KẾT CẤU MỚI TENSIONED BRACED RIBS IN ARCHITECTURAL PROJECTS

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.

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:

T H O M S O N L G T , C O N F L A N S S T E

-H O N O R I N E , F R A N C E , 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 ' /

N o n - L i n e a r Analysis

Fig 1

Fig 2 Thomson, France

Futt W n ,

Ties in compression

Linear Analysis S t e p 1

Linear Analysis S t e p 2

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)

S A N N I C O L A S T A D I U M R O O F , B A R I ,

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. "^C1-*^•jjafiuB• 9'i'_h

Fig 5 Aviary, HK

Fig 6 Aviary, HK

Fig 7 Aviary, HK

Y O U D E AVIARY, H O N G K O N G , 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

2 5 m

1 3 9 m m d i a CHS rib

Fig 10

L O U V R E , 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

C H U R S T A T I O N R O O F , S W I T Z E R L A N D

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

A C K N O W L E D G E M E N T S :

The work of the above projects was carried out by a number of people Those working on the particular topics discussed were:

Thomson J o h n 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

THREE WIDESPAN SPACE ENCLOSURES

Tim Macfarlane and Damian Murphy, Dewhurst Macfarlane and Partners

I N T R O D U C T I O N

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

P H I L A D E L P H I A R E G I O N A L

P E R F O R M I N G A R T S C E N T R E

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

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

B O S T O N C O N V E N T I O N C E N T R E

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

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 the erection and

fabrication process and reduced the overall weight to less

than 20 lbs/sq ft

The isolation of the roof from 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 of the 300 sq ft plan to each hall

The 60' length was established as the ideal length, both

for normal 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' long straight sections The only exception to this rule was the far corner pieces These were lifted as welded cruciform assemblies supported at three nodes by the boundary walls They offered a positional location at the 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 horizontal stiffness due to the natural 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