The attack spans of the West Gate Bridge are presently being retrofitted with advanced stuffs in the signifier of C fiber polymer laminates and cloths. This is to account for the planned addition of operational traffic lanes from 4 to 5 each manner.
Related plants from literature is discussed on assorted facets of the structural appraisal and modeling work carried out on the concrete viaducts and minor spans of the West Gate Bridge. This was done with the intent of deriving a better apprehension on the application of Finite Elements plan on Bridgess. A literature reappraisal was besides done on the C fiber polymer engineering.
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Background & A ; recent structural appraisal
Models were developed for both the steel and concrete subdivisions of the West Gate Bridge by the West Gate Bridge Strengthening Alliance in twelvemonth 2009 in order to measure the present capacity of the span and to develop an effectual strengthening option to achieve the coveted burden standards ( Taylor, Percy & A ; Allen 2009 ) . Harmonizing to Williams et Al. ( 2009 ) , the structural adequateness of the span was established with computing machine theoretical accounts which included assorted phases of the Bridgess during their life clip.
Furthermore, Service Limit State ( SLS ) and Ultimate Limit State ( ULS ) design envelopes were generated and assorted cheques were performed with conformity to the Austroads Bridge Design Code ( ABDC ) and AS 5100 design codifications. Harmonizing to Rombach and Specker ( n.d. ) , SLS includes full prestressing ( minimal compressive emphasis of 1 MPA ) and the shear transportation in the articulations. ULS considers the gap of the articulations and the burden transportation in the articulations.
Taylor et Al. ( 2009 ) besides demonstrated the use of Bridge Specific Assessment of Live Load ( BSALL ) and how informations of existent vehicles that travel over the West Gate Bridge was applied in the analysis, local traffic Weigh in Motion ( WIM ) information was developed for the West Gate Bridge beef uping undertaking.
In this literature reappraisal, computing machine theoretical accounts developed on the concrete span constituents ( Eastern and Western Approach Viaducts and the minor spans for the strengthening of the West Gate Bridge will be critically analysed.
Modeling is the doing an idealisation of a existent construction. Rombach ( 2004 ) sees the bulk of finite component method mistakes come from the modeling. Therefore, Biggs et Al. ( 2000 ) has employed several finite component schemes which include several premises to simplify the theoretical account development without any loss in the truth of the representation. Finite component schemes used by Biggs are shown in.
Table. Finite component schemes.
Component of Bridges
Finite Element Representations
Reinforced concrete deck
Shell elements and rebar elements
Radio beam elements
Radio beam elements
Simple supports of multipoint restraints
Surface force per unit area tonss
Consequently, Williams et Al. ( 2009 ) suggested that planetary theoretical accounts of the single constructions of West Gate Bridge were created utilizing chiefly beam elements. Selected parts were modelled utilizing elaborate shell elements in order to detect local effects. Sing the existent 3D geometry of the construction, the effects of the support conditions, phases of prestressing and the impermanent supports used during building are analysed.
Furthermore, Williams et Al. ( 2009 ) introduced the clip component into the building sequence of the theoretical account by including time-dependent effects of the beef uping. Such effects include the weirdo and shrinking of the concrete and steel relaxation.
Biggs et Al ( 2000 ) identified that the complexness of the stuff is the major factor which limits the capablenesss of the finite component method. Similarly, Rombach ( 2004 ) stated that ( Finite Element Method ) FEM is normally based on a linear-elastic stuff behavior with limited redistribution of member forces. In relevancy to the West Gate Bridge, the stuff belongingss of the viaducts were set harmonizing to the span specific design standards developed in January 2008 with measured values ( Williams, Pircher, & A ; Allen 2009 ) . This could be done by taking into history the subdivision belongingss of the constituents such as the shear slowdown belongingss during calculation.
Additionally, lading theoretical accounts which consists of force per unit area tonss applied to adorn elements were created for all lasting and transeunt effects and assorted traffic lading theoretical accounts were considered ( Williams, Pircher & A ; Allen 2009 ) . Study done by Biggs et Al. ( 2000 ) stated that the burden magnitudes corresponded to the tyre tons of a standard AASHTO-type, multiaxle truck, and the burden locations in relation to the tyre footmarks. Rombach ( 2004 ) believes that this may take to an addition of the existent country under burden in the computation of slabs under concentrated tonss.
Williams et Al. ( 2009 ) has performed a elaborate appraisal on the WGB prior to patterning. It is to verify the enforced building strategy through reappraisal of the original design, as-built drawings, building exposure, and interviews with building directors. As clip has been included as a 4th dimension in the manner, the original building theatrical production, the clip dependent effects ( weirdo and shrinking ) , the subdivision geometry and building burden on the suited subdivision belongingss has been simulated into the theoretical account. This was a ambitious undertaking since the viaducts consist of several pre-cast subdivisions erected and prestressed at different stages. However, harmonizing to Taylor et Al. ( 2009 ) , the Alliance has provided a set of ‘as built ‘ drawings to exemplify the completion of the pulling sets and cross mention them with on-site measurings and observations. Therefore, the obtained records are deemed accurate.
Williams et Al. ( 2011 ) on his paper on ‘Carbon fiber retrofitting of the West Gate Bridge ‘ described that the attack viaducts consists of three cell precast concrete box sections which were originally assembled span-by-span to organize a cardinal spinal column. The typical geometry of the precast spinal column section demoing tendon locations can be seen in.
Figure. Typical spine girder unit.
Impermanent supports were positioned under the first unit of the spinal column girder and the following span was constructed in the same technique. Precast cross cantilevers stick out at right angles from the spinal column to keep the staying breadth of the deck as shown in. These were erected and post-tensioned to the cardinal spinal column in order to transport a concrete slab constructed from precast panels and insitu concrete.
Figure. Placement of pre-cast subdivisions, transverse cantilevers and deck slab.
A position of the complete theoretical account of the eastern viaduct is shown in and a position of the span from underneath is shown in.
SOFiSTiK pre-processor ( based on an AutoCAD meat ) was used to execute construction input and the consequence of lasting tonss of the WGB ( Williams, Pircher & A ; Allen 2009 ) . Taylor et Al. ( 2009 ) sees SOFiSTiK as a finite component analysis and design bundle which allows for the integrating of building phase analysis, full 3D prestressed geometry definition including un-bonded sinews and clip dependent effects due to crawl and shrinkage. Additional burden conditions and analysis were evaluated in the theoretical account with a combination of graphical user interface and script linguistic communication of SOFiSTiK. Rombach ( 2004 ) sees that the design of a span is normally done individually for the transverse and longitudinal waies. Consequently, Taylor et Al. ( 2009 ) has presented both independent longitudinal analysis theoretical accounts and the transverse theoretical accounts for the concrete viaducts. The theoretical accounts and their confirmations are detailed in the undermentioned subdivisions.
Figure. Model of the attack viaduct on eastern side.
Figure. Bottom of the completed span – photographic position and elaborate theoretical account.
As discussed in Section, the original building procedure consisted of a span by span sequence. Detailed 3-dimensional line theoretical accounts were developed for the appraisal of the longitudinal behavior of the Western and Eastern ( as shown in ) . Harmonizing to Rombach ( 2004 ) , the span is modelled as an ordinary beam in a longitudinal theoretical account with a stiff cross-section with no deformations due to flexing or shear. It is so used to gauge the longitudinal, shear and tortuosity supports, the relevant support forces, the emphasiss, and the warp of the span.
In the context of WGB, the theoretical account for the concrete viaducts were integrated with the latest external prestressing beef uping plants aboard with the corresponding clip dependent effects to supply the ability to measure the consequence of the recent strengthening ( Taylor, Percy & A ; Allen 2009 ) .
Figure. Longitudinal Sofistik theoretical account.
In this theoretical account, Taylors et Al. ( 2009 ) have besides performed the influence lines rating for unrecorded burden application and super-positioning. The consequences were so confirmed against simplified SpaceGass theoretical accounts and close truth was found. From the longitudinal manner, important consequences obtained included the utmost fiber tensile and compressive emphasis ratings sing shear slowdown effects. The ultimate flexural, shear and torsional opposition were besides obtained.
Rombach ( 2004 ) analyzed the cross behaviour of a span by patterning the truss component of a ‘1 metre ‘ broad subdivision of the span. The variable deepness of the beams and the disposition of the axis of gravitation are taken into history. Similarly, cross analysis theoretical accounts by Taylor et Al. ( 2009 ) consist of a combination of home base and beam elements ( see ) . Plate elements were used to pattern the spinal column while beam elements were used to pattern the cantilever beams. These theoretical accounts typically simulated the original building sequence and included the clip dependent effects due to crawl and shrinkage.
This modeling by Taylor et Al. ( 2009 ) was besides undertaken utilizing Sofistik. It allowed for the combine of beam and home base elements with the integrating of building phase analysis, the 3D prestressed geometry and including the clip dependent behavior of concrete every bit good.
Figure. Local Sofistik theoretical account.
The purpose of these analyses was to gauge the cross flection of the spinal column and the capacity of the precast cantilever. Besides forces and minutes, the fiber tensile and compressive emphasis, ultimate flexural capacity of the precast cantilever beam were analysed exactly. The consequences of the appraisal were by and large in line with what was expected after the consequences were verified against simplified manus computations and SpaceGass theoretical accounts
The minor spans were designed and constructed as composite Bridgess with longitudinal steel I-sections and concrete deck slabs ( Williams, Pircher & A ; Allen 2009 ) . Detailed computing machine theoretical accounts were generated by sing the clip lines and building sequence ( ) . The subdivisions were modelled in consideration for the strains due to self-weight of the steel girders and the weight of the wet concrete during building prior to the hardening of composite province. As with the attack viaducts, assorted traffic lading theoretical accounts were considered in order to guarantee that the Bridgess are equal to transport the needed traffic burden.
Figure. Model of the Minor Spans.
Taylor et Al. ( 2009 ) stated that theoretical accounts of WGB were wind tunnel tested at the clip of its design in 1973. However since some of the strengthening options and proposed ascents will change the cross sectional profile of the span, it was considered indispensable to re-evaluate the span ‘s aerodynamic stableness. Therefore, Williams et Al. ( 2009 ) have re-evaluated the air current analysis of the WGB. A computational fluid kineticss ( CFD ) theoretical account of the cross-section was built in order to analyze the air current lading on the span utilizing an input in SOFiSTiK called crosswind. Wind effects due to sidelong air current applied at different angles ( see ) were examined. The consequences of these analyses were compared to the inactive air current burden as defined in the AS5100 and AS1170 design codifications.
Figure. Wind speed field around cross-section at -10 deg onslaught angle.
It is the nature of long span Bridgess with aerodynamic subdivisions that comparatively little alterations in certain sensitive locations along the span can hold a distinguishable consequence on the span ‘ behavior.
Analysis of structural appraisal
This subdivision will reexamine the proficient analysis and consequences obtained from the finite component theoretical accounts used to measure some of the of import features of the span behavior.
The viaducts were modelled and analysed as both a complete longitudinal series of beam elements over their full lengths and besides utilizing localized beam and home base elements.
Williams et Al. ( 2009 ) considered several attacks in analysis of the constructions for traffic burden. Similarly, Rombach ( 2004 ) agrees that assorted burden instances have to be considered in the design of a span construction. The burdens have to be combined in the most unfavorable mode. The relevant placement of the traffic loads such as acle tonss can be considered in two different ways. First, one can ‘drive ‘ the traffic tonss by the computing machine over the span in all different lanes. This consequences in tremendous figure of burden instances and a major computational attempt. The applied scientist has to cognize in progress which parts of the construction should be loaded to acquire the greatest member force. The constructions were foremost analysed for current burden conditions harmonizing to ABDC and AS5100 burden demands on 8-lane constellations. It is to make a baseline apprehension of the bing emphasis province. This attack so modified to the BSALL burden to be run over the 8-lane constellation and the proposed 10-lane concluding constellation after beef uping.
Once all inputs were elaborate and checkered, end product secret plans and tabular arraies were created to find beef uping options. Harmonizing to Williams et Al. ( 2009 ) , analysis for SLS emphasiss was able to supply secret plans of upper limit and minimal compaction and tenseness in the utmost fibers of the subdivision as seen in. These were oriented along the layout of the span profile to supply speedy mention to countries of involvement and targeted beef uping plants ( ) . Similiarly, The ULS forces used the gross subdivision belongingss and provided use factors alternatively of emphasiss.
Figure. Effective ( dark ) and gross cross-section in longitudinal way.
Figure. SLS stresses along the bottom fiber of the western viaduct.
Rombach and Specker ( n.d. ) have identified the critical subdivisions under the ultimate tonss as shown in.
Table. Critical subdivisions.
Mid of span
Greatest bending minute
First articulation after support
Great shear force but prestress force non uniformly distributed in cross-section
High concentrated tonss due to anchorage of sinews
High concentrated tonss due to sinews
Development of beef uping options utilizing extra longitudinal station tensioning was carried out following the same logic as for the original building. In parts of disobedience, such as tenseness in the bottom fiber of the spinal column girder at SLS, extra external web sinews were provided to better this tenseness ( ) .
Figure. PT stress diagrams.
Rombach and Specker ( n.d. ) proposed that the distortion features and bearing capacity of segmental Bridgess are subjected to the gap of the articulations, the local contact between the sinews and the concrete at the anchorages and deviators. Harmonizing to their findings, existent articulation can merely reassign normal and shear forces under compaction. As the normal emphasis becomes positive due to flexing, the joint contact is broken and no force is transmitted. Therefore, a simple non-linear stress-strain relationship is used for concrete harmonizing to ideal fictile theoretical account for the sinews. Similarly, Megally et Al. ( 2002 ) stated that contact elements at the interfaces allowed the compaction forces to develop at the articulations, but eliminated tenseness forces. In world, the epoxy between the sections does transport some tenseness until either the epoxy or the next concrete interruptions. The post-tensioning strand was modelled utilizing nexus elements which resisted merely axial force and provided the tenseness constituent necessary to defy the minutes created by the burdens.
Megally et Al. ( 2002 ) besides proposed that FEM used a linear-elastic constituent theoretical account for the concrete and did non account for any fictile distortions of the concrete or for suppression of the concrete. Besides, the research besides suggested that the burden on finite component theoretical account was terminated when the gap of the Centre articulation reached a point where the contact country was smaller than the contact elements. A complete concrete constituent theoretical account would hold to be created, and the computational demands would increase well.
By sing the premises and imitation of FEM by old research in this peculiar field, patterning by Williams et Al. ( 2009 ) has allowed for design optimization by changing the figure of strands per sinew every bit good as modifying the perpendicular beginnings to maximize eccentricities ( ) . Plots were automatically updated and consequences presented in a mode that enabled easy comparings. The long-run behavior of the strengthening was besides considered in this optimization procedure.
However, analysis by Williams et Al. ( 2009 ) has failed to turn to the chief behavior of the span under normal bending. Research by Rombach and Specker ( n.d. ) shows that when the span construction is under full compaction, segmental span behaves linear elastic like a massive one. Joints start to open and the warps exhibit a non-linear growing as the stiffness decreases. Failure occurred when sinews start to give and the impersonal axis is shifted into the top slab, doing the concrete to oppress.
Figure. 3-D representation of PT layout.
Transverse theoretical accounts
The localized transverse theoretical accounts allowed for a elaborate scrutiny of the single elements in the viaducts. Local wheel and axle tonss in assorted locations and combinations were considered to find the most utmost behavior of the deck, cantilevers, and spine girder webs and rims ( ) .
Figure. Local wheel burden of a deck subdivision.
Combinations were besides made to analyze planetary system behaviour by utilizing technology procedures uniting per centums of planetary and local forces. These theoretical accounts were besides used to analyze the effects of impermanent building lading including impermanent barriers and entree gauntries. Rombach ( 2004 ) believes that an insertion of the values of different support conditions ( to the full or partly restraint at the web supports ) and the location of the individual tonss is required. However, such analysis is more time-consuming than and FE analysis.
Harmonizing to Tang ( 2000 ) , the transverse analysis has assumed four series of finite-element trial tallies under different conditions. Test A assumed that minor clefts exist in the sheathing. Test B was analysed under the status of nothing snap and perfect bonding. One major longitudinal cleft bing in the sheathing was assumed for Test C. Test D examined the effects of temperature gradients merely.
The minor spans were modelled and subjected to lading utilizing a similar attack to what was performed on the concrete viaducts ( ) . Design lading envelopes were created to compare against subdivision capacities and plotted along the associated members to see countries of involvement. Additional capacity cheques were besides performed utilizing design spreadsheets and grillage package to verify the consequences from Sofistik.
Figure. Lane lading including UDL and point tonss.
Detailed 3D theoretical accounts of the wharfs were used to guarantee the capacity under the BSALL traffic lading for the 10-lane constellation was non exceeded. Non-linear concrete behavior and 2nd order effects were taken into history for these cheques ( ) .
Figure. Typical wharf theoretical account.
Wind lading in conformity with AS5100 and AS1170 was used for the elaborate modeling work. A CFD theoretical account was nevertheless set up to look into loading conditions on the deck at SLS and ULS air current speeds and to compare these burdens to those used. It was found that the disposition angle of the air current had a strong influence on the ensuing burden. However, in general it could be confirmed that the CFD theoretical account produced less conservative values.