Post-tensioned Thin Shells

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Tailor Made Concrete Structures – Walraven & Stoelhorst (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47535-8

Thin post-tensioned concrete shell structures

S. Dallinger & J. Kollegger

Institute of Structural Engineering, Vienna University of Technology, Vienna, Austria

ABSTRACT: Shells are optimal structures. They can carry maximum loads over long spans on all scales, fromnano-tubes to cooling towers with a very low amount of construction material. Today the use of shells is gainingmore importance in architectural designs for facades interior design and roof structures. For the creation of largesurface structures a viable connection technique is necessary. The connection of the elements will be established

by post-tensioning. This allows for a blunt connection, that is able to transfer normal forces and moments acrossthe connection. This connection technology was tested in experimental investigations. Finally, a feasibility study

was carried out by erecting a very slender arch using this connection technology.

1 INTRODUCTION

Shells are natural, logical and functional load carryingsystems. Nature has always been using these structureslong before architecture even existed. Examples areegg shells, nuts, beaks and cranial bones. If a space issurroundedby a minimal area of surface, theshellis thelogical optimum. Additionally, for the load transfer of

an uniformly distributed load, the shell structure is the perfect choice because mainly normal forces appear in the cross section (Billington 1965). Also in today’sarchitecture shells are very popular because of their elegant and spectacular design (Heinle and Schlaich1996).

2 CONNECTION TECHNOLOGY

Glass fibre and textile reinforced concrete are espe-cially suitable for shell structures due to their excellent

mechanical properties and their pronounced ductility.The use of textile reinforcement (Brameshuber 2006),(Hegger et al. 2006), increases the tensile strength of concrete which is low compared to its high compres-sive strength. Consequently, this composite materialis able to carry compressive and tensile loads withoutthe use of steel reinforcement. For thin shell concretestructures steel reinforcement is not applicable, as therequired concrete cover of 2 cm to 3 cm cannot beachieved. As textile reinforcement is not corrosive, therequired concrete cover only needs a thickness of threeto four millimetres.

This kind of concrete is usually produced as thin

prefabricated panels (Hegger et al. 2005), (Pachowand Lind 2004) with dimensions, which are suitable for

Figure 1. Plane surface structure element with post-tensioning cables.

transportation. For the creation of large surface struc-tures a viable connection technique, which is ableto transfer normal forces and moments across theconnection, is necessary.

Normally concrete elements are connected by the

grouting of overlapping steel reinforcement. If pre-fabricated elements and sloped surfaces are used, thistechnology will be very time-consuming and cost-intensive. This paper shall introduce a new joiningmethod, which makes it possible to connect prefab-ricated parts of glass fibre and textile reinforced concrete elements by means of post-tensioning. More-over, the advantages of post-tensioning are of use.

The key element of this joining technology con-sists of using pre-fabricated elements which areequipped with ducts during their production. Figure 1shows a plane surface structure element with tension-ing ducts and pre-stressing cables in one direction.

On-site these prefabricated elements are joined by post-tensioning cables. These post-tensioning cables

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Figure 2. Arch made of four curved surface structureselements.

are passed through the ducts to apply the post-tensioning to the elements. Figure 2 shows an archmade of four single curved surface structure ele-ments. In this figure the tensioning ducts and the

post-tensioning cables, which cross all four elements,are presented. Due to this preload force thewholecrosssection experiences compressive stress. Therefore, thestructure, which is made of several separate elements,acts like one monolithic structure – as if fabricated inone pour.

With this technology plane as well as single or dou- ble curved surface structures can be created. For theconstruction of shells it is advisable to generate a biax-ial post-tensioning state. This can be achieved by twoorthogonally arranged sets of post-tensioning cables.

By the post-tensioning process a state of compres-sive stress is created in the concrete. The external load has to reduce this compressive stress before tensioningstresses andcracks canappear. Structures made of con-crete, which stay free of cracks, have a higher exten-sional and bending stiffness than structures showingcracks. Post-tensioning causes the cracking of the con-crete under a higher external load and therefore thestructure experiences less deformation. Especially for thin walled surface structures, which have a non-linear load-deflection behaviour, this advantage can be veryuseful. On the one hand the deformations caused by

the external load can be minimised, on the other hand the stability of the construction can be improved.This new construction method and technique is

suited for application, when a fast erection on-site isrequired and the time-consuming setting up of form-work is not possible.The pre-fabricated parts areeasilytransported and assembled in dry construction, whichreduces the construction time on-site as well as thecosts.This technique also enables easy and fast assem-

bling and disassembling and is therefore a techniquefor temporary buildings, like pavilions and exhibitionhalls. Due to the formability of the surface structureelements, applications in the field of architecture are

infinite and enable architects to design a wide rangeof structures. Particularly for shells a fast, simple and

inexpensive building method is essential so that infuture these structures, which are fascinating becauseof their shape and thinness , are going to be used more often. Applications for shell structures can befound in various f ields of infrastructural facilities.Especially for pavilions, exhibition halls, stadiums,

churches and government buildings, where aesthet-ics and elegance are of enormous importance, shellsare favoured. Moreover, this joining technology can

be used in the field of facade technology, for curved roofs and lost formwork as well asin other fields wheredouble curved surfaces are requested.

3 EXPERIMENTAL INVESTIGATIONS

Two experimental series and one feasibility study onthe described joining technology were carried out. The

aim of the first experimental series was to detect theessential mechanical properties of the used glass fibrereinforced concrete plates. The second series consisted of testing the joining technology. To arrive at a sig-nificant conclusion, these first experiments dealt with

plane surface structures. By using these plane surfacestructures experiments are easily carried out becausemembrane forces do not have to be taken into accountand boundary conditions are clearly defined. The sim-

ple execution of the test and the simple state of stress inthe test specimens allow a better evaluation of the fail-ure mode and an exact identification of the mechanical

properties. Moreover, a feasibility study was carried out by erecting a very slender arch with the new con-nection technology. It is important to mention thatthese experiments are preliminary tests on this con-necting technology for thin post-tensioned concreteshell structures. Further experiments, especially ondouble curved surface structures, are planned.

3.1 Experiments on the connecting technology

In this experimental series, plane surface structure ele-

ments were joined together by post-tensioning and were then tested in a four-point-bending-test. Everytest specimen consisted of four plates. Each of these

plates had a dimension of 375× 270 mm and a thick-ness of 13 mm. During the production three tensioningducts were established in each plate. One duct waslocated in the centre of the cross section and the other two were situated in a distance of 125 mm. For theseexperiments the ducts were laid out eccentrically sothat the distance between the centre of a tensioningduct and the top surface with compressive stress in thetests amounted to 10 mm. The cross section of such a

plate is shown in Figure 3.

Four of these plates were connected with three post-tensioning cables with a diameter of 5 mm to one plate

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Figure 3. Half of the cross section of a plate with ducts in adistance of 125 mm.

Figure 4. Stress distributions in the cross section of the plate and in the interface due to post-tensioning and externalmoment.

of 375×1080 mm. The tensioning cables of speci-men 1 and 2 experienced a force of 3 kN; the posttensioning force of specimen 3 and 4 was equal to7 kN. These connected plates were tested in a four-

point-bending-test with a span of 930 mm. The applied forces as well as the displacement in the centre of thespecimen were measured. The connection is capableof transporting compressive and tensile forces as well

as bending moments. Figure 4 shows the stresses in thecross-section of a plate without cracks and in an inter-face. The cross section experiences a post-tensioning( P ) and a bending moment ( M ).

If the superposition of these loads ( P + M ) resultsin compressive stresses only then all interfaces remainclosed and the connected plates act like a monolithic

plate. Therefore a certain amount of tensile stress can be transported over the interface as long as this tensilestress is smaller than the compressive stress created

by the post-tensioning. However, if tensile stresses asa result of the superposition of the loads ( P + M ) occur

in the interface, it opens. Compared to the interface,the plate can at least bear a small amount of tensilestress – the tensile strength of the glass fibre or tex-tile reinforced concrete. Therefore the interface willalways open before the concrete starts to crack, whichleads to the ductile behaviour of the system.

Figure 5 shows the load deflection diagram of thefour experiments. No sudden failure can be detected in the specimens and in the area of the maximum load they behave almost ductile.

At the beginning the load deflection curve showed rising linear behaviour until the interface in the centreof the plate opened. The higher the post-tensioning,

the higher the force which caused the interfaces toopen. Afterwards the behaviour was not linear any

Figure 5. Load-deflection diagam of the connected plates.

Figure 6. Specimen prior to failure.

more because the interface between the plates contin-ued to open. The point at which the interface opened,the maximal load and the beginning of the burst out of the tensioning cables is marked in Figure 5.

This kind of failure was identical for each of thespecimens. The interface in the middle of the spanopened even wider by the increase of the deflec-tion. The other interfaces did not open because theyexperienced a smaller bending moment. Furthermoreno important deflections or scratches in the concrete

plates could be noticed. Thus the interface in the mid-dle of the plate defined the deflection figure as theother areas of the plate remained plane. The deflec-tion figure is almost V-shaped, shown in Figure 6. The

total failure occurred at a very high deflection level;the deviation force in the interface increased until thetensioning cable finally burst out of the concrete, asshown in Figure 6.

3.2 Arch made of curved surface structure elements

A feasibility study was made by erecting a very slen-der arch using this connection technology. For thisexperiment curved surface structure elements were

joined to one arch. This arch consisted of 39 ele-ments, with a size of 200× 100 mm and a thickness

of 13 mm. During the production of the curved sur-face structure elements flexible tensioning ducts were

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Figure 7. Axial force N, moment M and transverse force Q built up in an arch by centric post-tensioning.

inserted. Every element was equipped with one ductwhich was situated almost centrically. The bending of the elements was generated by placing the fresh con-

crete slabs on single curved formwork. The rise of the100 mm long elements amounted to 0, 7 mm onlyand is therefore a barely visible curving for these smallelements.

The 39 curved surface structure elements were kepttogether by one post-tensioning cable with a diameter of 5 mm.The post-tensioning force was increased untilthe interfaces were closed, a compression stress in theinterface was generated and the whole arch acted likeone monolithic structure.

As a result of centric post-tensioning in plane or curved shell structures – which aresupported restraint-

free – no external force appears. These structures onlyexperience a shortening along the centre line. This isalso applies to laminar centric post-tensioning struc-tures. Figure 7 shows the stress resultants of an arch,made of curved elements and experiencing centric

post-tensioning.Figure 8 shows the arch after the erection. The arch

has a span width of 3300 mm and a rise of 940 mm,therefore the arc length amounts to approximately3960 mm. From Figure 7 it can be noticed that this archis very slender. The slenderness describes the ratio of radius to shell thickness and amounts to 147,whichis a very high slenderness ratio. In comparison, theshell of an egg only has a ratio of approximately 60(r/t= 24 mm/0, 4 mm).

4 CONCLUSIONS AND FUTURE PROSPECTS

The production of thin post-tensioned concrete shellsusing prefabricated elements which can be connected

Figure 8. Post-tensioned arch made of 39 curved surfacestructure elements.

on site, will turn out to be a cost-effective, easy and time-saving method. For this construction procedurethe joining technology is of great importance. On theone hand an easy handling is required and on the other hand forces and moments have to be transported over the interfaces. This innovative joining technology for thin shells with post-tensioning presented in this paper shows that theconstructionof plane andcurved surfacestructure elements is possible and moments as well astensile forces can be carried across the interfaces.

REFERENCES

Billington, D. P. (1965). Thin Shell Concrete Structures.McGraw-Hill Book Company.

Brameshuber, W. (2006). State-of-the-Art Report of RILEM Technical Committee 201-TRC: Textile Reeinforced Con-crete. Ibac – RWTH Aachen University, Germany.

Hegger, J., W. Brameshuber, and N. Will (2006). Textile Reinforced Concrete: Proceedings of the 1st Interna-tional RILEM Symposium. RILEM Publications S.A.R.L,Aachen.

Hegger, J., N. Will, and S. Voss (2005). Extreme thin facade panels made of textile reinforced concrete. Concrete Plant + Precast Technology 2, 56–57.

Heinle, E. andJ. Schlaich (1996). Kuppeln aller Zeiten – aller Kulturen. Deutsche Verlags- Anstalt, Stuttgart.Pachow, U. and D. Lind (2004). Glassfiber-reinforced

concrete/textile-reinforced concrete: fundamentals, pro-cesses and applications. Concrete Plant + Precast Tech-nology 1, 18–30.

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Post-tensioned Thin Shells

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