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THE DEVELOPMENT OF AASHTO LRFD BRIDGETHE DEVELOPMENT OF AASHTO LRFD BRIDGE DESIGN SPECIFICATION AS N EXAMPLE OF PROBABILISTIC-BASED SPECIFICATIONS
State University of New York at BuffaloNovember 7 2011November 7, 2011
Presented ByWagdy G. Wassef, P.E., Ph.D.Modjeski and Masters, Inc.
A Brief Historyy• 1931 – First printed version of AASHO Standard
Specifications for Highway Bridges and IncidentalSpecifications for Highway Bridges and Incidental Structures
• 1970’s AASHO becomes AASHTO (1990’s AREA becomes (AREMA)
• Early 1970’s AASHTO adopts LFDL t 1970’ OMTC t t k li it t t b d• Late 1970’s OMTC starts work on limit-states based OHBDC
• 1986 AASHTO explores need to change1986 AASHTO explores need to change
Design Code ObjectivesDesign Code Objectives • Technically state-of-the-art specification. • Comprehensive as possible• Comprehensive as possible.• Readable and easy to use.• Keep specification-type wording – do not develop
a textbook.• Encourage a multi-disciplinary approach to bridge
design.g
Major ChangesMajor Changes•A new philosophy of safety - LRFD•The identification of four limit statesThe identification of four limit states•The relationship of the chosen reliability level, the load and resistance factors, and load models th h th f lib tithrough the process of calibration
– new load factors– new resistance factors
LRFD - Basic Design ConceptLRFD - Basic Design Concept
Some Algebra
QR
2Q
2RQ)-(R + =
2Q
2R +
Q - R =
x 1 = R = + + Q = R ii2Q
2R
22
ii
++Qx
=
2Q
2R + + Q
Load and Resistance Factor DesignLoad and Resistance Factor Design
• Σηi γi Qi ≤ Rn = Rri i i n r• in which:• i = D R I 0.95 for loads for max
1/( ) 1 0 f l d f i• = 1/(I D R) 1.0 for loads for min• where:• i = load factor: a statistically based multiplier on i y p
force effects• = resistance factor: a statistically based
multiplier applied to nominal resistancemultiplier applied to nominal resistance
LRFD (Continued)LRFD (Continued)• i = load modifier• D = a factor relating to ductilityD a factor relating to ductility• R = a factor relating to
redundancyf t l ti t• I = a factor relating to
importance• Qi = nominal force effect: a
deformation stress, or stress resultant
• R = nominal resistanceRn nominal resistance• Rr = factored resistance: Rn
Reliability Calcs Done for M and V –e ab ty Ca cs o e o a dSimulated Bridges Based on Real Ones• 25 non composite steel girder bridge simulations• 25 non-composite steel girder bridge simulations
with spans of 30,60,90,120,and 200 ft, and spacings of 4,6,8,10,and 12 ft.
• Composite steel girder bridges having the same parameters identified above.
• P/C I-beam bridges with the same parametersP/C I beam bridges with the same parameters identified above.
• R/C T-beam bridges with spans of 30,60,90,and 120 ft with spacing as above120 ft, with spacing as above.
Reliability of Std Spec vs. LRFD –y p175 Data Points
Major Changes j g• Revised calculation of load distribution
LtK
LS
2900S + 0.075 = g
3g
0.10.20.6
LtL2900 3
s
Circa 19901990
Major Changes (Continued)Major Changes (Continued)• Combine plain, reinforced and prestressed concrete.• Modified compression field/strut and tie• Modified compression field/strut and tie.• Limit state-based provisions for foundation design.• Expanded coverage on hydraulics and scour.• The introduction of the isotropic deck design.• Expanded coverage on bridge rails.• Inclusion of large portions of the AASHTO/FHWA g p
Specification for ship collision.
Major Changes (Continued)Major Changes (Continued)• Changes to the earthquake provisions to eliminate
the seismic performance category concept bythe seismic performance category concept by making the method of analysis a function of the importance of the structure.
• Guidance on the design of segmental concrete bridges – from Guide Spec.
• The development of a parallel commentary.p p y• New Live Load Model – HL93• Continuation of a long story
1923 AREA Specification
4k6k
16k24k
10-Ton15-Ton
8k14'
32k5.5'
20-Ton
VERY CLOSE!!
1928-1929 Conference Specification
6k14'24k
30'6k
14'24k
30'8k
14'32k
30'6k
14'24k
30'6k
14'24k
15-Ton 15-Ton 20-Ton 15-Ton 15-Ton
640 lb/ft
18,000 lb for Moment26,000 lb for Shear
640 lb/ft
1944 HS 20 Design Truck Added
Live Load Continued to be Debated• Late 60’s – H40, HS25 and HS30 discussed• 1969 SCOBS states unanimous opposition to• 1969 – SCOBS states unanimous opposition to
increasing weight of design truck – “wasteful obsolescence” of existing bridges
• 1978 – HS25 proposed again• 1979 – HS25 again – commentary –
– need for heavier design load seems unavoidableg– HS25 best present solution– 5% cost penalty
• Motion soundly defeated• Motion soundly defeated
“E l i L d ” B d TRB“Exclusion Loads” – Based on TRB Special Report 225, 1990
EXCL/HS20 Truck or Lane or 2 – 25 kips Axles @ 4 ft (110 kN @ 1.2 m)
Selected Notional Design LoadSelected Notional Design Load
HL-93
EXCL/HL 93 Circa 1992EXCL/HL 93 – Circa 1992
NCHRP 12-33 Project ScheduleNCHRP 12-33 Project Schedule
• First Draft - 1990 – general coverageFirst Draft 1990 general coverage• Second Draft - 1991 – workable• Third Draft - 1992 – pretty closep y• Fourth Draft - 1993 – ADOPTED!!• 12,000 comments• Reviewed by hundreds• Printed and available - 1994
Upgrades and Changes to 1990 T h lTechnology
• 1996 foundation data reinserted• 1996 foundation data reinserted.• New wall provisions – ongoing upgrade.• 2002 upgraded to ASBI LFRD Segmental Guide
Specs.• MCF shear in concrete simplified and clarified several
times – major update in 2002.times major update in 2002.• Load distribution application limits expanded several
time in 1990’s due to requests to liberalize.• More commentary added• More commentary added.
Upgrades and ChangesUpgrades and Changes• 2004 – major change in steel girder design in
anticipation ofanticipation of………• 2005 – seamless integration of curved steel bridges
ending three decade quest
Upgrades and Changes (Continued)Upgrades and Changes (Continued)
• 2005 – P/C loses updated• 2006 – complete replacement of Section 10 –
Foundation Design• 2006 – more concrete shear options2006 more concrete shear options• 2007 – big year
– Streamline MCF for concrete shear design1 000 year EQ maps and collateral changes– 1,000 year EQ maps and collateral changes
– Seismic Guide Spec - displacement based– Pile construction update
• 2008 - Coastal bridge Guide Spec
Where Do We Go From Here?
Where Do We Go From Here?Where Do We Go From Here?• The original AASHTO LRFD live load
t d b d l d tstudy was based on load measurements made in the 1970’s in Ontario. How this
l t t t d ’ l d ?relates to today’s loads?
Where Do We Go From Here?Where Do We Go From Here?• The specifications was calibrated for the
t th li it t t h th d fi iti fstrength limit state where the definition of failure is relatively simple: if the factored l d d th f t d i tloads exceed the factored resistance, failure, i.e. severe distress or collapse, will t k ltake place. What about service limit state and what is failure under service limit states?
Where Do We Go From Here?Where Do We Go From Here?Two Current Projects of Special Note:• SHRP R19 B - Bridge for Service Life
Beyond 100 Years: Service Limit State Design (SLS)
• NCHRP 12-83, Calibration of Service Limit ,State for Concrete
R19B Research TeamR19B Research Team
Modjeski and Masters, Inc.: John Kulicki, Ph.D., P.E.Wagdy Wassef, Ph.D., P.E.
University of Delaware: Dennis Mertz, Ph.D., P.E.University of Nebraska: Andy Nowak, Ph.D.NCS Consultants: Naresh Samtani, Ph.D., P.E.
NCHRP 12-83 Research TeamSame except that NCS Consultants are replaced with
Rutgers University: Hani Nasif, Ph.D., P.E.
Current General SLS’sCurrent General SLS s• Live load deflections• Bearings-movements and service forces• Settlement of foundations and walls
Current Steel SLS’sCurrent Steel SLS s• Permanent deformations in compact steel
tcomponents• Fatigue of structural steel, steel
reinforcement and concrete (through its own limit state)
• Slip of slip-critical bolted connections
Current Concrete SLS’sCurrent Concrete SLS s
• Load inducedLoad induced– Stresses in prestressed concrete under
service loadsservice loads– Crack control reinforcement
• Non Load induced• Non-Load induced– Shrinkage and temperature reinforcement
S litti i f t– Splitting reinforcement
Desired AttributesDesired Attributes
I SLS i f l? C it b• Is an SLS meaningful? Can it be calibrated?
• Does it really relate to service---or something else?
• Can (should) aging and deterioration be incorporated?p
• Can it reflect interventions?
General TopicsGeneral Topics
• Special challenges for SLS developmentSpecial challenges for SLS development• Survey of owners
U f WIM d t• Use of WIM data• Calibration process
General Topics (cont’d)General Topics (cont d)
• Improvements to current SLSImprovements to current SLS– Crack control in reinforced concrete
Tension in P/S beams– Tension in P/S beams– Load induced fatigue in steel and concrete
Use of Weigh In Motion Data– Use of Weigh-In-Motion Data
Current StatusCurrent Status
• Vetted WIM dataVetted WIM data– SLS Live Load live load model– Finite Life fatigue load modelFinite Life fatigue load model– Infinite Life fatigue load model
• Preliminary Betas for Service III (Tension inPreliminary Betas for Service III (Tension in P/s beams)
• Work on deflections• Work on deflections• Work on compiling info on joints and
bearingsbearings
Service and Fatigue LL has been a challenge
• Truck WIM was obtained from the FHWA and NCHRP Project 12-76
T t l b f d b t 60 illi• Total number of records about 60 million – about 35 million used
Initial Filtering Criteria For Non-Fatigue SLS (FHWA Unless Noted)
• Excluded Vehicles• Excluded Vehicles – Individual axle weight > 70kips -– GVW < 10– GVW < 10 – 7 >Total length >200 ft – First axle spacing <5 ft p g– Individual axle spacing < 3.4ft – 10 > Speed > 100 mph – GVW +/- the sum of the axle weights by more than 7%. – FHWA Classes 3 – 14
Additional FilteringAdditional FilteringFilter #1 – Questionable Records
1 - Truck length > 120 ft g2 –sum of axle spacing > length of truck. 3 - any axle < 2 Kips 4 - GVW +/- sum of the axle weights by more than 10%4 GVW +/ sum of the axle weights by more than 10% 5 - GVW < 12 Kips
Filter #2 – Presumed Permit TrucksFilter #2 Presumed Permit Trucks6 - Total # of axles < 3 AND GVW >50 kips 7 - Steering axle > 35 k8 – individual axle weight > 45 kips
Filter #3 – Traditional Fatigue Population9 - Vehicles with GVW <20 Kips
Filtering By Limit StateFiltering By Limit State• Vehicles Passing Filters #1 & #2 will be
d f lib ti f ll li it t tused for calibration of all limit states except for Fatigue, the limit state for permit
hi l d ibl St th IIvehicles and possibly Strength II.• Vehicles filtered by Filter #2 will be
considered Permit vehicles and will be reviewed and may be filtered further.
• Vehicles passing all three filters will be used for the fatigue limit stateg
WIM Data - FHWA• 14 sites –
Representing 1 year 4
5
Representing 1 year of traffic at most sites
• The maximum 2
3
aria
ble Arizona(SPS-1)
Arizona(SPS-2)Arkansas(SPS-2)
recorded GVW is 220 kips
• Mean values range 1
0
1
d N
orm
al V
a Colorado(SPS-2)Illinois(SPS-6)Indiana(SPS-6)Kansas(SPS-2)Louisiana(SPS-1)Maine(SPS-5)Mean values range
from 20 to 65 kips-3
-2
-1S
tand
ard
Minnesota(SPS-5)New Mexico(SPS-1)NewMexico(SPS-5)Tennessee(SPS-6)Virginia(SPS-1)Wisconsin(SPS-1)
0 50 100 150 200 250-5
-4
GVW [kips]
Wisconsin(SPS 1)Delaware(SPS-1)Maryland(SPS-5)Ontario
GVW [kips]
Analysis of the WIM Datay
• Live load effect – maximum moment andLive load effect maximum moment and shear
• Simple spans with span lengths of 30 60• Simple spans with span lengths of 30, 60, 90, 120 and 200 ftT k i t h• Trucks causing moments or shears < 0.15 (HL93) were removed
Removal of the Heavy Vehicles for SLSy
6New York 8382 Span 90ft
• Filter – trucks causing moments
h th 1 35(HL934
or shears more than 1.35(HL93 live load effect) were removed
• Number of trucks before filtering2
mal
Var
iabl
e
Number of trucks before filtering – 1,551,454
• Number of trucks after filtering –1 550 914
-2
0
Sta
ndar
d N
orm1,550,914
• Number of removed trucks – 540• Percent of removed trucks
-4
S
No Trucks Removed
• Percent of removed trucks –0.03%
0 0.5 1 1.5 2 2.5 3-6
Truck Moment / HL93 Moment
0.03% Trucks Removed
Multiple Presence Casesp
• Simultaneous f t koccurrence of trucks
on the bridge:
Filt b d ti
T1 T1
• Filter based on time of a record and a speed of the truck
Headway Distance max 200 ft Headway Distance max 200 ft
p
• Distance from the first axle of first truck
T2 T2
to the first axle of the second truck maximum 200 ft
Two cases of the simultaneous occurrencemaximum 200 ft occurrence
Correlation Criteria
• Both trucks have the same number of• Both trucks have the same number of axles
• GVW of the trucks is within +/- 5%
• All corresponding spacings between axles are within +/- 10%
Adjacent Lanes - Floridaj140
• Florida I10 – Time
100
120
cy
• Florida I10 – Time record accuracy 1 second
60
80
Freq
uenc• Number of Trucks :
1,654,004
20
40• Number of Fully Correlated Trucks: 2 518
0 20 40 60 80 100 1200
Gross Vehicle Weight - Trucks in Adjacent Lanes
2,518
• Max GVW = 102 kips
Adjacent Lanes – Florida2 518 f 1 654 0002,518 of 1,654,000
4
5
2
3ab
le
0
1
Nor
mal
Var
ia
3
-2
-1
Sta
ndar
d
0 50 100 150 200 250-5
-4
-3
Florida I10 - 1259 Correlated Trucks - Side by SideFlorida I10 - All Trucks
0 50 100 150 200 250
Gross Vehicle Weight
One Lane – Florida4 190 f 1 654 0004,190 of 1,654,000
5
2
3
4
le
0
1
Nor
mal
Var
iab
-2
-1
Sta
ndar
d N
5
-4
-3
Florida I10 - 4190 Correlated Trucks In One LaneFlorida I10 - All Trucks
0 50 100 150 200 250-5
Gross Vehicle Weight
Conclusions for Multiple Presencep
• Vehicles representing the extreme• Vehicles representing the extreme tails of the CDF’s need not be
id d t i lt l iconsidered to occur simultaneously in multiple lanes.
• For the SLS only a single lane live• For the SLS, only a single-lane live-load model need be considered.
Statistics of Non-fatigue SLS Live LoadStatistics of Non fatigue SLS Live Load
• Based on 95% limit:Based on 95% limit:– ADTT = I,000, Project Bias on HL 93 = 1.4– ADTT = 5,000, Project Bias on HL 93 = 1.45ADTT 5,000, Project Bias on HL 93 1.45
• COV = 12%• Based on 100 years:• Based on 100 years:
– Project Bias varies with time interval which will be reflected in calibrated load factorbe reflected in calibrated load factor
– Not strongly influenced by span length
Typical Results For SLS Live Load ModelTypical Results For SLS Live Load Model
Span 60 ft
1 20
1.40
1.60
0.80
1.00
1.20
Bias
ADTT 250
ADTT 1000
0.40
0.60ADTT 2500
ADTT 5000
ADTT 10000
0.00
0.20
1 10 100 1000 10000 100 years
DaysDays
Conclusion For Non-fatigue SLSConclusion For Non fatigue SLS
• Not necessary to envelop all trucks – SLSNot necessary to envelop all trucks SLS expected to be exceeded occasionally
• Some states with less weight• Some states with less weight enforcement may have to have additional considerations (site/region specific liveconsiderations (site/region specific live load)HL 93 d t bl ti l ti l SLS• HL-93 adaptable as national notional SLS live load model
Non-Fatigue SLS LL ModelNon Fatigue SLS LL Model
• Mean Bias and project LL model at meanMean, Bias and project LL model at mean plus 1.5 standard deviations tabulated with and without DLA for parameters:and without DLA for parameters:– 5 ADTTs = 250, 1,000, 2500, 5000 and 10,000– 10 Time periods = 1 day, 2 weeks, 1 month, 210 Time periods 1 day, 2 weeks, 1 month, 2
months, 6 months, 1 year, 5 years, 50 years, 75 years and 100 years6 S 30 ft 60ft 90ft 120ft 200 ft & 300ft– 6 Spans = 30 ft, 60ft, 90ft,120ft, 200 ft & 300ft
– With and w/o DLA
Fatigue SLS LL Model
Live Load For Fatigue II (finite fatigue life)
4
6NCHRP Data - Indiana
e oad o at gue ( te at gue e)
0
2
4
Nor
mal
Var
iabl
e
-4
-2
Sta
ndar
d N
Station - 9511Station - 9512Station - 9532Station - 9534Station - 9552Ontario
0 50 100 150 200 250 300-6
GVW [kips]
Ontario
•Miner’s law yields one effective moment per spanMiner s law yields one effective moment per span•Rainflow counting yields cycles per truck•Variety of spans and locations yields Mean, bias and COV
Examples Using FHWA WIM DataExamples Using FHWA WIM Data
33 *n
M p m 3
1eq i i
iM p m
M [kip-ft] for 3 sitesMeff [kip-ft] for 3 sites
30 ft (-184)* 60 ft (-360)* 90 ft (-530)* 120 ft (-762)* 200 ft (-1342)*
‐83 ‐204 ‐269 ‐408 ‐84583 204 269 408 845
‐90 -215 -300 -452 -896
‐86 -217 -291 -439 -91686 -217 -291 -439 -916
* Values in parentheses= current AASHTO fatigue moment
15 sites processed so far15 sites processed so far
Example Using FHWA WIM Data – 3 sites
/ Fat TrkeqM M
Fatigue II Load Factors for 3 sites30 ft 60 ft 90 ft 120 ft 200 ft
0.45 0.56 0.51 0.54 0.63
0.48 0.60 0.57 0.59 0.67
0.47 0.60 0.55 0.58 0.68
So far looks good now add cycles perSo far looks good, now add cycles per Passage and compare to current
Cycles Per Passagey g
4.00 Arizona (SPS‐1)
3.00
3.50 Arizona (SPS‐2)Arkansas (SPS‐2)Colorado (SPS‐2)D l (SPS 1)
Cy
2.00
2.50 Delaware (SPS‐1)Illinois (SPS‐6)Kansas (SPS‐2)Louisiana (SPS‐1)
ycle
33% damage increase
Current
0 50
1.00
1.50
Continuous Bridges
Louisiana (SPS 1)Maine (SPS‐5)Maryland (SPS‐5)Virginia (SPS‐1)
es
Current
0.00
0.50
30 80 130 180Span length
gMiddle Support Wisconsin (SPS‐1)
Span length
Rainflow Cycles - nrcRainflow Cycles nrc
Continuous SpansContinuous Spans
30 ft 60 ft 90 ft 120 ft 200 ft
3.13 3.03 3.38 3.02 2.36
3.09 2.85 3.00 2.76 2.38
3.30 3.30 3.52 3.04 2.44
Damage Factor Compared to CurrentDamage Factor Compared to Current
3/ rcFat Trkeq
nM M
Current =0.75
eqAASHTOn
Current 0.75
30 ft 60 ft 90 ft 120 ft 200 ft
0.52 0.71 0.66 0.68 0.73
0.57 0.74 0.71 .73 0.78
0 55 0 78 0 73 0 73 0 800.55 0.78 0.73 0.73 0.80
High = 0.87 or 116% of currentHigh 0.87 or 116% of current
MM Independent Check of UNLMM Independent Check of UNL
• UNL running all filtered trucks at a site usingUNL running all filtered trucks at a site using the time stamps– Traffic simulationTraffic simulation– Not individual trucks one at a time
• Test axle train evaluated by UNL and MMTest axle train evaluated by UNL and MM– 8 hypothetical trucks– 49 axles9 a es– 963 ft– 843,000 lbs
MM Independent Check of UNLMM Independent Check of UNL
• MM Cobbled together existing pieces:g g p– Variation of program MM used in early 1990’s truck
study that resulted in HL93 Loading modified to calculate moment time historiescalculate moment time histories
– Used rainflow counting algorithm based on ASTM E 1049 – 85 previously developed to process p y p pinstrumentation data for repair of in-service bridge to calculate cycles per truck; andMiner’s La to calc late Meq– Miner’s Law to calculate Meq.
MM Independent Check of UNLMM Independent Check of UNL• Results:
O l f i “ ti t d”– Only a few issues “negotiated”– Final results – damage factors – same for simple span,
very close for Neg moment at pier of continuous.y g p– Sometimes intermediate results varied – seemed to
depend maximum magnitude of small cycles (noise) th t i d lik d t thithat was ignored---like data smoothing
• Common sense check – MM found that i l t i l l d f t fequivalent single cycle damage factor for
the 8 truck train could be used as a i h k k d llcomparison check – worked well.
Does This Increase Make Sense?
2 000 000
2,500,000ations
1,500,000
2,000,000
k Co
mbina
500 000
1,000,000
er of Truck
0
500,000
65 70 75 80 85 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08
Numbe
196
197
197
198
198
199
199
199
199
199
199
199
199
199
199
200
200
200
200
200
200
200
200
200
Year
Does This Increase Make Sense?Does This Increase Make Sense?
120.0%140.0%
e1992‐19971992‐2002
40 0%60.0%80.0%100.0%
nt Cha
nge
‐20.0%0.0%20.0%40.0%
Perce
Truck Weight
Does This Increase Make Sense?
Current Status of LL StudiesCurrent Status of LL Studies
• Fatigue II Being calibrated now – Concrete and steel
• Fatigue I model being finalizedg g• Other SLS
– Design model will be HL93 factored per calibrationDesign model will be HL93 factored per calibration– LL was handed off to NCHRP 12-83 team for concrete
SLS calibration - working– SHRP team is following with deflections and foundations
Concrete-Related Limit StatesConcrete Related Limit States
LRFD Description Proposed SLS
articleDescription Proposed SLS
5.7.3.4Control of cracking bydistribution of reinforcement
Service I‐A:Crack control of R/C/
9.7.2.5Reinforcement requirementsfor concrete deck designedusing empirical method
Service I‐B:Crack control of R/C concrete deckdesigned using empirical methodusing empirical method designed using empirical method
5 9 4 2Stresses check at service IIIli it t t ft l f ll
Service III‐A: DecompressionService III‐B: Un‐cracked section (max t il t )5.9.4.2 limit state after losses‐fully
prestressed componentstensile stress)Service III‐C: Cracked section (specified crack width)
Reliability Indices of Existing P/S ConcReliability Indices of Existing P/S Conc. Bridges
Service III Limit State
Reliability Indices of Existing P/S Conc. B idBridges
345
dex
345
dex
-2-10123
0 20 40 60 80 100 120 140 160
Rel
ialb
ity In
d
βave=0
-2-10123
0 20 40 60 80 100 120 140 160
Rel
ialb
ity In
d
βave=0.2
Decompression Max. Allowable Tension
0 20 40 60 80 100 120 140 160Span Length (ft.)
0 20 40 60 80 100 120 140 160
Span Length (ft.)
45
β 2
Reliability index of existing bridgesAssuming ADTT 5000
2-10123
Rel
ialb
ity In
dex βave=2
Max. Allowable Crack Width (0.016 in., 1 year return period)
-20 20 40 60 80 100 120 140 160
Span Length (ft.)
Reliability Indices of Existing P/S Conc. B idBridges
Reliability index (return Period 1 year)
ADTTDecompression
Maximum Allowable Tensile
Stress
Maximum Allowable Crack
WidthS ess d1000 0.2 0.4 2.352500 0.1 0.3 2.205000 0 0 0 2 2 005000 0.0 0.2 2.0010000 ‐0.15 0.1 1.88
Proposed Target ‐0 0 * 0 2 2 0
Beta0.0 0.2 2.0
In any one year period the limit state will be exceeded in:500 of 1000 bridges for reliability index of 0.0g y23 of 1000 bridges for reliability index of 2.0
Reliability Indices of Bridges Designed to C t S ifi tiCurrent Specifications
234
dex 2
34
dex
-4-3-2-101
0 20 40 60 80 100 120 140 160
Rel
ialb
ity In
d
βave=‐0.15
-4-3-2-101
0 20 40 60 80 100 120 140 160
Rel
ialb
ity In
d βave=‐0.06
Decompression Max. Allowable TensionSpan Length (ft.)
0 20 40 60 80 100 120 140 160Span Length (ft.)
34
βave=1.9
Same existing bridges except No. of strands determined using current
specifications-4-3-2-1012
Rel
ialb
ity In
dex
Max. Allowable Crack Width (0.016 in., 1 year return period)
Reliability IndexAssuming ADTT 5000
0 20 40 60 80 100 120 140 160Span Length (ft.)
Reliability Indices of Bridges Designed to C t S ifi tiCurrent Specifications
Performance Level
ADTTDecompression
Maximum Allowable Tensile
Stress
Maximum Allowable Crack
WidthS ess d1000 0.05 0.26 2.202500 ‐0.05 0.11 2.065000 0 15 0 06 1 905000 ‐0.15 ‐0.06 1.9010000 ‐0.35 ‐0.21 1.80
In any one year period the limit state will be exceeded in:In any one year period the limit state will be exceeded in:660 of 1000 bridges for reliability index of -0.1529 of 1000 bridges for reliability index of 1.90
Parametric Study of Reliability IndexParametric Study of Reliability Index
Three cases were considered:Three cases were considered:• Bridges designed with various spacing,
span lengths and section typesspan lengths, and section types• Bridges designed with different span
l th d ti t b t i dlengths and section types but same girder spacing
• Bridges designed with different span lengths and girder spacing but same section types.
Parametric Study of Reliability IndexParametric Study of Reliability Index4.0
5.0
Inde
x
3 0
4.0
5.0
Inde
x
1.0
2.0
3.0
Rel
ialb
ity I
1.0
2.0
3.0
Rel
ialb
ity
Existing Bridges Redesigned Bridges
0.030.0 60.0 80.0 100 120 140
Span Length (ft.)
0.030.0 60.0 80.0 100 120 140
Span Length (ft.)
g g g g
• Various girder spacing, section types, and span lengthsspan lengths.
• ADTT = 5000M ll d k idth• Max allowed crack width
Conclusions Related to SLS for Concrete St tStructures
• Different limit states may require differentDifferent limit states may require different target reliability index to maintain current performanceperformance
Bluewater Bridge #2gFirst LRFD Major Bridge
Opened 1997Opened 1997