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

14

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

16

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

17

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

18

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

19

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

20

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

21

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

23

45Properties, Dimensions and Maximum Spans for AASHTO-PCI I-Girders

46Properties, Dimensions and Maximum Spans for AASHTO-PCI I-Girders

24

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

27

53Properties, Dimensions and Maximum Spans for AASHTO-PCI Box Girders

54Properties, Dimensions and Maximum Spans for AASHTO-PCI Box Girders

28

U-Beam Bridges55

U-BeamsU-Beams56

29

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

32

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

35

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

40

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

55

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?