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DESIGN SPECIFICATION AS N EXAMPLE OF
PROBABILISTIC-BASED SPECIFICATIONS
State University of New York at Buffalo,
Presented ByWagdy G. Wassef, P.E., Ph.D.
Modjeski and Masters, Inc.
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A Brief Histor 1931 First printed version of AASHO Standard
Structures 1970s AASHO becomes AASHTO (1990s AREA becomes
AREMA)
Early 1970s AASHTO adopts LFD Late 1970s OMTC starts work on limit-states based
OHBDC
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Technically state-of-the-art specification.
. Readable and easy to use. Keep specification-type wording do not develop
a textbook. Encourage a multi-disciplinary approach to bridge
desi n.
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A new philosophy of safety - LRFD
The relationship of the chosen reliability level, theload and resistance factors, and load models
roug e process o ca ra on new load factors new resistance factors
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-
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Some Algebra
2Q
2 RQ)-(R + =
2Q
2 R +
- =
x 1
= R = + + Q = R ii2Q
2 R
ii x
=
Q R + +
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Load and Resistance Factor Desi n
Q R = R in which: i = D R I 0.95 for loads for max = I D R . or oa s or m n where: = load factor: a statisticall based multi lier on
force effects = resistance factor: a statistically based
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i = load modifier =
R = a factor relating toredundancy
I = a ac or re a ng oimportance
Q i = nominal force effect: adeformation stress, or stressresultant
=n
R r = factored resistance: Rn
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Reliabilit Calcs Done for M and V Simulated Bridges Based on Real Ones
-with spans of 30,60,90,120,and 200 ft, andspacings of 4,6,8,10,and 12 ft.
Composite steel girder bridges having the sameparameters identified above.
P/C I-beam brid es with the same arameters identified above.
R/C T-beam bridges with spans of 30,60,90,and
, .
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Reliabilit of Std S ec vs. LRFD 175 Data Points
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Major Changes Revised calculation of load distribution
K S S + 0.075 = g g0.10.20.6
t s
Circa
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Combine plain, reinforced and prestressed concrete.
. 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 lar e ortions of the AASHTO/FHWA
Specification for ship collision.
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Changes to the earthquake provisions to eliminate
making the method of analysis a function of theimportance of the structure.
Guidance on the design of segmental concretebridges from Guide Spec.
The develo ment of a arallel commentar . New Live Load Model HL93 Continuation of a long story
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1923 AREA Specification
4k6k
16k24k
10-Ton15-Ton
8k14'
32k5.5 '
20-Ton
VERY CLOSE!!
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1928-1929 Conference Specification
6k14'
24k30'
6k14'
24k30'
8k14'
32k30'
6k14'
24k30'
6k14'
24k
15-Ton 15-Ton 20-Ton 15-Ton 15-Ton
640 lb/ft
18,000 lb for Moment26,000 lb for Shear
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1944 HS 20 Design Truck Added
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Live Load Continued to be Debated Late 60s H40, HS25 and HS30 discussed
increasing weight of design truck wastefulobsolescence of existing bridges
1978 HS25 proposed again 1979 HS25 again commentary
need for heavier desi n load seems unavoidable HS25 best present solution 5% cost penalty
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xc us on oa s ase onSpecial Report 225, 1990
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EXCL/HS20 Truck or Lane or 2 25kips Axles @ 4 ft (110 kN @ 1.2 m)
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HL-93
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-
-
Second Draft - 1991 workable Third Draft - 1992 rett close Fourth Draft - 1993 ADOPTED!!
12,000 comments Reviewed by hundreds Printed and available - 1994
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Upgrades and Changes to 1990ec no ogy
.
New wall provisions ongoing upgrade. 2002 upgraded to ASBI LFRD Segmental Guide
Specs. MCF shear in concrete simplified and clarified several
times ma or u date in 2002. Load distribution application limits expanded several
time in 1990s due to requests to liberalize.
.
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2004 major change in steel girder design in
2005 seamless integration of curved steel bridgesending three decade quest
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Where Do We Go From Here?
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The original AASHTO LRFD live load
s u y was ase on oa measuremen smade in the 1970s in Ontario. How thisre a es o o ay s oa s
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The specifications was calibrated for the
s reng m s a e w ere e e n on ofailure is relatively simple: if the factoredoa s excee e ac ore res s ance,
failure, i.e. severe distress or collapse, willa e p ace.What about service limit state and what is
failure under service limit states?
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Two Current Projects of Special Note:
SHRP R19 B - Bridge for Service LifeBeyond 100 Years: Service Limit StateDesign (SLS)
NCHRP 12-83 Calibration of Service LimitState for Concrete
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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.
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Live load deflections
Bearings-movements and service forces Settlement of foundations and walls
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Permanent deformations in compact steel
componen s Fatigue of structural steel, steel
reinforcement and concrete (through its
own limit state) Slip of slip-critical bolted connections
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Stresses in prestressed concrete under
Crack control reinforcement
- Shrinkage and temperature reinforcement
p ng re n orcemen
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s an mean ng u an ecalibrated?
Does it really relate to service---or
something else? Can (should) aging and deterioration be
incorporated? Can it reflect interventions?
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Survey of owners se o a a
Calibration process
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Crack control in reinforced concrete Load induced fatigue in steel and concrete - -
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SLS Live Load live load model Finite Life fati ue load model Infinite Life fatigue load model
P/s beams)
Work on compiling info on joints and
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Service and Fatigue LL has been achallenge
Truck WIM was obtained from the FHWA
and NCHRP Project 12-76 o a num er o recor s a ou m on
about 35 million used
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Initial Filtering Criteria For Non-FatigueSLS (FHWA Unless Noted)
Individual axle weight > 70kips -
7 >Total length >200 ft
First axle s acin Speed > 100 mph
GVW +/- the sum of the axle weights by more than 7%. FHWA Classes 3 14
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Filter #1 Questionable Records1 - Truck length > 120 ft2 sum of axle spacing > length of truck.3 - any axle < 2 Kips
- - 5 - GVW < 12 Kips
Filter #2 Presumed Permit Trucks 6 - Total # of axles < 3 AND GVW >50 kips7 - Steering axle > 35 k
8 individual axle weight > 45 kipsFilter #3 Traditional Fatigue Population
9 - Vehicles with GVW
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Vehicles Passing Filters #1 & #2 will be
use or ca ra on o a m s a esexcept for Fatigue, the limit state for permitve c es an poss y reng .
Vehicles filtered by Filter #2 will beconsidered Permit vehicles and will bereviewed and may be filtered further.
Vehicles passing all three filters will beused for the fati ue limit state
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WIM Data - FHWA
14 sites 4
5
of traffic at most sites The maximum 23
r i a
b l e Arizona(SPS-1) Arizona(SPS-2) Arkansas(SPS-2)
recorded GVW is 220kips
0
1
N
o r m a
l V Colorado(SPS-2)
Illinois(SPS-6)Indiana(SPS-6)Kansas(SPS-2)Louisiana(SPS-1)Maine(SPS-5)
from 20 to 65 kips-3
-2
-
S t a n
d a r 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
Delaware(SPS-1)Maryland(SPS-5)Ontario
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Anal sis of the WIM Data
shear , ,
90, 120 and 200 ft ruc s caus ng momen s or s ears
< 0.15 (HL93) were removed
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Removal of the Heav Vehicles for SLS
6New York 8382 Span 90ft
Filter trucks causing moments
4
or s ears more an .
live load effect) were removed
2
m a
l V a r i a
b l e
1,551,454
Number of trucks after filtering
-2
0
t a n
d a r d
N o r, ,
Number of removed trucks 540
-4
No Trucks Removed
0.03%
0 0.5 1 1.5 2 2.5 3-6
Truck Moment / HL93 Moment
0.03% Trucks Removed
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Correlation Criteria
axles
GVW of the trucks is within +/- 5% All corresponding spacings between
axles are within +/- 10%
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Ad acent Lanes - Florida140
100
120
y
record accuracy 1second
60
80
F r e q u e n
Number of Trucks :
1,654,004
20
40 Number of FullyCorrelated Trucks:
0 20 40 60 80 100 1200
Gross Vehicle Weight - Trucks in Adjacent Lanes
,
Max GVW = 102 kips
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Adjacent Lanes Florida
, o , ,4
5
2
3
b l e
0
1
N o r m a
l V a r i
-2
-1
S t a n
d a r d
-5
-4
-
Florida I10 - 1259 Correlated Trucks - Side by SideFlorida I10 - All Trucks
Gross Vehicle Weight
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One Lane Florida
, o , ,5
2
3
4
l e
0
1
o r m a l
V a r
i a b
-2
-1
S t a n d a r
d
-4
-3
Florida I10 - 4190 Correlated Trucks In One LaneFlorida I10 - All Trucks
0 50 100 150 200 250-
Gross Vehicle Weight
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Conclusions for Multi le Presence
tails of the CDFs need not becons ere o occur s mu aneous y n
multiple lanes.
, - -load model need be considered.
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-
ADTT = I,000, Project Bias on HL 93 = 1.4 ADTT = 5 000 Pro ect Bias on HL 93 = 1.45
COV = 12%
Project Bias varies with time interval which will
Not strongly influenced by span length
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Span 60 ft
1.40
1.60
0.80
1.00
.
B i a s ADTT 250
ADTT 1000
0.40
0.60ADTT 2500
ADTT 5000
ADTT 10000
0.00
0.20
1 10 100 1000 10000 100 years
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-
expected to be exceeded occasionally
enforcement may have to have additional
load)
- a ap a e as na ona no onalive load model
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- ,
plus 1.5 standard deviations tabulated with
5 ADTTs = 250, 1,000, 2500, 5000 and 10,000
10 Time eriods = 1 da 2 weeks 1 month 2 months, 6 months, 1 year, 5 years, 50 years, 75 yearsand 100 years
pans = , , , , With and w/o DLA
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Fatigue SLS LL Model
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Live Load For Fati ue II finite fati ue life6
NCHRP Data - Indiana
0
2
o r m a
l V a
r i a
b l e
-4
-2
S t a n
d a r d
Station - 9511Station - 9512Station - 9532Station - 9534
Station - 9552
0 50 100 150 200 250 300-6
GVW [kips]
Rainflow counting yields cycles per truckVariety of spans and locations yields Mean, bias and COV
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3*
n
1eq i i
i
eff
30 ft (-184)* 60 ft (-360)* 90 ft (-530)* 120 ft (-762)* 200 ft (-1342)*
90 -215 -300 -452 -896
- - - -
* Values in parentheses= current AASHTO fatigue moment
Example Using FHWA WIM Data 3
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Example Using FHWA WIM Data 3sites
/ Fat Trk eq M M Fatigue II Load Factors for 3 sites
30 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
,Passage and compare to current
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C cles Per Passa e
4.00 Arizona (SPS1)
3.00
3.50 Arizona (SPS2)
Arkansas (SPS2)Colorado (SPS2)C
2.00
2.50 e aware
Illinois (SPS6)Kansas (SPS2)
cl 33% damage increase
1.00
1.50
Continuous Bridges
Maine (SPS5)Maryland (SPS5)Virginia (SPS1)
es
0.00
.
30 80 130 180
Middle Support
Wisconsin (SPS1)
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- rc
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
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3/ rcFat Trk e
n M M
Current =0.75
AASHTOn
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
. . . . .
Hi h = 0.87 or 116% of current
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the time stamps Not individual trucks one at a time
8 hypothetical trucks 49 axles
963 ft 843,000 lbs
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MM Cobbled together existing pieces: Variation of program MM used in early 1990s truck
study that resulted in HL93 Loading modified to
Used rainflow counting algorithm based on ASTM E
1049 85 reviousl develo ed to rocessinstrumentation data for repair of in-service bridge tocalculate cycles per truck; and
ner s aw o ca cu a e eq.
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Results:
n y a ew ssues nego a e
Final results damage factors same for simple span,ver close for Ne moment at ier of continuous.
Sometimes intermediate results varied seemed todepend maximum magnitude of small cycles (noise)
a was gnore --- e a a smoo ng
Common sense check MM found that
equ va en s ng e cyc e amage ac or or the 8 truck train could be used as acompar son c ec wor e we .
Does This Increase Make Sense?
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Does This Increase Make Sense?2,500,000
t i o n s
1,500,000
, ,
C o m
b i n
1,000,000
r
o f T r u c
0
,
5 0 5 0 5 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8
N u m b
1 9
1 9
1 9
1 9
1 9
1 9
1 9
1 9
1 9
1 9
1 9
1 9
1 9
1 9
1 9
2 0
2 0
2 0
2 0
2 0
2 0
2 0
2 0
2 0
Year
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120.0%
140.0% 1992 19971992 2002
60.0%80.0%
100.0%
n t C h a n g
20.0%
0.0%
20.0%
.
P e r c e
Truck Weight
Does This Increase Make Sense?
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Does This Increase Make Sense?
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-
LRFD article
5.7.3.4 Control of cracking bydistribution of reinforcement
Service I A:Crack control of R C
9.7.2.5Reinforcement requirementsfor concrete deck designed
Service I B:Crack control of R/C concrete deck
Stresses check at service IIIService IIIA: DecompressionService IIIB: Uncracked section (max
. . . m s a e a er osses u yprestressed components
ens e s ressService IIIC: Cracked section (specified crack width)
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.
Bridges
Service III Limit State
Reliability Indices of Existing P/S Conc.
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r ges3
4
5
e x 345
e x
-2
-1
0
1
2
R e l
i a l b i t y
I n
ave=0
-2-1012
R e
l i a l
b i t y
I n
ave=0.2
Decompression Max. Allowable TensionSpan Length (ft.) Span Length (ft.)
4
5
Reliability index of existing bridgesAssuming ADTT 5000-1
0
1
2
3
R e l
i a l b i t y
I n d e x ave=2
Max. Allowable Crack Width (0.016 in., 1 year return period)
-0 20 40 60 80 100 120 140 160
Span Length (ft.)
Reliability Indices of Existing P/S Conc.
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r gesReliability index (return Period 1 year)
ADTTDecompression
Maximum
Allowable Tensile Stress
Maximum
Allowable Crack Width
1000 0.2 0.4 2.35
2500 0.1 0.3 2.20
. . .10000 0.15 0.1 1.88
Proposed Target *Beta
. . .
In any one year period the limit state will be exceeded in:500 of 1000 brid es for reliabilit index of 0.023 of 1000 bridges for reliability index of 2.0
Reliability Indices of Bridges Designed to
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urren pec ca ons234
e x 234
e x
-4-3-2-101
0 20 40 60 80 100 120 140 160
R e l
i a l b i t y
I n ave= 0.15
-4-3-2
-101
R
e l i a
l b i t y
I n ave= 0.06
Decompression Max. Allowable TensionSpan Length (ft.) Span Length (ft.)
3
4 ave=1.9
Same existing bridges except No. of strands determined using current
specifications-4
-3
-2
-1
0
1
2
R e l
i a l b i t y
I n d e x
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
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urren pec ca onsPerformance Level
ADTTDecompression
Maximum
Allowable Tensile Stress
Maximum
Allowable Crack Width
1000 0.05 0.26 2.20
2500 0.05 0.11 2.06
. . .10000 0.35 0.21 1.80
660 of 1000 bridges for reliability index of -0.1529 of 1000 bridges for reliability index of 1.90
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Bridges designed with various spacing,,
Bridges designed with different spaneng s an sec on ypes u same g r er spacing
Bridges designed with different spanlengths and girder spacing but samesection types.
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4.0
5.0
n d e x
4.0
5.0
I n d e x
1.0
2.0
3.0
R e l i a
l b i t y
1.0
2.0
.
R e l i a
l b i t y
Existin Brid es Redesi ned Brid es
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.)
Various girder spacing, section types, and.
ADTT = 5000 ax a owe crac w
Conclusions Related to SLS for Concrete
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ruc ures
target reliability index to maintain current
Bluewater Brid e #2
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First LRFD Major Bridge
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