Simplified Live Load Distribution Formula in AASHTO

8/10/2019 Simplified Live Load Distribution Formula in AASHTO

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Simpli f ied L ive L oad Di stribution

FormulaNCH RP 12-62 with Specif ication

Discussion

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.

Brian Goodrich

NCHRP Manager: David Beal, P.E.


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AASHTO SCOBS Main Session -- DelawareJuly 2007

Introductory Comments

Large step

Address all questions

Next step


3/129


Objective

Develop new recommended LRFD live-loaddistribution-factor design equations for shear and

moment that aresimplerto apply and have a

wider range of applicability than those inthe current LRFD. The need for refined methods

of analysis should be minimized.


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Accuracy

Simplicity

How

conservative?


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Advantages

Consistent approach for bridge types

Based upon lever rule (shear and one-lane

moment) and adjusted

Based uniform distribution (multiple-lanes

loaded and adjusted

Independently accounts for multiple

presence

Eliminates many limits on application


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Advantages

Independently accounts for variability of simpleanalysis with respect to rigorous

Independent of cross section and span lengths Same for positive and negative moment areas


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Advantages

Many pages shorter

Many variables, definitions, and

computations are eliminated

Once transformations are understood the

adjustments from lever/uniform are readily

seen

Well documented


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Advantages

Extensible within proposed framework

Different coefficients

Analysis variability is quantified

Recalibration

LRFR

Multiple presence

Safety net

Lower bound for rigorous analysis


9/129


Disadvantages

New and Different

Minor programming required

Minor training Empirically based

Rigorous analysis as standard practice will

be discouraged


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Status

Good input from T-05 and T-10

Need time to revise and relax some

simplification and improve accuracy

Community to re-review

Mid Year meeting to provide modifications

Re review and response/revisions


11/129


Message today

Is not

The Framework


12/129


More thanSimplification

NCHRP 12-62


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Three Separate Components

s m mmg m a LR or uniform b

Multiple Presence

Uncertainty associated with analysis

Structural Analysis


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Analysis Component


Structural AnalysisMoment in the Interior Girder, 2 - 4 Lanes Loaded, Location 104.00

y = 1.0105x - 0.003

R2

= 0.9509

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

Numberof

Lanes/NumberofGirders

Distribu

tionFactor(Calibrate

d)


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Uncertainty Component



Moment in the Interior Girder, 4 Lanes Loaded, Location 104.00. 3 & 4 lanes not

critical.

0

10

20

30

40

50

60

0-0.05

0.05-0.15

0.15-0.25

0.25-0.35

0.35-0.45

.45-0.55

0.55-0.65

0.65-0.75

.75-0.85

0.85-0.95

0.95-1.05

1.05-1.15

1.15-1.25

1.25-1.35

1.35-1.45

1.45-1.55

1.55-1.65

1.65-1.75

1.75-1.85

1.85-1.95

1.95-2.05

Ratio - Spec Dist Factor (Calibration, Multiple Presence, and Distribution Simplification Factors)/

Rigorous Distribution Factor w/ m

Frequency-%

Rigorous/Simple


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Multiple Presence Component


Multiple Presence


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Current

0.10.4 0.2

30.075

9.5 12.0

g

s

KS Smg

L Lt

Back out variability (12-26)?

Multiple presence - no


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Example

Current LRFD

y = 0.0487x + 0.191

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

6 7 8 9 10 11 12 13 14 15

Spacing, ft.

D L= 100ft, Kgterm1.1L = 150,Kgterm=1.1

L = 200 ft, Kgterm= 1.1

Linear (L= 150, Kgterm=1.1)

20.5' 0.19mg S

0.10.4 0.2

30.075

9.5 12.0

g

s

KS Smg

L Lt


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Simplification is more than

just simple computations

Dr. Mertz


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Perspective

History

Trends

New work


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Example

12-26 Std Specification

m = 1.0, 0.90, 0.75

12-26 LRFD

m = 1.2, 1.0, 0.85, 0.65


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Three Separate Components


Multiple Presence


Structural Analysis


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Questions


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End of talk


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Possible Questions/Issues

Different coefficients for number of lanes?

Change from unified approach tobestapproach for each type, i.e., LR, Uniform

adjusted Three girders

Boxes

Open sections

Skew adjustment for moment stiffness?

Combine slab on girder bridge types


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Lets begin


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AASHTO SCOBS Main Session -- Delaware

July 2007

The Challenge

3-D System

1-D Girderline


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July 2007

Literature Review

Current Specifications & Simplified

Approach

Modeling Techniques

Field Testing

Parametric Effects

Bridge Type

Nonlinear effects


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July 2007

Summary Table (NBI Data)

Type 1990-present Total Inventory

Steel Beam30.0% 42.8%

Concrete I29.8% 15.1%

Precast Concrete

Boxes with Shear Keys 11.2% 5.0%

Slabs 14.3% 15.8%

85.3% 78.7%

Bridge Percentages by Type


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July 2007

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 3.26

Steel I-Beam 163 n/a 12 205 2 15.5 4.42 12 0 66.1 0.4 4.53

Prestressed 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 5.5

Slab 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 3.11

Steel Spread Box 20 n/a 58 281.7 8.67 24 5 9.5 0 60.5 0.75 8.02

Precast Conc. Spread Box 4 1 - 6 44.38 81.49 5.67 13.75 7.75 8.75 0.00 48.49 1.68 2.03

Precast 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 5.11

Steel 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 3 653 Slab on RC, Prest., and

Steel 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 4.00 0.00 36.00 .00 0.00 .21 .60

Span Length (ft)

Parametric

Bridges N/A 74

Number ofSpans

Parameter RangesReference

Numberof

Bridges

Bridge TypesTotal No.

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

24

809

DataSource

NCHRP 12-

26

TN Tech

Set 1

1

2


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July 2007

Common

Database

FormatNCHRP 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 from

Virtis/Opis to supply real bridges to

both simplified and rigorous methods.

2. Tenn. Tech. DatabaseDetailed descriptions and rigorous

analysis are available from a recent

TT study for TN DOT. Results,

structural models, etc., are readily

available.

Data Sources

Condense to a

Common Database

A

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

the proposed method.


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July 2007

Rigorous Analysis (Basis)

SAP

AASHTO FE Engine Ansys

Common

Database

Format

NCHRP 12-50

Common Database

Format

NCHRP 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 Recently trying

AASHTO Virtis


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July 2007

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 DatabaseFormat

NCHRP 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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July 2007

Grillage Method (structural model)


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July 2007

Proposed Implementation

Two simple methods for types

Uniform

Lever rule

One set of coefficients (for number of lanes) Multiple presence based upon lanes loaded in simple

analysis

Simplification factor adjusts for variability

m mmg m a LR or uniform b


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July 2007

Influence Surfaces (structural model)

024

0 480

720

96

0

080

1

60

240

320

400

48

0

5

60

64

0

-20.00

0.00

20.00

40.00

60.00

80.00

100.00

Ordinate

Longitudinal location, in.


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July 2007

Automated Live Load Positioning

Critical live load placement

Actions (shear, moment,

reaction, translation)

Single and multiple lanesloaded

Critical longitudinal

position

Accounts for barrier, etc.

4-ft truck transverse truck

spacing

POI at least tenth points


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July 2007

Computation of Distribution Factor

/

rigorous

beam

igorous Action Number LanesDistribution Factor g

Action from Beamline

or same Longitudinal Position

MgM

( )design rigorousestimate beamM g

Research: 3-D to 1-D

spatial reduction

Application: 1-D to 3-D

spatial reduction


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July 2007

Exam le o Standard S eci ication

Results

Moment at 1.4

One-lane Loaded Exterior I-Girder

Std. S/D vs. Rigorous

y = 0.9914x + 0.2962

R2

= 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


Std.

Spec.(S/D)DistributionFactor

1

1

Unit slope = good

R2 = poor

PoorR2 = little

hope


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July 2007

Lever Rule Results

Moment at 1.4

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

y = 1.63x - 0.2644

R2 = 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


LeverRuleDistributionFac

tor

1

1

R2 = good

slope = poor

Apply affinetransformation


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July 2007

Moment at 1.4

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

y = 0.978x + 0.0413

R2

= 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


Calibrate

dLeverRuleDistributio

nFactor

1

1

Calibrated Lever Rule Results

R2 = good and is the

same

slope= good


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July 2007

Affine Transformation Concept

SimpleM

ethod

Rigorous Method

Original Simple

Method

Rotation to Unity

by multiplication

Raise or lower by

addition/subtraction


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July 2007

Affine Transformation Concept

SimpleMethod

Rigorous Method

amfor slope change

bmfor shift

10L

m s m m

g

W Nmg m a b m

N


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July 2007

Moment Distribution Factor Computation

Number of

Loaded

Lanes

Girder Distribution Factor Multiple Presence Factor

Use integer part of

m = 1.2Interior and

ExteriorOne

to determine number of loaded lanes

N for multiple presence.

Interior and

Exterior

Two or

more

Loaded

Lanes 10

c Lm s m m

g g

W Nmg m a b m

N N

12

cW

lanesm s m lever rule mg

Nmg m a g b m

N

Removed m

limit of 0.85


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July 2007

Multiple Presences

1 1.20

2 1.003 0.85

4 or more 0.65

Number of

Loaded

anes

Multiple

resence Factor

"m"

10c L

m s m m

g

W Nmg m a b m

N

Basic method: Lever or Uniform


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July 2007

MN DOT Manual

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

0 2 4 6 8 10 12 14 16

Spacing, ft.

D

Steel - a

Concrete-k

LRFD

S/11

Number of Girders: 6

Girder: MN BT72

de, ft. 1.5

Span Length, ft: 130

Kg term: 1.1

Girder: interior Lanes: multiple

two lane

four lanethree

lane


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July 2007

MN Manual

MNDesignManualBridge

00.1

0.2

0.3

0.4

0.5

0.60.7

0.8

0.9

4 6 8 10 12 14

NumberofGirders

Distribution,

Present

Proposed

Barrier Width,

ft.= 1.66

S, ft. = 9.00

L, ft. = 130.00

g s = 1.01

am = 1.23

bm = -0.12

MN manual


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July 2007

Moment in the Interior Girder, 2 Lanes Loaded, Location 104.00y = 0.9981x + 0.0023R

2= 0.9268

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


ProposedLRFDSpecificationDistribution

Factor(Calibr

ationOnly)

Issue of Loaded Lanes

Moment in the Interior Girder, 3 Lanes Loaded, Location 104.00y = 1.0532x - 0.0227

R2

= 0.9182

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


Pro

posedLRFDSpecificationDistribution

Factor(CalibrationOnly)

Moment in the Interior Girder, 4 Lanes Loaded, Location 104.00y = 1.1096x - 0.023R

2= 0.9455

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


ProposedLRFD

SpecificationDistribution

Factor

(CalibrationOnly)

Issue: Do we have separate coefficients

for number of lanes loaded?


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July 2007

Implementation DecisionAffine transformationSimple vs RigorousLanes

am, bm different ~10%4

am, bm slightly different ~5%3

am, bm used in original

calibration was conservative

and simple

2 Moment in the Interior Girder, 2 Lanes Loaded, Location 104.00y = 0.9981x + 0.0023

R2 = 0.9268

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


ProposedLRFD



Moment in the Interior Girder, 3 Lanes Loaded, Location 104.00y = 1.0532x - 0.0227R2 = 0.9182

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


ProposedLRFD



Moment in the Interior Girder, 4 Lanes Loaded, Location 104.00y = 1.1096x - 0.023R2 = 0.9455

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


ProposedLRFD




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July 2007

Implementation Decision

mg4

mg3

mg2

mg

0.65

0.85

1.0

m

am4, bm4

am3, bm3

am2, bm2

Coefs CriticalSimple vs

RigorousLanes

4

3

2 Moment in the Interior Girder, 2 Lanes Loaded, Location 104.00y = 0.9981x + 0.0023R2 = 0.9268

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 1.4Rigorous Distribution Factor

Pro

posedL

RFDSpecification

Distrib

ution



R2

= 0.9182

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


Propo

sedLRFDSpecificationDistrib

ution



R2

= 0.9455

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 DistributionFactor

Propo

sedLR

FD

Specification

Distrib

ution

Factor(Calibration

Only)



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July 2007

Implementation Decision

mg

mg

Determined

in simply

analysis

m

am, bm

Coefs CriticalSimple vs

RigorousLanes

2, 3, 4 Moment in the Interior Girder, 2 Lanes Loaded, Location 104.00y = 0.9981x + 0.0023R 2= 0.9268

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


ProposedLRFD

Specification

Distribution

Factor(Calibration

Only)



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July 2007

Steel-I Moment Interior 2-4 Lanes

Moment in the Interior Girder, 2 - 4 Lanes Loaded, Location 104.00y = 1.0105x - 0.003

R2 = 0.9509

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


Number

ofLanes/NumberofG

irders

Distri

butionFactor(Calibrat

ed)


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July 2007

Concrete-T Moment Interior 2-4 Lanes

Moment in the Interior Girder, 2 - 4 Lanes Loaded, Location 104.00y = 1.0111x + 0.0008

R2

= 0.9324

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


Numbero

fLanes/NumberofG

irders

DistributionFactor


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July 2007

CIP BoxesMoment Interior 2-4 Lanes


R2

= 0.6711

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


Numbe

rofLanes/NumerofG

irders

DistributionFactor(Calibra

ted)


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July 2007

Adjacent BoxesMoment Interior 2-4 Lanes


R2

= 0.8717

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


Number

ofLanes/NumerofGirders

DistributionFactor(Calibrat

ed)


57/129


July 2007

Perform simple analysis ( Lanes = 1, 2, 3, 4

)

Apple multiple presence

Select critical

Canadian Approach


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July 2007

Lever Rule Equations (aids)

Girder

Location

Numberof Loaded

Lanes Distribution Factor Range of Application Loading Diagram

Numberof Wheels

to Beam

2

2

3

4

1

1

2 or more

Exterior

1

2ed

S

e

e

d S ft

d S

31 e

d

S 6ed S ft

31 e

d

S 10e S ft

3 8

2

ed

S 10 16e S ft

16 20ed S ft e

d S

6'6' 4'

ed S

6' 6'4'

ed S

6'6' 4'

S

ed S

6'

Sde

6'

2 162 e

d

S S

Remove

Column,

T05 felt itwas

confusing


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July 2007

Calibration Coefficients (Shear)

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

Steel I-Beam a 0.70 0.13 0.83 0.11 1.04 -0.12 0.99 0.01

Precast Concrete I-Beam,Precast

Concrete Bulb-Tee Beam, PrecastConcrete Tee Section with Shear Keys

and with or without Transverse Post-

Tensioning, Precast Concrete Double

Tee with Shear Keys with or without

Post-Tensioning, Precast Concrete

Channel with Shear Keys

h, i, j, k 0.83 0.07 0.92 0.06 1.08 -0.13 0.94 0.03

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 Box

Beam d 0.85 0.00 0.82 0.04 1.19 -0.20 0.71 0.23

Adjacent Box Beam with Cast-in-Place

Concrete Overlay f

Adjacent Box Beam with Integral

Concrete g

Precast Concrete Spread Box Beam b, c 0.61 0.15 0.78 0.12 1.00 -0.11 0.83 0.07

Open Steel Box Beam c

Shear

Exterior Interior

One Loaded Lane Two or More Lanes One Loaded Lane

0.910.03

Two or More LanesASHTO

LRFD

Cross

Section

TypeStructure Type Lever Rule

Use Article 4.6.2.2.4

0.87 -0.051.00-0.101.050.03


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July 2007

a m b m a m b m a m b m a m b m

Adjacent Box Beam with Integral

Concrete g


Adjacent Box Beam with Cast-in-Place

Concrete Overlay f

Use Article 4.6.2.2.4

Precast Concrete Spread Box Beam b, c 0.110.79-0.17

-0.010.53

Cast-in-Place Concrete Multicell Box

Beam d

Cast -in-Place Concret e Tee Beam e

0.020.26 -0.010.83-0.150.59

Precast Concrete I-Beam,Precast

Concrete Bulb-Tee Beam, Precast

Concrete Tee Section with Shear Keys

and with or without Transverse Post-

Tensioning, Precast Concrete Double

Tee with Shear Keys with or without

Post-Tensioning, Precast Concrete

Channel with Shear Keys

h, i, j, k

-0.100.93-0.821.71-0.070.65-0.090.54

Steel I-Beam a

-0.051.14-0.411.40-0.141.110.150.65

Moment

Exterior Interior

One Loaded Lane Two or More Lanes One Loaded Lane Two or More Lanes

Lever Rule Uniform Lever Rule Uniform

0.53 -0.101.18-0.240.97-0.121.140.19

0.68 -0.121.23-0.411.33

0.62

Structure Type

ASHTO

LRFD

Cross

Section

Type

0.77-0.061.00-0.08

-0.201.250.14

Calibration Coefficients (Moment)


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July 2007

Example

104

2 6

6 120.9

2 10 2 10

0.9

0.53 0.9 0.19

0.67

exterior

Lever Rule

Calibrated m Lever Rule m

Calibrated

P PR P

g

g a g b

g

P/2 P/2


62/129


July 2007

Exterior One-Lane Moment

Moment in the Exterior Girder, 1 Lane Loaded, Location 104.00y = 1.0477x - 0.0032R2 = 0.8727

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, Including Multiple Presence

Proposed

LRFDSpecificationD

istribution

Factor,IncludingCalibration,Multiple

Presence,andDistributionSim

plification

Factors


63/129


July 2007

Shear Exterior Two Lanes

Shear in the Exterior Girder, 2 Lanes Loaded, Location 100.00y = 1.051x + 0.0145R2 = 0.9581

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


ProposedLRFDSpecificatio

nDistribution


Pre

sence,andDistributionS

implification

Factors


64/129


July 2007

Different Bridge

Types

S UP PO RTIN G C OM PO NENTS TYP E O F D EC K TYP IC AL C RO SS-SECTIO N

Steel Bea m Cast -in -place concr ete slab,precast concrete slab, steel

grid, glued/spiked panels,stressed wood

Closed Steel or Precast ConcreteBoxes Cast-in-place concrete slab

Open Steel or Precast ConcreteBoxes

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

Cast-in-Place Concrete MulticellBox

Monolithic concrete

Cast-in-Place Concrete Tee Beam Monolithic concrete

Precast Solid, Voided or Cellular

Concrete Boxes with Shear Keys

Cast-in-placestructural

concrete overlay

Precast Solid, Voided, or CellularConcrete Box with Shear Keys and

with or without Transverse Post-Tensioning

Integral concrete

Precast Concrete Channel Sectionswith Shear Keys

Cast-in-placestructuralconcrete overlay

Precast Concrete Double TeeSection with Shear Keys and with

or without Transverse Post-Tensioning

Integral concrete

Precast Concrete Tee Section with

Shear Keys and with or withoutTransverse Post-Tensioning

Integral concrete

Precast Concrete I or Bulb-TeeSections

Cast-in-place concrete,precast concrete

Wood Bea ms Cast-in- place concrete or plank, glued/spiked panels

or stressed wood


65/129


July 2007

Shear in the Exterior Girder, 1 Lane Loaded, Location 100.00y = 1.0272x - 0.0054R

2= 0.9889

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




Presence,andDis

tributionSimplification

F

actors

Concrete I Section ShearShear in the Interior Girder, 2 Lanes Loaded, Location 100.00y = 1.0413x + 0.0043

R2

= 0.887

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


ProposedLRFD



Presence,andDistributionSimplification

Factors

Shear in the Interior Girder, 1 Lane Loaded, Location 100.00y = 1.0192x + 0.0026R

2= 0.9146

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


ProposedLRFD




Factors

Shear in the Exterior Girder, 2 Lanes Loaded, Location 100.00y = 0.9747x + 0.0275R

2= 0.9756

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




Presence,andDis


F

actors

Interior One nterior Multiple

Exterior One xterior Multiple


66/129


July 2007

Moment in the Interior Girder, 2 - 4 Lanes Loaded, Location 104.00

y = 1.0105x - 0.003

R2

= 0.9509

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


NumberofLanes/NumberofGirders

DistributionFactor(Calibrated)

Moment in the Exterior Girder, 1 Lane Loaded, Location 104.00y = 1.0417x + 0.0049R

2= 0.9152

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




Presence,andDis


F

actors

Concrete I Section MomentMoment in the Interior Girder, 1 Lane Loaded, Location 104.00y = 1.0475x - 0.0074

R2

= 0.8786

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


ProposedLRFDSpecificationDistributionFactor

(Appendix),IncludingCalibration,Multiple


Factors

Moment in the Exterior Girder, 2 Lanes Loaded, Location 104.00y = 1.0236x + 0.0168R

2= 0.9408

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


ProposedLRFDSpec

ificationDistributionFactor

(Appendix),Includ

ingCalibration,Multiple

Presence,andDis


F

actors

nterior One Interior Multiple

xterior One Exterior Multiple


67/129


Statistical Comparison Conceptual

1.00

Standard

deviation

implified

rigorous

g

g

NumberofSamples

Mean


68/129


Shift Simple Upward by a factor

Simple / Rigorous

1.00

Increase by a factor that is related to the COV

Live Load Distribution Simplification =s


69/129


One-lane

wo or

more lanes One-lane

Two or

more lanes

Shear 1.02 1.02 1.02 1.04

oment 1.04 1.07 1.11 1.05

Shear 1.03 1.02 1.02 1.04

Shear 1.03 1.03 1.05 1.08

oment 1.02 1.05 1.13 1.05

Shear 1.05 1.02 1.04 1.03oment 1.17 1.04 1.18 1.06

Shear 1.02 1.03 1.03 1.03

oment 1.14 1.04 1.08 1.05Shear 1.03 1.06 1.15 1.10

Shear 1.00 1.00 1.00 1.00

oment 1.00 1.00 1.00 1.00

1.08


Moment 1.15 1.10 1.21

Precast Concrete Spread Box

Beam b, c

djacent Box Beam with Cast-in-

Place Concrete Overlay,

Adjacent Box Beam with

Integral Concrete

f, g

Cast-in-Place Concrete Tee

Beam e

ast-in-Place Concrete Multicell

Box d

Interior

Steel I-Beam a

h, k, i, j

Structure Type

AASHTO

RFD Cross

Section

ype Action

Exterior

Moment

recast Concrete I-Beam,Precast

Concrete Bulb-Tee Beam,

Precast Concrete Tee Section

with Shear Keys and with or

without Transverse Post-Tensioning, Precast Concrete

Double Tee with Shear Keys

ith or without Post-Tensioning,

Precast Concrete Channel with

Shear Keys

1.011.081.101.04

Analysis Simplification Factors, s


70/129


Example Continued

0.67

1.02 1.2 0.67

0.82

Calibrated

a

a

g g

mg

mg

Previous

Example

6 120.9

2 10 2 10

0.9

0.53 0.9 0.190.67

exterior

Lever Rule

Calibrated m Lever Rule m

Calibrated

P PR P

g

g a g bg


71/129


All effects are now separated andunderstandable

1.02 1.2 0.67

0.82

s

s

mg

mg

Variability in

analysis

Effect of Multiple

Presence

Analysis


72/129


Skew Adjustment

Load effect increases for shear

Load effect decreases for moment


73/129


Skew

Adjustments for shear

No iteration

Commentary M&M 20-07 Study (shear

adjustment spatial variation)

Neglect decrease for moment

Re-entered in Rev 1 of

Agenda


74/129


Skew Simplification (shear and reactions)Type of Superstructure

Applicable Cross-Sectionfrom Table 4.6.2.2.1-1 Skew Adjustment Factor

Range ofApplicability

Concrete Deck, Filled Grid,Partially Filled Grid, or Unfilled

Grid Deck Composite withReinforced Concrete Slab on Steel

Beams; Concrete T-Beams, T- and

Double T-Section

a, e, k and also i, jif sufficiently connected to

act as a unit

1.0 0.20tan 60

3.5 16.0

0 240

4b

S

L

N

Precast Concrete I, Bulb Tee

Beams, and Precast channel sectionswith Shear Keys

h, k 1.0 0.09 tan 60

3.5 16.0

0 240

4b

S

L

N

Cast-in-Place Concrete Multicell

Box

d 12.01.0 0.25 tan

70

L

d

0 60

6.0 13.0

0 240

35 110

3c

S

L

d

N

Concrete Deck on Spread Concrete

Box Beams

b, c

12.01.0 tan

6

Ld

S

0 60

6.0 11.5

0 140

18 65

3b

S

L

d

N

Concrete Box Beams Used inMultibeam Decks

f, g 12.01.0 tan

90

L

d

0 60

0 120

17 60

35 60

5 20b

L

d

b

N

312

g

s

K

t


75/129


Type of Superstructure

Applicable Cross-Section from Table

4.6.2.2.1-1 Skew Adjustment FactorRange of

Applicability

Concrete Deck, Filled Grid,Partially Filled Grid, orUnfilled Grid Deck Compositewith Reinforced Concrete Slabon Steel Beams; Concrete T-Beams, T- and Double T-Section

a, e, k and also i, jif sufficiently

connected to act as aunit

1.5

11 tanc

0.5

1 0.25 S

cL

If < 30o

thenc1= 0.0

If > 60o

use = 60o

30o 60o

3.5 S16.020 L 240

Nb 4

Precast Concrete I, Bulb TeeBeams, and Precast channelsections with Shear Keys

h, k 1.5

11 tanc

0.5

1 0.50

Sc

L

If < 30o thenc1= 0.0If > 60o use = 60o

30o 60o

3.5 S16.020 L 240

Nb 4

Concrete Deck on ConcreteSpread Box Beams, Cast-in-Place Multicell Box ConcreteBox Beams and Double T-

Sections used in MultibeamDecks

b, c, d, f, g 1.05 0.25 tan 1.0

If > 60o use = 60o

0o 60

o

Skew Simplification (moment)


76/129


77/129


Correction Factors for Load Distribution Factors

for Shear (Type "k" bridges)

1.00

1.05

1.10

1.15

1.20

1.251.30

1.35

1.40

1.45

1.50

0 10 20 30 40 50 60

Skew Angle

CorrectionFactor

LRFD Henry's


78/129


79/129


Diaphragm Stiffness Study

1'-9" 40'-6" 1'-9"

44'

4'-9" 11'-6" 11'-6" 11'-6" 4'-9"

9"

66"Web (Typ.)

Span Length = 2 x 153


80/129


Typical Framing Plan

19'-11" 19'-11" 19'-11" 21'-1" 25' 25' 21'-1" 19'-11" 19'-11" 19'-11"

60

25'25'18'-6" 25'25' 18'-6"25'

30

19'-11" 19'-11"


81/129


Stiffness of Cross Frame

L 4" x 4" x 5/16"

5'-6"W

eb

L

AEke

2sin2

in

k1706.25sin

ft

in12ft75.12

ksi29000in4.22

22

ek

Shear stiffness considered


82/129


Skew Adjustment Results

Skew, deg. Diaphragm Stiffness Moment Ratio Reference

0 1213 1.00

30 1185 0.98

60 1117 0.920 1.00

30 0.98

60 0.92

0 1130 1.00

30 885 0.78

60 800 0.71

Table L-18,

Figure L-139

Figure L-157

Figure L-175

~ no change

Zero, no diagphragms

Actual Estimate K = 170 k/in

Rigid

Steel Plate Girder Bridge

Four steel plate girders, two spans at 152 ft., spacing 11'-6"


83/129


84/129


Curvature

No change

W

1' 9" 1' 9"


85/129


Push-the-limits bridgesSSOverhang

1 -9

OverhangS

st

1 -9

Bridge

No.

Girder

Spacing,

S

(ft)

Recommended

minimum slab

thickness

(AASHTO STD

Table 8.9.2)

Slab

hickness,

ts

(in)

Span

Length, L

(ft)

Total

Bridge

idth, W

(ft)

No.of

girders

Overhang

(ft)

1 12 8.80 9.00 240 44 4 42 12 8.80 9.00 260 44 4 4

3 12 8.80 9.00 280 44 4 4

4 12 8.80 9.00 300 44 4 4

5 12 8.80 9.00 200 44 4 4

6 14 9.60 9.75 200 48 4 3

7 16 10.40 10.50 200 54 4 3

8 18 11.20 11.25 200 60 4 3

9 20 12.00 12.00 200 68 4 4

10 12 8.80 9.00 160 58 5 5

11 12 8.80 9.00 160 53 4 8.5


86/129


Many Parameter Studies

Skew

Diaphragm Cross-frame Stiffness

End Cross-frames

Intermediate Cross-frames

Typical Example

Span 1 Span 5


87/129


With Support

Diaphragms

With SupportDiaphragms

With Support

DiaphragmsR = 61.87 kipsDF = 0.876

R = 52.94 kipsDF = 0.870

R = 54.89 kips

DF = 0.778

R = 20.07 kips

DF = 0.330

R = 52.94 kips

DF = 0.870

R = 43.82 kips

DF = 0.621

R = 52.15 kips

DF = 0.739

R = 43.78 kips

DF = 0.720

1

1

1

R = 54.89 kips

DF = 0.778

R = 46.62 kips

DF = 0.660

25

R = 46.62 kips

DF = 0.660

p

5

5

R = 28.00 kips

DF = 0.460

R = 43.78 kips

DF = 0.72025

5

Span 5

25

R = 34.30 kips

DF = 0.564

60

30

R = 34.30 kipsDF = 0.564

R = 43.82 kips

DF = 0.621

R = 34.30 kipsDF = 0.564

R = 34.30 kips

DF = 0.564R = 43.82 kips

DF = 0.621

R = 43.82 kips

DF = 0.621

R = 28.00 kips

DF = 0.460

R = 52.15 kips

DF = 0.739

R = 20.07 kips

DF = 0.330

R = 61.87 kips

DF = 0.876


88/129


Regression Testing

Complete database used to compare:

LRFD

S/D

Rigorous Again, used 12-50

M t i th E t i Gi d 2 L L d d L ti 104 00

Moment in the Exterior Girder, 2 Lanes Loaded, Location 104.00y = 1.0128x - 0.0626R

2= 0.688

1 4


89/129


Moment in the Exterior Girder,2 Lanes Loaded, Location 104.00

0

10

20

30

40

50

60

-0.05

.05-0.15

.15-0.25

0.25-0.35

.35-0.45

.45-0.55

.55-0.65

.65-0.75

0.75-0.85

0.85-0.95

.95-1.05

1.05-1.15

1.15-1.25

1.25-1.35

1.35-1.45

1.45-1.55

1.55-1.65

1.65-1.75

1.75-1.85

1.85-1.95

1.95-2.05

Ratio- Appendix Dist Factor (Calibrated, withM ultiple Presence)/ 2005 AASHTO LRFD Distribution

Factor

Frequency-%

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

2005 LRFD Specifications Distribution Factor


Factor(Appendix),IncludingCalibration,

Mul

tiplePresence,andMethodFactors

Momentin the Exterior Girder,2 Lanes Loaded,Location 104.00

0

10

20

30

40

50

60

-0.05

.05-0.15

.15-0.25

0.25-0.35

.35-0.45

.45-0.55

.55-0.65

.65-0.75

0.75-0.85

0.85-0.95

.95-1.05

1.05-1.15

1.15-1.25

1.25-1.35

1.35-1.45

1.45-1.55

1.55-1.65

1.65-1.75

1.75-1.85

1.85-1.95

1.95-2.05

Ratio -Appendix Dist Factor (Calibrated, with Multiple Presence)/ Rigorous Distribution Factor w/ m

Frequency

-%


2= 0.9408

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


Proposed

LRFD


Factor(A

ppendix),IncludingCalibration,

Multiple

Presence,andMethodFactors


0

10

20

30

40

50

60

-0.05

.05-

0.15

.15-

0.25

0.25-

0.35

.35-

0.45

.45-

0.55

.55-

0.65

.65-

0.75

0.75-

0.85

0.85-

0.95

.95-

1.05

1.05-

1.15

1.15-

1.25

1.25-

1.35

1.35-

1.45

1.45-

1.55

1.55-

1.65

1.65-

1.75

1.75-

1.85

1.85-

1.95

1.95-

2.05

Ratio - 2005 AASHTO LRFD/ Rigorous DistributionFactor w/ m

Frequenc

y-%

Moment in the Exterior Girder, 2 Lanes Loaded, Location 104.00y = 0.773x + 0.2106R 2 = 0.7999

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


2005LRFDSpecificationDistributionFactor

Appendix Dist Factor (Calibrated, withMultiple

Presence)/2005 AASHTO LRFD


Presence)/Rig orous withmultiple presence

2005AASHTO LRFD/Rigorous

withmultiple presence

Average 0.87 1.00 1.20

Standard Deviation 0.18 0.10 0.26

Coefficient of Variation 20.77% 9.78% 21.29%

Count 72 72 72

Statistic

Methods Compared


2= 0.688

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


ProposedLRFD

Specific

ationDistribution

Factor(Appendix),Inclu

dingCalibration,

MultiplePresence,and

MethodFactors

Moment in theExterior Girder 2 Lanes Loaded Location 104 00


2= 0.688

1 4


90/129



0

10

20

30

40

50

60

-0.05

.05-0.15

.15-0.25

0.25-0.35

.35-0.45

.45-0.55

.55-0.65

.65-0.75

0.75-0.85

0.85-0.95

.95-1.05

1.05-1.15

1.15-1.25

1.25-1.35

1.35-1.45

1.45-1.55

1.55-1.65

1.65-1.75

1.75-1.85

1.85-1.95

1.95-2.05


Factor

Frequency-%

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




Mul



0

10

20

30

40

50

60

-0.05

.05-0.15

.15-0.25

0.25-0.35

.35-0.45

.45-0.55

.55-0.65

.65-0.75

0.75-0.85

0.85-0.95

.95-1.05

1.05-1.15

1.15-1.25

1.25-1.35

1.35-1.45

1.45-1.55

1.55-1.65

1.65-1.75

1.75-1.85

1.85-1.95

1.95-2.05


Frequency

-%


2= 0.9408

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


Proposed

LRFD


Factor(A


Multiple



0

10

20

30

40

50

60

-0.05

.05-

0.15

.15-

0.25

0.25-

0.35

.35-

0.45

.45-

0.55

.55-

0.65

.65-

0.75

0.75-

0.85

0.85-

0.95

.95-

1.05

1.05-

1.15

1.15-

1.25

1.25-

1.35

1.35-

1.45

1.45-

1.55

1.55-

1.65

1.65-

1.75

1.75-

1.85

1.85-

1.95

1.95-

2.05


Frequenc

y-%


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









Average 0.87 1.00 1.20



Count 72 72 72

Statistic

Methods Compared

Moment in the Exterior Girder, 2 Lanes Loaded, Location 104.00y = 1.0236x + 0.0168

R2

= 0.9408

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


ProposedLR

FD


Factor(Appe

ndix),IncludingCalibration,

MultiplePre

sence,andMethodFactors



2= 0.688

1.4


91/129



0

10

20

30

40

50

60

-0.05

.05-0.15

.15-0.25

0.25-0.35

.35-0.45

.45-0.55

.55-0.65

.65-0.75

0.75-0.85

0.85-0.95

.95-1.05

1.05-1.15

1.15-1.25

1.25-1.35

1.35-1.45

1.45-1.55

1.55-1.65

1.65-1.75

1.75-1.85

1.85-1.95

1.95-2.05


Factor

Frequency-%

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2 1.4




Mul



0

10

20

30

40

50

60

-0.05

.05-0.15

.15-0.25

0.25-0.35

.35-0.45

.45-0.55

.55-0.65

.65-0.75

0.75-0.85

0.85-0.95

.95-1.05

1.05-1.15

1.15-1.25

1.25-1.35

1.35-1.45

1.45-1.55

1.55-1.65

1.65-1.75

1.75-1.85

1.85-1.95

1.95-2.05


Frequency

-%


2= 0.9408

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


Proposed

LRFD


Factor(A


Multiple



0

10

20

30

40

50

60

-0.05

.05-

0.15

.15-

0.25

0.25-

0.35

.35-

0.45

.45-

0.55

.55-

0.65

.65-

0.75

0.75-

0.85

0.85-

0.95

.95-

1.05

1.05-

1.15

1.15-

1.25

1.25-

1.35

1.35-

1.45

1.45-

1.55

1.55-

1.65

1.65-

1.75

1.75-

1.85

1.85-

1.95

1.95-

2.05


Frequenc

y-%


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









Average 0.87 1.00 1.20



Count 72 72 72

Statistic

Methods Compared


2= 0.7999

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


2005LRFDS

pecificationDistributionFactor



2= 0.688

1.4


92/129



0

10

20

30

40

50

60

-0.05

.05-0.15

.15-0.25

0.25-0.35

.35-0.45

.45-0.55

.55-0.65

.65-0.75

0.75-0.85

0.85-0.95

.95-1.05

1.05-1.15

1.15-1.25

1.25-1.35

1.35-1.45

1.45-1.55

1.55-1.65

1.65-1.75

1.75-1.85

1.85-1.95

1.95-2.05


Factor

Frequency-%

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1 1.2 1.4




Mul



0

10

20

30

40

50

60

-0.05

.05-0.15

.15-0.25

0.25-0.35

.35-0.45

.45-0.55

.55-0.65

.65-0.75

0.75-0.85

0.85-0.95

.95-1.05

1.05-1.15

1.15-1.25

1.25-1.35

1.35-1.45

1.45-1.55

1.55-1.65

1.65-1.75

1.75-1.85

1.85-1.95

1.95-2.05


Frequency

-%


2= 0.9408

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


Proposed

LRFD


Factor(A


Multiple



0

10

20

30

40

50

60

-0.05

.05-

0.15

.15-

0.25

0.25-

0.35

.35-

0.45

.45-

0.55

.55-

0.65

.65-

0.75

0.75-

0.85

0.85-

0.95

.95-

1.05

1.05-

1.15

1.15-

1.25

1.25-

1.35

1.35-

1.45

1.45-

1.55

1.55-

1.65

1.65-

1.75

1.75-

1.85

1.85-

1.95

1.95-

2.05


Frequenc

y-%


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









Average 0.87 1.00 1.20



Count 72 72 72

Statistic

Methods Compared

App endix Dist Facto r (Calibrate d, with Multiple


App endix Dist Facto r (Calibrate d, with Multiple

Presence)/Rigo rous with multiple presence

2005 AASHTO LRFD/Rigorous

with multiple presence

Ave rage 0.87 1.00 1.20



Count 72 72 72

Statistic

Methods Compared


93/129


94/129


Shear Interior Two Lanes

Shear in the Interior Girder, 2 Lanes Loaded, Location 100.00y = 1.0411x + 0.0049R2 = 0.9

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



Fac

tor,IncludingCalibration,Multiple

Presence,andDistributionS

implification

Factors


95/129


Moment Exterior One Lane

Moment in the Exterior Girder, 1 Lane Loaded, Location 104.00y = 1.0477x - 0.0032R

2= 0.8727

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


Prop

osedLRFD



Pres

ence,andDistributionS

implification

Factors


96/129


Moment Exterior Two Lanes


2= 0.8566

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


Propo

sedLRFDSpecification

Distribution

Facto

r(Appendix),Including

Calibration,

Mu

ltiplePresence,andDi

stribution

SimplificationFactors


97/129


98/129


Moment Interior Multiple Lanes

Moment in the Interior Girder, 2 - 4 Lanes Loaded, Location 104.00y = 1.0105x - 0.003R2 = 0.9509

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


Number

ofLanes/NumberofGirders

DistributionFactor(Calibr

ated)

C t T B Sh


99/129


Shear in the Exterior Girder, 1 Lane Loaded, Location 100.00y = 1.0195x + 0.0042

R2

= 0.9309

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





implification

Factors

Concrete Tee Beams ShearShear in the Interior Girder, 2 Lanes Loaded, Location 100.00y = 1.0457x + 0.0051

R2 = 0.8371

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


ProposedLRFD




Factors

Shear in the Interior Girder, 1 Lane Loaded, Location 100.00y = 1.1279x + 0.0017R2 = 0.9168

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


ProposedLRFD




Factors


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


ProposedLRFD




implification

Factors

Interior One Interior Multiple

Exterior One Exterior Multiple

Concrete Tee Beams Moment


100/129



R2

= 0.9324

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


NumberofLanes/NumberofGirders

DistributionFactor

Moment in the Exterior Girder, 1 Lane Loaded, Location 104.00y = 1.0201x + 0.0051R2 = 0.9133

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


ProposedLRFD


Factor,IncludingCalibra

tion,Multiple

Presence,andDistribution

Simplification

Factors

Concrete Tee Beams MomentMoment in the Interior Girder, 1 Lane Loaded, Location 104.00y = 1.1225x + 0.0028

R2 = 0.7358

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


ProposedLRFD

SpecificationDistributio

n



Factors

Moment in the Exterior Girder, 2 Lanes Loaded, Location 104.00y = 1.0208x + 0.0285R2 = 0.9749

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


ProposedLRFD

Specificat

ionDistribution

Factor,IncludingCalibra

tion,Multiple

Presence,andDistribution

Simplification

Factors




101/129

Spread Box Beams Moment


102/129



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


ProposedLRFDSpe

cificationDistribution


MultiplePresenc

e,andDistribution

Simplifica

tionFactors

Spread Box Beams Moment

Moment in the Interior Girder, 2 Lanes Loaded, Location 104.00y = 1.065x - 0.0013R 2 = 0.9096

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





Factors

Moment in the Interior Girder, 1 Lane Loaded, Location 104.00y = 1.0651x + 0.0165

R2

= 0.6968

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


ProposedLRFDSpecificationDistributio

n


Presence,andDistributionSimplificatio

n

Factors


2= 0.8381

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


ProposedLRFD


Factor(Appendix),

IncludingCalibration,

MultiplePresenc

e,andDistribution

Simplifica

tionFactors



Need updated figure


103/129

Adjacent Boxes Moment (f & g)


104/129



R2 = 0.8717

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


NumberofLanes/NumerofGirders



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



Factor,IncludingCalibration,MultiplePresence,

andDistributionSim

plificationFactors

Adjacent Boxes Moment (f & g)Moment in the Interior Girder, 1 Lane Loaded, Location 104.00y = 1.0889x - 0.0066

R2 = 0.9117

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


ProposedLRFD

SpecificationDistributionFactor



Factors


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



Factor,IncludingCalibration,MultiplePresence,

andDistributionSim

plificationFactors



Adj t B Sh (d)


105/129


Shear in the Exterior Girder, 1 Lane Loaded, Location 100.00y = 1.0458x - 0.0032R 2 = 0.8782

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


ProposedLRFD


Factor,IncludingCalib

ration,Multiple


Factors

Adjacent Boxes Shear (d)Shear in the Interior Girder, 2 Lanes Loaded, Location 100.00y = 1.0334x - 0.0002

R2 = 0.7972

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





Factors

Shear in the Interior Girder, 1 Lane Loaded, Location 100.00y = 1.0424x + 0.001R 2 = 0.8017

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





Factors


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


ProposedLRFD


Factor,IncludingCalib

ration,Multiple


Factors



Adj t B M t (d)


106/129



R2 = 0.6711

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


NumberofLanes/NumerofGirders



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


ProposedLRFDSpec



Presence,andDi

stributionSimplification

Factors

Adjacent Boxes Moment (d)Moment in the Interior Girder, 1 Lane Loaded, Location 104.00y = 1.0575x - 0.0056

R2 = 0.8147

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


ProposedLRFDSpecificationDistributionFac

tor



Factors


2= 0.5726

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


ProposedLRFDSpec



Presence,andDi

stributionSimplification

Factors




107/129

Concrete I Section Moment


108/129



R2

= 0.9509

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 1.4Rigorous Distribution Factor

NumberofLanes/NumberofGirder

s


Moment in the Exterior Girder, 1 Lane Loaded, Location 104.00y = 1.0417x + 0.0049

R2

= 0.9152

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


ProposedLRFD

Spec

ificationDistribution


Presence,andDistrib

utionSimplification

Fact

ors

Concrete I Section MomentMoment in the Interior Girder, 1 Lane Loaded, Location 104.00y = 1.0475x - 0.0074

R2

= 0.8786

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


ProposedLRFDSpecificationDistributionFactor



Factors

Moment in the Exterior Girder, 2 Lanes Loaded, Location 104.00y = 1.0236x + 0.0168R2 = 0.9408

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


ProposedLRFDSpecifica

tionDistributionFactor

(Appendix),Including

Calibration,Multiple

Presence,andDistrib

utionSimplification

Factors




109/129


Three-girder bridges

Current uses Equations for boxes

Proposed requires lever rule

l


110/129


WS DOT Example

Three-girder tub

16 ft spacing

60 degree skew


111/129

Q D


112/129


Questions, Discussion

E d f T lk


113/129


End of Talk

Addi i l k


114/129


Additional work

Review/revise tub girder systems

Develop presentation materials to help explain this

in a more understandable manner

Suggestions welcome!

excellent 0.9

Sanders

and Elleby

AASHTO

Standard

S ecification

CHBD C L RF D Al te rn ate

for

oment

Uniform

Distribution

Lever Rule Best

Method

Lanes

Loaded

Girder

LocationsAction

Bridge

Set

Method

0.90 > good 0.80 0.80 > acceptable0. 70 0 .7 0 > p oo r 0.50 bad < 0.5


115/129


1 bad bad bad good bad excellent Lever

2 or more ad bad ad ood ad xcellent Lever

1 good good good good acceptable good Lever

2 or more ood ood good acceptable good xcellent Lever

1 bad bad bad acceptable bad poor good Lever

2 or more ad bad ad ood ad oor ood Lever

1 bad bad bad bad poor bad bad lternate

2 or more acceptable oor ccept able acceptable acceptable good acceptable Uniform

1 bad bad bad excellent poor excellent Lever

2 or more ad bad ad acceptable poor xcellent Lever

1 good good good excellent acceptable excellent Lever

2 or more ood ood good ood xcellent good Uniform

1 bad bad bad good bad poor excellent Lever

2 or more ad bad ad ood ad poor xcellent Lever

1 poor poor acceptable good good bad poor lternate

2 or more ood ood good ood good xcellent good Uniform

1 poor poor poor good good excellent Lever

2 or more oor oor poor xcellent xcellent xcellent Uniform

1 good good excellent excellent acceptable excellent Lever

2 or more xcellent ood xcellent ood xcellent good Uniform

1 poor poor poor good bad acceptable excellent Lever

2 or more oor oor poor xcellent ad xcellent xcellent Uniform

1 poor acceptable good excellent poor poor acceptable Lever

2 or more ood cce table ood xcellent oor xcellent oor Lever

1 acceptable good acceptable excellent good excellent Lever

2 or more ood ood good xcellent xcellent xcellent Lever

1 good excellent good good acceptable excellent Lever

2 or more xcellent excellent xcellent xcellent poor xcellent Lever

1 poor poor acceptable poor poor poor poor CHBDC

2 or more ood ood good ood ad poor good CHBDC

1 bad poor bad poor poor bad poor Lever

2 or more ad oor poor oor poor xcellent poor Uniform

1 bad bad bad good acceptable good Lever

2 or more ad bad ad acceptable acceptable xcellent Lever

1 bad good good acceptable poor good CHBDC

2 or more ad ood good ood poor acceptable LRFD

1 bad bad bad bad poor bad bad lternate

2 or more ad bad ad ad poor poor ad lternate

1 bad bad bad bad good bad bad lternate

2 or more ad bad ad oor good ad ad lternate

1 good good good excellent good excellent Lever


1 accepta ble a cceptable acceptable good acceptable excel lent Lever


1 poor poor poor acceptable acceptable poor acceptable lternate

2 or more oor oor poor ood acceptable

Documents

Simplified Live Load Distribution Formula in AASHTO