BridgeTech, Inc.

Simplified Live Load DistributionFormula

NCHRP 12-62

Research TeamJay A. Puckett, Ph.D., P.E.Dennis Mertz, Ph.D., P.E.X. Sharon Huo, Ph.D., P.E.

Mark Jablin, P.E.Michael Patrick, Graduate Student

Matthew Peavy, P.E.

NCHRP Manager: David Beal, P.E.

BridgeTech, Inc.

Objective The objective of this project is to develop new

recommended LRFD live-load distribution-factordesign equations for shear and moment that are

simpler to apply and have a wider range ofapplicability than those in the current LRFD.The need for refined methods of analysis shouldbe minimized.

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The Problem

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Basics Behavior

Stiff Deckrelativeto Girders –betterdistribution,moreuniform

All analysis and numericalapproaches attempt to quantify this

behavior

Somewhere between Equal (Rigidbody)and

Lever Rule

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AccuracySimplicity

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AccuracySimplicity

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Literature ReviewCurrent Specifications & Simplified

ApproachModeling TechniquesField TestingParametric EffectsBridge TypeNonlinear effects

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PI Bias for a Simple Method

• Analytically based approach

• Canadian SpecificationOrthotropic Plate Theoryspace

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NBI 1990 - mostrecent

NBI TotalInventory Number Skewed

14275 6626330.0% 43.8%

1464 30753.1% 63.4%

1811 3546

3.8% 62.0%360 3677

0.8% 65.3%629 11340

1.3% 40.3%5329 9514

11.2% 53.6%

933 1396

2.0% 49.0%

40 82

0.1% 9.2%

208 300

0.4% 35.3%

208 300

0.4% 35.3%

14168 2669129.8% 50.1%

1571 42133.3% 15.8%

6799 20728

14.3% 37.1%47587 353845 150825

100.0% 42.6%

Precast Solid, Voided, orCellular Concrete Boxes withShear Keys and with orwithout TransversePosttensioning

Open Steel or PrecastConcrete Boxes

Cast-in-Place ConcreteMulticell BoxesCast-in-Place Concrete TeeBeamPrecast Solid, Voided, orCellular Concrete Boxes withShear Keys

Steel Beam Cast in place concreteslab, precast concrete

Closed Steel or PrecastConcrete Boxes

Cast in place concreteslab

Cast-in-place concrete orplank, glued/spiked panelsor stressed wood

Precast Concrete ChannelSections with Shear Keys

Precast Concrete DoubleTee Section with Shear Keysand with or withoutTransverse Posttensioning

Precast Concrete I or Bulb-Tee Sections

Precast Concrete TeeSection with Shear Keys andwith or without TransverseReinforcement

Integral Concrete

Integral Concrete

Cast-in-place concreteoverlay

Integral Concrete

Cast-in-place concrete,precast concrete

Cast-in-place concreteslab, precast concrete slab

Monolithic Concrete

Monolithic Concrete

Cast-in-place concreteoverlay

j

slab on girders

slab on girders

slab on girders

monolithic slab and girders

monolithic slab and girders

slab on girders

i

h

g

slab on girders

slab on girders

slab on girders

slab on girders

Supporting Components Type of DeckAASHTO Letter

(see Table4.6.2.2.1-1)

2848

a

d

c

b

f

e

Number of BridgesAnalytical Group Type

28106

17766

5718

5633

151398

Q

4847

slab on girders

53285

Slabs Not Applicable Not Applicable Slabs

26629

l

k

slab on girdersWood Beams

Total:

55869

895

851

851 NB

IDat

abas

e

BridgeTech, Inc.

Summary Table (NBI Data)

Type 1990-present Total Inventory

Steel Beam 30.0% 42.8%

Concrete I 29.8% 15.1%Precast ConcreteBoxes with Shear Keys 11.2% 5.0%

Slabs 14.3% 15.8%85.3% 78.7%

Bridge Percentages by Type

BridgeTech, Inc.

min. max min max min max min max min maxConc. T-Beam 71 n/a 12 93 2.42 16 5 11 0 52.98 0.32 3.26Steel I-Beam 163 n/a 12 205 2 15.5 4.42 12 0 66.1 0.4 4.53Prestressed I-Beam 94 n/a 18.75 136.2 3.21 10.5 5 9 0 47.7 0.31 3.12Prestressed Conc. Box 112 n/a 43.3 243 6 20.75 n/a n/a n/a n/a 0.52 8.13R/C Box 121 n/a 35.2 147 6.58 10.67 n/a n/a n/a n/a 0.53 5.5Slab 127 n/a 14.2 68 n/a n/a 9.8 36 0 70 0.21 2.56Multi-Box 66 n/a 21 112.7 n/a n/a 0 11 0 55.8 0.22 5.96Conc. Spread Box 35 n/a 29.3 136.5 6.42 11.75 6 8.5 0 52.8 0.54 3.11Steel Spread Box 20 n/a 58 281.7 8.67 24 5 9.5 0 60.5 0.75 8.02Precast Conc. Spread Box 4 1 - 6 44.38 81.49 5.67 13.75 7.75 8.75 0.00 48.49 1.68 2.03Precast Conc. Bulb-Tee 4 2 - 6 115.49 159.00 8.33 10.29 8.25 8.27 0.00 26.70 1.43 4.97Precast Conc. I-Beam 3 3 - 5 67.42 74.33 9.00 10.58 8.25 8.75 0.00 33.50 1.45 1.53CIP Conc. T-Beam 3 4 - 5 66.00 88.50 8.17 12.58 7.00 9.00 0.00 31.56 1.91 2.74CIP Conc. Multicell 4 2 - 3 98.75 140.00 9.00 10.33 8.00 9.25 0.00 26.23 2.24 3.05Steel I-Beam 4 2 - 4 140.00 182.00 9.33 11.50 8.00 9.00 0.00 50.16 1.60 5.11Steel Open Box 2 1 - 3 170.67 252.00 9.00 9.38 8.50 8.50 4.50 31.95 3.28 7.00

LRFR 3 653Slab on RC, Prest., andSteel Girders 653 1 - 7 18.00 243.00 2.33 18.00 0.00 8.00 N/A N/A 0.38 5.22

Spread Box Beams 27 1 100.00 190.00 5.00 20.00 6.00 12.00 N/A N/A 1.40 8.00

Adjacent Box Beams 23 1 100.00 210.00 3.00 5.83 5.00 6.00 N/A N/A 1.13 9.60

Slab on Steel I-Beam 24 1 160.00 300.00 12.00 20.00 9.00 12.00 N/A N/A 2.76 6.82

Summary: 1560 1 - 7 12.00 300.00 2.00 24.00 0.00 36.00 0.00 70.00 0.21 9.60

Span Length (ft)

ParametricBridges

N/A 74

Number ofSpans

Parameter RangesReference

Numberof

BridgesBridge TypesTotal No.

Bridges Aspect Ratio (L/W)Skew Angle (deg)Slab Thickness (in)Girder Spacing (ft)

24

809

Dat

aS

ou

rce

NCHRP 12-26

TN TechSet 1

1

2

BridgeTech, Inc.

CommonDatabaseFormatNCHRP 12-50

1. NCHRP 12-26 BridgeDatabase800 + Bridges can be used in anautomated process to generatesimplified and rigorous analyses.

3. Virtis/Opis DatabaseBridges650+ bridges may be exported fromVirtis/Opis to supply real bridges toboth simplified and rigorous methods.

2. Tenn. Tech. DatabaseDetailed descriptions and rigorousanalysis are available from a recentTT study for TN DOT. Results,structural models, etc., are readilyavailable.

Data Sources

Condense to aCommon Database

A

4. ParametricallyGenerated Bridges74 Bridges were developed totest the limits of applicability ofthe proposed method.

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Rigorous Analysis (Basis)SAPAASHTO FE EngineAnsys

CommonDatabaseFormatNCHRP 12-50

Common DatabaseFormatNCHRP 12-50

A

B

BRASS-Girder (LRFD)TM

Simplified Analysis Methods: Standard Specifications (S over D) LRFD Specifications Rigid Method Lever Rule Adjusted Equal Distribution Method Canadian Highway Bridge Design Code Sanders

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Simplified Moment and Shear Distribution Factor Equations Specification and Commentary Language Design Examples Final ReportIterative Process Involving Tasks 7,8, and 9 through 12.

Common DatabaseFormatNCHRP 12-50

Studies Directed Toward: Skew Lane Position Diaphragms

B

Comparisons and Regression Testing (NCHRP 12- 50 Process)Tasks 6 & 9Regression testing on “real” bridges (Virtis/Opis database, NCHRP 12-26 database)(compare proposed method to current LRFD method)Comparisons from parametric bridges and rigorous analysis

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Grillage Method (structural model)

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Influence Surfaces (structural model)

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Automated Live Load Positioning

• Critical live load placement• Actions (shear, moment,reaction, translation)• Single and multiple lanesloaded• Critical longitudinalposition• Accounts for barrier, etc.• 4-ft truck transverse truckspacing• POI at least tenth points

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Computation of Distribution Factor

/

rigorous

beam

Rigorous Action Number LanesDistribution Factor g

Action from Beamlinefor same Longitudinal Position

Mg

M

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Using Distribution Factors

( )design rigorousestimate beamM M g

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Example of Standard SpecificationResults

Moment at 1.4One-lane Loaded Exterior I-Girder

Std. S/D vs. Rigorous

y = 0.9914x + 0.2962R2 = 0.3834

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Rigorous Distribution Factor

Std

.Spe

c.(S

/D)D

istr

ibu

tion

Fac

tor

1

1

Unit slope = good

R2 = poor

Poor R2 = littlehope

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Lever Rule ResultsMoment at 1.4

One-lane Loaded Exterior I-GirderLever Rule vs. Rigorous

y = 1.63x - 0.2644R2 = 0.8889

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Rigorous Distribution Factor

Lev

er

Ru

leD

istr

ibu

tion

Fac

tor 1

1

R2 = good

slope = poor

Apply affinetransformation

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Moment at 1.4One-lane Loaded Exterior I-GirderCalibrated Lever Rule vs. Rigorous

y = 0.978x + 0.0413R2 = 0.8889

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Rigorous Distribution Factor

Cal

ibra

ted

Lev

erR

ule

Dis

trib

utio

nFa

cto

r

1

1

Calibrated Lever Rule Results

R2 = good and is thesame

slope = good

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Affine Transformation ConceptSi

mpl

eM

etho

d

Rigorous Method

Original SimpleMethod

Rotation to Unityby multiplication

Raise or lower byaddition/substratio

n

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Affine Transformation (example)

1 1.63 0.2644y x 12

1.63 0.26440.1622

1.63 1.63 1.63y x

y x

13 2 0.1622 0.1622 0.1622 0.1622

1.63y

y y x x

( )

( )

( )

where1

0.61 and 0.16221.63

andis thecalibrated distribution factor, and

is the lever ruledistribution factor computed with the typical man

Calibrated lever rule m Lever rule m

m m

Calibrated lever rule

Lever rule

g a g b

a b

g

g

ualapproach.

Unitslope

Unitslope

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Affine Transformation ConceptSi

mpl

eM

etho

d

Rigorous Method

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Number ofLoadedLanes

Girder Distribution Factor Multiple Presence Factor

Use integer part of

m shall be greater than or equal to 0.85.

to determine number of loaded lanes formultiple presence.

Interior andExterior

Two ormore

LoadedLanes

m = 1.2Interior andExterior

One

10c st L

m ag g

W F Nmg m m

N N

12cW

Lm m lever rule m

g

Nmg m a g b m

N

Moment Distribution Factor Computation

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Multiple Presences

1 1.202 1.003 0.85

4 or more 0.65

Number ofLoadedLanes

MultiplePresence Factor

"m"

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Lever Rule Equations (aids)Girder

Location

Numberof Loaded

Lanes Distribution Factor Range of Application Loading Diagram

Numberof Wheelsto Beam

2

2

3

4

1

1

2 or more

Exterior

12 2

edS

6e

e

d S ft

d S

31 ed

S S 6ed S ft

31 ed

S S 10ed S ft

33 82 2

edS S

10 16ed S ft

16 20ed S ft ed S

6'6' 4'

ed S

6' 6'4'

ed S

6'6' 4'

S

ed S

6'

Sde

6'

2 162 ed

S S

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Calibration Coefficients (Moment)

a m b m a m b mSteel I-Beam aPrecast Concrete I-Beam kPrecast Concrete Bulb-Tee Beam kPrecast Concrete Double Tee withShear Keys with or without Post-Tensioning

i

Precast Concrete Tee Section withShear Keys and with or withoutTransverse Post-Tensioning

j

Precast Concrete Channel with ShearKeys h

Cast-in-Place Concrete Tee Beam e 0.65 0.15 1.40 -0.41Cast-in-Place Concrete Multicell BoxBeam

d

Adjacent Box Beam with Cast-in-Place Concrete Overlay

f

Adjacent Box Beam with IntegralConcrete g

Precast Concrete Spread Box Beam b, c 0.50 0.06 0.77 -0.17Open Steel Box Beam c Use Article 4.6.2.2.3

Moment

1.51 -0.690.41 -0.03

1.20 -0.370.61 0.16

Structure Type

AASHTOLRFD CrossSection Type

One Loaded LaneExterior Interior

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Calibration Coefficients (Moment)

a m b m a m b mSteel I-Beam aPrecast Concrete I-Beam kPrecast Concrete Bulb-Tee Beam kPrecast Concrete Double Tee withShear Keys with or without Post-Tensioning

i

Precast Concrete Tee Section withShear Keys and with or withoutTransverse Post-Tensioning

j

Precast Concrete Channel with ShearKeys h

Cast-in-Place Concrete Tee Beam e 0.65 0.15 1.40 -0.41Cast-in-Place Concrete Multicell BoxBeam

d

Adjacent Box Beam with Cast-in-Place Concrete Overlay

f

Adjacent Box Beam with IntegralConcrete g

Precast Concrete Spread Box Beam b, c 0.50 0.06 0.77 -0.17Open Steel Box Beam c Use Article 4.6.2.2.3

Moment

1.51 -0.690.41 -0.03

1.20 -0.370.61 0.16

Structure Type

AASHTOLRFD CrossSection Type

One Loaded LaneExterior Interior

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Calibration Coefficients (Shear)

a v b v a v b v a v b v a v b v

Steel I-Beam aPrecast Concrete I-Beam kPrecast Concrete Bulb-Tee Beam kPrecast Concrete Double Tee withShear Keys with or without Post-Tensioning

i

Precast Concrete Tee Section withShear Keys and with or withoutTransverse Post-Tensioning

j

Precast Concrete Channel with ShearKeys h

Cast-in-Place Concrete Tee Beam e 0.79 0.09 0.94 0.05 1.24 -0.22 1.21 -0.17

Cast-in-Place Concrete Multicell BoxBeam

d

Adjacent Box Beam with Cast-in-Place Concrete Overlay

f

Adjacent Box Beam with IntegralConcrete g

Precast Concrete Spread Box Beam b, c 0.63 0.14 0.79 0.12 0.85 -0.01 1.02 -0.10Open Steel Box Beam c Use Article 4.6.2.2.3

Structure Type

AASHTOLRFD CrossSection Type

ShearExterior Interior

One Loaded LaneTwo or More Lanes

LoadedOne Loaded

LaneTwo or MoreLanes Loaded

0.81 0.09 0.94 0.07

0.85 0.04 0.90 0.04 -0.06

1.09 -0.15 0.91

1.27 -0.22 1.04

0.05

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Structural Factor (Moment) MultipleLanes Loaded

Steel I-Beam aPrecast Concrete I-Beam kPrecast Concrete Bulb-Tee Beam kPrecast Concrete Double Tee withShear Keys with or without Post-Tensioning

i

Precast Concrete Tee Section withShear Keys and with or withoutTransverse Post-Tensioning

j

Precast Concrete Channel with ShearKeys h

Cast-in-Place Concrete Tee Beam e 1.10Cast-in-Place Concrete Multicell BoxBeam d

Adjacent Box Beam with Cast-in-Place Concrete Overlay f

Adjacent Box Beam with IntegralConcrete g

Precast Concrete Spread Box Beam b, c 1.00

Open Steel Box Beam cUse ExistingSpecification

Structure Type

AASHTOLRFD CrossSection Type

Two or moreloaded lanes

1.15

1.10

F st

UniformDistribution

Nlane / Ngirder

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Example

10’4’

2’ 6’

6 120.9

2 10 2 100.9

0.61 0.9 0.16

0.71

exterior

Lever Rule

Calibrated m Lever Rule m

Calibrated

P PR P

g

g a g b

g

P/2 P/2

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Calibration ResultsSlab-on-Girder Bridges

Type of Bridge

Slope Intercept R 2Figures a b a or F st b

RegressionPlot R 2

1 Lane 1.2386 -0.1112 0.9661 13a, N-125 0.8074 0.0898 0.81 0.09 13b, K-16 0.9656

2 or More Lanes 1.0657 -0.0713 0.9674 14a, N-117 0.9384 0.0669 0.94 0.07 14b, K-15 0.9485

1 Lane 0.9209 0.1355 0.9198 15a, N-93 1.0859 -0.1471 1.09 -0.15 15b, K-12 0.9198

2 or More Lanes 1.1041 -0.0553 0.9343 16a, N-85 0.9057 0.0501 0.91 0.05 16b, K-11 0.9343

CalibratedLever 1 Lane 1.6396 -0.2679 0.8894 17a, N-61 0.6099 0.1634 0.61 0.16 17b, K-8 0.8894

Henry'sMethod 2 or More Lanes 1.0440 0.1098 0.8757 18a, N-51 n/a n/a 1.15 n/a 18b, K-7 0.8757

CalibratedLever 1 Lane 0.8346 0.3076 0.4497 19a, N-29 1.1982 -0.3686 1.20 -0.37 19b, K-4 0.4508

Henry'sMethod 2 or More Lanes 1.0112 0.0658 0.9216 20a, N-19 n/a n/a 1.15 n/a 20b, K-3 0.9216

I-G

irder

s(a

,h,i

,j,k

)

Shea

r

CalibratedLever

Exterior

Interior

Mom

ent

Exterior

Interior

GirderLocationAction

BasicMethod

Calibration Constants

Lanes LoadedInitial Trend Line - Lever Rule and Henry'sMethod (Henry's Method already calibrated)

Computed CalibrationFactors (for LeverRule Calibration)

Recommended Calibration Factors

QuiteGood

(typical)

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Statistical Comparison Conceptual

1.00

Standarddeviation

simplified

rigorous

g

g

Num

ber

ofSa

mpl

es

Mean

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Shift Simple Upward by a factor

Simple / Rigorous1.00

Increase by a factor that isrelated to the COV

a

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Analysis FactorsType of Bridge

No. ofStd. Dev.

Offset

ComputedAnalysisFactor

RoundedAnalysis Factor

( b = 1)

No. of Std.Dev. Offset

ComputedAnalysis Factor

RoundedAnalysis Factor

(b = 0.5)

No. of Std. Dev.Offset

ComputedAnalysisFactor

RoundedAnalysis

Factor (b =S/R (S/R) -1 V S/R β ga ga (rounded) β ga ga (rounded) β ga ga (rounded)

1 Lane 13c 1.010 0.991 0.058 1.0 1.049 1.05 0.5 1.020 1.05 0.0 0.991 1.002 or More Lanes 14c 1.014 0.986 0.067 1.0 1.053 1.05 0.5 1.019 1.05 0.0 0.986 1.001 Lane 15c 0.999 1.001 0.069 1.0 1.069 1.10 0.5 1.035 1.05 0.0 1.001 1.002 or More Lanes 16c 1.000 1.000 0.102 1.0 1.102 1.10 0.5 1.051 1.05 0.0 1.000 1.00

CalibratedLever

1 Lane 17c 0.993 1.007 0.0921.0 1.099 1.10 0.5 1.053 1.05 0.0 1.007 1.00

Henry'sMethod 2 or More Lanes 18c 1.285 0.778 0.110 1.0 0.888 1.00 0.5 0.833 0.85 0.0 0.778 0.80

CalibratedLever

1 Lane 19c 0.996 1.004 0.244 1.0 1.248 1.25 0.5 1.126 1.15 0.0 1.004 1.00Henry'sMethod

2 or More Lanes 20c 1.139 0.878 0.068 1.0 0.945 1.00 0.5 0.912 0.95 0.0 0.878 0.90

FiguresAction

Interior

Exterior

Girder LocationBasic

Method

Interior

Exterior

CalibratedLeverS

hear

No. of Std. Dev. Offset b = 1 No. of Std. Dev. Offset b = 0.5 No. of Std. Dev. Offset b = 0.0

I-G

irde

rs(a

,h,

i,j,

k)

COVInverseRatio ofMeansLanes Loaded

Analysis Factor Computations

Mo

men

t

High dueto highCOV

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Example Continued

6 120.9

2 10 2 100.9

0.61 0.9 0.16

0.71

exterior

Lever Rule

Calibrated m Lever Rule m

Calibrated

P PR P

g

g a g b

g

0.71

1.05 1.2 0.71

0.89

Calibrated

a

a

g g

mg

mg

PreviousExample

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All effects are now separated anunderstandable

1.05 1.2 0.71

0.89a

a

mg

mg

Variability in

analysis

Effect of MultiplePresence

Analysis

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SkewAdjustments for shearNo iterationCommentary M&M 20-07 StudyNeglect decrease for moment

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CurvatureNo change

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Type of SuperstructureApplicable Cross-Section

from Table 4.6.2.2.1-1 Correction Factor

Range of

Applicability

Concrete Deck, Filled Grid,Partially Filled Grid, or UnfilledGrid Deck Composite withReinforced Concrete Slab on Steelor Concrete Beams; Concrete T-Beams, T- and Double T-Section

a, e and also h, i, j

if sufficiently connected toact as a unit

1.0 0.20 tan 0 603.5 16.020 240

4b

SL

N

Precast concrete I and bulb teebeams

K 1.0 0.09 tan 0 603.5 16.020 240

4b

SL

N

Cast-in-Place Concrete MulticellBox

D 12.01.0 0.25 tan

70L

d

0 60

6.0 13.020 240

35 1103c

SL

dN

Concrete Deck on Spread ConcreteBox Beams

B, c

12.01.0 tan6

Ld

S

0 60

6.0 11.520 140

18 653b

SL

dN

Concrete Box Beams Used inMultibeam Decks

f, g 12.01.0 tan

90L

d

0 6020 120

17 6035 60

5 20b

L

db

N

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Push-the-limits bridgesW

SSOverhang

1'-9"

OverhangS

st

1'-9"

BridgeNo.

GirderSpacing,

S(ft)

Recommendedminimum slab

thickness(AASHTO STD

Table 8.9.2)

SlabThickness,

ts

(in)

SpanLength, L

(ft)

TotalBridge

Width, W(ft)

No.ofgirders

Overhang(ft)

1 12 8.80 9.00 240 44 4 42 12 8.80 9.00 260 44 4 43 12 8.80 9.00 280 44 4 44 12 8.80 9.00 300 44 4 45 12 8.80 9.00 200 44 4 46 14 9.60 9.75 200 48 4 37 16 10.40 10.50 200 54 4 38 18 11.20 11.25 200 60 4 39 20 12.00 12.00 200 68 4 410 12 8.80 9.00 160 58 5 511 12 8.80 9.00 160 53 4 8.5

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Many Parameter StudiesSkew

Diaphragm Cross-frame Stiffness End Cross-frames Intermediate Cross-frames

Typical Example

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With SupportDiaphragms

With SupportDiaphragms

With SupportDiaphragms

R = 61.87 kipsDF = 0.876

R = 52.94 kipsDF = 0.870

R = 54.89 kipsDF = 0.778

R = 20.07 kipsDF = 0.330

R = 52.94 kipsDF = 0.870

R = 43.82 kipsDF = 0.621

R = 52.15 kipsDF = 0.739

R = 43.78 kipsDF = 0.720

1

1

1

R = 54.89 kipsDF = 0.778

R = 46.62 kipsDF = 0.660

25

R = 46.62 kipsDF = 0.660

Span 1

5

5

R = 28.00 kipsDF = 0.460

R = 43.78 kipsDF = 0.720

25

5

Span 5

25

R = 34.30 kipsDF = 0.564

60°

30°

R = 34.30 kipsDF = 0.564

R = 43.82 kipsDF = 0.621

R = 34.30 kipsDF = 0.564

R = 34.30 kipsDF = 0.564

R = 43.82 kipsDF = 0.621

R = 43.82 kipsDF = 0.621

R = 28.00 kipsDF = 0.460

R = 52.15 kipsDF = 0.739

R = 20.07 kipsDF = 0.330

R = 61.87 kipsDF = 0.876

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Regression TestingComplete database used to compare:

LRFD S/D Rigorous Again, used 12-50

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Is this simpler?

Consistent approach for most bridgetypes

Based upon lever rule (shear and one-lane moment) – and adjusted

Based uniform distribution (multiple-lanes loaded – and adjusted

Independently accounts for multiplepresence

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Is this simpler?Independently accounts for variability of

simple analysis wrt rigorousLever rule aids are provided in appendixNo iterative approach, i.e., independent of

cross section and span lengthsSame for positive and negative moment

areasSkew corrections are based upon S/L

(readily known)

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Is it simpler?

Many pages shorterMany variables eliminated from

notation and sectionOnce affine transformations are

understood the adjustments fromlever are readily seen

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Go to report

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Additional work

Recalibrate uniform method parallel thecalibrated lever

Improve one-lane loaded for momentReview/revise tub girder systems

Develop presentation materials to helpexplain this in a more understandable manner

Suggestions welcome!

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Questions, Discussion

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End of AASHTO Talk

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Extra slides

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Modeling Appendix

hh1

h2

le1

le2

li/2

li/2

li

il

tw

t1

2t

hs

twCentroid Axisof Box-Girder

ExteriorLongitudinal

Girder

InteriorLongitudinal

Girder

h

l e1

e2l

il

l e* Interior

LongitudinalGirder

ExteriorLongitudinal

Girder

Closed Section ForTorsional Rigidity

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Shear Distribution Factors for CIP Concrete Multicell

Box Beam Bridges -- Validation

Ext Int Exterior Interior Exterior Interior Exterior Interior1 L 0.620 0.344 0.618 0.338 0.29% 1.84%2 L 0.644 0.876 0.644 0.889 0.06% 1.45%3 L 0.654 0.900 0.653 0.915 0.25% 1.69%1 L 0.618 0.346 0.620 0.336 0.34% 3.03%2 L 0.637 0.885 0.640 0.891 0.51% 0.68%3 L 0.645 0.904 0.649 0.913 0.57% 0.93%1 L 0.643 0.317 0.639 0.310 0.63% 2.08%2 L 0.669 0.861 0.664 0.815 0.80% 5.36%3 L 0.679 0.885 0.672 0.877 1.00% 0.95%1 L 0.635 0.318 0.547 0.289 13.84% 9.10%2 L 0.667 0.854 0.606 0.759 9.06% 11.18%3 L 0.679 0.883 0.629 0.817 7.37% 7.50%1 L 0.722 0.264 0.718 0.257 0.43% 2.52%2 L 0.774 0.955 0.780 0.948 0.70% 0.65%3 L 0.779 1.022 0.784 1.033 0.67% 1.02%1 L 0.706 0.267 0.698 0.261 1.17% 2.26%2 L 0.767 0.941 0.769 0.930 0.15% 1.18%3 L 0.776 1.016 0.778 1.022 0.24% 0.63%1 L 0.652 0.317 0.658 0.314 0.88% 0.95%2 L 0.675 0.914 0.681 0.936 0.83% 2.40%1 L 0.642 0.319 0.645 0.335 0.43% 5.12%2 L 0.671 0.908 0.675 0.983 0.62% 8.30%

SAP2000 BTLiveLoader DifferenceBridgeType

TTUBridge No.

BridgeID No. Span LanesLoaded

BeamEnd

1

210141013

2

1

14 1011 1012

2

13

15

Mul

ticel

lBox

Bea

m

1

2

12 1007 1008

10101009

1

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excellent ≥0.9 bad < 0.5

Lever Rule Henry'sMethod

LRFD CHBDC STD Sanders BestMethod

1 excellent good good bad bad bad Lever2 or more excellent acceptable good bad bad bad Lever

1 excellent poor good good good good Lever2 or more excellent excellent excellent good good good Lever

1 good good good bad bad bad Lever2 or more good good good poor acceptable bad Lever

1 bad bad bad bad bad bad CHBDC2 or more acceptable excellent acceptable acceptable acceptable poor Henry's

1 excellent good good poor poor poor Lever2 or more excellent excellent excellent poor poor poor Lever

1 excellent poor excellent excellent good good Lever2 or more good excellent good excellent good excellent Henry's

1 excellent excellent good poor poor poor Henry's2 or more excellent excellent excellent poor poor poor Henry's

1 poor bad excellent acceptable poor poor LRFD2 or more poor excellent excellent good good good Henry's

1 excellent acceptable excellent poor acceptable bad Lever2 or more excellent excellent excellent acceptable acceptable poor Lever

1 excellent acceptable excellent acceptable good poor Lever2 or more good excellent excellent good excellent poor Henry's

1 poor poor poor poor poor poor CHBDC2 or more good excellent good poor acceptable poor Henry's

1 acceptable bad poor bad poor bad Lever2 or more poor excellent poor bad poor bad Henry's

1 excellent poor excellent acceptable acceptable poor Lever2 or more excellent excellent excellent good good acceptable Lever

1 excellent poor acceptable good excellent acceptable STD2 or more excellent excellent excellent good excellent acceptable Henry's

1 poor bad bad poor bad bad CHBDC2 or more acceptable good poor poor poor bad Henry's

1 bad excellent bad poor bad bad Henry's2 or more poor good poor poor poor bad Henry's

Method Rating Based on the Value of the Correlation Coefficient (R2) between Each SimplifiedMethod and Rigorous Analysis

LanesLoaded

GirderLocations

ActionBridgeSet

Method0.90 > good ≥0.80 0.80 > acceptable ≥0.70 0.70 > poor≥0.50

4

3

2

1

Moment

Moment

Shear

Moment

Shear

Moment

Shear

Shear

Exterior

Interior

Exterior

Interior

Exterior

Interior

Exterior

Interior

Exterior

Interior

Exterior

Interior

Exterior

Interior

Exterior

Interior

Slab On I

CIP Tees

SpreadBoxes

AdjacentBoxes

vvcc

vvcccvc

vvcc

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Basics Continued Deflection is the easiest state

variable to predictanalytically/numerically

Interior girder load effects areeasier to predict than exterior

Loads near midspan distributemore uniformly than loadapplied near supports.

Relative stiffness is primaryand flexure is more importantthan is torsion

Most important parameter isthe girder spacing (orcantilever span)

2

2

3

3

( )

( )

d wEI M x

dxd w

EI V xdx

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Prerequisites We are not proposing to take any one simplified

method “as is”. (unless it really works well). Analytically-based approaches can be

implemented at different levels (i.e., computestiffness parameters) – empirical methods cannot.

Analytically-based approaches can be more easilyextended (in case of limits of application), thanempirically-based methods.

Analytically-based approaches can be as simple asempirical approaches

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Task 1 -- Literature Review

Michael PatritchGraduate StudentTN Tech

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Task 1 -- Literature Critical Findings

Simplified methods Sanders and Elleby “Equal Distribution Method” – name is a

misnomer Canadian Standards Juxtaposition of stiffness extremes

Stiffness effectsTestingAnalysis and modeling

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Sanders and Elleby NCHRP study Limitations

Span to 120-ft Slab on Beam (Orthotropic Plate Theory) Multi beam (Articulated Orthotropic Plate) CIP Boxes (Folded Plate)

Considered Aspect ratio Relative long/trans flexural stiffness Relative torsonal stiffness

Field tests for some validation

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AASHTO LRFD NCHRP 12-26 Empirically based Includes stiffness parameters in equations “Ugly” equations Embedded multiple presence factors No rational analytical basis Resort to lever rule when empiricism fails Works reasonably well for interior girders Limitations are of concern

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Sanders and Elleby (cont)

3For10

5

3For3

17

23

105

/2

CN

D

CCNN

D

DSg

L

LL

DSwheelg /)( Double for

LFRDDesign Lane

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Equal Distribution Method (TN DOT)

All beams carry equal live load(interior/exterior)

g = NL/Ng

Interpolate number of lanesAdjust g by empirical factors from researchResearch is on interior beamsSimple but purely empiricalLimited sample for rigorous comparison

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TN DOT Equal Distribution Method

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Sanders and Elleby (cont)

21

1

1

2

tJJ

IGE

LW

C

0.6Concrete slab bridge

1.8Separated concrete box-beams

3.5

Nonvoided concrete beams(prestressed or reinforced)

4.8

Composite steel I-beams

3.0Noncomposite steel I-beams

Concrete deck:Beam and slab (includes

concrete slab bridge)

KBeam Type and DeckMaterialBridge Type

C = K(W/L)

but

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Canadian SpecificationAnalytically based upon orthotropic plate

theoryVery similar to Sanders and EllebyUse either stiffness parameter approach or

good estimation tables (easy)Few limitationsMore rational limits for skew and curvature

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Canadian Specification (cont) Slab Voided slab, including multi-cell box girders with sufficient

diaphragms, Slab-on-girders Steel grid deck-on-girders Shear-connected beam bridges in which the interconnection of

adjacent beams is such as to provide continuity of transverse flexuralrigidity across the cross-section

Box girder bridges in which the boxes are connected by only the deckslab and transverse diaphragms, if present

Shear-connected beam bridges in which the interconnection ofadjacent beams is such as not to provide continuity of transverseflexural rigidity across the cross-section

Numerous wood systems ….

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Canadian Specification (cont)

gNmMn

M Laneavgg

avggmg MFM

1001001 ef

mCC

F

NSF

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Canadian Specification (cont)

1001001 ef

mCC

F

NSF

LengthSpanKCF

Lane width effect

Lane position effect

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Canadian Specification (cont)Similar procedures for shear – different values

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Canadian Specification (cont)Skew limit

Plan View

BeamsonSlab

Slabs

LengthSpanangleskewWidthBridge

181

61

)tan(

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Canadian Specification (cont)

0.12

CurvatureofRadiusb

LengthSpan

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Kennedy and SennahSteel BoxesPossibly concrete with modificationsSimilar to LRFD approach (authors claim

better accuracy)Empirical “Ugly” equations

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European Practice

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Examples

AASHTO LRFDHenry (old method)CSASanders and Elleby

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Summary

Moment Shear Moment Shear Moment Shear Moment Shear

AASHTO LRFD 0.694 0.955 0.840 0.840 0.732 0.884 0.733 0.733Canadian Bridge Design Code 0.895 0.895 1.034 1.034 0.783 0.783 0.930 0.930Sanders and Elleby 0.710 0.710 0.710 0.710 0.946 0.946 0.946 0.946Equal Distribution Factor Method 0.774 0.774 0.774 0.774 0.655 0.655 0.655 0.655

Interior ExteriorPCI Example 4

Interior ExteriorMethodAISI Example 2

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Task 2 – Range of structural forms, materialsand range of application

Range of application There is no reason at this point to limit range of

application (we can include range outside ofconventional practice and geometries)

“All” parameters will be included in thedatabase

A large amount of data is available fromseveral sources (see Task 6 tables)

Additional data can be added

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Task 3 -- Analytical method Mathematical model

Equilibrium,compatibility, andconstitutiverelationships

Beam theory Kirchhoff plate theory Results in governing

ODE or PDF

4

4

p xd wdx EI x

4 ,p x yw

D

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Task 3 -- Analytical methodNumerical methods

Finite difference Finite element method (plate or shell elements) Grillage Finite Strip Method Harmonic analysis (Sanders and Elleby)

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Theorem Requirements

Calculated internal actions and appliedforces are in equilibrium

Materials and section/member behaviormust be ductile

Independent of themodeling assumptions!

No instability or fracture

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The lower bound theorem isone of the most importanttheorems/concepts instructural engineering.

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The lower bound theorem isone of the most importanttheorems/concepts instructural engineering.

Offers wonderful assurance as the modelsare often simple approximations to thereal world.

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Task 4 -- Process Detail and Chaining

Effort Do it? Sample1 12-50 -> BRASS -> Computation -> 12-50 Small yes2 12-50 -> BRASS -> Input File -> FEA -> 12-50 Large yes3 12-50 -> BRASS -> Input File -> FSM -> 12-50 Medium yes4 TT Set 1 -> Process 1 Small-> Small yes All5 TT Set 1 -> Process 2 Small -> Large yes All6 TT Set 1 -> Process 3 Small -> Medium yes All7 TT Set 2 -> Process 1 Small-> Small yes Typical8 TT Set 2 -> Process 2 Small -> Large yes Typical9 TT Set 2 -> Process 3 Small -> Medium yes Typical

10 CSA -> Process 1 Depends maybe11 CSA -> Process 2 Depends maybe12 CSA -> Process 3 Depends maybe13 Sanders -> Process 1 Small-> Small maybe14 Sanders -> Process 2 Small -> Large maybe15 Sanders -> Process 3 Small -> Medium maybe16 LRFR -> Process 1 Small-> Small yes Typical17 LRFR -> Process 2 Small -> Large yes Typical18 LRFR -> Process 3 Small -> Medium yes Typical

Process

NCHRP 12-50

Dat

abas

e

LRFR

Sanders

CSA

NCHRP 12-62

TN Tech, Set 1

12-26

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Task 4 -- Process Matrix

Notes NCHRP 12-50 TN Tech Set 1 NCHRP 12-26 CSA Sanders LRFRAASHTO Std S/D equation, program into an automated approach process 1 process 4 process 7 process 10 process 13 process 16AASHTO LRFD LRFD Eqs, program into an automated approach process 1 process 4 process 7 process 10 process 13 process 16AASHTO LRFD Lever Rule Program into an automated approach process 1 process 4 process 7 process 10 process 13 process 16AASHTO LRFD Rigid Method Program into an automated approach process 1 process 4 process 7 process 10 process 13 process 16Sanders Program into an automated approach process 1 process 4 process 7 process 10 process 13 process 16Canadian Specification (CSA) Program into an automated approach process 1 process 4 process 7 process 10 process 13 process 16Henry (Modified) Program into an automated approach process 1 process 4 process 7 process 10 process 13 process 16Rigorous FEA FEA engine and/or a commercial FEA engine process 2 process 5 process 8 process 11 process 14 process 17Rigorous FSM Available FSM program process 3 process 6 process 9 process 12 process 15 process 18

Met

hod

Comparison of Methods and AvailableDatabases of Bridges

DatabaseAASHTO Std Spec.AASHTO LRFDLever RuleRigid methodCSAModified HenryJOSERigorous FEARigorous FSM

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Task 6 – Parametric StudySlab on Steel Girders

321 Total Data Sets AASHTO Type A

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Task 6 – Parametric StudySlab on Precast I and Bulb Tee Girders

176 Total Data Sets AASHTO Type K

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Task 6 – Parametric StudySlab on Concrete Tees

74 Total Data Sets AASHTO Types E and J

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Task 6 – Parametric StudySlab Bridges – 127 Slab Data Sets

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Task 6 – Parametric Study Spread Concrete Boxes

94 Total Data Sets AASHTO Types B and C

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Task 6 – Parametric StudyAdjacent Concrete Boxes

307 Total Data Sets AASHTO Types D, F, and G

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Task 6 -- Wood BridgesWood bridges will not be addressed

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Additional Load Distribution Issues

Parameters Skew Barriers Diaphragms LocationSkew Yes Maybe Yes MaybeBarriers Maybe Yes Maybe YesDiaphragms Yes Maybe Yes MaybeLocation (e.g. Fatigue) Maybe Yes Maybe Yes

Additional Parameters

Perform separate parametric studies to focusexclusively on these effects

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Three primary questions for thepanel

Lane width to determine the number oflanes

Live load positionMultiple presence factors

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Number of Lanes Loaded

•Issue for ourstudy – not totaldesign load forgirder systems

•Integer numberor decimal value

•Should not beoverly sensitive tothe distributionfactor

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Live Load Position – Interior Girder

6-4-6-6 (critical)

6-4-6-4-6 (critical)

6-6-6-6-6 (critical)

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Live Load Position (exterior girder)

2-6-4-6-6

2-6-4-6-4-6

2-6-6-6-6-6

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Multiple Presence – separate fromlive load distribution

Task 6 distribution factors will be computed forone-, two-, three-, etc-lanes loaded. This could becombined, if necessary, later.

Research simplified methods will not include m. Rearch simplified methods will permit one-, two-,

three-, etc-lanes loaded to be computed andindependently applied.

The specification can clearly indicate (apriori)how the number of controlling lanes, i.e., it can beexplicit and simple.

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Example

0.65

0.85

1.0

1.2

MultiplePresenceFactor

z.Z3

w.W4 or more

y.Y2

x.X1

FactorRequired byMethod

Number oflanes loaded

Controls for Strength I