Overview of LRFD

Firas I. Sheikh Ibrahim, Ph.D., P.E.Firas I. Sheikh Ibrahim, Ph.D., P.E.

Senior Codes & Specifications EngineerSenior Codes & Specifications Engineer

Office of Bridge Technology Federal Highway Administration

Washington, DC

Evolution Of Design Specifications1931 - First AASHO Specs

Evolved into AASHTO Standard Specs (SLD, and LFD), and became a patch document with inconsistencies and gaps

1994 - Load and Resistance Factor Design (LRFD)

1998 - 2nd Edition of LRFD

2004 - 3rd Edition of LRFD

2007 – 4th Edition of LRFD

Service Load DESIGN

QR

NominalNominalResistanceResistanceRRn

Nominal Load Effect, Nominal Load Effect, QQn < nRRFSFS

Service Load Design (SLD):(ft)D + (ft)L ≤ 0.55Fy, or1.82(ft)D + 1.82(ft)L ≤ Fy

LFD Design EquationΣΣ γγi QQi << φφRRnwhere:where:γγi == Load factorLoad factorγγi QQi == Factored load, Factored load,

required capacity required capacity φφ == Resistance factorResistance factorφφ RRn== CapacityCapacity

nRφ

nRnQ

nQγ

Load Factor Design (LFD):1.3[1.0(ft)D + 5/3(ft)L] ≤ φFy, or1.3(ft)D + 2.17(ft)L ≤ φFy (φ by judgment)

Reliability of the Standard Specs

0

4

0 30 60 90 120 2000

4

0 30 60 90 120 2000

4

0 30 60 90 120 200

SPAN LENGTH (Feet)SPAN LENGTH (Feet)

RE

LIA

BIL

ITY

IND

EX

RE

LIA

BIL

ITY

IND

EX

1

2

3

1

2

3

1

2

1

2

3

555

4

5

0 30 60 90 120 200

NORMALLY DISTRIBUTEDQ AND R:

LOGNORMALLY DISTRIBUTEDQ AND R

2 2R Q

R-Qβ=σ +σ

⎛ ⎞⎜ ⎟⎝ ⎠2 2

R Q

RlnQ

β=V +V

Design Life is Design Life is 50 years

Service Life could be less than 50Service Life could be less than 50

Design & Service Life forThe Standard Specifications

LRFD Design SpecificationsLonger Design Life (Longer Design Life (75 years))

Allows use of High Performance Material; Service Allows use of High Performance Material; Service Life (>75 years)Life (>75 years)

Consistent Reliability and Safety Factors for all Consistent Reliability and Safety Factors for all bridges,bridges,

More Realistic Live Load Model, and Distribution More Realistic Live Load Model, and Distribution FactorsFactors

State of the Art Provisions and Design ProceduresState of the Art Provisions and Design Procedures

Basic LRFD Design EquationΣΣ ηηi γγi QQi << φφRRn = = RRrwhere:where:ηηii == ηηD ηηR ηηI

ηηii == Load modifierLoad modifierγγi == Load factorLoad factorQQi == Nominal force effect Nominal force effect φφ == Resistance factorResistance factorRRn== Nominal resistanceNominal resistanceRRr == Factored resistance = Factored resistance = φφRRn

nRφ

nRnQ

nQγ

Sample LRFD Design Equation:1.25(ft)D + 1.75(ft)L ≤ φFy (φ by calibration)

(new live-load model)

LRFD = More Identifiable Limit States

SERVICE LIMIT STATESERVICE LIMIT STATErelating to stress, deformation, and cracking relating to stress, deformation, and cracking

FATIGUE & FRACTURE LIMIT STATEFATIGUE & FRACTURE LIMIT STATErelating to stressrelating to stress range and crack growth under repetitive loads, and range and crack growth under repetitive loads, and material toughnessmaterial toughness

STRENGTH LIMIT STATE STRENGTH LIMIT STATE relating to strength and stability relating to strength and stability

-- (CONSTRUCTIBILITY)(CONSTRUCTIBILITY)

EXTREME EVENT LIMIT STATE EXTREME EVENT LIMIT STATE relating to events such as earthquakes, ice load, and vehicle anrelating to events such as earthquakes, ice load, and vehicle and d vessel collisionvessel collision

Load Combinations and Load Factors

Use One of These at a

Tim e

Load Com bination

Lim it State

DC DD DW EH EV ES

LL IM CE BR PL LS

WA

WS

WL

FR

TU CR SH

TG

SE

EQ

IC

CT

CV

STRENGTH-I

γp

1.75

1.00

-

-

1.00

0.50/1.20

γTG

γSE

-

-

-

-

STRENGTH-II γp

1.35

1.00

-

-

1.00

0.50/1.20

γTG

γSE

-

-

-

-

STRENGTH-III γp

-

1.00

1.40

-

1.00

0.50/1.20

γTG

γSE

-

-

-

-

STRENGTH-IV EH, EV, ES, DW DC ONLY

γp

1.5

-

1.00

-

-

1.00

0.50/1.20

-

-

-

-

-

-

STRENGTH-V

γp

1.35

1.00

0.40

1.00

1.00

0.50/1.20

γTG

γSE

-

-

-

-

EXTREM E-I

γp

γEQ

1.00

-

-

1.00

-

-

-

1.00

-

-

-

EXTREM E-II γp

0.50

1.00

-

-

1.00

-

-

-

-

1.00

1.00

1.00

SERVICE-I

1.00

1.00

1.00

0.30

0.30

1.00

1.00/1.20

γTG

γSE

-

-

-

-

SERVICE-II 1.00

1.30

1.00

-

-

1.00

1.00/1.20

-

-

-

-

-

-

SERVICE-III 1.00

0.80

1.00

-

-

1.00

1.00/1.20

γTG

γSE

-

-

-

-

FATIGUE-LL, IM & CE ONLY

-

0.75

-

-

-

-

-

-

-

-

-

-

-

Load Factors for PermanentLoads, γp

Load FactorType of Load Maximum Minimum

DC: Component andAttachments

1.25 0.90

DD: Downdrag 1.80 0.45DW: Wearing Surfacesand Utilities

1.50 0.65

EH: Horizontal EarthPressure

• Active• At-Rest

1.501.35

0.900.90

EV: Vertical EarthPressure

• Overall Stability• Retaining

Structure• Rigid Buried

Structure• Rigid Frames

1.351.351.30

1.351.95

N/A1.000.90

0.900.90

LRFD = More Accurate Live Load Model, HL-93Design Truck: ⇒

Design Tandem:Pair of 25.0 KIP axles spaced 4.0 FT apart

superimposed on

Design Lane Load 0.64 KLF uniformly distributed load 0.64 Kip/ft

+

or

or

25.0 KIP25.0 KIP

LRFD Negative Moment Loading

For negative moment (between points of permanent-load contraflexure) & interior-pier reactions, check an additional load case:

> 50’-0”

0.9 x

LRFD Fatigue Load

Design Truck only =>w/ fixed 30-ft rear-axle spacingPlaced in a single lane

1

TABLE 4.6.2.2.1-1 COMMON DECK SUPERSTRUCTURES COVERED IN ARTICLES 4.6.2.2.2 AND 4.6.2.2.3.

SUPPORTING COMPONENTS TYPE OF DECK TYPICAL CROSS-SECTION Steel Beam

Cast-in-place concrete slab, precast concrete slab, steel grid, glued/spiked panels, stressed wood

Closed Steel or Precast Concrete Boxes

Cast-in-place concrete slab

Open Steel or Precast Concrete Boxes

Cast-in-place concrete slab, precast concrete deck slab

Cast-in-Place Concrete Multicell Box

Monolithic concrete

Cast-in-Place Concrete Tee Beam

Monolithic concrete

Precast Solid, Voided or Cellular Concrete Boxes with Shear Keys

Cast-in-place concrete overlay

Precast Solid, Voided, or Cellular Concrete Box with Shear Keys and with or without Transverse Posttensioning

Integral concrete

Table 4.6.2.2.2b-1 Distribution of Live Loads Per Lane for Moment in Interior Beams.

Type of Beams

Applicable Cross-Section

from Table 4.6.2.2.1-1 Distribution Factors

Range of Applicability

One Design Lane Loaded: 0.10.4 0.3

30.0614 12.0

g

s

KS SL Lt

⎛ ⎞⎛ ⎞ ⎛ ⎞+ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠

Two or More Design Lanes Loaded: 0.10.6 0.2

30.0759.5 12.0

g

s

KS SL Lt

⎛ ⎞⎛ ⎞ ⎛ ⎞+ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠

3.5 16.020 2404.5 12.0

4s

b

SLt

N

≤ ≤≤ ≤≤ ≤≥

10,000 ≤ Kg ≤ 7,000,000

Concrete Deck, Filled Grid, Partially Filled Grid, or Unfilled Grid Deck Composite with Reinforced Concrete Slab on Steel or Concrete Beams; Concrete T-Beams, T- and Double T-Sections

a, e, k and also i, j

if sufficiently connected to act as a unit

use lesser of the values obtained from the equation above with Nb = 3 or the lever rule

Nb = 3

Live-Load Distribution FactorsMoments – Interior Beams

Notes: 1) Units are in LANES and not WHEELS!2) No multiple presence factor applied (tabulated equations)3) May be Different for Positive and Negative Flexure Locations!

Table 4.6.2.2.3a-1 Distribution of Live Load per Lane for Shear in Interior Beams.

Type of Superstructure

Applicable Cross-Section

from Table 4.6.2.2.1-1

One Design Lane Loaded

Two or More Design Lanes Loaded

Range of Applicability

0.3625.0

S+

2.0

0.212 35S S⎛ ⎞+ − ⎜ ⎟

⎝ ⎠

3.5 16.020 2404.5 12.0

4s

b

SLt

N

≤ ≤≤ ≤≤ ≤

≥

Concrete Deck, Filled Grid, Partially Filled Grid, or Unfilled Grid Deck Composite with Reinforced Concrete Slab on Steel or Concrete Beams; Concrete T-Beams, T-and Double T-Sections

a, e, k and also i, j if

sufficiently connected to act as a unit

Lever Rule Lever Rule Nb = 3

Live-Load Distribution FactorsShear – Interior Beams

Notes: Same for Positive and Negative Flexure Locations!

Table 4.6.2.2.2d-1 Distribution of Live Loads Per Lane for Moment in Exterior Longitudinal Beams.

Type of Superstructure

Applicable Cross-Section from Table

4.6.2.2.1-1 One Design Lane

Loaded

Two or More Design Lanes

Loaded Range of

Applicability g = e ginterior

0.779.1

ede = + -1.0 < de < 5.5 Concrete Deck, Filled Grid,

Partially Filled Grid, or Unfilled Grid Deck Composite with Reinforced Concrete Slab on Steel or Concrete Beams; Concrete T-Beams, T- and Double T- Sections

a, e, k and also i, j

if sufficiently connected to act as a unit

Lever Rule

use lesser of the values obtained from the equation above with Nb = 3 or the lever rule

Nb = 3

Live-Load Distribution FactorsMoments – Exterior Beams

Notes: distribution factor for the exterior beam shall not be taken to be less than that which would be obtained by assuming that the cross-section deflects and rotates as a rigid cross-section (SPECIAL ANALYSIS).

2bN

LNext

b

L

xeX

NN

=R ∑

∑+

Table 4.6.2.2.3b-1 Distribution of Live Load per Lane for Shear in Exterior Beams.

Type of Superstructure

Applicable Cross-Section from Table

4.6.2.2.1-1 One Design Lane

Loaded Two or More Design

Lanes Loaded Range of

Applicability g = e ginterior

0.610

ede = +

-1.0 < de < 5.5 Concrete Deck, Filled Grid, Partially Filled Grid, or Unfilled Grid Deck Composite with Reinforced Concrete Slab on Steel or Concrete Beams; Concrete T-

a, e, k and also i, j

if sufficiently connected to act as a unit

Lever Rule

Lever Rule Nb = 3

Live-Load Distribution FactorsShear – Exterior Beams

Notes: distribution factor for the exterior beam shall not be taken to be less than that which would be obtained by assuming that the cross-section deflects and rotates as a rigid cross-section (SPECIAL ANALYSIS)

2bN

LNext

b

L

xeX

NN

=R ∑

∑+

Live-Load Distribution FactorsExterior Girder – Lever Rule

2bN

LNext

b

L

xeX

NN

=R ∑

∑+

R = reaction on exterior beam in terms of lanes

NL = number of loaded lanes under consideration

e = eccentricity of a lane from the center of gravity of the pattern of girders (ft)

x = horizontal distance from the center of gravity of the pattern of girders to eachgirder (ft)

Xext = horizontal distance from the center of gravity of the pattern of girders to theexterior girder (ft)

Nb = number of beams or girders

Live-Load Distribution FactorsExterior Girder - Special

Analysis

Stay Tuned!

Simpler more reliable LL DF Eqns are proposed for ballot in

2007

Des

ign

Req

uire

men

tD

esig

n R

equi

rem

ent

TimeTime

First useFirst use

FailureFailure

TimeTime--tested satisfactory tested satisfactory performanceperformance

LRFD Calibration is Scientific & based on performance of prior design specs &

existing bridge inventory

Existing Existing bridgesbridges

(Standard (Standard Specs)Specs)

Determine Determine β β from reliability from reliability analysis analysis

Determine Target Determine Target Reliability Reliability ββTT

For LRFD Equation:For LRFD Equation:

Optimize Optimize γγii for all types of loads, load for all types of loads, load combinations, and bridgescombinations, and bridgesDetermine φ for elements and materials from reliability analysis

Σ ηiγiQi ≤ φRn

0

4

0 30 60 90 120 2000

4

0 30 60 90 120 2000

4

0 30 60 90 120 200

SPAN LENGTH (Feet)SPAN LENGTH (Feet)

RE

LIA

BILI

TY IN

DEX

REL

IAB

ILIT

Y IN

DE

X

1

2

3

1

2

3

1

2

1

2

3

555

4

5

0 30 60 90 120 2000

4

0 30 60 90 120 2000

4

0 30 60 90 120 2000

4

0 30 60 90 120 200

SPAN LENGTH (Feet)SPAN LENGTH (Feet)

RE

LIA

BILI

TY IN

DEX

REL

IAB

ILIT

Y IN

DE

X

1

2

3

1

2

3

1

2

1

2

3

555

4

5

1

2

3

1

2

3

1

2

1

2

3

1

2

3

1

2

3

1

2

1

2

3

555

4

5555

4

5

0 30 60 90 120 200

Reliability and Calibration ofStandard & LRFD Specifications

SPAN LENGTH (Feet)SPAN LENGTH (Feet)

1

2

3

1

2

3

1

2

1

2

3

555

4

5

00 30 60 90 120 200

3.5

00 30 60 90 120 200

00 30 60 90 120 200

RE

LIA

BIL

ITY

IND

EX

RE

LIA

BIL

ITY

IND

EX

0 30 60 90 120 200

NORMALLY DISTRIBUTEDQ AND R:

LOGNORMALLY DISTRIBUTEDQ AND R

2 2R Q

R-Qβ=σ +σ

⎛ ⎞⎜ ⎟⎝ ⎠2 2

R Q

RlnQ

β=V +V

Unified Steel Specifications

StraightCurved

One Specs!

Lateral Force Effects & “One-Third” Rule

Bending stress due to vertical loads

ytfbu

ncfbu

Fff

Fff

φ

φ

≤+

≤+

l

l

3131

lf

buf

Modified Compression Field Theory

01170801

2

1

2

22222

..f

f

])()([ff

'c

max

'c

'c

max

≤+

=

−=

ε

εε

εε

NodalZonesP

2

P

P2

CC

T T

C CStrut

Fill

Fill

Tie

Fill

Strut and Tie Method

Doremus Avenue Viaduct(Newark, NJ)

Rt. 9, Nacote Creek Bridge (South Jersey)

WSDOT Spliced I-GirdersTwisp River Bridge, Twisp, WA

SingleSingle--span span spliced concrete girders spanning concrete girders spanning 195 ft

2002 PCI

Award

21,542’ long bridge bridge Channel Spans: 207Channel Spans: 207’’--257257’’--250250’’--257257’’--207207’’continuouscontinuousPost-tensioned bulb-tee girders

FLDOTSt. George Island Bridge Apalachicola, FL

FLDOTHathaway Bridge , Panama City, FL

3,815’ longTwin 80Twin 80’’ wide wide roadwaysroadways330330’’ typical spantypical spanSegmental boxes

Long Span Bridges in LRFD? (Cooper River Bridge, SC)

Longest cable stay span in Longest cable stay span in North America, 1,546 feet. North America, 1,546 feet. (LRFD for Cable Loss)(LRFD for Cable Loss)

Long Span Bridges in LRFD? (Great River Bridge, Desha County, AR)

682 ft 682 ft -- 1,520 ft 1,520 ft –– 682 ft Cable682 ft Cable--Stay BridgeStay Bridge

Long Span Bridges in LRFD? (Hoover Dam Bypass Project)

Composite Composite Concrete Deck Concrete Deck Arch BridgeArch Bridge(~2,000 ft)(~2,000 ft)

Comprehensive and rationalComprehensive and rationalResult in more reliable structuresResult in more reliable structuresDesign Life is Design Life is ???? years years

SUMMARYLRFD

Comprehensive and rationalComprehensive and rationalResult in more reliable structuresResult in more reliable structuresDesign Life is Design Life is 75 years years

SUMMARYLRFD

THANK YOU

Firas I. Sheikh Ibrahim, Ph.D., P.E.Firas I. Sheikh Ibrahim, Ph.D., P.E.Senior Codes & Specifications EngineerSenior Codes & Specifications Engineer

Office of Bridge Technology Federal Highway Administration

HIBT-10, Room 3203 400 7th. St. SW

Washington, DC 20590 (202) 366-4598

Firas.Ibrahim@dot.gov

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