Bridge System Safety And Redundancy
NCHRP 12-86Bridge System Safety and RedundancyJune 24 -2104 Presentation toAASHTO T-5 Technical Committee for Loadsand Load DistributionProf. Michel Ghosn, Mr. Jian YangDepartment of Civil EngineeringThe City College of New York / CUNY1
Outline Background Redundancy Concepts Methodology System Factors Examples Refined Analysis Conclusions2
BackgroundTraditional Definitions: Fracture Critical Members: Steel tension members or steel tension components of members whose failurewould be expected to result in a partial or full collapse of the bridge (AASHTOMBE) Steel members whose failure is expected to result in inability of the bridge tosafely carry some level of traffic (live load) in its damaged condition (FHWA –Memo 2012) Redundancy: Is the quality of a bridge that enables it to perform its design function to safelycarry some level of load in a damaged state (AASHTO LRFD/FHWA) It can be provided in one or more of the following ways (FHWA):1. Load Path Redundancy: based on number of main supporting members2. Structural Redundancy: continuity over interior supports3. Internal Member Redundancy: built-up detailing to limit fracturepropagation3
BackgroundRedundancy and No. of BeamsIs a bridge with four equally loaded beams redundant ?4
BackgroundRedundancy and Beam SpacingIs a multi-beam bridge with large beam spacings redundant ?5
BackgroundContinuityMMfMfCompact SectionCompact SectionfCompact SectionNoncompactMMfNoncompact SectionMfCompact SectionfNoncompact SectionDo bridges with compact and noncompact negative sections behave similarly ?6
BackgroundBrittle Member FailuresShear failure of concrete membersFatigue & Fracture of steel membersShould redundancy be only investigated for steel members ?7
BackgroundDuctile Member FailuresColumn failuredue to EQ.Column failuredue to collisionShould redundancy be only investigated for brittle failures?8
BackgroundAASHTO LRFD 2012:Load Modifier9
BackgroundIssues: Load Modifiers: Determined by judgment rather than through a calibration process. No clear guidance on how to select the ductility or redundancy modifiers. Refined Analysis: Needs non-subjective and quantifiable benchmarks to determine acceptablelevels of redundancy.Previous Studies: NCHRP 406 / 458: Proposed an approach to evaluate redundancy in bridge systems. Developed criteria based on bridge configurations known to be redundant. Calibrated system factors to achieve consistent levels of system reliability. Proposed a refined analysis procedure for complex systems.10
BackgroundNCHRP 406 / 458 Definitions: Structural redundancy: Ability of a structural system to continue to carry some level of load after the failure ofone critical structural component. Failure can be ductile due to overloading or brittle due to some damaging event. System factor: Modifies design/safety check equationfsf R iQiNwhere RN:fs:f: i :Qi:fs 1 f R N i Qirequired member capacity accounting for bridge redundancy;system factor;member resistance factor as specified in the current AASHTO codes;load factor for load i;load effect of load i.11
NCHRP 12-86Research Objectives: Review NCHRP 406 and NCHRP 458 methodology and results; Develop a methodology to quantify bridge system reliability for redundancy; Consider entire system behavior under vertical load and lateral load; Take into account design inadequacies; Calibrate system factors that take into consideration system redundancy; Recommend revisions to the AASHTO LRFD Bridge Design Specifications, and the GuideManual for Condition Evaluation and Load and Resistance Factor Rating (LRFR) of HighwayBridges;12
Behavior of Bridge SystemsLoad CarryingCapacitySystem SafetyPintact LFuOriginally intact systemPfunctionality LFfAssumed linearbehaviorPmember LF1Redundancy Member SafetyRobustness Pdamaged LFdLFuLF1SystemSafety FactorLFdLF1Safety FactorDamaged structureDesign Live LoadFirst memberfailureUltimatecapacity ofdamaged systemLoss offunctionalityUltimatecapacity ofintact systemBridgeResponse
Performance under Vertical Load Measures of Redundancy for Bridge Systems under Vertical LoadThree deterministic measuresof system redundancy:Typical behavior of systems under vertical loadRu: System redundancy ratio for ultimate limit state;Rf: System redundancy ratio for functionality;Rd: System redundancy ratio for damaged condition.14
Performance under Lateral Load Measures of Redundancy for Bridge Systems under Lateral LoadTwo deterministic measuresof redundancy for lateral loadPuR fu Pp1PuPP1 ucRdu 1cRfu: System redundancy ratio for force-baseddesigns;Rdu: System redundancy ratio for displacementbased designsTypical behavior of systems under lateral load15
Reliability Indexes u system memberLF uLF 1 VLF2 VLL2 systemLF uLL VLF2 VLL2 memberLF 1LL VLF2 VLL2 damagedLF dLL VLF2 VLL2lnLF1 lnlnlnR D L1 D.F . LLL1D.F. Load distribution factorLL Effect of HL-93 truck load with no dynamic allowance and no lane load.16
Reliability Calibration of System Factors Calibration of system factor fsAnalyze systems known to be redundantComparefsf R N iQiTarget reliability indexmarginReliability index marginfor current designSystem ReliabilityMember Reliability u target system member u system memberNew Member DesignDeficit in the Reliability Index Margin* member* system system u target u 17
Analysis I-Girder Bridge for Vertical LoadTennessee Test (Burdette and Goodpasture)Abaqus FEM (Barth) SAP Grillage (NCHRP 12-86)18
Analysis for Lateral LoadTest by McLean et al (1998)SAP2000 (NCHRP 12-86)19
Analysis of Box-Girder Bridge for Vertical LoadLive load versus displacement considering boxdistortion20
Model for Bridges under Lateral Load Force-Based DesignPuPP1 u tunc Pu Pp1 Fmc C tconf tunc Fmc: multi-column factor;C : curvature factor; u : ultimate curvature; : curvature reduction factor for details tunc : average curvature for typical unconfinedcolumn; tconf : average curvature for a typical confinedcolumn.Typical behavior of systems under DistributedLateral Load21
Calibration for Lateral Load Risk Factor for Systems under Lateral Loads: s exp 2LF 2 LE u target exp u target System Factor for Bridges under Lateral Loads: u tunc Pufs s Fmc C sPp1 tconf tunc Constants u target target reliability index margin 0.50 dispersion coefficient 0.60 for Seismic loads 0.35 for Other loads22
fs for Bridges under Lateral Load 1/223
fs for Bridges under Lateral Load 2/224
Force-Based Model VerificationCan simplified model adequately representSAP 2000 analysis results ?(a) Two-Column Bents u tunc Pu Pp1 Fmc C tconftunc (b) Three-Column Bents(c) Four-Column Bents25
Displacement-Based Model VerificationCan one-column displacement adequatelyrepresent system displacement ?Multi-Cell Box Girder Bridge1816161414System displacment (in)System displacment (in)I-girder bridge121086Orig. Conf.Category CCategory BEqualline42121086Orig. Conf.Cat. C4Cat. B2Equalline00024681012One-column displacement (in)1416180246810121416One-column displacement (in)Displacement capacity of a bridge system is equal to the displacement capacity of its most criticalcolumn.26
fsu for I-girder Bridges under Vertical Load 1/3Where:D/R dead load to resistance ratio for the member being evaluated.LF1 load factor related to the capacity of the system to resist the failure of its most critical member.LF1 LF1 R D L1 LF1 LF1 R DL1 when whenLF1 1.0LF1 u target 0.85(1.3.6.1-1) 1 1LF 1.0LFR load carrying capacity.D dead load moment effect.L1 moment effect of applied live load due to two side-by-side LRFD design trucks applied at the middle ofthe span or due to two trucks in one lane applied in each of two contiguous spans.L1 D.F . LLD.F. load distribution factorLL effect of the LRFD design truck with no impact factor and no lane load.The negative superscript refers to negative bending and the positive superscript refers to positive bending.27
fsu for Narrow I-girder under Lateral Load 2/328
fsu for Box Bridges under Vertical Load 3/329
Ultimate Capacity Model Verification Unified Regression EquationPrestressed I-beams-simple span35Prestressed I-beams-continuousspanPrestressed box-simple spanLFu 1.16*LF1 0.75R2 0.98830steel box-simple span25Prestressed I-beam sensitivitycontinuous spanPrestressed I-beams-simple span20LFuPrestressed conc.box continuous15steel box simple span Effect ofspan lengthContinuous steel box supp.stiffreducedSteel box simple span Effect of boxsectionSteel box simple span Effect ofsteel box BM spac.and No.of BMssimple span I girder bridges105005101520253035LF1Relationship between LFu and LF1 for Bridge Superstructures30
fsd for Damaged I-girder under Vertical Load 1/3WhereRd redundancy ratio for damaged bridge systemsS beam spacing in feet. weight 1.23 0.23 beam (kip / ft ) d target -2.70 beam total dead weight on the damaged beam in kip per unit length.M transverse transverse 0.50 0.50 1.1013.5 kip. ft / ftMtransverse is the combined moment capacity of the slab and transverse members including diaphragmsexpressed in kip-ft per unit slab width.31
fsd for Narrow I-Girder Bridges 2/3Table C.1.3.6.1-2 Additional system factors for I-girder superstructures susceptible to damage to amain member under vertical loads.Bridge cross section typeSimple span andcontinuous prestressedconcrete I-girder bridgeswith 4 beams at 4-ftContinuous non-compactsteel I-girder bridges with4 beams at 4-ftSimple span andcontinuous compact steel Igirder bridgeswith 4 beams at 4-ftRedundancy ratio RdSystem factorRd 0.56 transverse weightRd 0.58 transverse weightfsd Rd0.47 (0.47 Rd )DRRd 0.64 transverse weight32
fsd for Damaged Box under Vertical Load 3/333
Model Verification for Damaged BridgesContinuous steel I-girder bridges1.201.00y -0.081x 1.35R² 0.96LFd/LF10.800.60Non-compact0.40Compact0.20y -0.081x 1.05R² 0.860.00051015Spacing /ftBox Girder BridgesFractured boxes2525y 0.72x2020y 0.82x - 4.14R² 0.9915105y 0.46xR² 0.93Narrow simple span w/ torsion one laneNarrow simple span w/ torsion two lanesNarrow simple span open box two lanesWide Simple span w/torsionWide Simple span open boxsimple span P/s box w/ torsionContinuous box noncompact001020LF13040LFdLFd15105Wide simple span Partial damageWide contiuous partial damage001020LF1304034
Single Cell and Multi-cell Box Bridges35
Implementation: Rating of Multi-Girder Bridge1. LRFR Rating Factor:VariableSymbolBending Moment CapacityRn7200 kip-ftMoment due to Dead LoadDn3500 kip-ftAASHTO Truck LoadLLHS201880 kip-ftAASHTO 3S-2 Legal loadLn1682 kip-ftDistribution FactorD.F.0.75Impact FactorIM1.33R.F . fRn D Dn 1.0 7200 1.25 3500 0.94 L Ln1.80 1682 0.75 1.332. Load Factor LF1:LF1 R D7200 3500 3.18D.F . LLHS 20 0.75 18803. System Factor:1 1.5 D / R 1 1.5 0.49 fs 1 1 1.0621 LF121 3.18 2Bridge Cross Section 6 beams at 8-ft24. System Rating:fs fRn D Dn 1.07 1.0 7200 1.25 3500R.F . 1.08 L Ln1.80 1682 0.75 1.3336
Implementation: System under Lateral Load1. Correction Factor of Column Curvature:Three-Column Bent M p beam M p columnM u column M p column 202, 000 198, 600 0.21214, 600 198, 6002. Reduced Curvature to that of Cap Beam: u column u beam0.21 5.74 10 4 in 1 1.21 10 4 in 1 9.03 10 4 in 13. System Factor:VariableSymbolPlastic Moment of cap beamMp beam202,000 kip-inPlastic Moment of columnMp column198,600 kip-inUltimate Moment of columnMu column214,600 kip-inUltimate Curvature of column u column5.74 10-4 in-1Ultimate Curvature of beam u beam9.03 10-4 in-1Lateral Load when 1st column failsPp15244.8 kip fs Fmc C u tunc tconf tunc 0.21(5.74 10 4 ) 3.64 10 4 0.75 1.16 0.24 0.82 3 41.55 10 3.64 10 4. Max. Allowed Lateral Load:PEQ fs Pp1 0.82 5, 244.8 kip 4300 kip37
Refined Direct Analysis1.3.6.1.1 Direct Redundancy Analysis for Bridges under Vertical LoadsFor trusses and arch bridges, bridges classified to be of operational importance, and for bridges not coveredin Tables 1. 3.6.1–1 through 1.3.6.1-4, the system factor of Equation 1.3.2.1-1 for the structural components of asystem subjected to vertical loads shall be calculated from the results of an incremental analysis using Equation1.3.6.1.-2:R f Rd Rfs min u ,, 1.301.100.50 1.3.6.1.-21.3.6.2.1 Direct Redundancy Analysis for Bridges under Horizontal LoadsFor bridges classified to be of operational importance and for bridges not covered in Table 1. 3.6.2- 1 that arebeing evaluated using the force-based approach, the system factor of Equation 1. 3.2.1-1 for the structuralcomponents of a system subjected to horizontal load shall be calculated from the results of a nonlinear pushoveranalysis using Equation 1.3.6.2-6:R RR fs min u , f , d 1.20 1.20 1.20 0.50 1.3.6.2-638
Refined Analysis of Truss Bridge1/239
Refined Analysis of Truss Bridge2/240
Conclusions Proposed a methodology to quantify bridge redundancy; Considered entire system behavior under vertical load and lateral load; Considered design inadequacies ; Found a unified approach for simple spans and continuous superstructuresystems subject to vertical loads; Found a unified approach for integral and non-integral column-superstructureconnections for systems subject to lateral load; Calibrated system factors that take into consideration system redundancy; Recommended revisions to the AASHTO LRFD Bridge Design Specifications,and the Guide Manual for Condition Evaluation and Load and ResistanceFactor Rating (LRFR) of Highway Bridges;41
AcknowledgmentsNCHRP: NCHRP 12-86 Project PanelResearch assistants: Senior Prog. Officer Waseem Dekelbab Mr. Jian Yang (CUNY)Research Team: Ms. Feng Miao (CUNY) Mr. David Beal. Mr. Giorgio Anitori (UPC) Spain Mr. Bala Sivakumar (HNTB). Mr. Graziano Fiorillo (CUNY) Prof. Dan Frangopol (Lehigh). Mr. Murat Hamutcuoglu (HNTB) Prof. Gongkang Fu (Ill. Inst. Tech.).Special Thanks: Mr. Alexandre Beregeon(CUNY/ENTPE) France Prof. Joan Ramon Casas (UPC) Spain Mr. Tuna Yelkikanat (CUNY) Prof Yongming Tu (Southeast Univ.) China Ms. Miriam Soriano (UPC) Spain Dr. Lennart Elfgren, (Luleå) Sweden42
QuestionsThank You!43
Narrow simple span_w/ torsion_one lane Narrow simple span_w/ torsion_two lanes Narrow simple span_open box_two lanes Wide Simple span_w/torsion Wide Simple span_open box simple span P/s box w/ torsion Continuous box_noncompact y 0.72x Model Verification for Damaged Bridges y -0.081x
Aluminum bridge crane isometric 11 Steel bridge crane plan view 12 Aluminum bridge crane plan view 13 Bridge Crane Systems & Dimensional Charts Installation Parameters 14 250 lb. capacity bridge cranes 15 - 17 500 lb. capacity bridge cranes 18 - 21 1000 lb. capacity bridge cranes 22 - 25 2000 lb. capacity bridge cranes 26 - 29 4000 lb. capacity .
For a complicated Modbus system, redundancy is extremely important. The MGate MB3660 Modbus gateways support redundancy for both the power input and Ethernet connection. The MGate MB3660 gateways come with dual AC or DC power inputs built in for power redundancy, and have dual Ethernet ports (with different IPs) for network redundancy.
Ring-fence and assimilation proposals (if applicable) Mitigation against compulsory redundancy, including voluntary redundancy and bumped redundancy The selection processes (see section 17 of the managers guidance) 2.1. Assimilations Where a service has been restructured and there is a pool of potentially ‘at risk’
redundancy patterns at different levels in the power hierarchy. For example, Figure 2 shows the power hierarchy for a single datacenter server room with xN/y distributed redundancy at the UPS level (x 4, y 3) and 2N redundancy at the PDU level; 2N redundancy is simpler and more maintainable
Digital Image Fundamentals 21 Data Redundancies Data redundancy is a central issue in digital image compression In digital image compression, three basic data redundancies can be identified and exploited Psychovisual redundancy Encoding redundancy Inter-pixel (a.k.a. spatial) redundancy
Dependability via Redundancy: Time vs. Space Spatial Redundancy -replicated data or check information or hardware to handle hard and soft (transient) failures Temporal Redundancy -redundancy in time (retry) to handle soft (transient) failures
Hammersmith Bridge Suspension Bridge, 2 piers (1887) 210m 13m No, on road only Steps footway/ road Narrow traffic lanes, 20000 veh/day 3,872 1,923 5,795 Barnes Footbridge Deck arch bridge, 2 piers (1895) 124m 2.4m No, foot bridge only Steps Runs alongside railway bridge 1,223 256 1,479 Chiswick Bridge Deck arch bridge, 2 piers (1933) 185m 21m .
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