 1.77, and 3.47, respectively. Table D-108 Summary Information of Bridges Designed with γLL=1.0 ( 0.0948t cf f â²= ) Cases Section Type Span Length (ft.) Aps (in2) # of Strands 1 1800-2 100 8.874 58 2 1800-2 120 10.71 70 3 1800-2 140 14.076 92 4 2100-2 160 21.266 98 5 2400-2 180 22.568 104 6 2400-2 200 27.342 126 D-192
Figure D-149 Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=1.0 ( 0.0948t cf f â²= ) Figure D-150 Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=5000), γLL=1.0 ( 0.0948t cf f â²= ) D-193
Figure D-151 Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=5000), γLL=1.0 ( 0.0948t cf f â²= ) Step 3: Propose new live load, dead load, and/or resistance factors Based on the calibration process shown in step 1 through step 3, it is observed that the uniform target reliability index can be achieved using a live load factor of 1.0. Therefore, for the scenario of ADTT equal to 5000 and maximum concrete tensile stress of 0.0948t cf f â²= , a new live load factor of 1.0 is proposed. D.4.3.2 Bridges Designed for Maximum Concrete Tensile Stress of 0.158âðâ²ð In this section, the calibration process for a selected bridge database (shown in Table D-109) is performed. Table D-109 Summary Information of Bridges Designed with γLL=0.8 ( 0.158t cf f â²= ) Cases Section Type Span Length (ft.) Aps (in2) # of Strands 1 1800-2 100 5.814 38 2 1800-2 120 9.18 60 3 1800-2 140 12.546 82 4 2100-2 160 19.096 88 5 2400-2 180 20.398 94 6 2400-2 200 25.172 116 Step 1: Calculate the reliability level of designs according to AASHTO LRFD Specifications (2010) (Figure D-152~Figure D-154) D-194
Figure D-152 through Figure D-154 show the reliability indices for the bridges designed using AASHTO type girders according to AASHTO LRFD specifications (2010). It is observed that the average reliability index for decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 0.82, 1.18, and 2.97, respectively. Live load factor of 1.0 will be used in next step. Figure D-152 Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=0.8 ( 0.158t cf f â²= ) Figure D-153 Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=5000), γLL=0.8 ( 0.158t cf f â²= ) D-195
Figure D-154 Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=5000), γLL=0.8 ( 0.158t cf f â²= ) Step 2: Redesign the bridges with live load factor of 1.0 (Figure D-155~Figure D-157) The bridges have been redesigned using a live load factor of 1.0. Please note that only the live load factor of Service III limit state is increased from 0.8 to 1.0, dead load and resistance factors were kept the same during the redesign. Table D-110 shows the design outcomes of the redesigned bridges. Figure D-155 through Figure D-157 show the reliability indices for the redesigned bridges using live load factor of 1.0. It is observed that the average reliability index of decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 1.09, 1.5, and 3.26, respectively. Table D-110 Summary Information of Bridges Designed with γLL=1.0 ( 0.158t cf f â²= ) Cases Section Type Span Length (ft.) Aps (in2) # of Strands 1 1800-2 100 7.65 50 2 1800-2 120 11.628 76 3 1800-2 140 15.3 100 4 2100-2 160 23.002 106 5 2400-2 180 24.304 112 6 2400-2 200 29.946 138 D-196
Figure D-155 Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=1.0 ( 0.158t cf f â²= ) Figure D-156 Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=5000), γLL=1.0 ( 0.158t cf f â²= ) D-197
Figure D-157 Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=5000), γLL=1.0 ( 0.158t cf f â²= ) Step 3: Propose new live load, dead load, and/or resistance factors Based on the calibration process shown in step 1 through step 3, it is observed that the uniform target reliability index can be achieved using a live load factor of 1.0. Therefore, for the scenario of ADTT equal to 5000 and maximum concrete tensile stress of 0.158t cf f â²= , a new live load factor of 1.0 is proposed. D.4.3.3 Bridges Designed for Maximum Concrete Tensile Stress of 0.19âðâ²ð In this section, the calibration process for a selected bridge database (shown in Table D-111) is performed for the scenario of ADTT equal to 5000. Table D-111 Summary Information of Bridges Designed with γLL=0.8 ( 0.19t cf f â²= ) Cases Section Type Span Length (ft.) Aps (in2) # of Strands 1 1800-2 100 5.202 34 2 1800-2 120 8.568 56 3 1800-2 140 11.934 78 4 2100-2 160 17.794 82 5 2400-2 180 19.096 88 6 2400-2 200 24.304 112 Step 1: Calculate the reliability level of designs according to AASHTO LRFD Specifications (2010) (Figure D-158~Figure D-160) Figure D-158 through Figure D-160 show the reliability indices for the bridges designed using AASHTO type girders according to AASHTO LRFD specifications D-198
(2010). It is observed that the average reliability index for decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 0.79, 1.14, and 2.92, respectively. Since the reliability indices are lower than target reliability index, live load factor of 1.0 will be used in next step. Figure D-158 Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=0.8 ( 0.19t cf f â²= ) Figure D-159 Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=5000), γLL=0.8 ( 0.19t cf f â²= ) D-199
Figure D-160 Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=5000), γLL=0.8 ( 0.19t cf f â²= ) Step 2: Redesign the bridges with live load factor of 1.0 (Figure D-161~Figure D-163) The bridges have been redesigned using a live load factor of 1.0. Please note that only the live load factor of Service III limit state is increased from 0.8 to 1.0, dead load and resistance factors were kept the same during the redesign. Table D-112 shows the design outcomes of the redesigned bridges. Figure D-161 through Figure D-163 show the reliability indices for the redesigned bridges using live load factor of 1.0. It is observed that the average reliability index of decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 1.00, 1.45, and 3.28, respectively. Table D-112 Summary Information of Bridges Designed with γLL=1.0 ( 0.19t cf f â²= ) Cases Section Type Span Length (ft.) Aps (in2) # of Strands 1 1800-2 100 6.732 44 2 1800-2 120 10.71 70 3 1800-2 140 14.688 96 4 2100-2 160 21.7 100 5 2400-2 180 23.436 108 6 2400-2 200 29.078 134 D-200
Figure D-161 Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=1.0 ( 0.19t cf f â²= ) Figure D-162 Reliability Indices for Bridges at Maximum Tensile Stress Limit State (ADTT=5000), γLL=1.0 ( 0.19t cf f â²= ) D-201
Figure D-163 Reliability Indices for Bridges at Maximum Crack Width Limit State (ADTT=5000), γLL=1.0 ( 0.19t cf f â²= ) Step 3: Propose new live load, dead load, and/or resistance factors Based on the calibration process shown in step 1 through step 3, it is observed that the uniform target reliability index can be achieved using a live load factor of 1.0. Therefore, for the scenario of ADTT equal to 5000 and maximum concrete tensile stress of 0.19t cf f â²= , a new live load factor of 1.0 is proposed. D.4.3.4 Bridges Designed for Maximum Concrete Tensile Stress of 0.253âðâ²ð In this section, the calibration for a selected bridge database (shown in Table D-113) is performed for a scenario of ADTT equal to 5000. Please note that the maximum allowable crack width is specified as 0.016 in for maximum allowable crack width limit state. Table D-113 Summary Information of Bridges Designed with γLL=0.8 ( 0.253t cf f â²= ) Cases Section Type Span Length (ft.) Aps (in2) # of Strands 1 1800-2 100 3.978 26 2 1800-2 120 7.344 48 3 1800-2 140 10.404 68 4 2100-2 160 16.058 74 5 2400-2 180 16.926 78 6 2400-2 200 22.134 102 D-202
Step 1: Calculate the reliability level of designs according to AASHTO LRFD Specifications (2010) (Figure D-164~Figure D-166) Figure D-164 through Figure D-166 show the reliability indices for the bridges designed using AASHTO type girders according to AASHTO LRFD specifications (2010). It is observed that the average reliability index for decompression limit state, maximum allowable tensile stress limit state and maximum allowable crack width limit state is 0.19, 0.55, and 2.79, respectively. Live load factor of 1.0 will be used to estimate the effect of changing live load factor on reliability level. Figure D-164 Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=0.8 ( 0.253t cf f â²= ) D-203
Figure D-165 Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=5000), γLL=0.8 ( 0.253t cf f â²= ) Figure D-166 Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=5000), γLL=0.8 ( 0.253t cf f â²= ) Step 2: Redesign the bridges with live load factor of 1.0 (Figure D-167~Figure D-169) In this step, the bridges were redesigned using a live load factor of 1.0. Please note that only the live load factor of Service III limit state is increased from 0.8 to 1.0, dead load and resistance factors were kept the same during the redesign. Table D-114 shows the design outcomes of the redesigned bridges. D-204
Figure D-167 through Figure D-169 show the reliability indices for the redesigned bridges using a live load factor of 1.0. It is observed that the average reliability index for the decompression limit state, the maximum allowable tensile stress limit state and the maximum allowable crack width limit state is 0.85, 1.23, and 3.04, respectively. Table D-114 Summary Information of Bridges Designed with γLL=1.0 ( 0.253t cf f â²= ) Cases Section Type Span Length (ft.) Aps (in2) # of Strands 1 1800-2 100 5.508 36 2 1800-2 120 9.18 60 3 1800-2 140 13.158 86 4 2100-2 160 19.964 92 5 2400-2 180 21.266 98 6 2400-2 200 26.908 124 Figure D-167 Reliability Indices for Bridges at Decompression Limit State (ADTT=5000), γLL=1.0 ( 0.253t cf f â²= ) D-205
Figure D-168 Reliability Indices for Bridges at Maximum Allowable Tensile Stress Limit State (ADTT=5000), γLL=1.0 ( 0.253t cf f â²= ) Figure D-169 Reliability Indices for Bridges at Maximum Allowable Crack Width Limit State (ADTT=5000), γLL=1.0 ( 0.253t cf f â²= ) Step 3: Propose new live load, dead load, and/or resistance factors Based on the calibration process shown in step 1 through step 3, it is observed that the uniform target reliability index can be achieved using a live load factor of 1.0. Therefore, for the scenario of ADTT equal to 5000 and maximum concrete tensile stress of 0.253t cf f â²= , a new live load factor of 1.0 is proposed. D-206
D.5 Selection of load and resistance factors for use in the AASHTO LRFD The detailed results presented above are summarized in Chapter 5 of the report. The proposed revisions to AASHTO LRFD are presented in Section 5.2.8 with the proposed revised specifications shown in Chapter 6. The detailed results presented above may be used by owners to revise their design requirements to fit special situations they may have. D-207
