design codes part 3 - wojskowa akademia techniczna · design codes –part 3 role of a code in the...
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DESIGN CODES – Part 3
Role of a Code in the Building Process
Code levels
Code Development Procedure- Scope of the Code
- Code objective
- Demand Function
- Closeness to the Target
- Code Format
Development of a Bridge Design Code (AASHTO)
Development of a Design Code for Concrete Buildings (ACI 318)
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Role of a Design Code
Parties involved in the building process: owner, designer, contractor, user-occupant
Conflicting interests
The Code establishes the acceptance criteria
Types and magnitude of loads and load combinations
Required minimum load carrying capacity
Required safety margin in terms of safety factor, reliability index, or probability of failure
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CENTRAL ROLE OF A DESIGN CODE
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DESIGN CODES –HISTORICAL PERSPECTIVE
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CODE LEVELS
Depending on the approach to reliability, there are four levels (categories) of design codes:
Level I Codes: use deterministic design formulas.
Level II Codes: reliability index is compared to the target value
Level III Codes: full reliability analysis is performed
Level IV Codes: reliability analysis and cost optimization
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CODE LEVELS
Level I Codes: These codes use deterministic design formulas. The safety margin is introduced through central safety factors (ratio of design resistance to design load) or partial safety factors (load and resistance factors).
Level II Codes: These codes define the design acceptance criterion in terms of the “closeness” of the actual reliability index for a design to the target reliability index or other safety related parameters.
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CODE LEVELS
- Level III Codes require a full reliability analysis to quantify the probability of failure of the structure under various loading scenarios. The acceptance criterion is defined in terms of the closeness of the actual reliability index to the optimum reliability level (or probability of failure).
- Level IV Codes use the total expected cost of the design as the optimization criterion. The acceptable design maximizes the utility function which describes the difference between the benefits and costs associated with a particular design.
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Code Development Procedure
The major steps involved in the development of a design code include:
Step 1. Define scope and data space.
Step 2. Define code objective(s).
Step 3. Establish frequency of demand.
Step 4. Select code space metric.
Step 5. Select code format(s).
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1. Scope of the Code
Define class of structures (building, bridge)
Function (office buildings, highway bridge, parking structure)
Materials (steel, reinforced concrete, wood)
Loads (wind, earthquake, ice)
Range of parameters (span range)
Limit states (flexural capacity, deflection)
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2. Define Code Objective
To achieve a negligible failure frequency with a reasonable material economy
Minimize total utility (difference between revenues and costs)
To design structures which can survive a pre-selected period of time with a reasonable probability of failure
To design structures with b close to bT (target reliability index)
To design structures with a safety factor not less than a pre-selected allowable value (allowable stress design)
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3. Establish Frequency of Demand
The basis is analysis of past and present practice
Determine the frequency of occurrence of a particular safety check
The most common load cases, e.g. determine frequencies for different ratios of D and L
Fuzzy values can be assigned: often, sometimes, rarely, unlikely
Future trends are more important than past and even present
The code should provide a good fit to bT for the most frequent design situations (e.g. most frequent load ratios)
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4. Closeness to the Target
Measure of closeness between the code and its objective
bT – b , this difference varies
Minimize (bT – b)2, or minimize |bT – b|
The best is to minimize
(bT – b)/d – 1 + exp [- (bT – b)/d]
Minimize the total cost
CT = CI + CF PF
where:
CI = initial cost (design and construction)
CF = cost of failure (almost constant)
PT = probability of failure
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Target Reliability Index
Selection criteria:
Consequences of failure
Marginal cost of reliability (cost to increase or decrease the reliability by a unit)
Reliability of structures designed using the current (old) code
Performance of structures designed using the current (old) code
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Utility vs. Target Reliability
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New Design vs. Existing Structure
For a new design, reliability can be increased with little extra cost
For an existing structure any strengthening can be prohibitively expensive
Current practice accepts lower reliability levels for existing structures
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System vs. Component
Structures are systems made of components
Series system (weakest link)
Parallel systems
Failure of a component may not mean failure of the system
Ductile and brittle components
Correlation between components
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Examples of the Target Reliability Indices for Bridge Components
bT = 3.5 Primary component
Multiple load path
bT = 5.0 Primary component
Single load path
bT = 2.0 Secondary component
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Examples of the Target Reliability Indices for Bridges
For steel, reinforced concrete, prestressed concrete girders,
bT = 3.5
For sawn wood bridge components,
bT = 2.0
For girder bridge as a system,
bT = 5.5-6.5
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5. Code Format
Simple or complex
Simple code – not good for closeness to the target
Complex code – not good for users
Allowable stress design
Stress due to design load < allowable stress
(safety reserve in the allowable stress)
Load and resistance factor design (LRFD)
Factored load < factored resistance
(safety reserve in load and resistance factors)
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Allowable Stress Design
D + L ≤ Fa
where: D = stress due to dead load
L = stress due to live load
Fa = allowable stress
Safety margin is mostly in the allowable
stress (conservatively low)
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Load and Resistance Factor Design (LRFD), or Limit States Design Codes
For each limit state
factored load ≤ factored resistance
Load and resistance factors serve as partial safety factors
They are determined using the code calibration procedure
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LRFD Philosophy
Define limit state function, e.g.
g = R – (D + L)
so that g < 0 means failure.
Safety reserve is represented by load and
resistance factors
gD D + gL L ≤ f R
where
gD > 1.0, gL > 1.0, f < 1.0
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Selection of New Load and Resistance Factors
Factored load and factored resistance correspond to the “design point”
The number of different load and resistance factors should be minimized
Load and resistance factors are rounded to the nearest 0.05
The same load factors for all materials
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Load Factors, g
Approximate formula for a load factorg = l (1 + n V)
where l = bias factor for the considered load
component
V = coefficient of variation for the considered load component
n = a constant, equal to about 2 for the ultimate limit states (bridge girders)
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Resistance Factors
A limited number of different resistance factors, f, is considered (they are rounded to the nearest 0.05)
Calculate reliability indices for each value of f
Select f that results in b’s closest to the target reliability index
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Future Trends in the Development of Design Codes
Improve statistical data-base for load and resistance parameters
Consider load sharing, redundancy, and brittleness/ductility
Develop system reliability models for structures rather than components
Determine the degree of correlation between load and resistance parameters
Verify boundary conditions for advanced structural analysis models (finite elements method)
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Example of Code CalibrationACI 318 Building Code
The basic document for design of concrete (R/C and P/C) buildings in USA
ACI 318 specifies resistance factors and design resistance
ACI 318 specifies load factors
ACI 318 does not specify design load, reference is made to other codes
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Why Calibration of ACI 318?
Current load factors were adopted in 1950’s
Introduction of the new code with loads and load factors, ASCE 7 (American Society of Civil Engineers)
Load factors specified in ASCE 7 are already adopted for steel design (AISC) and wood
Problems with mixed structures (steel and concrete)
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Load factors specified byACI 318 and ASCE 7
The design formula specified
by ASCE-7 Standard
1.4 D < f R
1.2 D + 1.6 L < f R
1.2 D + 1.6 L + 0.5 S < f R
1.2 D + 0.5 L + 1.6 S < f R
1.2 D + 1.6 W + 0.5 L + 0.5 S < f R
1.2 D + 1.0 E + 0.5 L + 0.2 S < f R
0.9 D – (1.6 W or 1.0 E) < f R
The design formula specified
by ACI 318-99 Code
1.4 D + 1.7 L < f R
0.75 (1.4 D + 1.7 L + 1.7 W) < f R
0.9 D + 1.3 W < f R
0.75 (1.4 D + 1.7 L + 1.87 E) < f R
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Objectives of Calibration of ACI 318
Determine resistance factor, f, corresponding to the new load factors (ASCE 7)
Reliability of the designed structures cannot be less the predetermined minimum level
Maintain a competitive position of concrete structures
If needed, identify the need for changes of load factors in the ASCE 7
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Considered Structural Components
Beams (reinforced concrete, prestressed concrete)
Slabs (reinforced concrete, prestressed concrete)
Columns (reinforced concrete, prestressed concrete, tied and spiral)
Plain concrete
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Considered Load Components
D = dead load
L = live load
S = snow
W = wind
E = earthquake
Load combinations
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Statistical Load Models
Time-varying loads
“Turkstra-Rule” – load combination model
The load models require further analysis, as the models used in this calibration are too conservative (in particular wind and earthquake)
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Assumed Statistical Data
Dead load l = 1.03-1.05, V = 0.08-0.10
Live load l = 1.00, V = 0.20
Wind l = 0.80, V = 0.35
Snow l = 0.80, V = 0.25
Earthquake l = 0.65, V = 0.55
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Considered Materials
Concrete (cast-in-place and precast)
Ordinary concrete
Light weight concrete (18 kN/m3)
High strength concrete
(f’c ≥ 45 MPa)
Reinforcing steel bars
Prestressing steel strands
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Reliability Index
The general format of the limit state function
g = R – Q = 0
2
Q
2
R
QR
b
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Considered Cases
Old
Statistical data for materials from 1970’s
Design according to ACI 318-99
New
Statistical data for materials from 2001-02
Design according to proposed ACI 318
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Reliability Indices for R/C Beams,
Flexure, Ordinary Concrete (D+L)
R / C B eam, F lexure
Old St at ist ical D at a
Exist ing D esign, C ast in Place
0
1
2
3
4
5
6
7
8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
D/ ( D+L)
f0.0
R/ C Be a m, Fl e x ur e
Ne w S t a t i st i c a l Da t a , P r opose d De si gn
Ca st i n P l a c e
0
1
2
3
4
5
6
7
8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
D/ ( D+L)
f0.5
f0.0
f0.5
OLD NEW
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Reliability Indices for R/C Beams,
Flexure, High Strength Concrete (D+L)
R / C B eam, F lexure
Old St at ist ical D at a
Exist ing D esig n, C ast in Place
0
1
2
3
4
5
6
7
8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
D / ( D +L )
f0.0
R / C B eam, F lexure
N ew St at ist ical D at a, Propo sed D esign
C ast in Place, S=0 .5L
0
1
2
3
4
5
6
7
8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
D / (D +L)
f0.5
f0.0
f0.5
OLD NEW
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Reliability Indices for R/C Beams,
Shear, Ordinary Concrete (D+L)
R/ C be a m, S he a r , Ol d S t a t i st i c a l Da t a ,
Ex i st i ng De si gn,
Ca st i n P l a c e
0
1
2
3
4
5
6
7
8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
D / ( D +L )
f0.5
R/ C be a ms, S he a r , Ne w S t a t i st i c a l Da t a ,
P r opose d De si gn,
Ca st i n P l a c e , S =0 . 5 L
0
1
2
3
4
5
6
7
8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
D/ ( D+L)
f0.0
f0.5
f0.0
OLDNEW
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Reliability Indices for R/C Beams,
Shear, High Strength Concrete (D+L)
R / C beam, Shear, Old St at ist ical D at a,
Exist ing D esign,
C ast in Place
0
1
2
3
4
5
6
7
8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
D / ( D +L )
f0.5
R/ C be a ms, S he a r , Ne w S t a t i st i c a l Da t a ,
P r opose d De si gn,
Ca st i n P l a c e , S =0 . 5 L
0
1
2
3
4
5
6
7
8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
D/ ( D+L)
f0.0
f0.5
f0.0
OLD NEW
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Reliability Indices for P/S Beams,
Flexure, Ordinary Concrete (D+L)
P/ S B eam, F lexure
Old St at ist ical D at a
Exist ing D esig n, Plant C ast
0
1
2
3
4
5
6
7
8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
D / ( D +L)
f0.0
P/ S B eam, F lexure
N ew St at ist ical D at a, Proposed D esign
Plant C ast , S=0 .5L
0
1
2
3
4
5
6
7
8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
D/ ( D+L)
f0.5
f0.0
f0.5
OLD NEW
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Reliability Indices for P/S Beams,
Shear, Ordinary Concrete (D+L)
P / S be a m, S he a r , Ol d S t a t i st i c a l Da t a ,
Ex i st i ng De si gn
P l a nt Ca st
0
1
2
3
4
5
6
7
8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
D/ ( D+L)
f0.5
P / S be a ms, S he a r , Ne w S t a t i st i c a l Da t a ,
P r opose d De si gn
P l a nt Ca st , S =0 . 5 L
0
1
2
3
4
5
6
7
8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
D/ ( D+L)
f0.0
f0.5
f0.0
OLD NEW
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Reliability Indices for R/C Slabs,
Flexure, Ordinary Concrete (D+L)
R/ C S l a bs, Fl e x ur e , Ol d S t a t i st i c a l Da t a ,
Ex i st i ng De si gn
Ca st i n P l a c e
0
1
2
3
4
5
6
7
8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
D / ( D +L )
f0.0
R/ C S l a bs, Fl e x ur e , Ne w S t a t i st i c a l Da t a ,
P r opose d De si gn
Ca st i n P l a c e , S =0 . 5 L
0
1
2
3
4
5
6
7
8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
D/ ( D+L)
f0.5
f0.0
f0.5
OLD NEW
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Reliability Indices for R/C Slabs,
Flexure, High Strength Concrete (D+L)
R / C Slabs, F lexure, Old St at ist ical D at a,
Exist ing D esign
C ast in Place
0
1
2
3
4
5
6
7
8
0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1. 0
f0.0
R / C Slabs, F lexure, N ew St at ist ical D at a,
Proposed D esign
C ast in Place, S=0 .5L
0
1
2
3
4
5
6
7
8
0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1. 0
D / ( D +L )
f0.5
f0.0
f0.5
OLD NEW
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Reliability Indices for P/S Slabs,
Flexure, Ordinary Concrete (D+L)
P / S S l a bs, Fl e x ur e , Ol d S t a t i st i c a l Da t a ,
Ex i st i ng De si gn
P l a nt Ca st
0
1
2
3
4
5
6
7
8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
D/ ( D+L)
f0.0
P / S S l a bs, Fl e x ur e , Ne w S t a t i st i c a l Da t a ,
P r opose d De si gn
P l a nt Ca st , S =0 . 5 L
0
1
2
3
4
5
6
7
8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
D / ( D +L )
f0.5
f0.0
f0.5
OLDNEW
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Reliability Indices for Post Tensioned Slabs,
Flexure, Ordinary Concrete (D+L)
Post -tensioned Slab, Old
Statistical Data, Existing Design
Cast in Place
0
1
2
3
4
5
6
7
8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
D / ( D +L )
f0.0
Post-tensioned Slabs, New
Statistical Data, Proposed
Design
Cast in Place, S=0.5L
0
1
2
3
4
5
6
7
8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
D/ ( D+L)
f0.5
f0.0
f0.5
OLDNEW
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Reliability Indices for Post Tensioned Slabs,
Flexure, High Strength Concrete (D+L)
Post -tensioned Slab, Old
Statistical Data, Existing Design
Cast in Place
0
1
2
3
4
5
6
7
8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
D / ( D +L)
f0.0
Post-tensioned Slabs, New
Statistical Data, Proposed Design
Cast in Place, S=0.5L
0
1
2
3
4
5
6
7
8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
D/ ( D+L)
f0.5
f0.0
f0.5
OLD NEW
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Reliability Indices for R/C Columns, Tied,
Ordinary Concrete (D+L)
R/ C Col umns, Ti e d ( f a i l ur e i n c ompr e ssi on) ,
Ol d S t a t i st i c a l Da t a , Ex i st i ng De si gn, Ca st
i n P l a c e
0
1
2
3
4
5
6
7
8
0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1. 0
D / ( D +L )
f0.0
R/ C Col umns, Ti e d ( f a i l ur e i n
c ompr e ssi on) , Ne w S t a t i st i c a l Da t a ,
P r opose d De si gn
Ca st i n P l a c e , S =0 . 5 L
0
1
2
3
4
5
6
7
8
0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1. 0
D / ( D + L)
f0.65
f0.0
f0.5
OLDNEW
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Reliability Indices for R/C Columns, Tied,
High Strength Concrete (D+L)
R / C C o lumns, T ied ( f ailure in
co mpressio n) , Old St at ist ical D at a,
Exist ing D esign, C ast in Place
0
1
2
3
4
5
6
7
8
0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1. 0
D / ( D +L )
f0.0
R / C C o lumns, T ied ( f ailure in
compression) , N ew St at ist ical D at a,
Proposed D esign
C ast in Place, S=0 .5L
0
1
2
3
4
5
6
7
8
0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1. 0
D / ( D + L)
f0.65
f0.0
f0.5
OLD NEW
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Reliability Indices for R/C Columns, Spiral,
Ordinary Concrete (D+L)
R / C C o l u mn s , Sp i r a l , ( f a i l u r e i n c o mp r e s s i o n ) , O l d
S t a t i s t i c a l D a t a , E x i s t i n g D e s i g n , C a s t i n P l a c e
0
1
2
3
4
5
6
7
8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
D / ( D +L )
f0.5
R / C C o l u mn s , Sp i r a l , ( f a i l u r e i n c o mp r e s s i o n ) , N e w
St a t i s t i c a l D a t a , P r o p o s e d D e s i g n , C a s t i n P l a c e ,
S= 0 . 5 L
0
1
2
3
4
5
6
7
8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
D / ( D +L )
f0.0
f0.5
f0.0
OLD NEW
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Reliability Indices for R/C Columns, Spiral,
High Strength Concrete (D+L)
R / C C o lumns, Sp iral, ( f ailure in
compressio n) , Old St at ist ical D at a,
Exist ing D esign, C ast in Place
0
1
2
3
4
5
6
7
8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
D / ( D +L )
f0.5
R / C C o lumns, Sp iral, ( f ailure in
co mpression) , N ew St at ist ical D at a,
Prop osed D esig n, C ast in Place, S=0 .5L
0
1
2
3
4
5
6
7
8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
D/ ( D+L)
f0.0
f0.5
f0.0
OLD NEW
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P / S Col umns Ti e d ( f a i l ur e i n c ompr e ssi on) ,
Ol d S t a t i st i c a l Da t a , Ex i st i ng De si gn, P l a nt
Ca st
0
1
2
3
4
5
6
7
8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
D/ ( D+L)
f0.0
P / S Col umns, Ti e d ( f a i l ur e i n c ompr e ssi on) ,
Ne w S t a t i st i c a l Da t a , P r opose d De si gn
P l a nt Ca st , S =0 . 5 L
0
1
2
3
4
5
6
7
8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
D/ ( D+L)
f0.65
f0.0
f0.5
Reliability Indices for P/S Columns, Tied,
Ordinary Concrete (D+L)
OLD NEW
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Reliability Indices for P/S Columns, Spiral,
Ordinary Concrete (D+L)
P / S C o l u mn s , Sp i r a l , ( f a i l u r e i n c o mp r e s s i o n ) , O l d
St a t i s t i c a l D a t a , E x i s t i n g D e s i g n , P l a n t C a s t
0
1
2
3
4
5
6
7
8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
D / ( D +L )
f0.5
P / S C o l u mn s , Sp i r a l , ( f a i l u r e i n c o mp r e s s i o n ) , N e w
St a t i s t i c a l D a t a , P r o p o s e d D e s i g n , P l a n t C a s t ,
S= 0 . 5 L
0
1
2
3
4
5
6
7
8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
D / ( D +L )
f0.0
f0.5
f0.0
OLD NEW
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Reliability Indices for Plain Ordinary Concrete Elements, (D+L)
P / S C o l u mn s , Sp i r a l , ( f a i l u r e i n c o mp r e s s i o n ) , N e w
St a t i s t i c a l D a t a , P r o p o s e d D e s i g n , P l a n t C a s t ,
S= 0 . 5 L
0
1
2
3
4
5
6
7
8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
D / ( D +L )
f0.0
f0.5
f0.0
P l a i n C o n c r e t e , ( f l e x u r e , c o mp r e s s i o n , s h e a r &
b e a r i n g ) , N e w St a t i s t i c a l D a t a , P r o p o s e d D e s i g n
C a s t i n P l a c e , S= 0 . 5 L
0
1
2
3
4
5
6
7
8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
D / ( D +L )
f0.60
f0.65
f0.0
OLD NEW
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Reliability Indices for Plain High Strength Concrete Elements, (D+L)
Plain C oncret e, ( f lexure, compression,
shear & bearing ) , Old St at ist ical D at a,
Exist ing D esign
C ast in Place
0
1
2
3
4
5
6
7
8
9
10
0 . 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 0 . 9 1. 0
D / ( D +L )
f0.65
Plain C oncret e , ( f lexure, co mpression,
shear & bearing ) , N ew St at ist ical D at a,
Proposed D esign
C ast in Place, S= 0 .5L
0
1
2
3
4
5
6
7
8
9
10
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
D / ( D +L)
f0.60
f0.65
f0.0
OLD NEW
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Reliability Indices for R/C Beams,
Flexure, Ordinary Concrete, (D+L+W)
R / C B eam, F lexure
Old Stat ist ical D ata
Exist ing D esign, C ast in P lace
0
1
2
3
4
5
6
7
8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
D / ( D +L)
f0.0
R / C B eam, F lexure
N ew St at ist ical D at a, Proposed D esign
C ast in Place
0
1
2
3
4
5
6
7
8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
D/ ( D+L)
f0.5
f0.0
f0.5
NEWOLD
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Reliability Indices for R/C Beams,
Flexure, Ordinary Concrete, (D+L+E)
R / C B eam, F lexure Old Stat ist ical D ata
Exist ing D esign, C ast in P lace
0
1
2
3
4
5
6
7
8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
D / ( D +L)
f0.0
R / C B eam, F lexureN ew Stat ist ical D ata, P ro po sed D esign
C ast in P lace
0
1
2
3
4
5
6
7
8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
D / ( D +L)
f0.5
f0.0
f0.5
OLD NEW
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Reliability Indices for R/C Beams,
Flexure, Ordinary Concrete, (D+L+S)
R / C B eam, F lexure
Old St at ist ical D at a
Exist ing D esign, C ast in Place
0
1
2
3
4
5
6
7
8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
D / ( D +L )
f0.0
R / C B eam, F lexureN ew Stat ist ical D ata, P ro po sed D esign
C ast in P lace
0
1
2
3
4
5
6
7
8
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
D/ ( D+L)
f0.5
f0.0
f0.5
OLDNEW
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Selected Range of Reliability Indices for Beams, designed according to “old” ACI 318
Range of Target Reliability Index for Beams
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
Reli
ab
ilit
y I
nd
ex
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Selected Range of Reliability Indices for Slabs, designed according to “old” ACI 318
Range of Target Reliability Index for Slabs
0.0
1.0
2.0
3.0
4.0
5.0
6.0
Reli
ab
ilit
y I
nd
ex
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Selected Range of Reliability Indices for Columns and Plain Concrete Elements,
designed according to “old” ACI 318
Range of Target Reliability Index for Columns and Plain
Concrete Elements
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
Reli
ab
ilit
y I
nd
ex
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Selected Target Reliability Indices
Structural type and limit state Range of β β T
R/C Beam cast-in-place, flexure 3.4-3.6 3.5
R/C beam plant cast, flexure 3.2-3.4 3.5
R/C Beam cast-in-place, shear 3.8-4.0 3.5
R/C beam plant cast, shear 4.1-4.2 3.5
P/S beam plant cast, flexure 4.2-4.4 3.5
P/C beam plant cast, shear 4.3-4.4 3.5
R/C slab cast-in-place 2.3-2.5 2.5
R/C slab plant cast 3.8-3.9 3.5
P/S slab plant cast 4.7-5.0 3.5
Post-tensioned slab cast-in-place 2.3-2.5 2.5
R/C column cast-in-place, tied 3.8-4.1 4.0
R/C column plant cast, tied 3.9-4.2 4.0
R/C column cast-in-place, spiral 4.0-4.4 4.0
R/C column plant cast, spiral 4.2-4.5 4.0
P/S column plant cast, tied 5.0-5.3 4.0
P/S column plant cast, spiral 5.8-6.2 4.0
Plain concrete, flexure, shear 5.7-6.2 4.0
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Recommended Resistance Factors for ACI 318
Structural type and limit state Resistance factors, φ
R/C Beam cast-in-place, flexure 0.90
R/C beam plant cast, flexure 0.90
R/C Beam cast-in-place, shear 0.85
R/C beam plant cast, shear 0.85
P/S beam plant cast, flexure 0.90
P/C beam plant cast, shear 0.85
R/C slab cast-in-place 0.90
R/C slab plant cast 0.90
P/S slab plant cast 0.90
Post-tensioned slab cast-in-place 0.90
R/C column cast-in-place, tied 0.75
R/C column plant cast, tied 0.75
R/C column cast-in-place, spiral 0.80
R/C column plant cast, spiral 0.80
P/S column plant cast, tied 0.75
P/S column plant cast, spiral 0.80
Plain concrete, flexure, shear 0.65
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Proposed Change in Load Factors (ASCE 7)
The design formula specified Proposed
by ASCE-7 Standard
1.4 D < f R 1.4 (D + L) < f R
1.2 D + 1.6 L < f R
1.2 D + 1.6 L + 0.5 S < f R
1.2 D + 0.5 L + 1.6 S < f R
1.2 D + 1.6 W + 0.5 L + 0.5 S < f R
1.2 D + 1.0 E + 0.5 L + 0.2 S < f R
0.9 D – (1.6 W or 1.0 E) < f R
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Reliability Indices for Beams, designed according to the “new” ACI 318
0
1
2
3
4
5
Re
lia
bilit
y In
de
x
Reliability Indices for Beams
target value
new , ordinary concrete
new , high strength concrete
new , light w eight concrete
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Reliability Indices for Slabs, designed according to the “new” ACI 318
0
1
2
3
4
5
Re
lia
bil
ity
In
de
x
Reliability Indices for Slabs
target value
new , ordinary concrete
new , high strength concrete
new , light w eight concrete
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Reliability Indices for Columns and Plain Concrete Elements, designed
according to the “new” ACI 318
0
1
2
3
4
5
6
7
8
Re
lia
bil
ity
In
de
x
Reliability Indices for Columns and Plain Concrete Elements
target value
new , ordinary concrete
new , high strength concrete
new , light w eight concrete
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Conclusions for ACI 318 Calibration
Quality of materials (concrete and reinforcing steel) have improved in the last 20-30 years
Reliability of structures designed according to “old” ACI 318 is now higher than the minimum acceptable level
Resistance factors can be increased by 10-15%. Therefore, for the new load factors (ASCE 7), “old” resistance factors are acceptable
Phase 2 of the Calibration continues, including eccentrically loaded columns, slabs and environmental loads
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Calibration of the AASHTO LRFD Design Code for Bridges
Basic design formula
gD D + gL L (1 + I) ≤ f R
In the AASHTO Standard Specifications (old)
1.30 D + 2.17 L (1 + I) ≤ f R
In the AASHTO LRFD Code (new)
1.25 D + 1.75 L (1 + I) ≤ f R
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AASHTO LRFD Code
1.25 D + 1.75 L (1 + I) ≤ f R
Load factors are determined so that for each
factored load, the probability of being
exceeded is about the same for all load
components.
Resistance factor is determined so that the
reliability index, b, is close to the target
value, bT.
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Limit States in AASHTO Code for bridges
Four types of limit states:
Strength limit state
Service limit state
Fatigue and fracture limit state
Extreme event limit state
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Strength Limit StateThis limit state relates to strength and
stability, local and global. The Code
specifies five strength limit states:
Strength I (normal vehicular use, no wind)
Strength II (permit vehicles, no wind)
Strength III (wind velocity > 55 mph)
Strength IV (high dead load to live load ratio)
Strength V (normal vehicular use with wind of 55 mph)
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Service Limit StateThis limit state relates to restrictions on stress,
deformation, crack width under regular service
conditions. The Code specifies three service limit
states:
Service I (normal use with 55 mph wind, control of crack width in R/C, compression in P/C)
Service II (overload provision, only for steel structures)
Service III (only for tension in P/C)
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Fatigue and Fracture Limit State
This limit state relates to restrictions on
stress range as a result of a single design
truck occurring at the number of expected
stress range cycles. It is intended to limit
crack growth under repetitive loads to
prevent fracture during the design life of the
bridge.
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Extreme Event Limit States
This limit state relates to the structural
survival of a bridge during a major
earthquake or flood, or when collided by a
vessel, vehicle, or ice flow, possibly under
scoured conditions. The Code specifies
two extreme event limit states:
Extreme Event I (earthquake)
Extreme Event II (ice load, collision by vessels and vehicles)
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General Form of a Limit State Function
factored load (Q) ≤ factored resistance (fR)
Q = S hi gi Qi ≤ f R
where Qi = load component “i”
hi = hD hR hI
gi = load factor “i”
f = resistance factor
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Load Modifiershi = hD hR hI
hD = a factor relating to ductility
hR = a factor relating to redundancy
hI = a factor relating to operational importance
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DuctilityThe structural system shall be proportioned and
detailed to ensure the development of significant
and visible inelastic deformations at the strength
and extreme event limit states before failure.
For strength limit state:
hD = 1.05 for nonductile components
hD = 1.00 for conventional designs
hD = 0.95 for components and connections with additional ductility-enhancing measures
For all other limit states:
hD = 1.00
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Redundancy
Multiple load path and continuous structures should be
used. Main elements whose failure is expected to cause
the collapse of the bridge shall be designated as failure-
critical (nonredundant).
For strength limit state:
hR = 1.05 for nonredundant members
hR = 1.00 for conventional levels of redundancy
hR = 0.95 for exceptional levels of redundancy
For all other limit states:
hR = 1.00
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Operational ImportanceThe owner may declare a bridge or any structural component and connection thereof to be of operational importance.
For strength limit state:hI = 1.05 for important bridgeshI = 1.00 for typical bridgeshI = 0.95 for relatively less important bridges
For all other limit states:hI = 1.00
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AASHTO Standard Specifications Load Factor Design
1.3 D + 1.3 (5/3) L (1 + I) ≤ f R
where: D = moment due to dead load
L = moment due to live load
I = dynamic load factor (impact)
R = moment carrying capacity
f = resistance factor
Safety margin is included in load and
resistance factors
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Resistance Factors in AASHTO Standard Specifications (2003)
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Reliability Indices for AASHTO Standard Specifications
Prestressed Concrete Girders, Moment
0
1
2
3
4
5
0 50 100 150 200
Span [ft]
Re
lia
bil
ity I
nd
ex
s = 12'
s = 10'
s = 8'
s = 6'
s = 4'
s = girder spacing
20 m 40 m 60 m
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Reliability Indices for AASHTO Standard Specifications
R/C T-Beams, Moment
0
1
2
3
4
5
0 50 100 150 200
Span [ft]
Re
lia
bil
ity I
nd
ex
s = 12'
s = 10'
s = 8'
s = 6'
s = 4'
s = girder spacing
20 m 40 m 60 m
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Reliability Indices for AASHTO Standard Specifications
Composite Steel Girders, Moment
0
1
2
3
4
5
0 50 100 150 200
Span [ft]
Re
lia
bil
ity I
nd
ex
s = 12'
s = 10'
s = 8'
s = 6'
s = 4'
s = girder spacing
20 m 40 m 60 m
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Reliability Indices for AASHTO Standard Specifications
Non-Composite Steel Girders, Moment
0
1
2
3
4
5
0 50 100 150 200
Span [ft]
Re
lia
bil
ity I
nd
ex
s = 12'
s = 10'
s = 8'
s = 6'
s = 4'
s = girder spacing
20 m 40 m 60 m
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Reliability Indices for AASHTO Standard Specifications
Prestressed Concrete Girders, Shear
0
1
2
3
4
5
0 50 100 150 200
Span [ft]
Re
lia
bil
ity I
nd
ex
s = 12'
s = 10'
s = 8'
s = 6'
s = 4'
s = girder spacing
20 m 40 m 60 m
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Reliability Indices for AASHTO Standard Specifications
R/C T-Beams, Shear
0
1
2
3
4
5
0 50 100 150 200
Span [ft]
Re
lia
bil
ity I
nd
ex
s = 12'
s = 10'
s = 8'
s = 6'
s = 4'
s = girder spacing
20 m 40 m 60 m
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Reliability Indices for AASHTO Standard Specifications
Steel Girders, Shear
0
1
2
3
4
5
0 50 100 150 200
Span [ft]
Re
lia
bil
ity I
nd
ex
s = 12'
s = 10'
s = 8'
s = 6'
s = 4'
s = girder spacing
20 m 40 m 60 m
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LOAD FACTORS
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Load and Resistance Factor Design
(AASHTO LRFD Code)
1.25 D + 1.75 L (1 + I) ≤ f R
where: D = moment due to dead load
L = moment due to live load
I = dynamic load factor
R = moment carrying capacity
f = resistance factor
Load and resistance factors are determined
in the calibration process
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Reliability Indices for AASHTO LRFD (1998), Steel Girders, moment
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Reliability Indices for AASHTO LRFD (1998), R/C T-Beams, moment
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Reliability Indices for AASHTO LRFD (1998), Prestressed Concrete Girders, moment
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Reliability Indices for AASHTO LRFD (1998), Steel Girders, shear
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Reliability Indices for AASHTO LRFD (1998), R/C T-Beams, shear
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Reliability Indices for AASHTO LRFD (1998), Prestressed Concrete Girders, shear
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Effect of Code Calibration
Prior to calibration, there is a considerable spread of reliability indices
After calibration, the reliability indices are close to the target value
Example is calibration of the AASHTO code for highway bridges
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Reliability Indices for AASHTO (2002) and AAHSTO LRFD (2004) -
Moment
0
1
2
3
4
5
0 1 2 3 4 5
b, AASHTO Standard 2002)
b, A
AS
HT
O L
RF
D (
2004)
Prestressed Concrete
Reinforced Concrete
Steel - Composite
Steel - Non Composite
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Reliability Index for AASHTO (2002) and AASHTO LRFD (2004) -Shear
0
1
2
3
4
5
0 1 2 3 4 5
b AASHTO Standard (2002)
b, A
AH
ST
O L
RF
D (
20
04
)
Pretressed Concrete
Reinforced Concrete
Steel
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Conclusions
Limit state design or LRFD codes provide for a consistent reliability level
The format is flexible, and it can be used for new structural types, new materials
Improved quality can be reflected in increased resistance factors and reduced load factors