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RiskAnalysis
for
BridgesAndrzej S. Nowak
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Department of Civil Engineering
Outline
Importance of bridges
Natural and man-made hazards Risk analysis procedures
Target reliability
Implementations
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Department of Civil Engineering
Bridges in USA
Bridges are structures with span larger than 20 ft
There are 584,000 highway bridges (4 millionpaved roadway)
Interstate highway network consists of about50,000 miles of highways and 54,800 bridges
Traffic growth: number of vehicles and weight oftrucks
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Department of Civil Engineering
National Bridge Inventory (NBI)
NBI is maintained by the Federal HighwayAdministration (FHWA)
Total number of bridges in NBI is 584,000
NBI includes bridge location, structural type,material, number of spans, span length(s), width,and rating factors
Federal Aid Highway Bridges owned by State
DOTs (about 50%)
Off System Highway Bridges owned by Counties,Cities and private owners
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Department of Civil Engineering
Importance of Bridges
Local and national economy (transportation)
Considerable national investment
Need to access affected regions during disasters
(floods, hurricanes, earthquakes) Strategic importance for national defense, terrorist
attacks
Showcase for technological progress, signature
bridges
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General Problems
Most bridges were built in 1950s and 1960s Bridges deteriorate due to aging, increased live
loads, cracking, corrosion, environmental effects(freeze and thaw cycles), fatigue
Many bridges (30%) are either structurallydeficient or functionally obsolete. They needrepair, rehabilitation or replacement
Available funds are limited. How to use thelimited resources in the most efficient way?
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Needs
Rational bridge design codes
Efficient procedures for evaluation of existingbridges (actual loads, actual load carrying
capacity) Efficient methods for repair and rehabilitation
Rational protective and preventive measures(maintenance, monitoring, security devices)
Methods for prediction of future changes
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Current Trends
Reliability-based design codes, load and resistancefactor design (LRFD)
Advanced finite element methods (FEM)
Non-destructive evaluation techniques (NDT) Weigh-in-Motion (WIM) measurement of trucks
Bridge management system (BMS)
Focus on accelerated repair, rehabilitation andreplacement
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Department of Civil Engineering
Future Developments
Performance-based design
Life-cycle optimization
High-performance materials
Computer-aided analysis and design
Remote sensing and monitoring of structuralperformance
Security considerations (protective design) Minimization of interference with traffic
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Natural Hazards
Wind (hurricanes, tornadoes)
Snow and ice
Floods (tsunami) Earthquakes
Temperature effects
Material degradation
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Schoharie Creek Bridge
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Depth of Scour
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Damaged Plinth
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Department of Civil Engineering
Man-Made Hazards
Inadequate maintenance (corrosion,cracking)
Overloads (weight, height) Collisions vehicles and vessels
Acts o vandalism, intentional damage
Terrorist attacks, explosions, fires
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Department of Civil Engineering
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Department of Civil Engineering
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Department of Civil Engineering
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Department of Civil Engineering
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Department of Civil Engineering
Extreme Events
Very small probability of occurrence
Very severe consequences
Approach: Prevent, reduce probability of
occurrence
Reduce consequences, contain thedamage
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Department of Civil Engineering
Basic Questions
How to measure probability of failure
and reliability?
What is the target reliability, oracceptable probability of failure?
How to implement it in engineering
practice?
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Department of Civil Engineering
Safety Measure
Probability of failure, PF
Reliability index,
Simple formula Iterative procedures
Monte Carlo simulations
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Reliability Index,
Mean (R-Q)
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Reliability Index,
For a linear limit state function, and R and Q bothbeing normal random variables
2
Q
2
R
QR
+
=
R = mean resistanceQ = mean load
R = standard deviation of resistance
Q = standard deviation of load
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Reliability index and probability of failure
PF 10-1 1.28
10-2 2.33
10
-3
3.09
10-4 3.71
10-5 4.26
10-6 4.75
10-7 5.19
10-8 5.62
10-9 5.99
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Department of Civil Engineering
Target Reliability Index
If reliability index is too small there are problems, even structural
failures If reliability index is too large the
structures are too expensive
Hi i l P i
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Historical Perspective
Trial and error, past experience, judgment
Allowable stress design, central safetyfactor
Partial safety factors (limit state design, orload and resistance factor design)
Life-cycle analysis, optimization of the total
cost, cost-benefits ratio
Selection Criteria for the
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Selection Criteria for theTarget Reliability Index
Consequences of failure
Economic analysis (costs)
Past practice
Human perception
Political decisions
T t R li bilit I d
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Target Reliability Index major considerations
Redundancy and Ductility
Element and system reliabilityNew design and existing structure
Important and ordinary structures
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Structural Systems
Series systems weakest linksystems, to be avoided
Parallel systems componentsshare the load, preferred systems
Avoid brittle materials and elements,
use ductile materials and elements
Th k t li k
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Department of Civil Engineering
The weakest link
determines the strength
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Department of Civil Engineering
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Department of Civil Engineering
Target Reliability Indices inAASHTO Bridge Design Code
3.5 for steel and prestressed
concrete components
2 for wood components 5-6 for structural systems
0-1 for serviceability limit states
(deflection, decompression)
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Department of Civil Engineering
Target Reliability by ISO-2394
Relative costs of safety
measures
Consequences of Failure
small some moderate great
High 0 1.5 2.3 3.1
Moderate 1.3 2.3 3.1 3.8
Low 2.3 3.1 3.8 4.3
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Department of Civil Engineering
Proposed Target Reliability for ACI 318
Relative costs of
safety measures
Consequences of Failure
small some moderate great
High 0 1.5 2.5 3
Moderate 1 2.5 3 4
Low 2 3 4 4.5
I l t ti f th
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Department of Civil Engineering
Implementation of thetarget reliability
Design by load and resistance factors, fool-proof design, protective design
Construction quality control of materials and
workmanship, fool-proof construction Proper use and operation, maintenance,
preventive repairs
Preventive measures, monitoring, diagnostictesting
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Golden Gate Bridge, San Francisco
built in 1933-1935, span of 1280 m
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Golden Gate Bridge
San Francisco
Sunshine Skyway Bridge, Tampa, Florida
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Sunshine Skyway Bridge, Tampa, Florida
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