MIT WestGate Bridge

8/11/2019 MIT WestGate Bridge

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Lessons Learned in the Design and Erection of Box Girder Bridges fromthe West Gate Collapse

by

Alia Christine Burton

S.B., Civil EngineeringMassachusettsInstitute of Technology, 2005

Submitted to the Departmentof Civil and EnvironmentalEngineering inPartialFulfillmentof the Requirements for the Degree of

Master of Engineeringin Civil and EnvironmentalEngineeringat the

MassachusettsInstitute of Technology

June 2007

C 2007 Alia ChristineBurton. All rights reserved.

The author herebygrants to MIT permissionto reproduceand to distributepubliclypaper and electroniccopies of this

thesis documentin whole or in part in any mediumnowknown orhereafter created.

Signatureof Author ......... ............... , .. .. .v. ...................................Department of Civil andEnvironmentalEngineering

May 21, 2007

Certified by ................ ................... .................. .......JeromeJ. onnor

rofessor of Civil and EnvironmentalEngineeringThesis Supervisor

Accepted by .......... ............................................... .......................- DanieleVeneziano

Chairman, DepartmentalCommitteefor Graduate Students

ARCHIVES

MASSACHUSETTS INSTITUTEOF TECHNOLOGY

JUN 0 7 2007

LIBRARIES


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Lessons Learned in the Design and Erection of Box Girder Bridges fromthe West Gate Collapse

by

Alia Christine Burton

S.B., Civil EngineeringMassachusettsInstitute of Technology, 2005

Submitted to the Departmentof Civil andEnvironmentalEngineeringon May 21st 2007 in Partial Fulfillmentof theRequirements for the Degree of Master of Engineeringin

Civil and Environmental Engineering

ABSTRACT

The West Gate Bridge, intendedto span the Yarra Riverin Australia, collapsedduring itsthird year of construction in 1970. Investigationinto the project revealed numerousissuesin the bridge's design and construction.The West Gate Bridge is one of a numberof boxgirder bridgesbuilt during the mid 2 0 th century, and was oneof four to fail in a three yearperiod.

An overview of the design and erection issues is presented, particularlythose dealingwith thin elementsin compression.A comparisonof momentsand stresses resulting fromthe use of concrete blocks and jacks to reduce the camber difference encounteredon span10-11 shows that the latter methodwould have been preferable.

The failure of three other box girder bridges between1969 and 1971, and the requiredstrengthening of dozens of others, reveal the lack of understanding of the slendercompressiveelementspresent in such structures.

A brief literature review presentsthe bucklingand deformation modes found instiffenedplates under compressive loading, showing the developmentof understanding of thesesystems from papers written or published in 1997, 2001, 2004 and 2006- over threedecades after the West Gate collapse.

Criteria by AASHTO andby B. H. Choi and C. H. Yoo for the minimum moment ofinertia of longitudinal andtransverse stiffeners of box girders are presented. The resultingvalues are compared to the moment of inertia of sections used to strengthen the WestGate Bridge after the collapse of a similar bridge. Thiscomparison shows that therequirementsare quite sensitiveto scale and can provide inconsistent requirements forstiffness. Thus, thereis currently a lack of guidance andregulation from codes for thedesign of wider single-cell boxgirders. The complex andnon-linear nature of the slenderelements in compression used in box girders does not allow the extrapolationof simplerrules developed for the design of smaller bridges.Despite the complex behavior of box


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girders, they offer a numberof advantagesand further researchis needed to improve theiranalysis,design, construction,repair and maintenance.

Thesis Supervisor: JeromeJ. ConnorTitle: Professor of Civil and Environmental Engineering


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Acknowledgements

I wish toacknowledgeProfessor Connor for his guidancethroughout the program and mymother, who held my hand three hundredmiles away.


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Table of Contents

1. INTRODUCTION ....................................... 112. BACKGROUND ............................................................................................................... 12

2.1. INITIAL DESIGN .............................................................. 122.2. CONTRACTUAL RELATIONSHIPS........................... ......................... 162.3. CONSTRUCTION ............................................ ................. 172.4. THE COLLAPSE ............................................................... 18

3. ADVANTAGES AND DISADVANTAGES OF BOX GIRDERS ....................................... 24

3.1. A DVANTAG ES .................................................................................... 243.2. D ISA DVANTA GES ....................................................................................................................... 25

4. WEST GATE BRIDGE ISSUES .................................................. 26

4 .1. D ESIG N .................................................................................................. .......................... ... 264 .2. E REC T IO N ............................................................................................................... 354.3. COMPARISON OF USE OF CONCRETE KENTLEDGES WITH JACKING ..................................... 37

5. OTHER FAILURES ................................................................................................................... 43

5.1. FOURTHDANUBE BRIDGE.................................................. 435.2. M ILFORD H AVEN B RIDGE........................................................................ ............................. 445.3. RHINE BRIDGEIN KOBLENZ ....................................... ........................... 475.4. IMPACTS ON OTHER BRIDGES ................... ................................. 50

6. BEHAVIOR OF STIFFENED PANELS .................................................................................. 52

6.1. A CONTRIBUTION TO THESTABILITY OFSTIFFENED PLATES UNDER UNIFORM COMPRESSION(1997) 526.2. STIFFENED STEEL PLATES UNDER UNIAXIAL COMPRESSION(2001)............................... . 54

6.3. BUCKLING OF STIFFENED PLATES WITH BULB FLAT FLANGES (2004) ................................. 567. STIFFNESS REQUIREMENTS FOR STIFFENERS OF COM PRESSION PANELS.......... 59

7.1. RESEARCHBY CHOI AND YOO (2006) ................................... ........ ....................... 597.2. COMPARISON OF STIFFENER REQUIREMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

8. RECENT EXAMPLE OF A SUCCESSFUL BOX GIRDER BRIDGE................................ 69

9. CONCLUSION .................................................. 71

10. REFER EN CES ............................................................................................................................. 73

11. APPENDICES ................................................. 76

8


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List of Figures

FIGURE 1: PLAN VIEW ................................................ 13FIGURE 2: ELEVATION, PLAN ANDSECTIONVIEWS ................................................................ .. 14FIGURE 3: PHOTOGRAPHOF BRIDGE MODEL.................................................................... 14

FIGURE 4: ASSEMBLY DIAGRAM................................................................. 15FIGURE 5: ELEVATION AND PLAN OF COLLAPSEDSPAN .......................................................... .. 19FIGURE 6: SHORTLY AFTER COLLAPSE.......................................................................... ......................... 20FIGURE 7: IMPACT OF COLLAPSEFORCED A STEEL BEAM THROUGH CONCRETEOF DECK ........................... 20FIGURE 8: COLLAPSEDDECK VIEWED FROM NEIGHBORING PIER. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . 21FIGURE 9: CLOSE-UPOF SHATTERED BOX STRUCTUREOF DECK .............................................................. .. 21FIGURE 10: D YNAMICS OF FAILURE................................................................................ .......................... 22FIGURE 11: SKETCHOF C O LL A PS E. . . . . . . . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . .......................... 23FIGURE 12: SIDEVIEW OFBRITANNIA BRIDGE.................................................... 24FIGURE 13: CROSS-SECTIONOF BRITANNIA BRIDGE.................................................................. 24FIGURE 14: MOMENT UNDERSELF-WEIGHTAND KENTLEDGES................................................... 38FIGURE 15: MOMENT UNDERSELF-WEIGHTAND JACKING.... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38FIGURE 16: STRESS IN TOP FLANGE FROM SELF-WEIGHTAND KENTLEDGES........................................... 39FIGURE 17: STRESS IN TOP FLANGEFROM SELF-WEIGHTAND JACKING ...................................................... 39

FIGURE 18: STRESS IN BOTTOM FLANGE FROM SELF-WEIGHTAND KENTLEDGES..................................... 40FIGURE 19: STRESS IN BOTTOM FLANGEFROM SELF-WEIGHTAND JACKING........................................... 40FIGURE 20: MILFORD HAVENBRIDGE AFTER COLLAPSE......................................................... 46FIGURE 21: SCHEMATIC DIAGRAM OFBRIDGE AND FAILURE..................................... ........................ 46FIGURE 22: DIAPHRAGMOVER PIER 6 OF MILFORDHAVEN BRIDGE............................... .......... 47FIGURE 23: SCHEMATIC DIAGRAM OF FAILUREOF KOBLENZ BRIDGE........................................................ 49FIGURE24: BOTTOMFLANGE SPLICEOF KOBLENZ BRIDGE.................................... ...................... 49FIGURE 25: SCHEMATIC DIAGRAM OF CONSTRUCTION JOINTSAND THEIR INFLUENCEON FAILURE ............... 50FIGURE 26: VARIOUS BUCKLING MODESOF STIFFENED PLATES.............................. ........................ 53FIGURE 27: TYPICAL BUCKLINGMODES ..................................................................................... .............. 55FIGURE 28: LOAD VERSUS DEFORMATION BEHAVIOR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55FIGURE 29: VARIOUS MODES OF DEFLECTION .. . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . . . .. . . . . . . . . 58FIGURE 30: COLUMNAPPROXIMATION OF A TYPICAL STIFFENED FLANGE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61FIGURE 3 1: TYPICAL BUCKLING MODE SHAPES................................................................. 63FIGURE 32: ULTIMATE FAILURE MODESOF TRANSVERSELY STIFFENED FLANGES...................................... 65FIGURE 33: SIDE VIEW OFSTORROW DRIVE CONNECTOR BRIDGE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70FIGURE 34: SIDE VIEW OFSTORROW DRIVE CONNECTOR BRIDGEDURING CONSTRUCTION......................... 70


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List of Tables

TABLE 1: COMPARISON OF MOMENT AND STRESSESFROM SELF-WEIGHT, KENTLEDGES ANDJACKING.......... 41TABLE 2: COMPARISON OF REQUIRED STIFFNESSES.................................. ...................................... 67


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1. Introduction

This thesis will explore issuesin the design, erection,and behavior of box girder

bridges using the West Gate Bridge collapseas a case study. The behavior of the thin

compressive elements in box girders is complex andwas not well understood at the time

the West Gate Bridge, andother similar bridges,were designed and erected.This lack of

understanding resultedin several failuresof bridgesof this type.

We will begin withan overview of the West Gate Bridge project, the box girder bridge

as a structural system, and key designand construction issues specific to the West Gate

Bridge. Thechallenges encounteredin the design and erectionof the West Gate Bridge

are numerous andthis paper does not aim to conduct a full account or analysis of them

all. However, keyconcerns of calculations of loads and stresses duringthe constructionand service conditions will be noted. Particular attentionis paid to matters regarding

elementsof the bridge under compressive loading.

One of the critical challenges in the erection phase was the presence of large

differences in camber of two similar sets of half spans. Two tactics for removing the

camberdifference of span 10-11 will be compared.A brief presentationof failures of box

girder bridgesconstructedduring the same time periodwill follow.

Next, a summary of the understandingof buckling and failure modesof stiffened

panels under compressive loading as described in papers written or published in 1997,2001, and 2004 is presented. An overview of design criteria suggestedby AASHTO

(AmericanAssociationof State Highway and TransportationOfficials) and by B. H. Choi

and C. H. Yoo (2006) for the minimum moment of inertia of stiffening elements follows.

These design requirements will be compared to one another and to the properties of the

stiffeningelementsused in the West Gate Bridge.


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2. Background

On October 15, 1970, the West Gate Bridge dramatically collapsed duringthe third

year of its construction,killing 35 membersof the workforce [6].

The bridge was chosento replace the existing ferry crossing of the Yarra River in

Melbourne,Victoria, Australia. Constructionof the foundations started in April 1968 and

the bridge was scheduled for completionin early 1971 [6].

The bridge would have been the largest built in Australia (Hitchings169), and now

follows Houghton Highwayas the second longestin the country [15].

2.1. Initial DesignThe total lengthof the West Gate Bridge is 2,585 m and the width is 37 m. It has two

four 17 m wide lane lanes, separated by a median strip. The bridge was to consist of

spans of varying lengths in either prestressed concreteor steel. The centralsteel main

span over the Yarra River is 336 m long with shorter spans on either side, for a steel

structure with a total length of 859 m. There are ten approach spans on the western

approach and thirteen approach spans on the eastern approach, each of prestressed

concrete and67 m in length [6].


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Figure 1: Plan view

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ELEVATION

Crown of roadExpansion 192.175Epansonjoint Pinjonlt Pin oint jont

irm i Fix = ixed

it fcontrctSSaondE Limitofcontracts andE

a: PLAN

> Cross m at\,i , O'6' crs

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% 1:40 1:40L panddown constanton concaveside

/ Variable gap/ ection from Box 16 to mid span o

-Section at max superelevation at box Iponvex side of curve

TAPER - OUT OF SUPERELEVATION ON CONVEX SIDE

Figure 2: Elevation, plan and section views

The central three steel spans form a cable-stayed structure supported from two

central steel towers rising 46 m above the roadway. The navigational clearance provided

is 54 m above the low water level [6].

Figure 3: Photograph of bridge model


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The central span structure consists of a simple central tower with cable stays

anchored within the central cell of the box girder. This arrangementhas been foundbest

suited to the roadway layout, since the tower and anchoragescan be accommodatedin the

central median strip between the lanes. Inequalitiesof loading on the two lanes are dealtwith by providingadequate torsional stiffness in the deck structure [6].

The hollow box section consists of a trapezoidalsection 4.05 m deep, 19.06 m wide

along the bottom flange, and 25.47m at the top flange. Minimizingplate thickness was

one of the primary aims of the design since most of the problems associated with the

production and welding of high yield steel would be eliminated. The boxes are made up

from stiffened panels for standardizationand economy. The box girder is divided into

three compartmentsby verticalwebs and outer inclined web panels.Each web and flange

plate is 16 m long and stiffened with either bent plates, angles, or bulb flats welded to

them. All web andbottom flange splices connectingthese panels are made with grip bolts

[6].

Figure 4: Assembly diagram


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The cable-stayedsystem operates only between columns 11 and 14. Spans 10-11 and

14-15 are therefore unstayed box girders, rollersupported at the outermost ends but pin

supportedand continuousat the inner ends. Therefore,the investigationinto the causes of

failure of span 10-11 was limited to a comparatively simple structural system(Royal

Commission36).

2.2. Contractual Relationships

In 1961, the Lower Yarra CrossingAuthority (LYCA)was established as a non

profit company to construct and operate a bridge crossing the Lower YarraRiver. In

1965, LYCA had informal talks with consulting engineers Maunsell and Partnersof

Melbourne. Maunsell and Partners had limited experiencein major bridge designand in1966, they recommended thatLYCA approach the internationally recognizedfirm

Freeman, Fox and Partners (FF&P)of London. FF&P hada world reputation for their

work on such structures as the Forth Road Bridge(1963) and the Severn Bridge(1968)

[6].

Time was very important becauseof the high level of interest charges to LYCA. In

order to meet the completion deadlineit was decided fromthe beginning that detailed

designs must be rapidly prepared so that tenderscould be called for constructionas soon

as possible [6].

In 1967, LYCA formally appointedthe two firms as joint consultants for detailed

design up to the preparation of tender documents.The contracts for foundationwork and

concrete construction were awardedto John HollandConstruction (JHC) of Melbourne in

1968. The contract for steelwork constructionwas awarded to World Services and

Construction(WSC), a subsidiaryof a Dutch constructioncompany, also in 1968. By the

end of 1969, it was apparent thatWSC was falling behind the construction schedule for

steelworkerection [6].

To avoid furtherdelay LYCA made new contractual arrangementsin which WSC

continued to make the steel parts for the bridge but JHC was to erect and join the

steelworktogether. This is a specializedarea in which JHC lacked experience[6].


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2.3. Construction

The foundations, which involved sinking cylinder and driving octagonal steel piles,

were started in April 1968 and ended without incidentin September 1969 [6].

Cantilevered forms wereused to construct the concretepiers in 2.44 m sections. Foursets of formworkwere used so that the four piers couldbe constructed simultaneously.

The 67 m approach spans consisted of eighteen spine beam units whichwere

manufactured on site. Special equipmentwas designed and built to lift and handle the

units into position [6].

Each steel box of the central span structureconsisted of twenty-one stiffened plate

panels which were fabricated in two workshops at the bridge site. Plate steel was

prepared to specialspecificationsand rigorously tested for such properties as strength and

impact resistance[6].

By October 1970, twelve pairs of half boxes had been erected on the east bank

extending from Pier 15 to a point mid-way between Piers 13 and 14. Span 10-11 had

been started on the west bank. The three middle spans- 11-12, 12-13 and 13-14 - were

designed to be erected by the cantilevermethod in which sectionsof the steel box were

raised and attached to the last section. Thiscould havebeen done from one pier only or

from both endsso that the cantilevered spans met in the middle- however, this stage was

not reachedin construction.

Span 10-11 and span 14-15 were designed to be erected in a different fashion by

assembling each span in two halves on the ground in full length and half width. Each

span was then lifted into position at the top of the piers. The next stage, which proved

extremelydifficult,was to join the two half spans together [6].

The erection of span 14-15 gave an indication of the problems to be expected with

the chosen erection procedure. The boxes were bolted together on temporary staging at

ground level. When the span was lifted off the temporary staging the upper plates of the

boxes buckled at the unsupported edges. Thus, inadequate temporary bracing led tosignificant compression instability. When both halves were jacked and placed on the

piers, a 90 mm (3.5 in) difference in camber was observed.To eliminate this difference,the end of the south half span was jacked up to about twice the camber difference, andwhen aligned, the two halves were jacked together, closing the horizontal gap. Some


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local buckling remainedand this was pressed out using long bolts tightened on stiff

beams. Working from both ends left one section in the middle where the buckles

remained. Theonly way to remove these, in the opinion of the engineers, was to undo

some of the bolts connectingthe stressedstructure, and when displacementhad eased out

the buckles, replace the boltsafter enlargingthe holes [6].

The first half spans werejoined successfullyby WSC, with a system of hydraulic

jacks to ensure thatthe total load of the partly constructed span would be more or less

equally shared betweenall the trestles. However,when JHC took overthis assembly,they

had difficultyin understandingthe logicbehind this system [6].

The success of the erection of span 14-15 lead to a "degree of unconcern" when

similar problems were encounteredon span 10-11 [6].

The Collapsed Span

At the time when span 10-11 was partially assembledon the ground, the contract for

steel erection was awardedto JHC. Similar to the constructionof span 14-15, span 10-11

was also erected by assemblinghalf spans and joining them together after placingthem

on the piers [6].

The half boxes were surveyed for alignmenton the ground, but due to temperature

changes and the fact that one half span had a crane on it, thesurveys were likely to be

inconsistentand unreliable [6].

When the two sections werebrought together afterbeing lifted onto the piers, the

difference in camber was foundto be as much as 114 mm (4.5 in). JHC proposed to use

10 8-tonne kentledges (concrete blocks) placed near the midspan, to remove the

difference. With seven of these blocks in place a major bucklehad occurredin the upper

panel of the north span.In order to allow thebuckle to be removed, bolts connectingthe

transverse splicein the top deck near the mid span were undone [6].

2.4. The Collapse

On October 15, after about sixteen bolts hadbeen loosed, therewas significant

slipping of the two plates relative to one another such that the loosened bolts were

jammed tightly into their holes and couldnot be removed [6].


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After about 30 bolts were removed,a dramatic changetook place. First, the buckle

spread into the adjacent outer panels, accompaniedby the buckling failure of the upper

part of the inner web plate. Plasticcreep in the steel, and possibly the effect of thermal

changes, all contributed to a slow diffusionof yielding, which lasted50 minutes beforethe finalcollapse [6].

Images captured following the failure andsketchesof the collapse are shown below.

Figure 5: Elevation and plan of collapsed span

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L...1,,,,Pc4 ,,_,... ,,__r , ) 4vwJcrt Q: , * j' " ' t/ ?ae i, i .S ., or,d i


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Figure 6: Shortly after collapse

Figure 7: Impact of collapse forced a steel beam through concrete of deck


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Figure 8: Collapseddeck viewed from neighboringpier

Figure 9: Close-up of shattered box structure of deck


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Figure 10: Dynamics of failure


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L

Figure 11: Sketch of collapse


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3. Advantages and Disadvantages of Box Girders

Robert Stephenson, an English civil engineer, first decided on light metal

construction for the rational use of material for the Britannia Bridgein 1850. This

structure was a continuous girderof puddle iron with maximum spans of 142 m in the

form of a box. He is consideredto be ahead of his time, and his ideawas not followedup

until a century later (Inst. Civil Engineers21). Stiffened steel plate box girders for bridge

construction were first developed andused in Germany in the 1950s for post-war

reconstruction. Stiffened plates are basic components of many structures, including

bridges,buildings, automobiles,aircrafts, offshoreplatforms, and naval vessels [8].

The main advantagesand disadvantagesof box girderbridges are describedbelow.

Figure 12: Side view of Britannia Bridge

Figure 13: Cross-section of Britannia Bridge

3.1. Advantages

During the mid 20 th century, engineers favored the box girder, pioneered by

Freeman, Fox and Partners, because of its relative lightness, speedof construction and

cost. They said box girders could cut cost of constructionby between 30 and 50 percent

(Hitchings 98).

Because box girders are closed-section members, they are often used in highway

bridges because of their high torsionalrigidity, economy, appearance, and resistance to


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corrosion. With their wide bottom flanges, relativelyshallow depths can be used

economically. And for continuous box girders, intermediatesupports often can be

individual, slender columnssimply connectedto concealed cross frames (Brockenbrough

11.56).

3.2. Disadvantages

Because relatively thinmembers take significantcompressive forces, bucklingis a

key design concern forsteel box girders. Moreover, the behavior of this system is very

complex and requires a high design effort. A view contradictory to the previous

subsection is that box girder bridgesare more expensive to fabricate, andmay also be

more difficult to maintain because of the need for access toa confined space inside the

box [4].

At the time of the publication of Steel Box Girder Bridges by the Institutionof Civil

Engineers in 1973, there was no comprehensivetheory that embraced all the stability

problems typical of steel box girders. This is because a number of factors work together

to make it difficult to analyze the physical nature of the problem, such as: a) the complex

form of the cross-section and the difficulty of taking into account the interaction of its

various parts, b) the compound and three dimensional stateof stress and c) the non-

linearity of geometry and of the constitutive laws of the material, both of which much be

consideredfor a correct interpretationof the problem(Inst. CivilEngineers25).

Informationderived from experimentswas also insufficientwith only one person - P.

Dubas - havingworked in the field at the time (Inst. CivilEngineers 25).


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4. West Gate Bridge Issues

4.1. Design

The design process of the original West Gate Bridge had manycomplications, and

calculations containednumerous errors in arithmetic andin engineeringprinciple. This

subsection is intended only to highlight certain issues relating to engineering practice,

and to the events leadingto the collapseof the bridge.

Administrative Matters

A number of administrative,communicationand managerialproblems characterized

the design and erectionof the bridge.In writing the report, the Royal Commision foundithard to determine the sequence of calculationsmade because neither Freeman,Fox and

Partners (FF&P) nor WorldServices and Construction(WSC) made a regular practice of

dating or signing their calculations. WSC repeatedly requested designcalculations from

FF&P but were often leftwithout a response.

WSC also facedlabor problemson site, including disputes,strikes, protest meetings,

walk-offs and absenteeism. John Holland Construction (JHC) also experienced

challengeswhen they tookover the steel erection, as the companyhad no experience with

box girder constructionand was stronglyopposed by FF&P [6].

General Design

Overall, the design - as a process and as a deliverable - was troubled. Because the

Lower Yarra Crossing Authority (LYCA) was very concernedabout having the bridge

completed on time, it was decided that detaileddesigns were to be rapidly prepared so

that tenderscould be calledfor constructionas soon as possible [6].

Almost the only calculationswhich FF&P presentedto the Royal Commission(after

the collapse)relating to the tender design were the computeroutputs made in early 1967.

Neither Sir G. Roberts nor Dr. W. C. Brown, senior engineersof FF&P, would admit to a

knowledge of the details of the computerprogram used to make their calculations.And,

in setting up a model for the program, sweeping simplifications weremade when

representing the structure (Royal Commission52).


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Brown, saidthe "bridge was a new development.The design remainedin a complete

state of flux for some considerable time...because this type of bridge involves new

concepts and calls for muchthought to arrive at acceptablepractical solutions." While the

box girder bridge was ahighly advanced systemand had been popular for only a shorttime, FF&P actuallyhad great dealof experience withbox girder bridges, includingthose

with trapezoidal sections andwith cablestays (Royal Commission49).

FF&P stated that tender design was preliminary only andthat they would have

expected the contractor to introduce changes when preparing workingdrawings. Yet, the

tender drawings showthat design detailsare fully worked out, to the location of every

bolt (Royal Commission49).

FF&P's design activity was at a very low level from early 1969 until April 1970,

when, in the opinion of the Royal Commission,they should have been checkingthe final

design of the structure. Their own checks, madeat the end of 1968, showed stresses in

some areas considerably higher than permitted by any code. Construction, meanwhile,

was proceeding despitethe unsatisfactorystate of the calculations (Royal Commission

51).

Specificdesign issues are addressed in the following sections.

Loading

The self-weightand dead load reactions on piers were determinedearly in the design

by FF&P and were generally agreed upon by WSC, A.P. Sewell of JHC and J.J. Grassl,consulting engineer. The reactions on two piers due to live load were found to be 280

tons by FF&P while A.P. Sewell and G. Maunsell found about845 tons. This major

discrepancyis explained in the following paragraphs(Royal Commission47).

Early in 1967, Maunsell was anxious to find reaction values so that they could

proceed withthe design of concrete piers. A calculation done by FF&P in April of that

year showed that the live load reactions were assessedby a simple proportion of the deadload reactions(Royal Commission47).

Roberts stated that the live loads in question were preliminary only, but there is no

evidence that estimates of live load reactions were everrevised. And, the values obtained


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at that time appear to have beenin use by both FF&P and Maunsellright up to the time of

failure (Royal Commission47).

There was also a discrepancyon the number of lanes needed forthe basic function of

the bridge, as well as in the live load reduction.One of LYCA's design requirements was

that planning shouldbe made for "four lanes of traffic with a breakdown lane allowing

for a possible extensionto five lane operation withouta breakdown lane." Thus, the two

55 ft 2 in carriageways would be required by the NAASRA (National Association of

Australian State Road Authorities)to carry ten lanesof traffic. However,FF&P designed

the bridge to carry eight lanes of traffic. According to the AASHO (American

Association of State Highway Officials), and hencethe NAASRA, code,FF&P could

reduce live loadby 25%, which is based on statistical grounds. However, the values onthe curve used by FF&P were already calculated assuming75% of the lanes would be

fully loaded (RoyalCommission46).

Factors of Safety

In statements to LYCA, FF&P made it clear that where appropriate,the design

stresses wouldbe in accordance with BS 153 (British Standard),including the increase of

30 percent above workingstressesfor the erection conditions (RoyalCommission42).

The safety factor for the service condition is 1.70, although it would be morecorrect

to describe this as a load factor- the factor by whichthe factored loads must be multiplied

for yielding of some structuralmember to occur. The elasticanalysis made in design

must account for all factors involved,particularly when dealing withpanels of plating

under compression or shear (RoyalCommission42).

BS153 setout various combinationsof forces which must be taken into account. In

presenting the stress analysisfor the service condition,FF&P included only the dead and

live load and ignored othereffects such as wind pressure,temperature, and resistanceof

expansion bearing to movement. The neglect of these minor effects reduced the safety

factor, and they weremore dangerousbecause their significance, neither individuallynor

collectively, was assessed (RoyalCommission42).

The safety factor has a particularly high significance in the design of this bridge

because of the uncertaintyassociatedwith stiffenedplates under compression.In addition


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to the possible initial distortions and locked-in stresses, thereis also considerable

difference of opinion on the exact manner in which suchpanels behave whenloaded to

failure. Furthermore, when failure occurs, it will usually be catastrophic (Royal

Commission43).Experts could not agree on the determinationof the theoretical failure loads for the

panels, and thus, the appropriate allowable working stress. Therefore, the factor of

ignorance for these elements is large. It would appear inappropriateto use the same

safety margin as that used for elements whose behavioris more certain, suchas simple

beams. Given this,the Royal Commissionbelieved the factor of 1.31 (1.70/1.30) wastoo

low for the design of compressionpanels in a box girder (43).

Finally, the FF&P design calculationsbarely contain any statement on, or values of,allowable stressor any comparisonsof allowable or actual stresses. In some of the rare

cases where valuesare given, BS153 has been used.

Stiffened Panels in Compression

The stiffened panelsof the upper flange were intendedto work compositelywith the

concrete deck in the service condition to add significantly to the stability of the upper

sections. However, for the pre-concretedstages of erection it was necessary to provide

stiffening sufficientto stabilize the parts of the upper flange which were in compression.

It was thefailure of these panelsthat led to the collapse (RoyalCommission37).

This stiffening included longitudinal bulb flats and transverse stiffeners. The

connectiondetails wereflawed in that the transverse stiffenerswere connectedonly to the

bulb flats and therefore, only indirectly connected to the flange plate in many cases.

These fish plates (or, K-plates), used to splice the bulb flats, were not designed with

consideration of their high slenderness ratio and eccentricity. For this reason, the

connection of the longitudinal stiffeners was less strong than the elements themselves

(Royal Commission37-8).The effective length of 0.71 (fixed-pinned condition) for the stiffened panel and K-

plates used by Dr. W. C. Brown was also a point of disagreement because they werebased upon assumptions that the panels would be bent slightly downwards initially andwould behave as if fixed. The Royal Commission determined that this assumptionwas


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unacceptable because these conditionswere not met on site. They doubt that the

assumption would have been justifiable even if the conditions had been met (Royal

Commission45).

FF&P used the simple theory of bending to calculate the buckling load of the

stiffened plates. However, the Royal Commission claimed this theory could lead to

significant errors due to the fact that plane sections, on bending, do not necessarily

remain plane(RoyalCommission37).

The critical stress for buckling of longitudinally stiffenedpanels betweentransverse

beams was found to be 18.3 tons/in2 (40.4 ksi) - only slightly higher than theEuler value

for one longitudinally stiffenedpanel and its attached plate, whichwas 17.7 tons/in2

(39.0 ksi). The Royal Commission asserts that failure would occurat a stress well belowthe elastic crippling stress because of the imperfections of flatness inherent in any

practical panel and the limits imposed bythe onset of yield (Royal Commission54).

The classical theory of elasticity gives three modes of buckling for such panels in

compression.While FF&P gave a formulas for the most complex mode (which is also the

least practical fornormal design purposes)to WSC, there is no evidence that FF&P used

the method for either the tender design or post-tendercheck (RoyalCommission55).

Furthermore,the formulas forthe various bucklingmodes only give elastic critical

stress. They can be of some help in determining the appropriate allowablestress, but

other factors such as the yield stress, the initial unfairness of the panels and the

appropriatesafety factor must be taken into account.

Lastly, there is no evidence that post-bucklingbehaviorwas investigated.And, in the

design, FF&P ignoredthe presenceof the splices in the way it might affect the stabilityof

the panels (RoyalCommission55-56).

Factors Not Addressed in Report of Royal Commission

While the report presented by the Royal Commission is very comprehensivein the

review of calculations and design features of the West Gate Bridge, we may note that

certain typesof loading werenot discussedby the designers or contractors,nor by the

Commission.


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These include seismic loading,dynamic loading andresponse, and fatigue. It could

be that these effects were not consideredas often in that timeperiod. Or, the reason could

be that the factors were not considered relevant for the inquiry given that they did not

directly relateto the collapse.

Shear lag

Calculations by FF&P did not account for shear lag effects in the webs and

diaphragms, which involve the distributionof load between inner and outerwebs (Royal

Commission61).

The Royal Commission states that the distribution is not a statically determinate

problem and a reasonably complex analysis would be needed to get a meaningful

distribution(Royal Commission62).

After the collapse, Maunsell,London performed finite element analysisand

calculated shear lag effects of up to 80 percent. In certain locations of the box girder,

Maunsell, London's analysis showed peakstresses caused by shearlag in excess of the

yield stress andthere wereareas of up to about 30 ft2 where thestress wasnever less than

90 percent of the yield stress (Royal Commission62).

After the Milford Haven Bridge collapse in June 1970, FF&P used a 50/50

distribution, then59/41 and 42/58 distributions,where the outer webstake 59 and 42

percent of the total shear and the innerwebs take 41 and 58 percent. The analysis by

Maunsell, London foundthat a distribution of 40/60 seemed more rationalwhen

considering compatibilityof shear deflectionsin the four webs (Royal Commission62).

The assumption that the loadfolloweda 50/50 distributionwould imply overstressed

conditions in the bolted connections between the webs and the load bearing diaphragm

(Royal Commission62).

ErectionWhen the principle dimensions of the bridge had been established and the tender

design was carried out in mid-1967, it appears that no serious consideration was given to

potential erection schemes,even though one of the computer runs was claimed to be an"erection analysis." The analysis made at that time was limited to an examination of


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stresses in the steel bridge except for the concrete deck and another similaranalysis for

the stresses in the bridge with all the concrete in place and already hardenedin order to

act compositely withthe steel (RoyalCommission41).

The instantaneous placement and hardening of the whole concrete deck cannotbe

considered a practical condition and one can assume that any practical scheme for

concreting would be likely to impose higher stresses at some placesduring erection


By adopting this oversimplified approach, FF&P achieved a design which they

believed was satisfactory for the service condition, but required considerableextra

strengthening at many places to meet the stresses imposed by any practicalerection

scheme (Royal Commission41).According to B. W. Smith, the erection stages of a large bridge are often the most

critical fromthe point of view of safety. As erection continues,additional elements may

be added to parts of the structure already erected.These may include deck panels,

concrete, or additional crossmembersto be integrated witha spine that is already erected.

This will affect the stiffness on the part of the structurealready erected and consequently,

it will behave differently when subjectedto loadings in its stiffened state. This must be

consideredin large-span bridges, as the effects of deformations and locked-in stresses can

be significant. An incremental loading approachis suggested for analysis that addresses

these changes [20].

Other effects on stresses

BS153, and all other codes on the design of bridges call for consideration of

secondary effects from wind, temperature (uniform and differential), stresses

permanently induced by erectionforces, stresses induced by settlement of supports, and

stresses caused by creep effects in the concrete of the composite deck (Royal

Commission60).

Wind stresses could have been relatively highbecause the half girders would have

not only a larger coefficientof drag than the more streamlinedfull section, but also a

much smaller section modulus for bending in the horizontal plane (Royal Commission

61).


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The bridge is most sensitive to differential temperaturebetween the upper and lower

flanges. And, it is most sensitive to this effect duringthe erection stages before the

concrete deck is placed (Royal Commission61).

The method of erecting spans 10-11 and 14-15 in two halves meant that unless thetwo halves were made with exactlythe same camber, permanently locked-up stresses

would be induced when bringing the two halves to the same level (RoyalCommission

61).

Other erection-inducedstresses would occurif the cantileverswere not set out to the

correct profile,so that theirreactions onto the piers would be other than thoseassumed in

the calculations. There was some evidence that thishad already happened when

cantilevering out from pier 14 towards the temporary prop on the east side (Royal

Commission61).

The concrete deck had been assumed to work in a compositemanner with the steel,

as long as the concrete remained uncracked.The creep of concrete understress would

gradually change the stressdistribution, and this effect also could become significant


FF&P stated that they considered stresses induced by wind and temperature, butdid

not produce calculations showing the effects of these stresses. The wind pressure on the

bridge during erectionwas estimated to be as high as 2.1 tons/in2 (4.6 ksi) at box 17. The

magnitude of the temperature-induced stress depends on the differential, but a rough

estimate could be 1 ton/in2. The permanent stress induced fromreducing the camber

difference between the half spans was approximately1 ton/in2 (Royal Commission61).

While none of the secondary effects are very large, they could have dangerously

reduced the safety margin. The effects probably wouldnot act together for a cumulative

effect at any one point, but it is suggested that certain combinations are statistically

probable and should have beeninvestigated(Royal Commission61).

Strengthening Following the Collapse of the Milford Haven Bridge

WSC found certain areas of the structure where additional stiffening was needed.

According to their calculationssome of this extra strengtheningwas required not only for

the erection conditions but for the service condition as well. Most of the strengthening


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added to the West Gate Bridge after the Milford Haven failure wasfor the strengthening

of details overlookedearlier (Royal Commission59-60).

Since the Milford Haven Bridge was of a somewhat similar designand becuase

FF&P were thedesigners of both bridges,LYCA arranged forG. Maunsell and company

in London, to make an immediate checkof the design of the steel spansin the West Gate

Bridge. Followingthe Milford Haven collapse,certain steps were takento strengthen the

steel spansof the West Gate Bridge (Royal Commission12, 59-60).

The main steps, taken in certain boxes,were:

* doubling thelongitudinal stiffeners

* substitutionof angle splices forthe K-plates

* increasingthe number of bolts in the transverse seam* connectingthe main diaphragmto the outer sloping webs

* additionof 15 in channels as further transverse stiffeners

* additional longitudinaland transverse stiffenersto the outer slopingwebs

* additionof reinforcingplate aroundthe opening forthe main tower in box 17

* massive strengtheningof transverse diaphragms

* concreting in of K-plates on the already erected east span14-15 (Royal

Commission60).

The Report of the Royal Commissionstated that while this stiffening was vitally

necessary, none of it directly affected the section which collapsed. Theyalso believed

there are a number of places in the box girder which would fail to meet the requirement

even after the post Milford Haven stiffening had beenadded (Royal Commission60).

As an example of a more comprehensive design, the planning for the new bridge

crossing the Lower Yarra River included wind tunnel tests, carried out by theaerodynamics divisions of the natural physical laboratories at England and Monash

Universities. The model tests showedthat the bridge would behavesatisfactorilyin wind

speeds of twice the maximumvalue to be expected in a 100 year period (Hitchings 171).


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4.2. Erection

In addition to concerns raised in the design process, there were numerous challenges

encounteredin the erection of steel workfor the West GateBridge.

Bulge

In early September 1970, a bulge was found in the sloping outer web around the

south 8-9 splice. This bulge tookthe form of a dishing inwardsof the web to a maximum

of about 1 1Ain. It covered a roughly circular area witha diameterof about 10 ft, but was

difficult to see because of lighting and the perspective of observers (Royal Commission

29).

It was established that the bulge was the result of a fabrication distortionor an

accident in erection which had gone unnoticed for two months. It was uncertain thatthe

outer web plating had notbecome unstable due to the stresses in it and that the situation

would notworsen as further boxes were cantilevered out (RoyalCommission29).

Transition Curves

The transition curves of the approach viaducts were carried overonto the steel

bridge. The twist of the boxes on the convex side of the curve- the north boxes of span

10-11 and the southboxes of span 14-15 - amountedto 23 minutes of arc (0.38 degrees)

per 100-ft length. To achieve this twist when fabricatingthe boxes, it was necessary for

all the panels involved in the twist to be made as rhomboids, slightly off the perfect

rectangle. In practice the panels themselveswere kept rectangularbut the holes around

the edge were set out on lines whichformed a rhomboid.The use of transition curves on

the steel bridge was seen to have introduced significant complicationin detailing and

resulted in many non-standardpanels (Royal Commission36).

Events Leading Directly to Collapse

As discussed in a previous section, the 14-15 and 10-11 spans were erected by

assembling, lifting and joining half-spans. This methodwas consideredunusual and had

not been attempted anywhere else in the world. Especiallygreat care would have been


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required to reduce any camber difference, but was not exercised (Royal Commission 16),[6].

The Royal Commissionasserts that the difficulty in getting the two half girders to

the correct relative positions throughouttheir lengths was due to the fact that the camber

curves on the two halves were different not only in amplitude but also in shape.

Therefore, even when connectionshad been made at a number of diaphragmsit was still

necessary to use large forces to make the remaining parts fit (RoyalCommission22).

A more detailed descriptionof the events leading to failure, beginning with the

observed differencein camber and resultingin the creation of a hinge was presented in

Chapter 2.

This subsection ends with a simple suggestion for the loosening of the bolts in orderto remove the buckles in the upper flange. Temporary supports below the box girder

would have reducedthe positive bending momentin the middle of the span, reducing the

compressive andtensile stressesin the flanges.The removal of bolts at the center of the

girder, while successful on span 14-15, could be thought to create a hinge if the

compressive and tensile stressesbecome too high. The hinge would create a mechanism,

as the ends of the girder have almostno moment capacity.

The bolts were jammed tightly into their holes afterabout sixteen had beenremoved

in the method chosen;the decrease in moment andin compressive stressin the top flange

through temporary supportsor jacks would have made this job easier and safer.

While this simple tactic would noteliminate the more seriousissues with the design

and erection of the bridge, it would have reducedstresses in the girder whilecalculations

continued to be made and extra strengtheningwas added. More importantly,it could have

saved human life on the site.

Following the October 1970 disaster the erection method of the new bridge crossing

the Yarra River was changed suchthat each box-girder was cantileveredonto an existing

box-girder. Overhead crane and underpinningprops were used to provide extrasafety and

ease of operation (Hitchings171).


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4.3. Comparison of use of concrete kentledges with jacking

This sectionof the chapter quantifies the benefits of jacking to remove the 114 mm

(4.5 in) camber difference found when trying to join the halves of span 10-1 1. Rather

than applying gravity load to reduce the vertical camber of one half span, jacking could

have beenused to increase thevertical camber of the other half span.

The deformnation resulting from the 80 tonne (176.4 kips) load, both modeled as a

point load and as three point loads, was used to estimate the moment of inertia of the half

box section. These values werecompared withcalculations made based on the geometry

of the cross-section. The schemes of kentledge and jack placement are listed and

described below.

* Kentledge Load Scheme 1: The load of the kentledgeswas modeled as a point

load at the midpoint of the span.* Kentledge Load Scheme 2: Four kentledge blocks are placed at the midpoint of

the span and three kentledgeblocks are placed atone third of the length from the

ends. Thisscheme is probably the more realistic of the two kentledgeschemes.

* Jacking Scheme 1: The jacking force is modeled as a point load at the center of

the span. The force is equal in magnitude to and opposite in direction of the

concentratedforce in Kentledge Load Scheme 1.

* Jacking Scheme 2: The jacking force is modeled as a point load at the midpoint

of the span and two pointloads one third the length of the span from theends. The

three forces are equal and were recalculated to achieve the desired displacementat

the midpoint. This scheme is more realistic than Jacking Scheme 1 nd is more

appropriate if a small number of jacks, each with a relatively high capacity, is

available on the site.

* Jacking Scheme 3: The jacking force is modeled as five point loads with spacing

equal to one sixth the length of the span. The five forces are equal and were

recalculated to achieve the desired displacement at the midpoint. This scheme ismore realistic than Jacking Scheme 1 and is more appropriate if there are more

jacks with lower capacityavailable on the site.

Stresses that might result from wind, temperature, erection were each estimated at Iton/square inch, or 6.615 ksi in total (Royal Commission 61). These were added to the


38/96

compressive and tensile stresses at the top and bottom of the flange, respectively, for

conservative treatment. The following graphs and table show the moment and stresses

present on the entire length of the half spans.

Figure 14: Moment under self-weight and kentledges

Figure 15: Moment under self-weight and jacking

Moment Under Self-Weight and Kentledges

U

5000

10000

15

20000

25000E30000

35000

40000

4 5 00 0

-- Self-Weight

S- - Kontledges(Scheme 1)

- Kentledges(Scheme 2)

250 300 3550 100 150 200

Position (ft)

Moment Under Self-Weight and Jacking

0

5000

10000

15000

E

20000

25000

30000

SSelf-Weight

- -Jacking(Scheme 1)

Jacking(Scheme 2)

Jacking(Scheme 3)1

0 50 1 15 200 25 3 35

Position (if)

45


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Compressive Stress in Top Flange:Self-Weight and Kentledges

I

/I

/\\ /\\ /

\ . /

\\ /

\ / //

\ //

N.. . -.. -,, . , , .-

t

-- Self-Weight

K----Kentledges(Scheme 1)

- Kentledges(Scheme 2)

0 50 100 150 200 250 300 350

Position (ft)

Figure 16: Stress in top flange from self-weight and kentledges

Figure 17: Stress in top flange from self-weight and jacking

2

4

6

3 8

C,10

12

14

16

Compressive Stress in Top Flange:Self-Weight and Jacking

0

2

4

6

8

10

Self-Weight

- - - Jacking(Scheme 1)

Jacking(Scheme 2)

Jacking(Scheme 3)

0 50 1 15 200 25 3 35

Position (ft)

.v0 5 1 15 2 25

3 35

Position

(ft)


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Tensile Stress in Bottom Flange:Self-Weight and Kentledges

u

2

4

6

8

A 10

12

14

16

18

20

- Self Weight

- - - Kentledges(Scheme 1)

Kentledges(Scheme )

300 35000 15 200 25

Position (ft)

Figure 18: Stress in bottom flange from self-weight and kentledges

Figure 19: Stress in bottom flange from self-weight and jacking

0 50

Tensile Stress in Bottom Flange:Self-Weight and Jacking

0

2

4

6

8

10

12

-- Self-Weight

--- Jacking(Scheme 1)

-Jacking(Scheme 2)

. Jacking(Scheme 3)

0 50 100 150 200 250 300 350

Posi t ion (ft)

20

0 50 1 15 225 3 35

Position(ft)


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y, (fi) yt, (ft) I (ft) a, , (ksi)5.96 7.33 115.60 6.615

Self-Weight Kentledge Kentledge Jacking Jacking JackingOnly Scheme1 Scheme 2 Scheme 1 Scheme 2 Scheme3

Max Moment(kip-ft) 26674 42880 39639 12905 13141 13728Percent Difference 0% 61% 49% -52% -51% -49%

Top Flange:o (ksi) 9.56 15.36 14.20 4.62 4.71 4.92

plus o, (ksi) 16.17 21.98 20.82 11.24 11.32 11.53

Bottom Flange:a, (ksi) 11.74 18.87 17.45 5.68 5.78 6.04

plus a,,, (ksi) 18.35 25.49 24.06 12.29 12.40 12.66

Table 1: Comparison of moment and stresses from self-weight, kentledges and jacking

Conclusion

Jacking Scheme 1 results in the lowest bendingmoment, and the lowest stresseson

the half span. It may not be feasible to provide one jack with a capacity of 80 tonnes

(176.4 kips), but the goal of the contractor shouldbe to provide the most upward force as

close to the midspan as possible.

Kentledge Scheme1 resulted in the highest bendingmoment, and highest stresses at

the midspan. The worst case arises when concentratingthe downward force closest to the

midpoint- thus, it would be better to distribute the load and keepsome weight away from

the center of the span if weight is used to remove camber.

The stresses calculated in both kentledge schemes are between 14-19 ksi for both

flanges. Yet, when adding the approximatestresses thatmight have resulted from wind,

temperature (uniform and differential) and erection forces, the maximum stresses are

between 20-26 ksi.

The stresses in the top flange of span 10-11 would be the greatest concern during

construction because of the potential compressiveinstability of the flanges working

without a concrete deck. The range of allowable stress given by BS153 for l/r values

ranging from 50-90 is 6.8-10.9 tons/in2, or 15.0-24.0 ksi (Royal Commission59). The

maximum compressive stresses under the two kentledge schemes are just below the


42/96


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5. Other Failures

While box girder bridges offer the benefits mentioned in Chapter 3, they were not

very well understood at the time. Including the WestGate collapse, therewere fourfailures of box girderbridges of somewhat similar designduring construction in different

parts of the world from 1969 to 1971. Remarkably, no two of these failures much alike.

All four, however, were associated with instabilityof thin platesin compression[14].

The main causesof these failures were: a) the application of buckling theory with

inadequate factors of safety, and b) poor detailing rules andthe absence of fabrication

tolerances [14].

The bridges thatfailed were,in chronological order:

* The Fourth Danube Bridge (Vienna, Austria,November6, 1969)

* The MilfordHaven Bridge (now,the Cleddau Bridge) (United Kingdom,June

2, 1970)

* The West Gate Bridge(Melbourne,Australia,October, 15, 1970)

* The RhineBridge (Koblenz,West Germany,November, 10, 1971) [14].

5.1. Fourth Danube BridgeThe Fourth Danube Bridge consisted of twin box girders in three spans of 393 ft, 688

ft, and 269 ft. During construction,bucklingwas foundon both box girders at two points:

at the center of the 393 ft span, and about 197 ft from the right bankpier in the center

span. The resulting shorteningof the superstructure damagedthe abutment bearings and

support at the pier. The closing point,havingonly fourweb plates with small flanges, had

to withstand the full dead weightmoment of the steel loads, andthe web plates were

stressedbeyond the elastic limit.As a result, the smallupper flanges were twisted and the

upper sections of the webs plasticallybuckled(Xanthakos 508).Three causesfor the buckling were expressed:

1) The theoreticalbuckling stress curve used as a basis for the safety checkwas 7%

higher than the actual buckling stresses in the elastic-plastictransitional range, and the

bottom plates wherethe damageoccurredwere within this rangeof maximumdeviation.


44/96

2) Deformations caused by welding seams in the bottom plate and its ribs and

variations in plate thicknessrepresented deviationfrom the assumed ideal straightplane

of the panel.

3) Differential temperature in the deck-steel box system,particularly a temperature

drop during the night, was stated as the principal cause. The roadway deckwas heated

above air temperature under sunshine, but cooling after sunset caused additional

compressionstresses in the bottomplates (Xanthakos 508).

5.2. Milford Haven Bridge

The Milford Haven Bridge, locatedin Wales, UK, had many featuresin common

with the West Gate Bridge, includingthe use of a trapezoidal box girder.It consisted of awelded box girder superstructurewith a main span of 700 ft and was claimedto be

Europe's longest bridge withoutcable support. The trapezoidal box is 20 ft deep, 66 ft

wide at the top,and 22 ft wide at the bottom (Xanthakos507). The box girderwas much

smaller in width but much largerin depth thanthe West GateBridge. It was also a single

cell sectionhaving no internal webs(Royal Commission26).

The collapse, however,was dissimilar to that of the West Gate Bridge in that it

originated at a point of negative moment overone of the columns when a span was being

cantileveredout, whereasin the West Gate Bridge, the failure was ata region of positive

moment near the center of what was, at the time, a simply supportedspan (Royal

Commission 12).

It is clear from the reports of the failure that it was initiated by bucklingof the

support diaphragm at the root of the cantilever being erected. This diaphragm was

subjected to a hogging bending momentand a large vertical shear force.The diaphragm

was torn away from the sloping websnear the bottom of the box, allowing bucklingof

the lower web and bottom flange to take place [14].

The diaphragm plate nearthe outer bottom cornerswas subjected to a complex

combinationof actions. The shearof the transverse girder anddiffusion of the point load

from the bearings was compoundedwith out-of-plane bendingeffects caused by bearing

eccentricityand the effects of inclination of the webs of the main bridge girder which

producedadditionalhorizontalcompressiveaction [14].


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As the diaphragmbuckled it shortened, reducingthe overall depth of the box girder;

the tendency of the bottom flange to buckle was increased by this reduction of distance

between flanges,which increasedthe force needed in each flange to carry the moment

with a reduced lever arm. The weakened section was unableto sustain the momentsimposed and thecantilever rotated about the virtual hinge that was formed (Royal

Commission12).

Xanthakos notesthree unforeseen hazardsin the construction of the Milford Haven

Bridge: a) the diaphragm couldhave been as much as % in out of flat, making it

susceptible to local buckling, b) the bearing on the pier was out of line with the neutral

axis of the diaphragm and could impose bendingmoment, and c) some bolts intended to

be loose in oversized holes were tight, and under loadmovement they couldhave tornthe

longitudinal stiffenersfrom the bottom flange and made itunstable in compression.Inaddition, subsequent calculations indicated that the diaphragmwould be prone to failure

when the reactions at the pier supportingthe cantilevered span exceeded900 long tons.

At the time of failure the reactionwas 963 long tons (507-8).


46/96


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In i l.-.,

Figure 22: Diaphragm over Pier 6 of Milford Haven Bridge

5.3. Rhine Bridge in Koblenz

The center span of the Koblenz Bridge over the Rhine River collapsed during

constructionon November 10, 1971, when erection had almost reached the mid-point of

the 235 m span. The bridge was a single steel box, 16.4 m wide at the top plus

cantilevers,and 11 m wide at the bottom. The box was erectedby cantilevering,with 85tons beinglifted at a time [14].

The bottom flange was stiffened longitudinally by T-stiffeners, and the box was

stiffened transverselyby frames with diagonals made of 300 mm diameter steel tubes. All

site joints were welded, a relatively new techniquein Germany at the time. As shown in

the following figure, a 460 mm gap was provided in the longitudinal T-stiffeners of the

lower flange to permit the passage of automatic weldingequipmentmaking the transverse

butt weld splicing the flange plate.The T-stiffenerwas then itself spliced by welding in

two plates, with the plate splicingthe web of the stiffener being just 460 mm long and

butt welded. To avoid a local concentration of residual welding stresses, this plate was

not welded to the bottom flange of the box, but was set with its bottom edge 30 mm clear

of the flange. The platesplicing the table of the T-stiffener was lappedon top of the ends

of the two T sections [14].

S3 -;JII ~L 410 U,'. 11 -

Elevation Section

,I I


48/96

It was determined that:

* The bottom flange plate, which carriedlarge compressive stresses during

construction, wasunsupportedover a 460 mm length at each site splice.

* The main butt weld in the bottom flange plate was atthe center of this 460 mm

length, possibly introducinga slight lack of straightness.

* The centroid of the splice of the T-stiffener wasalmost certainlyfurther from the

flange than that of the T itself, causing an eccentricity that put the flangeplate undera

larger compressivestress at this point [14].

The followinginvestigation showed thatthe bottom flange platecould carry its stress

safely if out-of-straightnesswas no more than 0.95 mm on the 460 mm unsupportedlength. Infact the plate was out-of-straightby as much as 2 mm at some points[14].

The failure began whenthe flange plate suddenly foldedup at the splice into the 30

mm recess. Much of the stress that should have been carried by the plate was

consequently thrownoff onto the T-stiffeners. They were then takingthree times their

design stress, and they buckled as well, leading toglobal collapse [14].

An inquiry into the failure concluded thatthere had been no negligence. The design

calculationshad all been done correctly accordingto the methods normallyused at that

time in Germany. However, it was the methodsthat needed revision[14].

A report by the Technical University of Karlruhe indicated that the Rhine River

Bridge failed because of inadequate stiffeningacross the transverse weld seam in the

lower flange. Without direct support, the flange plate had a theoretical safetyfactor of

1.79, but in the presence of the smallestwave in the flange platethis factorwas reduced

to 1.0. The conclusion was reached thatthe linear theory used to calculate the critical

buckling stress on the steel plates was inadequate (Xanthakos508-9).


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Figure 25: Schematic diagram of construction joints and their influence on failure

5.4. Impacts on Other Bridges

According to Hitchings, the West Gate Bridge was one of the world's most

troublesome, costly and controversial projects.More than fifty bridges throughoutEurope

were closed down for examination afterthe collapse, and thirty-four of these had to be

strengthened beforebring reopened(5).

One example of a bridge whose design was altered as a result of the failures is the

Erskine Bridge, a box girder bridge which openedin July 1971, spanning the River Clyde

in west central Scotland.It was under constructionwhen the Milford Haven and West

Gate Bridges collapsed. Calculationsin design were remade andit was found that it

would fail tomeet in the middle. As a result, two cable stayswere added to the box girder

structure as support [9].

These failures drew attentionto several fundamental problems associated with the

ultimate limit stateof box girder bridges, such as: a) the margin of safety during

Staggered deck platejoints (3 sections perjoints (3ections per Welded joints between adjacenttrough length) 16m long trough units

Steel plate overjoint in eachstiffener

One open bulkhead per unit (300mm diagonaltubes and cross beams set back from troughjoint)

Prior to failure

Deck flange rotates

After failure

noed bulkhead

ttom flange folds alonga of trough joint


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construction as it relates to theoretical aspectsof failure probabilities,b) the inadequacy

of linear buckling theoryfor sections thatare wide in comparison to their length, and c)

the understanding of the ultimate capacity of partially completed steel box girders

(Xanthakos509).


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6. Behavior of Stiffened Panels

This chapter providesan overview of the modes of buckling of stiffened panels as

understoodfrom 1997 to 2004.

6.1. A contribution to the stability of stiffened plates under uniform compression

(1997)

This paper first presents a comprehensive literature review of research done on the

stability of stiffened platesunder compressive load, covering global (or overall)buckling,

local buckling, ultimatestrength, andsensitivityto imperfection.

Six modes of bucklingare presented:

Mode I (Fig. 26 a) - This mode is symmetric andis commonly knownas global or

overall mode. It occurs whena wide plate buckles together withthe stiffener, which may

be considered "light."

Mode II (Fig. 26 b) - This mode is antisymmetric andis commonly knownas the

local mode. It occurs when the stiffener is flexurally stiff and torsionally weak.In this

case, the stiffener subdivides the plate into several segments of width "S," with

longitudinal edges almostrotationallyfree.

Mode III (Fig. 26 c) - This is an intermediate modethat is possible if the stiffener is

not flexurallystiff.

Mode IV (Fig. 26 d) - This is a symmetric modethat is possible if the stiffener is

both flexurally and torsionally stiff. In this case, the longitudinal edge of each panel is

rotationally clamped,leading to a higher bucklingload for eachpanel than in Mode II.

Mode V and VI (Fig. 26 e and f) - These modes occurif the stiffener is slender and a

torsional bucklingmode or localbuckling of the plate componentsof the stiffener results

without participationof the plate [2].


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ia)- Mode [ ib)- Mode 11

ic0- Mode Ill d)- Mdxle IV

'e)- Mode V (rb- Mode VI

Figure 26: Various buckling modes of stiffened plates

Combinations of these buckling modes are also possible when two or more local

modes interact. Therefore, the buckling mode of the structure depends onthe geometric

characteristicsof the attached stiffener [2].

Despite the wide literature on stiffened plates, littleis known aboutthe geometric

proportionsof the plate andstiffeners requiredto triggerthese bucklingmodes [2].

From a design perspective, it is important to first study the geometric interaction

between the plate and the stiffener elements, and to showthe transitionfrom the overallto the local mode. Then,it might be possible to proportion the structure to either buckle

locally orin a global mode. The ultimatestrengthof the structurecan then be determined

based on this information [2].

The second part of the paper presents theoretical formulations for the stability

analysisof stiffenedplates underuniform compression.The strain energycomponents fo r

the plate and stiffener elements are derived in terms of the out-of and in-planedisplacement functions and sequential quadratic programming is used to find the

buckling load of the structure for the given plate/stiffenergeometric proportions.Theefficiencyof this methodis comparedwith the finiteelementmethod [2].


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6.2. Stiffened steel plates under uniaxial compression (2001)

Stiffened plates under uniaxial compression or under combined bending and

compression can buckle in one of four forms:

Plate-inducedbuckling (Fig. 27 a) and stiffener-inducedoverall buckling (Fig. 27 b):Overall buckling (sometimes referred to as Euler buckling) is characterized by the

simultaneous buckling of the stiffener and the plate. If the buckling occurs with the

stiffener on the concave (compression)side of the plate, overall bucklingis said to be

stiffener-induced.If the stiffener is on the convex side of the plate, overallbuckling is

said to be plate-induced. These two failure modes are typically characterizedby a very

stable post-buckling responsewhere buckling is characterized by a sharp change in

stiffness.

Plate buckling (Fig.27 c):

Plate buckling failure is characterizedby buckling of the plate between the stiffeners,

resulting in a load redistributionfrom the plate to the stiffeners. This failure mode tends

to have a more significant drop in load carrying capacityin the post-bucklingrange than

the overallbuckling failure modes.

Stiffener tripping(Fig. 27 d):

Stiffener trippingis characterizedby the rotation of the stiffener aboutthe stiffener-

to-plate junction. Therefore, it is a form of lateral-torsionalbuckling where torsion takes

place about this junction. As opposed to other modes of failure, stiffener tripping

generally results in a sudden loss of load carrying capacity. Becauseof this suddendrop

in capacity accompanying stiffener tripping,this mode of failure is considered a more

critical failure mode than the other stiffened plate failuremodes previously identified.

However, this failure modehas received far less attention than the other modes [19].


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(d)

Figure 27: Typical buckling modes

The following figure illustrates load versus deformationbehavior of the modes

described above. These relationshipswere also observed experimentally[19].

1.2Overall Buckding(Plate induced)

1 . 0 .--- __ __ _

/ OverallBuckling (Stiffener induced)S 0.8 -... . . - ------------

P 0.6 - - . Plate Buckling

0.4

0.2Stiffener Tripping

0.00.000 0.002 0.004 0.006 0.008 0.010 0.012

U 1/Lu

Figure 28: Load versus deformation behavior

The failure modes observedwhen a stiffenedplate is subjected to a concentric load

consist of overall buckling, plate buckling, or a combinationof these twomodes, referred

to as "interaction buckling." In all the cases investigatedwith stiffened plates subjectedto

axial load only, no failure took place by stiffener tripping. Both the plate buckling and

plate-induced overall buckling behaviors are considered to be stable failure modes,characterized by a very slow decrease in capacity. However, the interaction between


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save significant repair and maintenancecosts over the lifetime of the vessel [8]. These

benefitsmay be related to thoseof usingbulb flatsin bridges.

The investigationof stiffened plates is carried out in three general forms: theoretical,

using classical and emerging theory; numerical, using finite element methods andcomputer-aidedsimulation; and experimental,using stiffened plates under compressive

loading. Most of what is known of the behavior of bulb flat stiffenedplates appears to

come from numerical and experimentalinvestigations. The paper attempts to consider

new theoretical insights into the behaviorof stiffenedplates [8].

Previously, the onlypublishedwork on bucklingbehavior of bulb plates consisted of

Chou (1997), Chou and Chapman(2000) and Chou et al. (2000). Their analysis idealizes

the bulb flat flangeas an equivalent angle flange, treating the bulb flat cross section like a

rectangular cross section with regard to the bulb flat torsional and warping properties.

Danielson and Wilmer show that this idealization creates errorin the calculation of the

bulb flat stiffener's torsional rigidity, resulting in conservative estimates. Finite element

analysis shows that the torque-carryingcapacity of a bulb flat stiffener(with no structural

flaws) is greater than that of an angle stiffenerwith an equivalent area [8].

The authors used an energy method to derive general expressions to predict the

buckling stress due to stiffener tripping of a simply supported rectangular stiffened plate

subjected to axial compression. The onset of stiffener tripping negates the stiffener's

support to the plate panel and leads to the eventual collapseof the structure[8].

For stiffeners with a bulb flat flange, the values predicted with a simple formula are

less than 4% higher than the finite element results [8].

The modesof deflection identified in the paper are:

Mode 1 (Fig. 29 a) - This mode is described as a bending of the web in one half-

wave anda rotation of the flange about a point at the top of the web. There is no flange

bending along its length. This mode could occur when the flange bending stiffness is

large comparedto the flange torsionaland webbendingstiffnesses.Mode 2 (Fig. 29 b) - This deflection corresponds to a significant bending of the

flange and web with no flange torsion. This mode could occur when the flange torsional

stiffness is large comparedto the flangeand web bendingstiffnesses.


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Mode 3 (Fig. 29 c) - This deflection correspondsto the flange exhibiting a

combinationof bending and twistingwhile the web tends to remain straight. Thismode

could occur when the web bending stiffness is large comparedto the flange torsional and

bending stiffnesses. This case is likely to occur when the flange offers little or noadditionalstiffness to the platestructure comparedto the contribution of the web [8].

- -)

Figure 29: Various modes ofdeflection

-


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7. Stiffness Requirements for Stiffeners of Compression Panels

7.1. Research by Choi and Yoo (2006)

In light of the complex nature of the behavior and analysis of stiffened panelsundercompressionthere are few, if any, "hard and fast" rules to their design. Several codes,

including Eurocode,British Standard, and AASHTO(AmericanAssociation of State and

Highway Transportation Officials) specify minimum stiffnesses for transverse and

longitudinal stiffeners of compression panels. However, these requirements are for

narrower box girders with fewer longitudinalstiffeners, compared to the West Gate

Bridge. Thischapter will show that extrapolationof AASHTO requirementsfor single-

cell box girders of larger scales (greaterwidth and more longitudinal stiffeners) is not an

effective method for the designof such a structure.

Choi and Yoo say the AASHTO requirementsare inconsistent. In recent yearssome

confusion has arisen due to the differentrules adopted in the AASHTO specifications

guiding the design of transverse flange stiffeners. Articles10.39.4.4.1 and 10.39.4.4.2

state that the transverse stiffeners mustbe proportionedso that the moment of inertia of

each stiffener aboutan axis throughthe centroid of the section and parallelto its bottom

edge is at least equal to:

I, =0.10(n +1) 3 W3 fs A()E a

where:

w = width of flange between longitudinal stiffeners ordifference from a web to the

nearest longitudinalstiffener

Aj= area of the bottom flange, including longitudinal stiffeners

a = spacingof transverse stiffeners

E = modulus of elasticity

fi = maximum longitudinalbending stress in the flange of the panels on eitherside ofthe transverse stiffeners [5].

Because Af and f, are mutually interdependent, there can be a large number of

combinations of these two parameters thatsatisfy the equation. Therefore, the proper


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choice of the parameters is an iterative process in which the designer's intuition is

significant [5].

The Eurocode specification for stiffness of transverse stiffeners requires a

"complicated iterative process" becauseof parameters thatare interdependentor directlycoupled with It, [5].

Article 10.51.5.4.4 of the load factor design of AASHTO requires the minimum

stiffness fortransverse stiffeners to be:

I s = p t w (2)

where p = 0.125k 3 for n = 1 and (p = 0.07k 3n 4 for n = 2, 3, 4, or 5. k is a bucklingfactor

which shouldnot exceed 4. These rules are the same as those adoptedin the 2 nd editionof

the AASHTO LRFD manual. Morerecently, the 3

rdedition of the AASHTO LRFD

manual uses equation (1) for the design of transverse stiffeners and equation(2) for the

longitudinal stiffeners. It has been suggestedthat equation(2) requires an unreasonably

high value of ridigity, especially when the number of longitudinal stiffeners becomes

large. Choi and Yoo believe that an overly conservative approachhas been adopted

during the course of simplifying and extrapolating the limited research results for

multiple stiffeners. Recognizing this "awkwardness," the latest AASHTOspecifications

suggest that the number of longitudinal stiffeners should be preferably limitedto two.

The authors say that a thorough examination is clearly required to clarify this issueofrequiredminimum stiffness [5].

Yoo et al. numerically identified the minimum stiffnessrequirement for longitudinal

flange stiffeners andproposed a new equation that couldrationally replacethe current

AASHTO design standard. This relationshipis:

I, = 0.3a 2 ntf3w (3)

where a = a / w = aspect ratioof a subpanelof a stiffened flange[5].

The term "subpanel" refers to a portion of a steel panel bounded by adjacent

longitudinalstiffenersor webs and their adjacenttransverse stiffeners[5].

Transverse stiffenersused as bracing members for longitudinal stiffeners should

have sufficient bending stiffness to effectively restrainthe longitudinal stiffeners. This

requirement pertainsto both the "column behavior" model adopted in Eurocode and BS


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5400 and the "plate behavior" approach adopted in AASHTO. As the aspect ratio of the

subpanel is one of the most influential parameters determiningthe minimumstiffness ofthe longitudinal stiffener, it should also be an equally important parameter defining the

required strength andspacingof adjacent transversestiffeners [5].The authors say that there are no reliable design guides that rationally define the

minimum stiffnessrequirement and the spacing of transverse stiffeners,particularlyfor

the "plate behavior" approach adoptedby AASHTO[5].

The data resulting froma series of non-linear incremental analyses and elastic

buckling analyseswas reduced by means of a regression processto extract analytical

equations. The validity of these equations wasthen tested usingthe results of parametric

studies for the minimum stiffness requirementof transverse stiffeners[5].

td)

Lki. udinSlif ener

Sliri

t

-tQ

I=.

IZ= ------A=

ColumnApproximaliin

ip ,

cQ.I

Q = k '

P [) I~c'

(h~) C

Figure 30: Column approximation of a typical stiffened flange

The figure above gives an overview of the column approximation of a typical

longitudinallyand transverselystiffened flange.


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Fig. 30 (a) shows the stiffened flange, Fig. 30 (b) shows the laterallybraced column

approximation, Fig. 30 (c) shows behavior when the transverse rigidity k, is sufficient,

and Fig. 30 (d) shows the simple beam approximationof a transverse stiffener.

In both the "columnbehavior" and "platebehavior" concepts, the roleof a transversestif

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