Load Rating of Riveted Steel Load Rating of Riveted Steel

Arch Bridge Connections Arch Bridge Connections

David V. Jauregui, PhD, PEDavid V. Jauregui, PhD, PE

November 28November 28thth, 2013, 2013

SapienzaSapienza University of RomeUniversity of Rome

OverviewOverview

•• IntroductionIntroduction

•• Load Rating MethodLoad Rating Method

•• Load Rating of: Load Rating of: Stringers SplicesStringers Splices

Spandrel SplicesSpandrel Splices

Column SplicesColumn Splices

Arch Ribs SplicesArch Ribs Splices

•• Conclusions & Recommendations Conclusions & Recommendations

•• IntroductionIntroduction

•• Load Rating MethodLoad Rating Method

•• Load Rating of: Load Rating of: Stringer SplicesStringer Splices

Spandrel SplicesSpandrel Splices

Column SplicesColumn Splices

Arch Rib SplicesArch Rib Splices

•• Conclusions & Recommendations Conclusions & Recommendations

IntroductionIntroduction Bridge BackgroundBridge Background

•• Name: The Los Alamos Canyon Bridge Name: The Los Alamos Canyon Bridge

(a.k.a. the Omega Bridge)(a.k.a. the Omega Bridge)

•• Steel arch riveted bridgeSteel arch riveted bridge

•• Designed & built in 1951 following 1944 AASHTO Designed & built in 1951 following 1944 AASHTO

specificationsspecifications

•• Carries traffic from town of Los Alamos and the LANL Carries traffic from town of Los Alamos and the LANL

(Los Alamos National Laboratory)(Los Alamos National Laboratory)

•• Bridge reduced the travel distance from 1.9 miles on a Bridge reduced the travel distance from 1.9 miles on a

steep grade to 820 ft: critical for emergency vehiclessteep grade to 820 ft: critical for emergency vehicles

•• Owned and maintained by the LANLOwned and maintained by the LANL

IntroductionIntroduction Research ObjectivesResearch Objectives

Connections commonly assumed to have equal or greater Connections commonly assumed to have equal or greater capacity than the members they adjoincapacity than the members they adjoin

Failure of connections could be criticalFailure of connections could be critical

•• Provide the LANL with upProvide the LANL with up--toto--date rating factors for the date rating factors for the Omega Bridge splice connectionsOmega Bridge splice connections

LRFD is the required method of design by FHWA since LRFD is the required method of design by FHWA since October 2007: Need for rating methodology consistent October 2007: Need for rating methodology consistent with the design method. with the design method.

No guidance in rating connectionsNo guidance in rating connections

•• Provide guidance in load rating connections using LRFR Provide guidance in load rating connections using LRFR method to bridge engineersmethod to bridge engineers

Connections commonly assumed to have equal or greater Connections commonly assumed to have equal or greater capacity than the members they adjoincapacity than the members they adjoin

Failure of connections could be criticalFailure of connections could be critical

•• Provide the LANL with upProvide the LANL with up--toto--date rating factors for the date rating factors for the Omega Bridge splice connectionsOmega Bridge splice connections

LRFD is the required method of design by FHWA since LRFD is the required method of design by FHWA since October 2007: Need for rating methodology consistent October 2007: Need for rating methodology consistent with the design method. with the design method.

No guidance in rating connectionsNo guidance in rating connections

•• Provide guidance in load rating connections using LRFR Provide guidance in load rating connections using LRFR method to bridge engineersmethod to bridge engineers

IntroductionIntroduction Research AidsResearch Aids

•• 2003 AASHTO Manual for Condition Evaluation and Load 2003 AASHTO Manual for Condition Evaluation and Load

and Resistance Factor Rating of Highway Bridgesand Resistance Factor Rating of Highway Bridges

•• Research by Tuyen (2005)Research by Tuyen (2005)

•• RISA for structural analysisRISA for structural analysis

•• MathCAD to calculate rating factorsMathCAD to calculate rating factors

•• Others: Original plans of the bridge, AISC steel manual, etc.Others: Original plans of the bridge, AISC steel manual, etc.

Load Rating Method: Load Rating Method: LRFRLRFR

Load Rating MethodLoad Rating Method LRFR LRFR

•• Load rating provides the basis for determining the safe load Load rating provides the basis for determining the safe load

capacity of a bridge in terms of a rating factor.capacity of a bridge in terms of a rating factor.

•• Rating factor is the ratio of the available to required live loaRating factor is the ratio of the available to required live load d

capacity:capacity:

0.1capacity load live Required

capacity load live Available≥=RF

Load Rating MethodLoad Rating Method LRFR LRFR

•• Three Stages of load rating in LRFR:Three Stages of load rating in LRFR: Design Load RatingDesign Load Rating

Legal Load RatingLegal Load Rating

Permit Load RatingPermit Load Rating

Start

Design Load Check

(HL-93)

Inventory Level Reliability

RF > 1-No Restrictive Posting

Requireda

-May be evaluated for

permit vehicle

RF <1

Check at operating

level reliability

RF > 1

RF <1

Legal load Rating

AASHTO or State legal loads

Evaluation level reliability

Higher Level Evaluation

(Optional)

-Refined analysis

-Load testing

-Site-specific load factors

-Direct safety assessment

RF <1

-Initiate load posting and/or repair/rehab

-No permit vehicles

-No restrictive

posting requiredb

-May be evaluated

for permit vehicles

RF > 1

RF > 1RF <1

a For AASHTO legal loads and state legal loads

within the LRFD exclusion limitsb For AASHTO legal loads and state legal loads

having only minor variations from the

AASHTO legal loads

Load Rating MethodLoad Rating Method LRFR LRFR

( )IMLL

DWDCRRF

LL

DWDCnsc

+

−−=

1γ

γγφφφ

General Equation for LRFR:General Equation for LRFR:

wherewhere RF = Rating FactorRF = Rating Factor

φφcc, , φφss = Condition and system factor, respectively= Condition and system factor, respectively

φφRRnn = Splice capacity= Splice capacity

γγDCDC, , γγDWDW, , γγLLLL = factors for dead load due to components and attachments, = factors for dead load due to components and attachments, wearing surface, and live load, respectivelywearing surface, and live load, respectively

DC, DW, LL = effects due to dead load due to components and DC, DW, LL = effects due to dead load due to components and attachments, wearing surface, and live load, respectivelyattachments, wearing surface, and live load, respectively

IM = Dynamic load allowance (or impact factor)IM = Dynamic load allowance (or impact factor)

Load Rating MethodLoad Rating Method LRFR LRFR

( )IMLL

DWDCRRF

LL

DWDCnsc

+

−−=

1γ

γγφφφ

Super Structure Condition RatingsSuper Structure Condition Ratings: 5.0 and higher:: 5.0 and higher:

Condition Factor, Condition Factor, φφcc = 0.95 = 0.95 (LRFR Table C6(LRFR Table C6--1 and 61 and 6--2)2)

System Factor, System Factor, φφss:: 1.0 for stringers1.0 for stringers

0.9 for spandrel beam, columns, and 0.9 for spandrel beam, columns, and arch ribsarch ribs

Redundant stringer systems

between floor beams

Riveted members in two-

girder/truss/arch bridges

(LRFR Table 6-3)

Load Rating MethodLoad Rating Method LRFR LRFR

( )IMLL

DWDCRRF

LL

DWDCnsc

+

−−=

1γ

γγφφφ

Load Factors:Load Factors: γγDCDC = = 1.251.25

γγDW DW = = 1.51.5

γγLLLL = = 1.75 1.75 for inventoryfor inventory

1.35 1.35 for operatingfor operating

Load Rating MethodLoad Rating Method LRFR LRFR

( )IMLL

DWDCRRF

LL

DWDCnsc

+

−−=

1γ

γγφφφ

For each member, distribution factor for different force effectsFor each member, distribution factor for different force effectsmust be applied: i.e., DFmust be applied: i.e., DFmomentmoment or DFor DFshearshear

( )[ ]IM1Truck Lane DF Effect Load Live LL ++= γ

Controlled by larger effect between HSControlled by larger effect between HS--20 or Design Tandem20 or Design Tandem

8k

32k 32k

14ft 14 to 30 ft

HS-20 (Longitudinal)

25k 25k

4 ft

Design Tandem (Longitudinal)

Lane Load = 0.64 klf

(a) TRUCK LOADS: HS-20 and Design Tandem

(b) LANE LOAD

8k

32k 32k

14ft 14 to 30 ft

HS-20 (Longitudinal)

25k 25k

4 ft

Design Tandem (Longitudinal)

Lane Load = 0.64 klf

(a) TRUCK LOADS: HS-20 and Design Tandem

(b) LANE LOAD

Load Rating MethodLoad Rating Method LRFR LRFR

•• Three Stages of load rating in LRFR:Three Stages of load rating in LRFR: Design Load RatingDesign Load Rating

Legal Load RatingLegal Load Rating

Permit Load RatingPermit Load Rating

Load Rating ofLoad Rating of

Stringer SpliceStringer Splice

Rating Stringer SpliceRating Stringer Splice Basic Information Basic Information

•• 2 Exterior Stringers:2 Exterior Stringers: ASTM ASTM A36A36 Steel (Steel (FFyy = 36 = 36 ksiksi) ) –– W21x83W21x83

•• 4 Interior Stringers:4 Interior Stringers: ASTM ASTM A7A7 Steel (Steel (FFyy = 33 = 33 ksiksi) ) –– W21x62W21x62

•• Total of 27 spans:Total of 27 spans: Six approach spans of 31 Six approach spans of 31 ftft on each end on each end

15 interior spans of 29.5 15 interior spans of 29.5 ftft over archover arch

•• Total of 26 splices:Total of 26 splices: 6 6 ftft from the floor beam supportsfrom the floor beam supports

South

6’-9”

6’-9”

7’-4 1/2”

7’-4 1/2”

3@ 6’-9”

Interior StringersExterior Stringers Spandrel Beams Floor Beam

Stringer Splice

31’ 31’ 31’ 31’ 31’ 31’ 29.5’ 29.5’ 29.5’ 29.5’ 29.5’ 29.5’ 29.5’

14’-9”

SP#1 SP#2 SP#3 SP#4 SP#5 SP#6 SP#7 SP#8 SP#9 SP#10 SP#11 SP#12 SP#13

6’-0”

(Typical)

407’-3”

CL Bearing

Abutment #1

Arch CL

Rating Stringer SpliceRating Stringer Splice Splice ConfigurationSplice Configuration

•• Same splice configuration for both interior and exterior stringeSame splice configuration for both interior and exterior stringersrs2’- 6 1/2”

1 1/2” Min.4 SPA @ 3”

= 1’- 0”1 1/2” Min.

7/8”φ H.S. Bolts

(Typical)

PL 5/16” x 12 1/2” x 1’- 6”

(Both Sides of Web)1 1/2”

Min.

1/2”

Max. 3” (Typ.)

1 1/2”

Min.

PL 7/8” x 8 1/4” x 2’- 6 1/2”

(Typ. Both Flanges)

12 1/2”

5 S

PA

@ 3

”

= 1

’-3”

1’-

6”

1 1/2” Min.

(Typ.)

1 1

1/1

6”

2’- 6 1/2”

1 1/2” Min.4 SPA @ 3”

= 1’- 0”1 1/2” Min.

7/8”φ H.S. Bolts

(Typical)

PL 5/16” x 12 1/2” x 1’- 6”

(Both Sides of Web)1 1/2”

Min.

1/2”

Max. 3” (Typ.)

1 1/2”

Min.

PL 7/8” x 8 1/4” x 2’- 6 1/2”

(Typ. Both Flanges)

12 1/2”

5 S

PA

@ 3

”

= 1

’-3”

1’-

6”

1 1/2” Min.

(Typ.)

1 1

1/1

6”

Rating Stringer SpliceRating Stringer Splice LoadsLoads

•• Dead load applied to the stringers:Dead load applied to the stringers:

••Interior Stringer Interior Stringer –– WWDead Dead = 556 lb/ft= 556 lb/ft

••Exterior Stringer Exterior Stringer –– WWDeadDead = 609 lb/ft= 609 lb/ft

•• Live load applied using Live load applied using moving loadmoving load tool in RISA:tool in RISA:

Rating Stringer SpliceRating Stringer Splice LoadsLoads

•• Used Influence Line for lane load placementUsed Influence Line for lane load placement

0.64 klf 0.64 klf 0.64 klf

Rating Stringer SpliceRating Stringer Splice Force Distribution on Force Distribution on the Crossthe Cross--SectionSection

TwebPL

TflangePL

CwebPL

CflangePL

NA

dwebPL

dflangePL

Flange

PL

Web

PL c

Stress, σ Force = σ x AiStress at

outermost surface

Stress at inside

edge of Flange PL

Stress at outside

edge of Web PL

Splice 1 controls for both moment and shear!Splice 1 controls for both moment and shear!

Rating Stringer SpliceRating Stringer Splice Limit StatesLimit States

•• Limit States for the Flange PL Group:Limit States for the Flange PL Group:

Yielding on the gross sectionYielding on the gross section

Fracture on the net sectionFracture on the net section

Block ShearBlock Shear

Shear strength of the rivetsShear strength of the rivets

Bearing strength of the platesBearing strength of the plates

•• Limit States for the Web PL Group:Limit States for the Web PL Group:

Yielding on the gross sectionYielding on the gross section

Fracture on the net sectionFracture on the net section

Shear strength of the rivetsShear strength of the rivets (for a single rivet)(for a single rivet)

Bearing strength of the platesBearing strength of the plates (for a single rivet)(for a single rivet)

Rating Stringer SpliceRating Stringer Splice Limit StatesLimit States

Tensile Limit States (kip)

Stringer Yielding on

Gross Area

Fracture on

Net Area

Block

Shear

Shear Strength

of Rivets

Bearing Strength

of Plate

Interior 214.4 270.7 610.7 126.3 831.6

Exterior 233.9 237.9 550.5 126.3 730.8

Shear Limit States (kip)

Stringer Yielding on

Gross Area

Fracture on

Net Area

Shear Strength

of Rivetsa

Bearing Strength

of Platea

Interior 200.5 222.8 25.26 24.50

Exterior 218.7 195.8 25.26 16.82

a Values for a single rivet

Rating Stringer SpliceRating Stringer Splice Combined Loading at WebCombined Loading at Web

eVMM T ⋅+=2

2

12

++=

VRRV yxR

Total Moment on web splice PLTotal Moment on web splice PL Resultant shear due to moment and Resultant shear due to moment and

direct shear:direct shear:

V/12 V/12

V/12

R1

R2

R3

R4

Rx4

Ry4

V

M

c.g. of Web PL

e

c.g. of Rivet Group

MT = M + Ve

V

V

Rating Stringer SpliceRating Stringer Splice Distribution FactorsDistribution Factors

Moment DFMoment DF Shear DFShear DF

One Lane One Lane

LoadedLoaded

Two or More Two or More

Lanes LoadedLanes Loaded

1.0

3

3.04.0

1..0.1214

06.0

+=

s

g

imLt

K

L

SSg

1.0

3

2.06.0

2..0.125.9

075.0

+=

s

g

imLt

K

L

SSg

0.2536.01..

Sg iv +=

0.2

2..3512

2.0

−+=

SSg iv

Interior Stringer: Interior Stringer: LRFD Table 4.6.2.2.2bLRFD Table 4.6.2.2.2b--11

All All Range of ApplicabilityRange of Applicability are metare met

Rating Stringer SpliceRating Stringer Splice Distribution FactorsDistribution Factors

Moment DFMoment DF Shear DFShear DF

One Lane One Lane

LoadedLoaded

Two or More Two or More

Lanes LoadedLanes Loaded

Exterior Stringer: Exterior Stringer: LRFD Article 4.6.2.2.2dLRFD Article 4.6.2.2.2d

Lever RuleLever Rule

2..2.. imem geg ⋅=

Lever RuleLever Rule

2..2.. ivev geg ⋅=

One Lane One Lane

Loaded Loaded -- RBMRBM

Two or More Two or More

Lanes Loaded Lanes Loaded --RBMRBM

Rigid Body MotionRigid Body Motion

Rigid Body MotionRigid Body Motion

Rigid Body MotionRigid Body Motion

Rigid Body MotionRigid Body Motion

Rating Stringer SpliceRating Stringer Splice Distribution FactorsDistribution Factors

Moment Shear Moment Shear

0.494 0.630 0.667 0.667

0.627 0.725 0.621 0.580

One Lane

Loaded0.451 0.451

Two or more

Lanes Loaded0.632 0.632

0.627 0.725 0.667 0.667Controlling DF

N/A

Interior Stringer Exterior StringerDF Type

Rigid

Body

Motion

One Lane Loaded

Two or More Lanes

Loaded

Rating Stringer SpliceRating Stringer Splice Rating FactorsRating Factors

Inventory Operating Inventory Operating Inventory Operating

Interior 1.10 1.43 2.30 2.98 1.19 1.54

Exterior 1.02 1.32 2.43 3.15 1.33 1.72

Stringer

Moment

(Flange Splice Plates) Web splice plates Single Rivet

Shear

Load Rating ofLoad Rating of

Spandrel SpliceSpandrel Splice

Rating Spandrel SpliceRating Spandrel Splice Basic InformationBasic Information

•• 2 Spandrel Beams:2 Spandrel Beams: ASTM A7 Steel (FASTM A7 Steel (Fyy = 33 ksi) = 33 ksi)

•• Total of 21 spans:Total of 21 spans: Three approach spans of 62 ft on each end Three approach spans of 62 ft on each end

15 interior spans of 29.5ft over arch15 interior spans of 29.5ft over arch

•• Total of 26 splices:Total of 26 splices: First five splicesFirst five splices: 15.5 ft from pier and : 15.5 ft from pier and

skewback column supportsskewback column supports

Remaining splicesRemaining splices: 7.25 ft from arch column : 7.25 ft from arch column

supportssupports

South

6’-9”

6’-9”

7’-4 1/2”

7’-4 1/2”

3@ 6’-9”

Interior StringersExterior Stringers Spandrel Beams Floor Beam

62’ 29.5’ 29.5’ 29.5’ 29.5’ 29.5’ 29.5’ 29.5’

14’-9”

SP#1 SP#3 SP#4 SP#5 SP#6 SP#7 SP#8 SP#9 SP#10 SP#11 SP#12 SP#13

407’-3”

CL Bearing

Abutment #1

Arch CL

62’ 62’

SP#2

15.5’ Typ.

7.25’ Typ.

Rating Spandrel SpliceRating Spandrel Splice Splice ConfigurationSplice Configuration

3”

4”

16 @ 3”

5”

3”

3”

2.5” 4”

3”

4” 2.5”

12 ½” x 5/16” x 5’-0”

12 ½” x 5/16” x 4’-8”

12 ½” x 5/16” x 2’-1”

12 ½” x 5/16” x 1’-5”

5 ¼” x 1/2” x 3’-6 ½”

6” x 1/2” x 3’-6 ½”

6” x 5/8” x 3’-6 ½”

7” x 1/2” x 3’-6 ½”

3 ½” x 3 ½” x ½ x 2’-0 ½”

3”

3”

3” 1.75”1.5”

Rating Spandrel SpliceRating Spandrel Splice Limit StatesLimit States

Yielding on

Gross Area

Fracture on

Net AreaBlock Shear

Shear Strength

of Rivets

Bearing Strength of

Plate

Top Flange 464.1 556.9 544.5 353.6 722.8

Bottom Flange 382.4 426.9 643.5 353.6 1726

Moment Limit States (kip)

Plate Group

Yielding on

Gross Area

Fracture on

Net Area

Shear

Strenght of

Rivetsa

Bearing Strength

of Platea

Web 623.7 881.7 25.3 23.0

Shear Limit States (kip)

Plate Group

aa For a single rivetFor a single rivet

Rating Spandrel SpliceRating Spandrel Splice Distribution FactorsDistribution Factors

•• One spandrel beam on each edge of the bridge widthOne spandrel beam on each edge of the bridge width

Considered as an Considered as an exterior beamexterior beam for moment DFfor moment DF

•• Use the lever rule to determine moment distribution factors:Use the lever rule to determine moment distribution factors:

1.7641.764 4 lanes loaded4 lanes loaded

2.0942.094 3 lanes loaded3 lanes loaded

1.9291.929 2 lanes loaded2 lanes loaded

1.3281.328 1 lane loaded1 lane loaded

Includes the multiple Includes the multiple

presence factorpresence factor

Controls!Controls!

•• LRFD Table 4.6.2.2.3.bLRFD Table 4.6.2.2.3.b--1 states the distribution factor for 1 states the distribution factor for

shear of an exterior beam is also determined using the lever shear of an exterior beam is also determined using the lever

rule: DFrule: DFmomentmoment = DF= DFshearshear

Rating Spandrel SpliceRating Spandrel Splice Rating FactorsRating Factors

RFi RFo

S1 1.27 1.65

S6 1.33 1.72

S1 0.92 1.20

S6 0.92 1.20

Critical SpliceMoment Rating

Top FL Plate

Group

Bottom FL

Plate Group

RFi RFo

4.00 5.19

0.90 1.16

Shear RatingCritical Splice

Web Splice Plates

Single Rivet

Moment Rating FactorMoment Rating Factor Shear Rating FactorShear Rating Factor

Splice S1 had larger moment Splice S1 had larger moment

due to truck load in magnitudedue to truck load in magnitude

Load Rating ofLoad Rating of

Column SpliceColumn Splice

Rating Column SpliceRating Column Splice Basic InformationBasic Information

•• Total of 20 columns:Total of 20 columns: 4 Pier columns4 Pier columns

2 Skewback columns2 Skewback columns

14 Arch columns14 Arch columns

•• Splices in six tallest columns: 55 ft below the deck gradeSplices in six tallest columns: 55 ft below the deck grade

S1

S3 S4

S2

S5 S6

Fixed

PinnedRoller

Arch Column Splices

Skewback Column

SpliceSkewback Column

Splice

Rating Column SpliceRating Column Splice Splice ConfigurationSplice Configuration

5 @ 3”

5 @ 3”

3.5”

1.5”

1.5”

1.5” 1.5”

4 @ 3”

3.5”

3”

3”

1.25”

1.25”

Arch Column SpliceArch Column Splice

24.5”

4 Angles

4” x 4” x 1/2”

4 Plates

24” x 1/2”

24”

4 Angles

5” x 5” x 3/4” x 3’- 1/2”

8 Plates

12” x 1/3” x 1’- 3”

Rating Column SpliceRating Column Splice Splice ConfigurationSplice Configuration

Skewback Column SpliceSkewback Column Splice

24” x ½”4” x 4” x ½”

48”

48.5” back to back

48” x ½”

4 Angles: 5” x 5” x ¾” x 3’-6 ½”

2 Plates: 12” x 3/8” x 3’-4”

8 Plates: 12” x 3/8” x 1’-4”

12” 42.5”

4 @ 3”

16”

2”

Rating Column SpliceRating Column Splice Modeling: MemberModeling: Member

•• The riveted connection stiffness is uncertainThe riveted connection stiffness is uncertain

•• Two models: COLUMN and BEAMTwo models: COLUMN and BEAM--COLUMNCOLUMN

•• Actual connection stiffness somewhere in between COLUMN Actual connection stiffness somewhere in between COLUMN

and BEAMand BEAM--COLUMN modelsCOLUMN models

•• Previous work found that Previous work found that BEAMBEAM--COLUMNCOLUMN model yielded model yielded

significantly significantly smaller rating factorssmaller rating factors: thus, chosen as : thus, chosen as critical modelcritical model..

Rating Column SpliceRating Column Splice Limit StatesLimit States

Flange Plates:Flange Plates:

Gross yieldingGross yielding

Net fractureNet fracture

Block shearBlock shear

Shear strength of rivetsShear strength of rivets

Bearing strength of PLBearing strength of PL

Angles:Angles:

Gross yieldingGross yielding

Net fractureNet fracture

Block shearBlock shear

Shear strength of rivetsShear strength of rivets

Bearing strength of PLBearing strength of PL

PL based PL based

Limit StatesLimit States

Rivet based Rivet based

Limit StatesLimit States

Total Capacity = smaller ofTotal Capacity = smaller of

[[φφRnRnFlangePLFlangePL + + φφRnRnAnglesAngles]]PLPL--BasedBased

[[φφRnRnFlangePLFlangePL + + φφRnRnAnglesAngles]]RivetRivet--BasedBased

Rating Column SpliceRating Column Splice Limit StatesLimit States

Gross Yield Net Fracture Block Shear Rivet Shear Plate Bearing

Plates 297.0 330.0 240.9 252.6 501.2

Angle 412.1 538.3 1073 151.5 1743

Control

Plates 356.4 429.0 419.5 252.6 501.2

Angle 412.1 538.3 1344 176.8 2055

Control

Plate-Based Limit States (kips)Rivet -Based Limit States

(kips)Splice

Arch

Column

768.5 429.3

Skewback

Column

Component

653.0 404.1== ==

Controls tension capacity Controls tension capacity for Arch Column Splice!for Arch Column Splice!

Rating Column SpliceRating Column Splice SecondSecond--Order EffectOrder Effect

•• No bracing between columns: Sway FrameNo bracing between columns: Sway Frame

•• For a beamFor a beam--column in sway frame, the maximum first order column in sway frame, the maximum first order

moments are amplified using the second order effect given in moments are amplified using the second order effect given in

LRFD Article 4.5.3.2.2bLRFD Article 4.5.3.2.2b

•• NonNon--sway and sway moments must be amplified by nonsway and sway moments must be amplified by non--sway sway

((δδbb) ) and sway (and sway (δδss) magnification factors) magnification factors

•• Previous work determined Previous work determined δδbb = = δδss = 1.0= 1.0

Rating Column SpliceRating Column Splice SecondSecond--Order EffectOrder Effect

End Moment

Max.

Moment

δb < 1.0

Splice Location

First-Order

Moment

Amplified

Moment

Moment

End Moment

Max. Moment

δb >1.0

Splice Location

First-Order

MomentAmplified

Moment

Moment

Lower LimitLower LimitHigher LimitHigher Limit

RangeRange

Rating Column SpliceRating Column Splice Distribution FactorsDistribution Factors

•• Columns in eastern arch rib controlledColumns in eastern arch rib controlled

•• Live load distribution factors determined using the same Live load distribution factors determined using the same

method as the spandrel beammethod as the spandrel beam

DFDFmomentmoment = DF= DFshearshear = 2.094= 2.094

Rating Column SpliceRating Column Splice Rating FactorsRating Factors

RFi RFo RFi RFo RFi RFo

Arch S5 1.41 1.83 0.65 0.84 1.03 1.34

Skewback S2 3.79 4.91 1.84 2.38 2.81 3.65

Average

Moment Rating Factors

Splice δb = 1.0 @ splice δb > 1.0 @ splice

RFi RFo RFi RFo

Arch S5 8.39 10.9 1.93 2.50

Skewback S2 36.8 47.8 6.95 9.01

Web Splice Plates Single Rivet

Shear Rating Factors

Splice

Load Rating ofLoad Rating of

Arch Rib SpliceArch Rib Splice

Rating Arch Rib SpliceRating Arch Rib SpliceBasic InformationBasic Information

•• Total of 15 arch rib segments per arch planeTotal of 15 arch rib segments per arch plane

•• Center 13 arch rib segments are splicedCenter 13 arch rib segments are spliced

(Labeled as S7 through S19 below)(Labeled as S7 through S19 below)

7

8

910

11 12 13 14 1516

17

18

19

Arch Rib Splice #Pinned Pinned

South

North

Rating Arch Rib SpliceRating Arch Rib Splice Splice ConfigurationSplice Configuration

46” x 3/4”

8” x 8” x 3/4”

71 1/2” x 1/2”

18 1/2” x 3/4” x 3’ 9”

18 1/2” x 3/4” x 9”

7 1/4” x 7 1/4”

x 7/8” x 3’ 6 ½”

12 1/2” x 5/8” x 2’ 0”

Rating Arch Rib SpliceRating Arch Rib SpliceModeling: MemberModeling: Member

RIGID Model PINNED Model

Skewback

ColumnSkewback

Column

Quarter Point

Arch Splice Quarter Point

Arch Splice

1.0 rad 1.0 rad

1.0 1.45

•• Two models considered: RIGID and PINNEDTwo models considered: RIGID and PINNED

•• Used Influence Line to determine which model produces lower Used Influence Line to determine which model produces lower rating factorsrating factors

Rating Arch Rib SpliceRating Arch Rib Splice Second Order EffectSecond Order Effect

•• LRFD Article 4.5.3.2.2c specifies live load moments in arch ribsLRFD Article 4.5.3.2.2c specifies live load moments in arch ribs

including impact including impact ““shall be increased by the moment magnification shall be increased by the moment magnification

factor, factor, δδbb””

0.1

1

≥

−

=

e

u

mb

P

P

C

φ

δ

( )2

2

u

eKl

EIP

π=

lluu = half of the arch length= half of the arch length

K = f (type of arch, riseK = f (type of arch, rise--toto--span ratio of span ratio of arch)arch)

CCmm = 1.0= 1.0

Dead Load HS-20 Lane

S9 1015 43.8 70.4 1.31

S17 1015 42.5 52.8 1.30

Moment Amplification

Factor, δb

Axial Forces (kips)Splice

Rating Arch Rib SpliceRating Arch Rib SpliceDistribution FactorsDistribution Factors

•• Arch ribs in eastern arch rib controlledArch ribs in eastern arch rib controlled

•• Live load distribution factors determined using the same Live load distribution factors determined using the same

method as the spandrel beammethod as the spandrel beam

DFDFmomentmoment = DF= DFshearshear = 2.094= 2.094

Rating Arch Rib SpliceRating Arch Rib SpliceRating FactorsRating Factors

Inventory Operating

S9 0.82 1.06

S17 0.84 1.09

Splices

Moment

(Flange Splice Plates)

Inventory Operating Inventory Operating

S7 13.5 17.5 2.58 3.35

S8 13.8 17.9 2.68 3.47

S11 9.4 12.2 2.37 3.07

S14 8.1 10.4 2.66 3.45

S17 15.8 20.5 2.70 3.50

Single Rivet

Shear

Splices Web Splice Plates

Conclusions & Conclusions & RecommendationsRecommendations

ConclusionsConclusions

RFi RFo RFi RFo RFi RFo

Interior Stringer 1.10 1.43 2.30 2.98 1.19 1.54

Exterior Stringer 1.02 1.32 2.43 3.15 1.33 1.72

Spandrel Beam 0.92 1.20 4.00 5.19 0.90 1.16

Splice

Shear

Web Splice Plates Single RivetMoment

South

Critical Spandrel Splice

(S4) for Shear

31’ 31’ 31’ 31’ 31’ 31’ 29.5’ 29.5’ 29.5’ 29.5’ 29.5’ 29.5’ 29.5’

14’-9”

CL Bearing

Abutment #1

Arch CL

Critical Spandrel Splice

(S1) for Moment

Critical Interior and Exterior Stringer

Splice (S1) for Shear and Moment

All splices rated All splices rated greater than 1.0 at greater than 1.0 at operating:operating:

No posting requiredNo posting required

Safe for AASHTO Safe for AASHTO and State legal loads and State legal loads without major without major variation from variation from AASHTO legal loadsAASHTO legal loads

Floor SystemFloor System

ConclusionsConclusions Columns & Arch RibsColumns & Arch Ribs

Critical Arch Column Splice (S5)

for Shear and Moment

Critical Skewback Column Splice

(S2) for Shear and Moment

South

North

Critical Arch Rib Splice (S9)

for Moment

Critical Arch Rib Splice (S14)

for Shear - Web Splice Plates Critical Arch Rib Splice (S11)

for Shear – Single Rivet

RFi RFo RFi RFo RFi RFo

Arch Column 1.03 1.34 8.39 10.88 1.93 2.50

Skewback Column 2.81 3.65 36.85 47.77 6.95 9.01

Arch Rib 0.82 1.06 8.05 10.4 2.37 3.07

SpliceMoment

Shear

Web Splice Plates Single Rivet

All splices rated All splices rated greater than 1.0 at greater than 1.0 at operating:operating:

No posting requiredNo posting required

Safe for AASHTO Safe for AASHTO and State legal loads and State legal loads without major without major variation from variation from AASHTO legal loadsAASHTO legal loads

RecommendationsRecommendations

•• Load test recommended to better estimate the rotational Load test recommended to better estimate the rotational

stiffness of the riveted connections for the spandrel beams, stiffness of the riveted connections for the spandrel beams,

columns, and arch ribscolumns, and arch ribs

•• Uncertainty in secondUncertainty in second--order effect of column splice moments: order effect of column splice moments:

Lower end amplified moment rated as low as 0.84 at operating. Lower end amplified moment rated as low as 0.84 at operating.

A thorough examination of column splice strongly A thorough examination of column splice strongly

recommendedrecommended

A more detailed analysis of the secondA more detailed analysis of the second--order effect order effect

recommended in future analysisrecommended in future analysis

RecommendationsRecommendations

•• Several rivets reported missing during last inspectionSeveral rivets reported missing during last inspection

Recommended to identify missing rivets and replace themRecommended to identify missing rivets and replace them

•• Lateral load analysis due to wind and earthquake load Lateral load analysis due to wind and earthquake load

recommendedrecommended

•• 33--D finite element model recommended to better evaluate the D finite element model recommended to better evaluate the

member and splice forces and refine the analysismember and splice forces and refine the analysis

ReferencesReferencesAmerican Association of State Highway and Transportation Officials (AASHTO). (2003). Manual for Condition Evaluation

and Load and Resistance Factor Rating (LRFR) of Highway Bridges, Washington, DC.

American Association of State Highway and Transportation Officials (AASHTO). (2004). LRFD Bridge Design Specifications,

3rd Edition, Washington, DC.

American Institute of Steel Construction (AISC). (2001). Manual of Steel Construction: Load and Resistance Factor Design,

3rd Edition, Chicago, IL.

FDOT (Florida Department of Transportation). 2007. 24 August 2007

<http:www.dot.state.fl.us/structures/LoadRatingSummit/AskTheProfessor.htm>

Garrett, Gregory P. “Analytical Load Rating of an Open-Spandrel Arch Bridge: Case Study.” Journal of Bridge Engineering

(January/February 2007): 13-20.

Gaylord, Edwin H., Charles Gaylord, and James Stallmeyer. Design of Steel Structures, 3rd Edition. New York: McGraw-Hill,

1992

McCormac, Jack C., and James K. Nelson Jr. Structural Steel Design: LRFD Method, 3rd Edition.Upper Saddle River, NJ:

Prentice Hall, 2002

Salmon, Charles G. and John E. Johnson. Steel Structures: Design and Behavior, 4th Edition. New York: Harper Collins, 1996

Tuyen, Nguyenngoc. Load Rating of a Riveted Steel Arch Bridge. Las Cruces, NM: New Mexico State University, 2005

Vinnakota, Sriramulu. Steel Structures: Behavior and LRFD. New York: McGraw-Hill, 2006

Questions?Questions?Questions?Questions?