NCHRP 12-86
Bridge System Safety and Redundancy
Prof. Michel Ghosn, Mr. Jian Yang
Department of Civil Engineering
The City College of New York / CUNY
June 24 -2104 Presentation to
AASHTO T-5 Technical Committee for Loads
and Load Distribution
1
Background
Redundancy Concepts
Methodology
System Factors
Examples
Refined Analysis
Conclusions
2
Outline
Background
Traditional Definitions:
Fracture Critical Members: • Steel tension members or steel tension components of members whose failure
would be expected to result in a partial or full collapse of the bridge (AASHTO
MBE)
• Steel members whose failure is expected to result in inability of the bridge to
safely 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 safely
carry 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 members
2. Structural Redundancy: continuity over interior supports
3. Internal Member Redundancy: built-up detailing to limit fracture
propagation 3
Background
Redundancy and No. of Beams
4
Is a bridge with four equally loaded beams redundant ?
Background
Redundancy and Beam Spacing
5
Is a multi-beam bridge with large beam spacings redundant ?
Background
6
Do bridges with compact and noncompact negative sections behave similarly ?
Compact Section
f
M
Compact Section
f
M
Compact Section
f
M
Continuity
Noncompact Section
f
M
Compact Section
f
M
Noncompact Section
f
M
Noncompact
Background
Brittle Member Failures
7
Shear failure of concrete members
Fatigue & Fracture of steel members
Should redundancy be only investigated for steel members ?
Background
Ductile Member Failures
8 Should redundancy be only investigated for brittle failures?
Column failure
due to collision
Column failure
due to EQ.
Background
AASHTO LRFD 2012:
9
Load Modifier
Background
Issues:
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 acceptable
levels of redundancy.
10
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.
Background
NCHRP 406 / 458 Definitions:
Structural redundancy: • Ability of a structural system to continue to carry some level of load after the failure of
one critical structural component.
• Failure can be ductile due to overloading or brittle due to some damaging event.
System factor: • Modifies design/safety check equation
N
s i iR Qf f
where RN: required member capacity accounting for bridge redundancy;
fs: system factor;
f : member resistance factor as specified in the current AASHTO codes;
i : load factor for load i;
Qi: load effect of load i.
11
N
i iR Q f 1
s f
NCHRP 12-86
Research 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 Guide
Manual for Condition Evaluation and Load and Resistance Factor Rating (LRFR) of Highway
Bridges;
12
Pdamaged = LFd
Pmember = LF1
Pfunctionality = LFf
Pintact = LFu
First member
failure
Loss of
functionality
Ultimate
capacity of
intact system
Load Carrying
Capacity
Bridge
Response
Originally intact system
Assumed linear
behavior
Damaged structure
Ultimate
capacity of
damaged system
Redundancy =
1LF
LFu
Design Live Load
Safety Factor
Member Safety
System Safety
Robustness = 1LF
LFd
System
Safety Factor
Behavior of Bridge Systems
Performance under Vertical Load
Typical behavior of systems under vertical load
Measures of Redundancy for Bridge Systems under Vertical Load
Ru: System redundancy ratio for ultimate limit state;
Rf: System redundancy ratio for functionality;
Rd: System redundancy ratio for damaged condition.
Three deterministic measures
of system redundancy:
14
Performance under Lateral Load
Pu
PP1
Typical behavior of systems under lateral load
Measures of Redundancy for Bridge Systems under Lateral Load
15
Rfu: System redundancy ratio for force-based
designs;
Rdu: System redundancy ratio for displacement
based designs
1
1
ufu
p
ucdu
c
PR
P
R
Two deterministic measures
of redundancy for lateral load
16
Reliability Indexes
2 2
lnu
system
LF LL
LF
LL
V V
1
2 2
ln
member
LF LL
LF
LL
V V
2 2
lnd
damaged
LF LL
LF
LL
V V
1
1
R DLF
L
1 . .L D F LL
D.F. = Load distribution factor
LL = Effect of HL-93 truck load with no dynamic allowance and no lane load.
1
2 2
ln
u system member
u
LF LL
LF
LF
V V
Reliability Calibration of System Factors
Calibration of system factor fs
*
targetsystem system u u
Deficit in the Reliability Index Margin
17
Analyze systems known to be redundant
System Reliability Member Reliability Compare
targetu system member Target reliability index
margin
u system member Reliability index margin
for current design
New Member Design
N
s i iR Qf f
*
member
18
Tennessee Test (Burdette and Goodpasture)
Abaqus FEM (Barth) SAP Grillage (NCHRP 12-86)
Analysis I-Girder Bridge for Vertical Load
19
Test by McLean et al (1998)
SAP2000 (NCHRP 12-86)
Analysis for Lateral Load
20
Analysis of Box-Girder Bridge for Vertical Load
Live load versus displacement considering box
distortion
Model for Bridges under Lateral Load
Pu
PP1
Typical behavior of systems under Distributed
Lateral Load
Force-Based Design
1
u tunc
u p mc
tconf tunc
P P F C
Fmc: multi-column factor;
C : curvature factor;
u : ultimate curvature;
: curvature reduction factor for details
tunc : average curvature for typical unconfined
column;
tconf : average curvature for a typical confined
column.
21
Calibration for Lateral Load
Risk Factor for Systems under Lateral Loads:
1
u tuncus s mc s
p tconf tunc
PF C
P
f
22
2 2u target
u targetexp expLF LE
s
System Factor for Bridges under Lateral Loads:
u target = target reliability index margin = 0.50
= dispersion coefficient = 0.60 for Seismic loads
= 0.35 for Other loads
Constants
23
fs for Bridges under Lateral Load 1/2
24
fs for Bridges under Lateral Load 2/2
Force-Based Model Verification
25
Can simplified model adequately represent
SAP 2000 analysis results ?
1
u tunc
u p mc
tconf tunc
P P F C
(c) Four-Column Bents
(a) Two-Column Bents
(b) Three-Column Bents
Displacement-Based Model Verification
26
0
2
4
6
8
10
12
14
16
18
0 2 4 6 8 10 12 14 16 18
Syst
em
dis
pla
cme
nt
(in
)
One-column displacement (in)
I-girder bridge
Orig. Conf.
Category C
Category B
Equalline
0
2
4
6
8
10
12
14
16
0 2 4 6 8 10 12 14 16
Syst
em
dis
pla
cme
nt
(in
)
One-column displacement (in)
Multi-Cell Box Girder Bridge
Orig. Conf.
Cat. C
Cat. B
Equalline
Displacement capacity of a bridge system is equal to the displacement capacity of its most critical
column.
Can one-column displacement adequately
represent system displacement ?
27
fsu for I-girder Bridges under Vertical Load 1/3
Where:
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.
+ +
11 1 +
1 1
when 1.0LFR D
LF LFL LF
(1.3.6.1-1)
11 1
1 1
= when 1.0LFR D
LF LFL LF
R = 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 of
the span or due to two trucks in one lane applied in each of two contiguous spans.
1 . .L D F LL
D.F. = load distribution factor
LL = 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.
u target = 0.85
28
fsu for Narrow I-girder under Lateral Load 2/3
29
fsu for Box Bridges under Vertical Load 3/3
30
Unified Regression Equation
Relationship between LFu and LF1 for Bridge Superstructures
0
5
10
15
20
25
30
35
0 5 10 15 20 25 30 35
LFu
LF1
Prestressed I-beams-simple span
Prestressed I-beams-continuousspanPrestressed box-simple span
steel box-simple span
Prestressed I-beam sensitivity-continuous spanPrestressed I-beams-simple span
Prestressed conc.box_continuous
steel 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 bridges
LFu=1.16*LF1+0.75
R2=0.988
Ultimate Capacity Model Verification
31
fsd for Damaged I-girder under Vertical Load 1/3
Where
dR = redundancy ratio for damaged bridge systems
S beam spacing in feet.
1.23 0.23 ( / )weight beam kip ft
beam = total dead weight on the damaged beam in kip per unit length.
0.50 0.5013.5 . /
transversetransverse
M
kip ft ft
Mtransverse= is the combined moment capacity of the slab and transverse members including diaphragms
expressed in kip-ft per unit slab width.
d target = -2.70
≤ 1.10
32
fsd for Narrow I-Girder Bridges 2/3
Table C.1.3.6.1-2 Additional system factors for I-girder superstructures susceptible to damage to a
main member under vertical loads.
Bridge cross section type Redundancy ratio dR System factor
Simple span and
continuous prestressed
concrete I-girder bridges
with 4 beams at 4-ft
0.56d transverse weightR
0.47 (0.47 )
dsd
d
R
DR
R
f
Continuous non-compact
steel I-girder bridges with
4 beams at 4-ft
0.58d transverse weightR
Simple span and
continuous compact steel I-
girder bridges
with 4 beams at 4-ft
0.64d transverse weightR
33
fsd for Damaged Box under Vertical Load 3/3
34
y = 0.46x R² = 0.93
0
5
10
15
20
25
0 10 20 30 40
LFd
LF1
Box Girder Bridges
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 + 1.05 R² = 0.86
y = -0.081x + 1.35 R² = 0.96
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0 5 10 15
LFd/L
F 1
Spacing /ft
Continuous steel I-girder bridges
Non-compact
Compact
y = 0.82x - 4.14 R² = 0.99
0
5
10
15
20
25
0 10 20 30 40
LFd
LF1
Fractured boxes
Wide simple span_Partial damage
Wide contiuous_partial damage
35
Single Cell and Multi-cell Box Bridges
36
Implementation: Rating of Multi-Girder Bridge
Variable Symbol
Bending Moment Capacity Rn 7200 kip-ft
Moment due to Dead Load Dn 3500 kip-ft
AASHTO Truck Load LLHS20 1880 kip-ft
AASHTO 3S-2 Legal load Ln 1682 kip-ft
Distribution Factor D.F. 0.75
Impact Factor IM 1.33
1. LRFR Rating Factor:
1.0 7200 1.25 3500
. . 0.941.80 1682 0.75 1.33
n D n
L n
R DR F
L
f
1
20
7200 35003.18
. . 0.75 1880HS
R DLF
D F LL
2 2
22
1
1 1.5 / 1 1.5 0.491 1 1.06
1 1 3.18s
D R
LF
f
1.07 1.0 7200 1.25 3500. . 1.08
1.80 1682 0.75 1.33
s n D n
L n
R DR F
L
f f
2. Load Factor LF1:
3. System Factor:
4. System Rating:
Bridge Cross Section 6 beams at 8-ft
37
Implementation: System under Lateral Load
Variable Symbol
Plastic Moment of cap beam Mp beam 202,000 kip-in
Plastic Moment of column Mp column 198,600 kip-in
Ultimate Moment of column Mu column 214,600 kip-in
Ultimate Curvature of column u column 5.74×10-4 in-1
Ultimate Curvature of beam u beam 9.03×10-4 in-1
Lateral Load when 1st column fails Pp1 5244.8 kip
1. Correction Factor of Column Curvature:
2. Reduced Curvature to that of Cap Beam:
3. System Factor:
4. Max. Allowed Lateral Load:
202,000 198,6000.21
214,600 198,600
p beam p column
u column p column
M M
M M
4 4 41 1 10.21 5.74 10 10 9.01.2 101 3
u column u beam
in in in
4 4
3 4
0.21(5.74 10 ) 3.64 10 0.75 1.16 0.24 0.82
1.55 10 3.64 10
u tunc
s mc
tconf tunc
F C
f
1 0.82 5,244.8 4300EQ s pP P kip kip f
Three-Column Bent
Refined Direct Analysis
38
1.3.6.2.1 Direct Redundancy Analysis for Bridges under Horizontal Loads
For bridges classified to be of operational importance and for bridges not covered in Table 1. 3.6.2- 1 that are
being evaluated using the force-based approach, the system factor of Equation 1. 3.2.1-1 for the structural
components of a system subjected to horizontal load shall be calculated from the results of a nonlinear pushover
analysis using Equation 1.3.6.2-6:
min , , 1.201.20 1.20 0.50
fu ds
RR R f
1.3.6.2-6
1.3.6.1.1 Direct Redundancy Analysis for Bridges under Vertical Loads
For trusses and arch bridges, bridges classified to be of operational importance, and for bridges not covered
in 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 a
system subjected to vertical loads shall be calculated from the results of an incremental analysis using Equation
1.3.6.1.-2:
min , ,1.30 1.10 0.50
fu ds
RR R f
1.3.6.1.-2
Refined Analysis of Truss Bridge 1/2
39
40
Refined Analysis of Truss Bridge 2/2
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 superstructure
systems subject to vertical loads;
Found a unified approach for integral and non-integral column-superstructure
connections 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 Resistance
Factor Rating (LRFR) of Highway Bridges;
41
Acknowledgments
NCHRP:
NCHRP 12-86 Project Panel
Senior Prog. Officer Waseem Dekelbab
42
Research assistants:
Mr. Jian Yang (CUNY)
Ms. Feng Miao (CUNY)
Mr. Giorgio Anitori (UPC) Spain
Mr. Graziano Fiorillo (CUNY)
Mr. Murat Hamutcuoglu (HNTB)
Mr. Alexandre Beregeon
(CUNY/ENTPE) France
Mr. Tuna Yelkikanat (CUNY)
Ms. Miriam Soriano (UPC) Spain
Research Team:
Mr. David Beal.
Mr. Bala Sivakumar (HNTB).
Prof. Dan Frangopol (Lehigh).
Prof. Gongkang Fu (Ill. Inst. Tech.).
Special Thanks:
Prof. Joan Ramon Casas (UPC) Spain
Prof Yongming Tu (Southeast Univ.) China
Dr. Lennart Elfgren, (Luleå) Sweden
Questions
Thank You!
43