mit westgate bridge
TRANSCRIPT
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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
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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
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% 1:40 1:40L panddown constanton concaveside
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-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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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
(Royal Commission41).
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
(Royal Commission61).
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
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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
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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.
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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).
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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
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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