1
AASHTO-LRFD Bridge Design
Riyadh Hindi, PhD, PEng
Evolution of Design Methodologies
Background of LRFD Specifications
Calibration
Major Changes
2
Evolution of Design Methodologies
1. Service Load Design (SLD)(aka Allowable Stress Design, ASD; or Working Stress Design, WSD) Dead, live, & other loads assumed of
equal importance (stresses summed up) Assumes linear elastic concrete stress-
strain fc 0.40 fc fy 24 ksi (Grade 60)
Evolution of Design Methodologies2. LFD Methodology
Strength Design Method (Load Factor Design, LFD) Nonlinear concrete stress-strain
(equivalent rectangular stress block for ease of use)
Tension steel yields before concrete crushes ductile behavior
Live load more variable than dead load Arbitrary load factors 1.3[1.0D + (5/3)(L+I)]
3
Evolution of Design Methodologies
3. LRFD MethodologyLoad and Resistance Factor Design Recognizes variability of loads and
resistances Consistent Reliability Index, , at
Strength Limit State Calibrated load and resistance factors 1.25D + 1.75(L+I)
AASHTO Bridge Design Specifications Standard Specifications for Highway Bridges,
17th Edition, 2002 AASHTO LRFD Bridge Design Specifications,
- Investigation begun in 1986- Development begun in 1988- 1st Edition, 1994- 2nd Edition, 1998- 3rd Edition, 2004- 4th Edition, 2007- 5th Edition, 2010- Originally US and SI units. Now US units only
4
AASHTO Ballots on the LRFD Specifications
May 1993To adopt the final draft of the NCHRP
12-33 document as the 1993 LRFDSpecifications for Highway Bridge Designand in 1995 consider phasing out the currentStandard Specifications.
May 1999After the 1999 meeting, discontinue
maintenance of the Standard Specifications(except to correct errors), and maintain theLRFD Specifications.
AASHTO Recommendation LRFD Implementation Plan (2000) All new bridges on which States initiate
preliminary engineering after October 1, 2007, shall be designed by the LRFD Specifications
States unable to meet these dates will provide justification and a schedule for completing the transition to LRFD.
For modifications to existing structures, States would have the option of using LRFD Specifications or the specifications which were used for the original design.
5
Objective of the LRFD
Develop a comprehensive and consistent Load and Resistance Factor Design (LRFD) specification that is calibrated to obtain uniform reliability (a measure of safety) at the strength limit state for all materials.
The specification also addresses the following limit states in the design process:
Service Limit State Fatigue and Fracture Limit State Strength Limit State Extreme Event Limit State
Calibration
Selection of a set of s and s to approximate a target level of
reliability in an LRFD-format specification.
6
Calibration Consists of Up to Three Steps:
Reliability-based calibration
Calibration or comparison to past practice
Liberal doses of engineering judgment
LRFD Calibration
Only the strength limit states of the LRFD Specifications are calibrated based upon the theory of structural reliability wherein statistical load and resistance data are required.
The other limit states are based upon the design criteria of the Standard Specifications and/or related state-of-the-art information.
7
Calibration to Past Practice
The strength limit states of the LRFD Specifications are calibrated to yield reliability comparable to past practice.
The other limit states are calibrated to yield member proportions comparable to past practice.
Statistical Data
Variability in Loads Traffic: Cars, Trucks (Different Number
of Axles), etc.
Variability in Resistances Concrete Compressive Strength Reinforcing Steel Yield Strength Cross-Section Geometry Location of Reinforcement
8
LRFD Calibration
Qmean
Rmean
Qn
Rn
Qn Rn
f(R,Q)
R,Q
The target Reliability Index is a unique quantity.
Many different sets of s and s can be selected to achieve the target Reliability Index .
Reliability Index
9
LRFD Calibration
Qmean
Rmean
Qn RnQn
Rn
f(R,Q)
R,Q
Qmean
Rmean
Qn Rn
f(R,Q)
R,Q
Qn
Rn
LRFD Calibration
10
R-Q
(R-Q)mean
Graphical definition of reliability index
LRFD Calibration
LRFD Calibration
Reliability Indices
0
1
2
3
4
5
Span Length
LFD Range LRFD Range
30 60 90 120 200, ft
11
Major Changes
Parallel Commentary
Unified Concrete Provisions
Shear Design
- Modified Compression Field Theory
- Strut-and-Tie Model
- Interface (Horizontal) Shear
Partial Prestressing
Unified Design Provisions for Reinforced and Prestressed Concrete
Emphasize common features Eliminate duplication Unify design procedures Promote the notion of structural
concrete Introduce partially prestressed
concrete
12
Other Major Changes
Limit States
Distribution Factors
Load Factors and Combinations
Vehicular Live Loads
Dynamic Load Allowance (IM)
Vessel Collision
LRFD Notation and Units
)psi(f5.7)psi(f6)psi(f3)psi(f2
fff
c
c
c
c
se
*su
s
Std Specs
)KSI(f24.0)KSI(f190.0)KSI(f0948.0)KSI(f0632.0
fff
c
c
c
c
pe
ps
pu
LRFD Specs
13
Basis of LRFD Methodology
iiQi Rn (1.3.2.1-1)
For loads where max. value of i is used:i D R I 0.95
For loads where min. value of i is used:i 1 D R I ) 1.00
i = load modifier
Load Modifier, iLRFD 1.3.3-.5
D = ductility factor= 1.05 for non-ductile components= 0.95 for ductile components
R = redundancy factor= 1.05 for nonredundant members= 0.95 exceptional levels of redundancy
I = operational importance factor= 1.05 for critical/essential bridges= 0.95 for less important bridges
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Ductility Factor, D
LRFD C1.3.3
This factor is related to structural behavior, not material behavior. Inelastic behavior Warning of failure
Therefore, properly designed reinforced concrete components are considered ductile, even though plain concrete is a brittle material.
Ductility Factor, D
15
Resistance Factors,
LRFD 5.5.4.2
Tension-controlled sections RC 0.90Tension-controlled sections P/S 1.00Compression-controlled sections 0.75Shear and torsion normal weight conc. 0.90Shear and torsion lightweight conc. 0.70Bearing 0.70
What LRFD is NOT?
New limit states New, more complex live-load
distribution factors New unified-concrete shear design
using modified compression-field theory
Strut-and-tie model for concrete Many other state-of-the-art additions
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AASHTO LRFD Bridge Design Specifications - Chapters
1. Introduction2. General Design and Location Features3. Loads and Load Factors4. Structural Analysis and Evaluation5. Concrete Structures6. Steel Structures7. Aluminum Structures
AASHTO LRFD Bridge Design Specifications - Chapters
8. Wood Structures9. Decks and Deck Systems10. Foundations11. Abutments, Piers, and Walls12. Buried Structures and Tunnel Liners13. Railings14. Joints and Bearings
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Concluding Remarks
Improvement over ASD and LFD
Uniform reliability index for the strength limit states
Provides a framework for future improvements
Incorporates state-of-the-art design procedures
PreliminaryDesign
PreliminaryDesign
2010 BridgeProfessors Workshop
2010 BridgeProfessors Workshop
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PRELIMINARY DESIGNPRELIMINARY DESIGN1. What is Preliminary Design?
2. Selection Criteria and AASHTO Specifications
3. Types of Concrete Bridges
a) Standard Sections
b) Girder Selection Aids
1. What is Preliminary Design?
2. Selection Criteria and AASHTO Specifications
3. Types of Concrete Bridges
a) Standard Sections
b) Girder Selection Aids
Preliminary Design Definition
Design Considerations Safety Economy Durability Aesthetics
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All Existing U.S. Bridges 2003 NBI Data58.0%
31.2%
8.4%
1.5% 0.5% 0.4%0.0%
10.0%
20.0%
30.0%
40.0%
50.0%
60.0%
=250
Maximum Span (ft)
Total Built = 475,000 Bridges
Bridges Built, 2003 NBI Data
0%
10%
20%
30%
40%
50%
60%
1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000
Year Built
Perc
ent B
uilt
P/S
Steel
RC
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AASHTO Bridge Design Specifications
Standard Specifications No Longer Apply
LRFD Specifications Govern Since October
2007
State Practices
40Concrete Bridge Types Slab Bridges I-Girder Bridges Box-Girder Bridges U-Beam Bridges Segmental Bridges Spliced-Girder Bridges Arch Bridges Cable-Stayed Bridges
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41Preliminary Design
CIP Reinforced Short Span Bridges Slab Bridges T-Beam Bridges
Precast, Prestressed Standard AASHTO/PCI Girders
I-Girders and Bulb-Tees Box Girders
Standard Regional Girders
42Bridge Selection GuideWSDOT
0 90 180 270 360 450 540 630
PipeConcrete Culvert
Plate ArchRC Slab
RC Tee BeamRC Box Girder
PT Conc Box GirderSegmental PT Box Girder
PS Conc SlabPS Conc Deck Bulb Tee
PS Conc GirderSteel Rolled Girder
Steel Plate GirderSteel Box Girder
Steel TrussTimber
Glulam TimberCable Stay Bridge
Suspension BridgeFloating Bridge
Arch BridgeMoveable Span Bridge
Tunnel
Span Range (ft)
22
43Slab Bridges
Simple, easy to construct Well-suited for spans up to about 50 ft Cast-in-place or precast. Reinforced or prestressed Can be made continuous with abutments and piers to
mobilize the frame action
44I-Girder Bridges
Most popular bridge type For spans up to about 160 ft. Common sizes: AASHTO/PCI Type I-VI (28 to 72)
and Bulb-Ts (54, 63, and 72)
Walnut Lane Bridge, Philadelphia, PA
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45Properties, Dimensions and Maximum Spans for AASHTO-PCI I-Girders
46Properties, Dimensions and Maximum Spans for AASHTO-PCI I-Girders
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47Properties, Dimensions and Maximum Spans for PCI Bulb Tee Girders
48Properties, Dimensions and Maximum Spans for PCI Bulb Tee Girders
25
49Properties, Dimensions and Maximum Spans for New England Bulb Tee Girders
50Properties, Dimensions and Maximum Spans for New England Bulb Tee Girders
26
2.51Design Charts for I-Girders
Illinois DOT
52Box Girder Bridges
Second-most popular after the I-girder bridges Common sizes: AASHTO/PCI Type BI-BIV (27 to 42) Span Range: 60 ft 105 ft. Use of side-by-side boxes without a wearing course
offers speedy construction
FHWA Showcase Bridge, Cambridge, OH 115-6 Span
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53Properties, Dimensions and Maximum Spans for AASHTO-PCI Box Girders
54Properties, Dimensions and Maximum Spans for AASHTO-PCI Box Girders
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U-Beam Bridges55
U-BeamsU-Beams56
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57Segmental Bridges
Economical, durable, aesthetically pleasing Span-by-span or balanced cantilever construction Post-tensioned or/and Cable-stayed Typical segment type: Concrete box Cast-in-place or precast Perfectly suited for gradual and sharply curved alignments
Sagadahoc Bridge, Bath-Woolwich, ME, Span 420
Hanging Lake Viaduct
I-70 in Glenwood, Colorado Segmental precast concrete bridge Balanced Cantilever construction
58
30
59Spliced Girder Bridges
Innovative technique for very long spans Long-segment precast prestressed girders spliced Spans of more than 300 ft have been achieved
Shelby Creek Bridge, KY, Span 250 ft.
S 274th Green River BridgeKent, Washington
60
31
S 274th Green River BridgeKent, Washington
61
62Arch Bridges
Most efficient shape for supporting gravity loading
Cast-in-place or precast
The longest existing concrete arch bridge: Wanxian Bridge, China. Span = 1378 ft. The first segmental precast
concrete arch bridge in the U.S.: The Natchez Trace Parkway, Franklin, Tennessee. Dual Spans of 582 ft. and 462 ft
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63Cable-Stayed Bridges
Structurally efficient use of materials. Concrete in compression and steel stays in tension. Economical and aesthetically pleasing. Most popular type for signature bridges. The longest concrete cable-stayed bridge in the U.S.:
Dames Point, Jacksonville, Fl. Main Span = 1300 ft
Zakim Bunker Hill Bridge
Located in Boston, MA over Charles River Part of the Central Artery Project
64
33
3.65
Loads and Load Distribution
Overview of Presentation
Calibration (Load and Resistance Factors)
New Load Model Refined Load Distribution
3.66
34
3.67LRFD Limit States The LRFD Specifications require examination of
several load combinations corresponding to the following limit states: STRENGTH LIMIT STATE
strength and stability
SERVICE LIMIT STATEstress, deformation, and cracking
FATIGUE & FRACTURE LIMIT STATEstress range
EXTREME EVENT LIMIT STATE earthquakes, ice load, and vehicle and vessel collision
3.683.4.1 Load and Load Designation
STRENGTH I : normal vehicular use without wind
STRENGTH II : owner design / permit vehicles without wind
STRENGTH III : bridge exposed to wind exceeding 55 mph
STRENGTH IV : very high dead-to-live load ratios
STRENGTH V : normal vehicular use with 55 mph wind
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3.69
3.4.1 Load and Load Designation
SERVICE I : normal operational use of the bridge with a 55 mph wind and nominal loads. Also control cracking of reinforced concrete structures.
SERVICE II : control yielding of steel structures and slip of connections
SERVICE III : control cracking of prestressed concrete superstructures
SERVICE IV : control cracking of prestressed concrete substructures
FATIGUE : repetitive vehicular live load and dynamic responses under a single truck
3.701.3.2 Limit States
iiQi Rn = Rr Eq. (1.3.2.1-1)where:i =Load Modifier
= D R I 0.95, where a max. value of i is used
= < 1.00, where a min. value of i isused
i = Load factor = Resistance factorQi = Nominal force effectRn = Nominal resistanceRr = Factored resistance
= R
IRD
1
Load modifier factors:D = DuctilityR = RedundancyI = Operational importance
36
3.713.3.2 Load and Load DesignationDD = downdragDC = dead load of structural
components and nonstructural attachments
DW = dead load of wearing surfaces and utilities
EH = horizontal earth pressureEL = accumulated locked-in
force effects resulting from the construction process, including the secondary forces from post-tensioning
ES = earth surcharge loadEV = earth fill vertical pressureBR = vehicular braking forceCE = vehicular centrifugal forceCR = creep
CT = vehicular collision forceCV = vessel collision forceEQ = earthquakeFR = frictionIC = ice loadIM = vehicular dynamic load
allowanceLL = vehicular live loadLS = live load surchargePL = pedestrian live loadSE = settlementSH = shrinkageTG = temperature gradientTU = uniform temperatureWA= water load and stream
pressure WL= wind on live loadWS= wind load on structure
Table 3.4.1-1 Load Combinations and Load Factors 3.72
37
Load Combination for Prestressed ConcreteStrength Limit State
Increased vehicular live load Reduced load factors Result: Design effects are similar to Std Specs
Service Limit State Increased vehicular live load Same stress limits Result: Design effects are significantly more
restrictive than designs using Std Specs Service III added to address this difference by
reducing live load effects
3.73
Table 3.4.1-2 Load Factors for Permanent Loads, p3.74
38
Total Vehicular LL(HL-93)
Design TruckOR
Design Tandem
PLUS
Design Lane LoadDesign Lane Load
Design TandemDesign Truck
3.6.1.2.1 Design Vehicular Live Loads3.75
3.76
The dynamic load allowance in Table 1 is an increment to be applied to the static wheel load to account for wheel load impact from moving vehicles.
Sources of dynamic effects on bridges Hammering at surface discontinuities Dynamic response of bridge as a whole
3.6.2.1 Dynamic Load Allowance (Impact)
39
3.77
For design of most bridge components for all limit states except fatigue
The LRFD Specifications simply require a constant magnification (IM) of 33% to be applied to the design truck or design tandem only
The magnification (IM) is not applied to the design lane load
This simple approach is based on a study that found the most influential factor affecting dynamic impact is roadway surface roughness
Commentary has more background
3.6.2.1 Dynamic Load Allowance (Impact)
3.785.5.4.2 Resistance Factors
Std SpecsLRFD 5.5.4.2
Flex RC 0.90 0.90Flex PS 1.00 1.00
Shear RC 0.85 0.90Shear PS 0.90 0.90
Compression 0.70 / 0.75 0.75Bearing 0.70 0.70
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Table 4.6.2.2.1-1 Common Superstructures
4.6.2.2.1 Simplified Distribution Factors
To use the simplified distribution factors the following conditions must be met
Width of deck is constant
Number of beams, Nb 4
Beams are parallel and of the same stiffness
The roadway part of the overhang, de 3.0 ft
Curvature is less than 4
Section appears in Table 4.6.2.2.1-1
41
3.81
Table 4.6.2.2.2b-1 Distribution of Live Loads Per Lane for Moment in Interior Beams
Notes: 1) Units are in LANES and not WHEELS!2) Limits of applicability are from parametric study3) No multiple presence factor applied (tabulated equations)4) May be different for positive and negative flexure locations5) Use more conservative of 1 or 2 lanes loaded6) Note that minimum no. of girders, Nb, is 3
Distribution Factors for I-Beams - Moment
The live load distribution factor for moment for interior beams with 2 or more lanes loaded
Nb 4
10,000 Kg 7,000,000
3.82
42
Longitudinal Stiffness ParameterThis term gives an indication of the relative stiffness between the beam (longitudinal) and deck (transverse)
For preliminary design, this term may be taken as 1.10
3.83
> 1, the inverse of ratio (n) for section propertiessince it is transforming beam to deck
Distribution Factors for I-Beams - Shear
The live load distribution factor for shear for interior beams with 2 or more lanes loaded
3.84
43
Distribution Factors for I-Beams Moment with Skew
Bending moments in interior and exterior beams on skewed supports may be reduced using the following multiplier
3.85
Distribution Factors for I-Beams Shear with Skew
Shear in exterior beams at the obtuse corner of the bridge may be reduced using the following multiplier
This formula is valid for < 60
3.86
44
3.874.6.2.2 Lever Rule
4.6.3 Refined Methods of Analysis
Nine methods are listed in Article 4.4 including Finite element method Finite difference method Grillage analogy method Yield line method
3.88
45
89
Flexure & Shear Design
90Learning Objectives
Unified Design Provisions for Flexure and Axial Load
Modified Compression Field Theory (MCFT) for Shear Design
46
91Flexural Design Provisions in AASHTO
AASHTO Standard Section 8 Reinforced Concrete Section 9 Prestressed Concrete
AASHTO LRFD Section 5 Concrete Structures
Reinforced concrete Prestressed concrete Partially prestressed concrete (New in
LRFD)
92AASHTO Standard
Maximum reinforcementReinforced Concrete
max = 0.75 bal (8.16.3.1)Prestressed Concrete
(pf*su/fc) 0.36 1 (9.18.1)
47
93Unified Design Provisions for Reinforced and Prestressed Concrete Flexural and
Compression Members
LRFD 5.7
Beams Ductile behaviorColumns Non-ductile behavior
Factors selected based on behavior
94Unified Design Provisions Key Concept
Strength reduction factor, ,depends on
maximum net tensile strain, t ,at nominal resistance, Mn
48
955.2 - Definitions
Net Tensile Strain - The tensile strain at nominal resistance exclusive of strains due to effective prestress, creep, shrinkage, and temperature.
965.2 - Definitions
Extreme Tension Steel The reinforcement (prestressed or nonprestressed) that is farthest from the extreme compression fiber.
49
975.2 - Definitions
t = Net tensile strain dt = Depth to extreme tension steel
dt
t
0.003
ColumnStrainBeam
985.2 - Definitions
t = Extreme tension steel strain at nominal resistance, due to applied loads
t
c a = 1c C
T
Pn
Mn
0.003
50
995.2 - Definitions
Compression-Controlled Strain Limit The net tensile strain (t ) at balanced strain conditions. See Article 5.7.2.1.
1005.7.2.1 Balanced Strain Condition
fy /Es (or 0.002)
0.003
51
1015.2 - Definitions
Compression-Controlled Section A cross section in which the net tensile strain (t ) in the extreme tension steel at nominal resistance is less than or equal to the compression-controlled strain limit.
[Usually 0.002]
1025.2 - Definitions
Tension-Controlled Section A cross section in which the net tensile strain (t ) in the extreme tension steel at nominal resistance is greater than or equal to 0.005.
52
1035.5.4.2 Resistance Factors
P/S
Transition Tension -Controlled
Compression-Controlled
1.00
R.C.
t = 0.002 t = 0.005
0.90
0.75
Net Tensile Strain
1
cd15.065.0 t
1
cd25.0583.0 t
104Effect of Variation in
Design flexural members as tension-controlled sections. Adding reinforcement beyond this limit reduces , because of reduced ductility, resulting in no gain in design strength
It is better to add sufficient compression reinforcement to raise the neutral axis and make the section tension-controlled
53
105Effect of Variation in
= As/bd
Mnbd2
10610.3.3-4 Strain Conditions
Compression-Controlled
Tension-ControlledTransition
c 0.375 dt0.375 dt < c < 0.6 dtc 0.6 dt
0.002 < t < 0.005
0.0030.003c = 0.003
t 0.005t 0.002
54
107Ductility ComparisonStandard vs. LRFD Specs.
108Example R.C. Beam
Given: fc = 4 ksi; fy = 60 ksiAssume steel yieldsT = Asfy = 3(0.79)60 = 142.2 kipsa = T/(0.85 fcb) = 3.49 in. c = a/1 = 4.1 in.Mn = T [dt-(a/2)] = 1672 in.-k = 139.3 ft-kc/dt = 4.1/13.5 = 0.304 < 0.375 ort = 0.003 [(dt-c)/c] = 0.0069 in./in. Tension-controlledMr = Mn = 0.90 (139.3) = 125.4 ft-k
a = 1c C
Tt
c
0.00312
3#8dt = 13.516
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5.8 Shear and Torsion
5.8.1.1 Flexural Regions Sectional Design Method Modified Compression Field Theory (MCFT)
5.8.1.2 Regions Near Discontinuities Strut-and-Tie (5.6.3)
109
110
where:Vc = concrete contribution
Vc =
=
Vs = stirrup contribution
=
Vp = vertical component of the prestressing force
5.8.3.3 Nominal Shear Resistance
pvvcn
pscn
Vdbf25.0VVVVV
psi) in (f dbf
ksi) in f( dbf0316.0'cvv
'c
cvv'c
cotds
fAv
yv
56
Modified Compression Field Theory (1986)111
Source: Collins Mitchell, 1991
112Reinforced Concrete = Cracked Concrete + Reinforcement
Panel Loaded in shear
57
113Stresses between Cracks
Calculated average stress
Tension Stiffening114
58
115Stress Transfer at a Crack
Local stresses at crack
116
Vci limited by:
- Width of crack, w
- Size of aggregate, a
Aggregate InterlockDetail at crack
59
117Average Stress Strain Relationships for Concrete in Tension
Diagonal Cracks Diagonal Compression118
60
119
0.11708.01
ff
])()(2[ff
1'c
max2
2'c
2'c
2max22
Average Stress-Strain Relationship for Concrete in Compression
where
Based on three principles:
Equilibrium
Compatibility
Stress-Strain Relationship
Modified Compression Field Theory
61
1.121
STRUCTURAL CONCRETE
Concrete
Reinforcement
Reinforced Concrete
Prestressed Concrete
1.122
Basic Concept Strong in Compression Weak in Tension
Characteristics of Concrete
62
1.123Typical Stress-Strain Curve for Concrete
1.124Behavior of Plain Concrete Members
63
1.125Typical Stress-Strain Curve forMild Reinforcing Steel
1.126Behavior of Reinforced Concrete Members
64
1.127Typical LoadDeflection Behavior of Unreinforced and Reinforced Concrete Beams
1.128Prestressed Concrete: General Principles
65
1.129Methods of Prestressing Concrete MembersPretensioning:
Post-tensioning
1.130Behavior of Prestressed Concrete Members
66
1.131Typical Load Deflection Behavior of Unreinforced, Reinforced and Prestressed Concrete Beams
1.132Stress-Strain Curves for Prestressing Strand and Mild Reinforcement
67
1.133Concepts of Prestressing
Maintain gross section properties for improved stiffness
Transform concrete from a material that cracks into an elastic uncracked material
Balance applied loads
Combination of concrete with very high strength reinforcement
Provide active force to close cracks due to overloads
1.134Load Balancing
68
1.135Need for High Strength Steel to Achieve Prestress
1.136Partial Prestressing
Partially prestressed members are allowed to crack at service loads Reduces Required prestress force Reduces excess section strength Generally requires addition of mild
reinforcement Stiffness is reduced deflections and fatigue
should be investigated Recognized in LRFD Specs
- No specific guidance for design- Partial prestress ratio, PPR, defined in LRFD
5.5.4.2.1
y spy ps
py ps
fAfAfA
PPR
69
1.137
Strength Limit State Flexure
Strength Limit State Shear
Fatigue Limit State Flexure
Service Limit State - Crack Control- Deformations Optional
Extreme Events
Design of Reinforced Concrete Members
1.138Design of Prestressed Concrete Members
Service Limit State Flexure- determine magnitude and location of P/S force- stress limits- stages of construction- almost always governs
Strength Limit State Flexure
Strength Limit State Shear
Fatigue Limit State Flexure
Service Limit State Deformations- optional
Extreme Events
70
Deck Design
Refined Methods (4.6.3.2)
Approximate Methods Empirical Method (9.7.2) Strip Method (4.6.2.1.1., App. A4
+ Section 5)
Overhang Design (9.7.1.5)
139
140Deck Design
71
141
Live Load: HL-93
Deck Concretefc = 4 ksiwc = 150 pcf
Nonprestressed Reinforcementfy = 60 ksiEs = 29,000 ksi
DimensionsThickness = 8.0 in. (9.7.1.1 & 13.7.3.1.2)Cover = 2.5 in. (Top) (5.12.3)
= 1.0 in. (Bottom) (5.12.3)
Future Wearing Surface Allowance: FWS = 30 psf
Problem Definition
1429.7.2 Empirical Method Based on extensive research
Load resistance mechanism Internal arching action
FEM verification
Factor of safety 8.0
No analysis required
Isotropic reinforcement
Not applicable to overhang design
72
1439.7.2.4 Empirical Method Design Conditions
Diaphragms at lines of support Concrete and/or steel girders Cast-in-place composite deck Uniform depth Effective length-to-depth ratio
6 to 18 Effective length
13.5 ft., maximum
(9.7.2.3)
1449.7.2.4 Empirical Method Design Conditions
Core depth 4.0 in., minimum
Slab thickness 7.0 in., minimum
Minimum overhang-to-depth ratio 5 3, if barrier is composite
fc - 4 ksi, minimum
Deck is composite
73
1459.7.2.5 Empirical Method Reinforcement
Bottom Layer, each way: 0.27 in.2 / ft.(#5 bars @ 13.5 in. spacing As,provd = 0.276 in.2 / ft.)
Top Layer, each way: 0.18 in.2 / ft.(#4 bars @ 13 in. spacing As,provd = 0.185 in.2 / ft.)
Grade 60 steel
Outermost bars in direction of effective length
Maximum spacing 18 in. o.c.
Reinforcement doubled in end zone if skew exceeds 25
1469.7.2.5 Empirical Method Final Design
74
1474.6.2.1.1 Strip Method Continuous beam loaded with truck axle loads Equivalent strip widths interior, exterior, and
overhang (Table 4.6.2.1.3-1) DL moments on a per foot width basis LL moments:
Moving load analysis Truck axles moved laterally Multiple presence factors Dynamic load allowance Total moment divided strip width
LRFD Table A4.1-1 (used in this design example)
148Strip Method
Overhang design (9.7.1.5)
Limit states
Service: crack control
Fatigue: need not be checked
Strength: factored moments
Extreme event: vehicular collision
75
149Strip Method DL Moments
C = 10 or 12 Self weight = 8(150)/12
= 100 psf = 0.1 ksf
CwM
2
.ft/.ftkip 81.010
9x1.0M2
DL
.ft/.ftkip 24.010
9x03.0M2
FWS
Future wearing surface = 30 psf = 0.3 ksf
150Strip Method LL Moments
Table A4-1 Span = 9 ft. Critical section for negative moment
(4.6.2.1.6) (1/3) bf = 14 in. (governs) 15 in. Use 12 in. (conservative)
.ft/.ftkip29.6M posLLI -
.ft/.ftkip71.3M negLLI -
76
151Strip Method Service LS Moments
Service Limit State:
Negative Interior Moment:
Mneg = -(0.81+0.24+3.71) = -4.76 kip-ft. / ft.
Positive Moment:
Mpos = (0.81+0.24+6.29) = 7.34 kip-ft. / ft.
152Strip Method Strength LS Moments
Strength Limit State
Negative Interior Moment:
Mneg,str = -(1.25x0.81 + 1.5x0.24 + 1.75x3.71)
= -7.87 kip-ft. / ft.
Positive Moment:
Mpos,str = 1.25x0.81 + 1.5x0.24 + 1.75x6.29
= 12.38 kip-ft. / ft.
77
153Strip Method Flexure Design Mneg,str = -7.87 kip-ft. / ft.
Try No. 5 at 10 in. o.c.
As = (12/10)(0.31 in.2/bar)
= 0.372 in.2 / ft.
in. 0.65 85.0
547.085.0ac
2ad
bfA
M ysn bf85.0fA
a 'c
ys
.in 547.0a 12)(0.85)(4)(
)(0.372)(60
flexure for0.9 section controlled-tension ,Therefore
005.0021.0003.0*65.0
65.019.5003.0*c
cdsection controlled mpressionTension/Co Check
tt
154Strip Method Flexure Design
2ad
bfA
M ysn
ft./ft.-kip 23.8)2547.019.5(
)12()60)(372.0)(90.0(Mn
Mn = 8.23 kip-ft. / ft. > Mneg,str = 7.87 kip-ft. / ft. O.K.
78
155Strip Method Crack Control
Maximum spacing of tension reinforcement
LRFD Article 5.7.3.4 applies if fMneg > 0.8fr
Therefore, Article 5.7.3.4 applies
ksi38.0424.0*8.0f24.0*8.0f8.0 'cr
ksi 38.0ksi 45.0
68*1212*76.4f2Mneg
156Strip Method Crack Control Maximum spacing of tension reinforcement
dc = cover extreme tension fiber to center of extreme reinf.
= 2.5 (clear cover) + 0.625 (diameter of No. 5 bar)/2
= 2.81 in.
css
e d2f700
s
exposure 2Class for 75.0,where
e
77.1)81.28(7.0
81.21)dh(7.0
d1c
cs --
fs = Stress in reinf. based on cracked section analysis
79
157
M
b
d s
c
s
fc
fs
NeutralAxis
kds
13kds
jd = (1 - )dk3s s
Elevation Section Strain Stress Resultant Forces
C
T
Figure 3: Reinforced concrete rectangular beam section at service load
Strip Method Crack Control Calculate fs
158Strip Method Crack Controlwhere:
M = -4.76 kip-ft./ft.As = No. 5 at 10 o.c. = 0.31/10*12 = 0.372 in.2/ ft.ds = 8 2.5 0.625/2 = 5.19 in.
sss jdA
Mf =
n = modular ratio = Es / Ec = 29,000 / 3,830 = 7.57. Use 8 6 OK(LRFD 5.7.1) ksi 830,30.4)150.0)(000,33(fw000,33E 5.1'c5.1cc
bdAs
00597.0)19.5)(12(
372.0
nnn2k 2 -
265.0)8)(00597.0()8)(00597.0()8)(00597.0)(2(k 2 -
3k1j - 912.03/265.01j ksi 4.32)19.5)(912.0)(372.0(
)12*76.4(fs
80
159Strip Method Crack Control
Provided No. 5 at 10 in. o.c. > 3.53 in. o.c. N.G.
Reduce spacing to 7 in. o.c.Revised maximum spacing = 7.2 in. O.K.
Therefore, for negative interior moments: Provide #5 @ 7 in. o.c. (As prov'd = 0.53 in.2 / ft.)Mneg provd = 11.5 kip-ft./ft.
Similar calculations for Mpositive suggestNo. 5 at 8 in. o.c. are adequate (As, provd = 0.465 in2/ft.)Mpos provd = 13.3 kip-ft./ft.
.in53.381.2*24.32*77.1
75.0*700d2
f700
s css
e ==
160Strip Method Distribution Reinforcement(LRFD 9.7.3.2)
At bottom In secondary direction Percent of reinforcement for Mpositive
As = 0.67(0.47 in.2 / ft.) = 0.31 in.2 / ft.
Provide #5 @ 12 in. o.c. (As prov'd = 0.310 in.2 / ft.)
ft. 8.5 in. 102 6- 108 S where %,67S
220
Governs 67% ,%67%755.8
220
81
161Strip Method Shrinkage & Temp. Reinf.
28.10.5 .Eq 60.0A11.0
18.10.5 .Eq f)hb(2
bh3.1A
s
ys
Maximum spacing: 3*8=24 in or 18 in (governs)
Provide No. 4 @ 18 in. o.c. (As prov'd = 0.27 in2 / ft.)
11.0A therefore ,085.060*)8510(*2
8*510*3.1A
:deck of width full Consider:1 Method
ss
42 6 = 510 in8 in
11.0,087.060*2496*3.1
24)012(*2968*12
12:22
ss AthereforeA
inperimeterDryinginArea
indeckofwidthunitConsiderMethod
12 in
8 in
162Strip Method Minimum Reinforcement
ft./ft.-kip7.9 in.-kip 94.7 )6
8*12(*74.0M2
cr
Mr lesser of 1.2 Mcr or 1.33 Mu (LRFD 5.7.3.3.2)
crcr SfM
Mpos provd = 13.3 kip-ft/ft and Mneg provd = 11.5 kip-ft/ft> 9.5 kip-ft/ft OK
ksi 74.0437.0f37.0f cr
ft/ft-kip 47.1638.12*33.11.33Mft/ft-kip 47.1087.7*33.11.33M
(governs) ft/ft-kip 5.99.7*2.1M2.1
strpos,
strneg,
cr
82
163Empirical vs. Traditional
Total reinforcement per square foot of deck:
Empirical method:2[0.276 + 0.185] = 0.922 in.2 / ft. (- 41%)
Traditional method:0.53 + 0.465 + 0.310 + 0.27 = 1.575 in.2 / ft. (+ 71%)
164Overhang Design Design Case 1: DL and trans. & long. Vehicle impact forces
Load & Resistance Factors = 1.0. extreme event limit state
Design Case 2: DL & vert. vehicle impact forces
Load & Resistance Factors = 1.0. extreme event limit state
Typically does not govern for concrete barriers
Design Case 3: Strength I Limit State
1.25DC + 1.5 DW + 1.75 (LL+IM)
83
165Vehicle Impact Forces Extreme Event Test Vehicle TL4
(LRFD 13.7.2)Design Forces and Designations
Ft Transverse Force 54 KIPFL Longitudinal Force 18 KIPFv Vertical Force Down 18 KIPLt and LL 3.5 FTLv 18 FTHe min (Height of impact above deck) 32 INH Minimum Height of Barrier 32 IN
166Safety BarrierStrength of Barrier: ILDOT F-Shape Concrete Barrier
84
167Strength of Barrier Yield Line Case 1
168Strength of Barrier Yield Line Case 2
85
169Distribution of Mc and T
T over Lc+ H (Case 2)
T over Lc+2H (Case 1)
At the inside of barrier M over Lc
170
Rw for barrier = 61.6 kip
61.6 kip > Ft = 54 kip OK
Strength of Barrier
kip 134.4
ft
:1Case Line Yield
HLMMM
LLR
MMMHLLL
ccwb
tcw
c
wbttc
2
1
2
882
2
7.13822
controls kip, 61.6
ft6.3
:2Case Line Yield
HLMMM
LLR
MMMHLLL
ccwb
tcw
c
wbttc
2
2
2
22
22
86
171Flexural Design of Deck At the inside face of the barrier:
MDC = (8/12)*(0.150)*(1.5)2 / 2 = 0.06 kip-ft. / ft.Mbarrier = (0.450)*(1.5)2 / 2 = 0.34 kip-ft. / ft.Mc = 13.9 kip-ft. / ft. (Flexural strength of barrier about hor. axis)
Design forces for deck (at inside face of barrier):M = MDC + Mbarrier + Mc
= 0.06 + 0.34 + 13.9= 14.30 kip-ft. / ft.
P = T1 (yield line case 1) = 6.94 kip / ft., at centroid of deck
P
M
h d
172Reinforcement at Top of Deck
P
M C
T+P
h da
Strains Stresses Forces
As = 0.185 in.2 / ft. (Empirical design No. 4 @ 13 o.c.) T1 = T + P T1 = T + P = 0.185x60 = 11.1 kip / ft. C = 11.1 - 6.94 = 4.16 kip / ft. a = 4.16/(0.85x12x4) = 0.10 in. c = a/0.85 = 0.10/0.85 = 0.12 in. de = 8 2.5 0.5/2 = 5.25 in.
22222 1ahPadThdPadCMn
87
173Reinforcement at Top of Deck
Mn = 2.53 < M = 14.30 kip-ft. / ft. NG
P
M C
T+P
h da
Strains Stresses Forces
.ft/.ftkip53.2.ft/.inkip3.30210.0
2894.6
210.025.51.11Mn
.ft/.ftkip0.15.ft/.inkip7.179292.0
2894.6
292.006.54.44Mn
Mn = 15.0 > M = 14.30 kip-ft. / ft. OK
Provide additional No. 7 at 13 in. o.c.alternating with No. 4 at 13 o.c. As = (0.20+0.60)/13*(12) = 0.74 in.2 / ft. T = 0.74x60 = 44.4 kip / ft.
174
Away from barrier: Dispersion at 30 to 45 deg
88
175
Thank YouQuestions?