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This During the last 12 years several of us in Ove Arup Partners, stimulated by the late Peter Rice, have pursued through various projects an interest in tensile systems which provide restraint to slender arches. The most recent of these is the Saga project which John Thornton has presented in a separate paper From Schlumberger to the Dynamic Earth A Sequence of Membrane Roofs 1. paper therefore looks at some of Sagas antecedents. Some of these have cable nets or textile membranes prestressed onto them, others are deadweight glass roofs. In each case it is the geometric stiffness of the tie restraint system which is significant rather than the levels of prestress applied. Each project has relied on the use of nonlinear analysis software to develop and justify structural behaviour. The software is based upon the Dynamic Relaxation technique originated by Alistair Day 2 and it explicitly models the following effects: • Large displacements • Change of stiffness of beam elements due to the axial forces and moments developing within them • Tie and membrane element forces go to zero if they attract zero strain.
297 TENSIONED BRACED RIBS IN ARCHITECTURAL PROJECTS Brian Forster, Ove Arup & Partners, London This During the last 12 years several of us in Ove Arup & Partners, stimulated by the late Peter Rice, have pursued through various projects an interest in tensile systems which provide restraint to slender arches. The most recent of these is the Saga project which John Thornton has presented in a separate paper - "From Schlumberger to the Dynamic Earth - A Sequence of Membrane Roofs" [1]. paper therefore looks at some of Saga's antecedents. Some of these have cable nets or textile membranes prestressed onto them, others are deadweight glass roofs. In each case it is the geometric stiffness of the tie restraint system which is significant rather than the levels of prestress applied. Each project has relied on the use of non-linear analysis software to develop and justify structural behaviour. The software is based upon the Dynamic Relaxation technique originated by Alistair Day [2] and it explicitly models the following effects: • Large displacements • Change of stiffness of beam elements due to the axial forces and moments developing within them • Tie and membrane element forces go to zero if they attract zero strain. Day [3] has described the software and its use in the design development of the first of the following projects: THOMSON LGT, CONFLANS STE- HONORINE, FRANCE, 1985 Here it was required to cover a 100m long x 18m wide internal "street" with a PTFE/glass membrane roof. The buildings on either side of the street have quite different stiffnesses. One is a 2 storey insitu concrete frame, the other a tall single storey steel shed. Directly coupling them together with a purely tensile membrane was simply not sensible because of the scale of the displacement that would be imposed upon the membrane, by the relative movement of the buildings. The preferred architectural solution was to use a closed framework across which spanned tensioned braced arch ribs support panels of membrane (fig. 1). The whole framework was fixed to one building and released from the other. However for reasons of cost the truss was realised as fig. 2 with slender struts forming the bottom member of a 3 dimensional truss with tensile shear bracing. \ ' 50.8kN ' / Non-Linear Analysis Fig 1 Fig 2 Thomson, France Futt W nd , Ties in compression Linear Analysis Step 1 Linear Analysis Step 2 Fig 3 Thomson, France Fig 4 Bukit Jalil Station, KL Day's paper [3] compares the results of using both N-L and linear analyses. The latter involved multiple steps and was awkward and slower to carry out. This was because under wind load loading some of the diagonal ties go slack with consequent changes in the geometric stiffness of the structure. This means when using a linear analysis method the structure has to be re-analysed with those members removed as fig. 3. A larger version of the Thomson roof covers the STAR LRT station at Bukit Jalil in Kuala Lumpur. The station serves the National Stadium and was built for the 1998 Commonwealth Games (fig. 4). 299 SAN NICOLA STADIUM ROOF, BARI, ITALY, 1989 This project was built for the 1990 Football World Cup held in Italy. The architect, Renzo Piano, conceived the stadium superstructure tier as a flying saucer hovering above the arena (fig. 8). So the superstructure and the roof have a simple rounded shape and it was important that the roof be composed as a series of simple calm sunshades. There are 26 of these cantilevering up to 27m from the back of the concrete upper tier. The infilling structure within each canopy is minimal through the use of slender tubular ribs curved to follow the profile of the roof (fig. 9). Each is braced with a system of "chord-ties" - a set of 3 tie rods springing from each end of the rib and joining to the 1/5th points of each arc (fig. 10). Under the downward load the chord-ties act to reduce the buckling length of the rib by resisting its in-plane deformation. Straight lateral tubes, used to stabilise the ribs out-of- plane, complete the framework producing an architectural effect similar to that of a Japanese screen. "itJIf. "^C 1 -*^•jjafiuB• 9' i '_h Fig 5 Aviary, HK Fig 6 Aviary, HK Fig 7 Aviary, HK 300 YOUDE AVIARY, HONG KONG, 1990 This project was named after the eminent botanist and is a sub-tropical aviary situated in an urban park in Central district on Hong Kong island (fig. 5). The aviary straddles a steep sided twisting valley on the lower slopes of the Peak. It was made tall enough to accommodate existing mature trees and consequently has a maximum clear internal height of 30m (fig. 6). Woven stainless steel mesh forms the enclosing skin. This is suspended from a cable net system prestressed against 3 tubular arches. The largest of these is 560mm diameter and spans 62 metres. This equates to a span/depth ratio of 110 indicating the stiffening effect that the cable net provides to the arch (fig. 7). It was found that the bending stiffness of the arch elements in relation to the axial stiffness of the cables influenced the size of bending moments developing in each arch. Simply increasing the arch size attracted more moment. The trick was to use thick wall tubes giving the highest bending capacity (section modulus) but with the lowest bending stiffness (moment of inertia) for cable net stiffness (area). Stability analyses performed on a full model showed that the nets sufficiently constrained the 60m arch to buckle in its second mode. Fig 9 Bari Stadium. Italy 25m 139mm dia. CHS rib Fig 10 Fig 8 Bari Stadium. Italy LOUVRE, PARIS This project, completed in 1994, involved covering the three open courtyards of the Richelieu wing of the museum, to give enlarged gallery space for sculpture (fig. 11). The dimensions of the structural elements were an important consideration in the roof design, not only to reduce the visual 'weight' but also to avoid casting deep shadows at floor level within the new sculpture courts. The courtyards taper in plan and spans vary from 28- 41m. The principal means of support are tied arches with radial ties providing restraint to in-plane buckling of each arch member (typically a 139 dia. CHS). A spine truss mediates between the stiffness of the hipped ends and the interior arches. Fig 11 Louvre, France 302 CHUR STATION ROOF, SWITZERLAND This project was the outcome of a public competition won by architects Richard Brosi and Robert Obrist. The roof is a fully glazed vault covering both railway and bus stations in a single span of 52m (fig. 12). The primary structure is a 10m deep tied arch with intermediate radial ties providing restraint to buckling of the principal compression members. Each "arch" is a pair of 460mm dia. CHS slightly inclined to one another as they pass over the vault but converging elegantly onto a common springing point (fig. 13). The inclination of the ribs when combined with the longitudinal purlins obviated the need for any other bracing. The main support columns occur at 15m spacing and are composed of a pair of 406 dia. CHS and cantilever from below (fig. 14). They were chosen so as to be strong and stiff enough to resist lateral wind but, importantly, not so stiff as to generate untoward resistance to arch spread under snow load or thermal expansion. For a tie braced arch of this type it is not possible to verify stability using a conventional "Code" approach. As with the previous structures the Arup programme FABLON was used to simulate elastic buckling of the framework and capacity checks were performed using a Merchant-Rankine approach in a manner consistent with Code requirements. This project received the ECCS Steel Award of 1993. Fig 12 Chur Station, Switzerland Fig 13 Chur Station, Switzerland Fig 14 Chur Station, Switzerland ACKNOWLEDGEMENTS: The work of the above projects was carried out by a number of people. Those working on the particular topics discussed were: Thomson John Hewitt, Brian Forster, Alistair Day Bukit Jalil Stadium : Tristan Simmonds, Andrew Trotman, Brian Forster Youde Aviary : John White, Amanda Gibney, Brian Forster San Nicola Stadium .Tristram Carfrae, Brian Forster, Peter Rice Richelieu Wing : Alexandre Cot, Alistair Lenczner, Peter Rice Chur Station : Alistair Hughes, Matthew Lovell, Peter Rice References: 1. Taylor W., Thornton J: From Schlumberger to the Dynamic Earth, a Sequence of Membrane Roofs , International Symposium on Widespan Enclosures, University of Bath, April 2000. 2. Day A.S: An Introduction to Dynamic Relaxation, The Engineer 219, 1965. 3. Day A.S., Haslett T., Carfrae T., Rice P: Buckling and Non-Linear Behaviour of Space Frames, First International Conference on Lightweight Structures in Architecture, Sydney, Australia 1986. 304 THREE WIDESPAN SPACE ENCLOSURES Tim Macfarlane and Damian Murphy, Dewhurst Macfarlane and Partners INTRODUCTION We are currently constructing three projects in the USA with roofs spanning between 180' and 420'. The design approach to each roof is fundamentally different and this paper will discuss in broad terms the different approaches. PHILADELPHIA REGIONAL PERFORMING ARTS CENTRE The roof geometry is a classical barrel vault within which two major performance spaces sit as self-contained structures (fig 1). The brief called for a completely glazed roof surface with transparent end walls to the barrel to achieve maximum transparency. The major axis of the vault is 350 ft long and the diameter of the vault is 174 ft. From the outset studies were carried out to find a structural system that would align with the glazing bars to ensure that only the primary system would be visible, to achieve the greatest transparency. A folded plate barrel vault constructed of vierendeel frames was adopted, which allowed for simple flat glass panels measuring 3'2" x 7'1" to be framed onto the vierendeel members (Fig 2). The vierendeel frames are fabricated from 5"x4" and 5"x5" tubes with wall thickness altered to reflect the changes in force between the crown and the springing 305 Fig 2 point. The fabrication process involves constructing 4 segments 1_ folds wide, welded and jigged in the workshop and bolted on site at the member mid points. The sections will all be painted with the finish coat applied prior to erection. Fire protection which was required for the lower 20 ft. of the trusses was achieved using a combination of sprinklers and intumescent paint. The glazed panels will be installed in bands of 3 units on a minimal aluminium frame and the joints between panels will be sealed with site-applied silicon. The total weight of steel is 825 tons which is equivalent to 27.0 lbs/ft2 of plan area. The vierendeel frames provide stiffness in the longitudinal direction as well as the span direction, therefore no additional wind bracing elements are required, resulting in a clean uniform structure. End Wall Design The height of the end walls (Fig 3) varies from 84 ft at the crown to 0 at the springing point. Laminated glass panels _" thick measuring 5' 9"x 4'2" are attached to 7/8" diameter steel cables which are suspended from a steel arch and tensioned by attaching cast iron weights of up to 12 tons to each cable. The cables deflect horizontally under wind load up to 2'8" in the centre and the weights which are attached to the adjacent roof structure via a linked arm move up to 3" vertically to accommodate the deflection of the wall. This arrangement ensures that the load on the steel arch remains constant and that vertical deflection of the arch structure remains unchanged during variable wind pressure. The weights are linked together to ensure that should a cable fail, the weight will be retained in place by the adjacent cables. Wind tunnel studies were carried out to ensure that the load variation in pressure which could occur would not cause unpredictable relative movement between adjacent cables. The project will be completed in December 2001. BOSTON CONVENTION CENTRE The Boston Convention Centre (Figures 4 and 5) will occupy a site some 1800 feet by 500 feet wide with its major entrance addressing the revitalized old dock area and its rear end abutting the finer scale of residential South Boston. Architecturally the 3 storey service buildings and hotels were designed as access strips running down each side of the 5 single storey visitor halls. Each hall measured 300 feet square on plan and with the front end of the building the final 300 x 300 space was a three storey volume with reception and public function suites. The roof to the convention halls and reception area was conceived as a continuous surface 300 feet wide x 1800 feet long, changing in profile from an arched section at the entrance end with its crown 120 feet above ground, to a flat section at the residential end with an elevation of 40 feet. At first sight the roof surface looks like a section of a regular solid. The geometry however was more complex than this and each section through the roof had a different radius, crown and springing dimension. Initially a strategy was developed which separated the roof from the adjacent service buildings and from the bridge elements which connected these structures. This resulted in a number of solutions which involved supporting each individual hall roof with 300 x 300 foot spans from up to eight columns set 60 foot in from the 306 [...]... fourth node for the 4 internal support columns which were then swung into place The remaining members were then lifted into place, building out from the corners using simply supported connections toward the centre defining the roof surface at the connection points, as construction progressed This configuration resulted in a 2-way spanning diagonal co-planar configuration, offering both vertical and... the adjacent service buildings and bridge links was reconsidered It was established that the roof could be supported from and braced by these elements, by introducing a sliding joint that could accommodate thermal movement but was capable of supporting vertical and horizontal wind and earthquake forces Working with a nominal 60' long W14 section, a surface was created by building out from the corners...Fig 6 free edges The columns and steel roof trusses for this structure were inevitably large (each one unique), resulting in average weights of 25 lbs/sq ft for the roof steelwork Value engineering came close to reducing the architectural gesture of a continuous roof plane to a series of flat stepped surfaces At the eleventh hour a solution was found which simplified... transportation and because at the steepest curved section of the roof, a chord of 60' would result in a maximum difference of only 2" between the actual and ideal position of the beam, which could be easily accommodated in the purlin connections The construction involved lifting each steel beam into place, as a planar single 60' long member or as a 120' long trussed element fabricated on the ground from 60'... triangulation inherent in its constructional logic Metal deck on purlins or pre-fabricated triangular panels were then erected to complete the surface The 120' long fabricated king post trusses provided an excellent opportunity to incorporate the service walkways designed to run at 60' centres above the exhibition hall 308 Fig 7 DAVID L L A W R E N C E C O N V E N T I O N CENTRE, PITTSBURGH The initial... convention hall in Pittsburgh took its formal inspiration from the three suspension bridges which cross the Allegheny River just downtown from the building's riverside site (Fig 6) To accommodate site geometry, a trapezoidal plan shape generated three halls 300' long by widths varying from 430' to 320' The cross section of the building resembled a suspension cable bridge cut at mid-span (Fig 7) The principal... (Fig 7) The principal carrying cable started at a height of 74' above ground level and climbed to an elevation of 180' It was supported by a steel mast and by its continuation from the mast to a connection 54' above ground back down to the building frame on its south elevation To coordinate with the ideal grid of 60' at the lower conference hall levels, cables and their supporting frames on the north... become known, were set with this spacing The triangulated bow and stern frames transmitted the tension forces from the main cables to the foundation and to the foundation level/conference hall level couple, which countered the large horizontal forces generated by the suspension cable Tie down cables were introduced to control wind uplift and overall deflection At the principal bridge connection and end... directly to the building structure to limit the cable live load deflection to 8 inches This was necessary as free live load deflection of up to 3 feet would otherwise have been encountered, which would have made the attachment of the vertical walls exceptionally difficult and awkward looking The curved metal roof deck was supported by fabricated metal steel trusses spanning 60 feet onto the main cables The... was supported by fabricated metal steel trusses spanning 60 feet onto the main cables The cables comprising 7 no 3 " strands were designed to carry a maximum tension load of 3,600 kips The mast section was 40" diameter steel and the maximum steel truss sections were fabricated from steel plate weighing 1000 lb/ft