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