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