Redundancy in Long Span Bridges for Risk

Mitigation in a Multi-Hazard Environment

Prof. Michel Ghosn, Jian Yang

The City College of New York/CUNY

AASHTO Technical Subcommittee T-1

Bridge Security and Hazards

April 21, 2015

1

FHWA P.M.: Mr. Waider Wong

Presentation Outline

Background

Research Objectives

Review of Previous Work

Research Approach

Preliminary Results

Summary

2

FHWA TOPR2: Redundancy in Long Span Bridges for Risk Mitigation in a Multi-Hazard Environment

Bridges are designed so that the capacity of each component

exceeds the effects of design load combinations

Structural systems optimized to meet member design criteria

may not provide sufficient levels of redundancy to withstand

an accidental single point failure or local damage

Most known catastrophic bridge collapses have been initiated

by a single member or a localized failure

No design criteria are available to consider the consequences

of a single point failure on structural system integrity 3

Problem Statement

4

Definition of Redundancy

Redundancy is the ability of a bridge to continue to safely

carry some level of load in a damaged state (AASHTO

LRFD/FHWA)

Damage can be due to:

Overloading of members of originally intact systems

Slow-progressing damage due to various deterioration mechanisms

Sudden local damage due to human-made or natural hazards

Background

Two-Parallel Truss Bridge in Minneapolis

I-35W Mississippi River Bridge Collapsed on August 1, 2007

The gusset plates were part of a “non-redundant” design.

Source: http://blog.cleveland.com/business/2008/06/fiberoptic_sensors_could_head.html

5

Background

Two-Parallel Truss Bridge in Mount Vernon, Washington

I-5 Skagit River Bridge Collapsed on May 23, 2013

Sway struts were hit directly by truck damaging the compression chords.

Source: Wikipedia

6

Sway Struts

Compression Chords

Background

The 1940 Tacoma Narrows Bridge

Collapsed in a 42 miles per hour (68 km/h) gust on November 7, 1940

Source : Wikipedia

7

Drastic Torsional (twisting) Movement 600 foot section dropped into the water

Motions produced by fluttering increased tension beyond the strength of hangers. Once a few hangers

failed, the weight of the deck caused unzipping of adjacent hangers.

Background

Tongmai Suspension Bridge in Tibet

Collapsed on Aug. 2, 2013

Main span: 210 m

Total length: 258 m

Before collapse

Source: http://epaper.gxnews.com.cn/ddshb/html/2013-08/04/content_2255803.htm Source: http://cswb.changsha.cn/html/2013-08/04/content_5_7.htm

After collapse

8

Collapse was initiated when one suspender failed in badly

deteriorated bridge due to the crossing of a 20-ton truck

.

Background

Queensboro Bridge in New York City

9 September 2nd 2013 truck fire on Queensboro Bridge causing local damage but no collapse

Photo: ABC news http://7online.com/archive/9208672/#gallery-1

Photo : Twitter/NY Scanner

Photo: NBC news http://www.nbcnewyork.com/news/local/Queensboro-Bridge-Truck-Fire-Ed-Koch-Delay-FDNY-Official-222063031.html

Background

Mathews Bridge – Jacksonville Florida

10

Barge collision with Mathews Bridge causing severe local damage but no collapse

Photo: Will Dickey/The Times-Union

Terry Wright, who works for Great Lake Dredge and Dock near

Talleyrand, took this photo

Photo: Terry Wright

Background

No criteria for quantifying redundancy in long span bridges

Design guidelines for buildings, may not be suitable for bridges

Differences in the configurations of structural systems as well as nature

and intensity of their permanent, live and transient loads 11

ASCE 7-2012

FEMA, 1997

GSA 2000

DoD 2002

Previous NCHRP work focused on short to medium span bridges under

slow damage

Current building codes and specifications that consider progressive

collapse of long span bridges:

Issues:

TOPR2 Research Objectives

Develop a methodology for routine evaluation of redundancy in complex bridge systems

Calibrate a practical simplified analysis procedure including system and load factors for progressive collapse analysis

Provide illustrations for design and evaluation of suspension, cable-stayed and arch bridges

12

Research Team:

City University of New York

• Michel Ghosn – Principal Investigator

• Anil Agrawal - IDIQ program manager

HNTB Corp.

• Ted Zoli

• Bala Sivakumar

• John Bryson

Weidlinger Associates

• Mohammed Ettouney

Figures of bridges

4. Nonlinear

Analysis

7. Compare

system safety,

stability and

Reliability

indices

8. Parametric

Analysis

5. Output

2. Identify likely damage

scenarios

5.c

P damage slow

5.d

P damage dynamic

Select Bridges

1.a

Arch**

1.b

Cable Stayed**

1.c

Suspension**

3. Nonlinear Finite

Element Model

Originally

Intact Bridge

9. Hardening

Retrofit Scheme

Slow

Damage

Sudden dynamic

Damage

2.a slow

damage

scenario

2.b dynamic

single point

Slow

Damage

Sudden

Damage

with Energy

Release

Member

Capacity

Ultimate

Capacity

Loading

Vertical Horizontal

5.a

P member

5.b

P ultimate intact P functionality

6. Compare

R u , R f ,

R d_slow ,

R d_dynamic DCI

1. Original Design

10. Hardened Design

** Bridge types shown are for illustrative

purposes only. The actual bridges to be

studied will be determined in Task 1 –

Literature Review. ,

Res

earc

h P

lan

- F

low

Ch

art

Research Objectives

14

Failure of Suspenders or Partial Damage to Main Cable

Partial Damage to Tower

Partial Failure of Deck

Goal: Practical procedure to evaluate ability of system to sustain some damage without collapsing

Previous Work

15

Protocols for assessing redundancy

in short/ medium span bridges

NCHRP Reports 406 and 776 (Ghosn et al,

1998, 2014) Calibrated a methodology and

criteria to evaluate the redundancy in highway

bridges

PennDOT redundancy provisions

Extreme event load combinations specifically

focused on evaluating fracture critical elements

Hubbard, Shkurti, & Price of HNTB (2004);

Hunley & Harik (2007); Barth (2013), applied

NCHRP 406 method to Marquette Interchange

WI project, analysis of steel box-girder bridges,

and analysis of a truss bridge

Jackson County Little Mill Creek bridge

www.veritassteel.com

Marquette Interchange

Previous Work

16

Qualitative Analysis of Suspension

Bridge Redundancy

HANGERS GIRDERS

MAIN CABLES TOWER

Haberland, Haß & Starossek (2012)

Hangers are critical components of

a suspension bridge whose failure

may cause zipper-type collapse

Robustness of a suspension bridge

can be enhanced by providing

alternative load paths or by

segmenting bridge girder or the

suspension system

Previous Work

17

Qualitative Analyses of Suspension

Bridge Redundancy

Zoli & Steinhouse (HNTB)

Suspender loss, main cable and tower

damage are primary concerns for

progressive collapse of suspension bridges

Potential for unzipping is high for

suspension bridges with deep stiffening

trusses

Large factor of safety for suspenders is

very desirable

Previous Work

18

Qualitative Analysis of Suspension

Bridge Reliability

Sgambi, Bontempi, Biondini &

Frangopol

Multiple failure modes, load

combinations and material and

geometric nonlinearity increase

problem complexity

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

Member Safety

System Safety

Robustness = 1LF

LFd

Redundancy Concept

Basis of criteria: Bridges with 4 beams or more have been

recognized to provide adequate levels of redundancy

LFu/LF1 > 1.30 LFf/LF1 > 1.10 LFd_slow/LF1 > 0.50

Criteria based on behavior of short to medium span girder

bridges

Sudden failures were not analyzed for progressive

collapse 20

NCHRP 406 Redundancy Criteria

21

Structural Reliability

22

Reliability Index

Safety Margin

Z=R-S

23

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

2 2

ln

u system member

u

LF LL

LF

LF

V V

Basis of criteria: Bridges with 4 beams or more have been

recognized to provide adequate levels of redundancy

f > 0.85 f > 0.25 f > -2.70

Criteria based on behavior of short to medium span girder

bridges

Sudden failures were not analyzed for progressive

collapse 24

NCHRP 406 Relibaility-Based Redundancy Criteria

Application: Redundancy In Truss Bridge

25

NCHRP 776

• 110 ft Total Span

• 14 ft Bay span

• 24 ft Wide

• 2 Side by Side Truck Load

Simple Supported Real Bridge

Analysis of Originally Intact Truss Bridge

26

NCHRP 776

• Intact Bridge

• Full Capacity

• LFu / LF1 = 1.35

0

1

2

3

4

5

6

7

8

9

10

0 5 10 15 20 25

LF

Displacement [in]

ULTM

LF1

Damaged Truss

27

NCHRP 776

• Damaged Bridge

• Compression Chord

CM01

CM03

CM02

0

1

2

3

4

5

6

7

8

9

10

0 10 20 30

LF

Displacement [in]

ULTM

LF1

CM01

CM02

CM03

Redundancy in Truss Bridge

28

NCHRP 776

Analysis

Case

LFu/LF1

Ultimate

limit state

of originally

intact

bridge

LFf/LF1 Functionality

limit state

of originally

intact

bridge

LFd/LF1

Redundancy

ratio for

damaged

bridge

scenarios

LF100/LF1

for

damaged

bridge

scenarios

ULTM 1.35 1.29 -

TM01 - 1.31 1.23

CM01 - 0.57 0.40

CM02 - 0.67 0.40

CM03 - 0.30 0.21

VM01 - 1.35 1.29

VM02 - 1.35 1.29

VM03 - 1.30 1.25

VM04 - 1.27 1.14

DM01 - 1.23 0.91

DM02 - 1.37 1.35

DM03 - 1.41 1.40

Redundancy in Steel Box-Girder Bridge

29

• Three Spans Continuous

• 180 ft Each Span

• 2 Side by Side HS-20 Trucks

• K-Braces at 45 ft [L/4]

NCHRP 776

Component

Cross

section

type

Width

[in]

Thickness

[in]

Box Web (x2) [BW] Plate

12.0 0.75

Box Bottom Flange [BF] 72.0 2.0

Cross Frame [LK] L-Profile

6.0 1.0

Bottom Cross Frame [LK] 6.0 1.0

Deck Concrete 514.0 9.0

Box-Girder Intact Structure

30

Ratios :

• LFu / LF1 = 1.94 > 1.30

• LFf / LF1 = N/A

NCHRP 776

LF1

Box-Girder Damage Scenarios

31

NCHRP 776

Braces Removed [DB01] 6’’ Through Section Fracture [DB02]

15’’ External Web and Half

Flange Removed [DB03] 80’’ External Web and Half

Flange Removed [DB04]

Redundancy in Box-Girder Bridge

32

LF1

Analysis

Case LFu/LF1 LFf/LF1 LFd/LF1 LF100/LF1

BULTM 1.94 -

DB01 - 1.24 -

DB02 - 1.39 -

DB03 - 1.81 -

DB04 - 1.50 -

NCHRP 776

Continuous steel box

girder bridges have very

high levels of redundancy

Dynamic Progressive Collapse Analysis Procedure

33

1. From static analysis of originally intact bridge determine internal forces, P0, in elements to be removed. 2. Change structural geometry by replacing element susceptible to damage by static force P0. 3. Apply dynamic impulsive force P(t) in opposite direction of static force P0. 4. Determine if system response will exceed capacity.

Dynamic Analysis Procedure for a SDOF System

34

Dynamic time history analysis process using simple member snapping approach

Comparison between structural analysis software and theoretical dynamic response

35

Results confirm that member snapping approach is as accurate as theoretical analysis

Comparisons of dynamic response Comparisons of dynamic amplification factor

Proposed Simplified Progressive Collapse Analysis

36

Pseudo Static Analysis of Damaged Bridge

Research will determine appropriate dynamic amplification and safety factors for use during simplified pseudo static progressive collapse analysis to evaluate level of redundancy in complex bridge systems similar to GSA method used for buildings

1.5E+03

2.0E+03

2.5E+03

3.0E+03

3.5E+03

4.0E+03

4.5E+03

5.0E+03

0 1 2 3 4 5 6 7 8 9 10

Ad

jace

nt

Han

ger

Forc

e P

(k

N)

Time (sec.)

Static Response

Pseudo Static Response

Minimum Required Capacity

Dynamic amplification (to be determined)

Safety factor (to be determined)

Preliminary Results

37

Suspension Bridge

• 820 ft-2,723 ft-820 ft

• 93 ft Wide Steel Box

• 41 ft+70@37.7ft+41 ft Suspender Spacing

• Suspender Strength: 1,005 kips/suspender

• Concrete Compressive Strength f ’c : 7.25 ksi • Tower stiffness(EI/l3/leg) @ top: 68 kip/ft; (EI/l3/leg) @ bottom: 128 kip/ft

• Tower stiffness(EA/l/leg) @ top: 2.5x105 kip/ft; (EA/l /leg) @ bottom: 4.5x105 kip/ft

Actual Simple Span Bridge

Live Load Model

38

Variable Design value (4 lanes) Bias Mean value

1 event 2.37 kip/ft 0.969 2.30 kip/ft

1 week 2.37 kip/ft 1.136 2.69 kip/ft

1 year 2.37 kip/ft 1.206 2.86 kip/ft

75 year 2.37 kip/ft 1.266 3.00 kip/ft

Preliminary Results

39

Effect of Td on Adjacent Hanger Force

(1) Td=1ms

(2) Td=10 ms

(3) Td=100 ms

(4) Td=1000 ms

Max is 2802 kN at 83 ms

Max is 2740 kN at 83 ms

Max is 2449 kN at 140 ms

Max is 2198 kN at 1050 ms

1.5E+03

2.0E+03

2.5E+03

3.0E+03

0 1 2 3 4 5 6 7 8 9 10H

anger

Forc

e

(kN

) Time (sec.)

1.5E+03

2.0E+03

2.5E+03

3.0E+03

0 1 2 3 4 5 6 7 8 9 10

Hanger

Forc

e

(kN

)

Time (sec.)

1.5E+03

2.0E+03

2.5E+03

3.0E+03

0 1 2 3 4 5 6 7 8 9 10

Hanger

Forc

e

(kN

)

Time (sec.)

1.5E+03

2.0E+03

2.5E+03

3.0E+03

0 1 2 3 4 5 6 7 8 9 10

Hanger

Forc

e

(kN

)

Time (sec.)

Preliminary Results

40

Effect of Damping on Dynamic Amplification Factor

Damage Concerns

41

Lateral load on partially

damaged tower

V V

w

Vertical load on damaged deck

Damaged cable and suspenders

Partial cable

damage

Partial tower

damage

Partial deck

damage

Preliminary Results

42

Live load factor versus reliability index for different bridge damage scenarios

Establish the relationship between the dynamic progressive collapse reliability of each design and the live

load multiplier l.

Suspension Bridge

Preliminary Results

43

Pushdown Analysis Results

Suspenders designed for

safety factor S.F.=3.5

Thick arrow:

System capacity

Thin arrow:

First member failure

Analysis Cases LF1 LFu or LFd Ru or Rd

Intact 11.1 15.0 1.35>1.30 10.0-8.0>0.85

1 hanger ruptured 11.1 9.78 0.88>0.50 9.47-8.0>-2.7

3 hangers ruptured 11.1 8.77 0.79>0.50 8.87-8.0>-2.7

5 hangers ruptured 11.1 3.51 4.91-8.0<-2.7

0.0E+00

5.0E+04

1.0E+05

1.5E+05

2.0E+05

2.5E+05

3.0E+05

3.5E+05

4.0E+05

4.5E+05

5.0E+05

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0

Live

load

(kN

)

Displacement (m)

Pushdown Analysis

Intact

1 hanger damaged

3 hangers damaged

5 hangers damaged

LF1

LFu

l collapse

Damage 1 Collapse

Live load

multiplier l

Bridge Damage Level

Collapse

Damage 2

Expected Outcome

l 2

l 1

Envisioned Performance Based Design Criteria

LFu

LF1

Expected Outcome

45

Performance-based design to study the ability of a bridge with a

certain level of damage to still sustain sufficient level of load

A structural engineer will be able to design a reliable system by simply

performing an incremental static analysis without the need to perform a

nonlinear dynamic analysis

Target safety factors for different levels of damage can be extracted

based on experience with the performance of bridges that have survived

significant damage or from reliability indexes

Preliminary analysis demonstrates the feasibility of the proposed

research approach and consistency of results with previous NCHRP

studies

Summary

46

We described ongoing work supported by FHWA to study Redundancy in

Long Span Bridges for Risk Mitigation in a Multi-Hazard Environment

TOPR2 Objective is to develop a methodology to quantify redundancy in

complex bridge systems

Study will determine appropriate live load multiplier (considering dynamic

amplification and safety factor) for use during simplified progressive

collapse analysis to evaluate level of redundancy in complex bridge

systems similar to GSA method for buildings

We will provide illustrative applications for design of long span bridges

Questions

Thank You!

47