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RELIABILITY OF REINFORCED CONCRETE SHELL STRUCTURES

I. Bucur-Horváth, A. Hedes

Technical University of Cluj-Napoca, C. Daicoviciu Street 15, 400020 Cluj-Napoca, Romania

[email protected], [email protected]

ABSTRACT

The paper is going to follow the shell structures evolution in a historical perspective, necessary to draw correctconclusions on the present state of art concerning theoretical and practical aspects of using reinforced concreteshell structures. Researches put into evidence the mechanical reasons of creating membranes. That is to induceas much as possible a membrane state of stresses in the shell structure. The relation between form andmechanical behaviour of the shell structures is emphasized in general and on some examples in particular aswell, in order to put in evidence the great possibility of influencing the reliability of shell structures by form andconstructive conceiving. Actual problems of the mechanical modeling and computing are discussed.Considerations about reliability and the main fields of using reinforced concrete shell structures are related.

Keywords: Shell structures, history, structural forms and mechanical behaviour, reliability.

1. INTRODUCTION

The compressed curved structural forms are well known from ancient times. As well, vaulted and domestructures made of compressive-resistant materials (stone, roman concrete, brick) are accompanying the wholedevelopment of the architectural forms [1]. The revival of the resistant carcasses as shell structures coincideswith the epoch of the reinforced concrete affirmation in the second half of the 19th century. Due to its specialqualities, constructors and innovators were competed each other in finding rational fields of application of thenew material. Among the issues, one of the more important structural achievement was that of reinforcedconcrete thin shells: recipients (reservoirs, water towers, silos), shell roofs and also hydro-constructions (dams).An entire technical innovation movement and scientific emulation was created in connection with the reinforcedconcrete objects generally and with the reinforced concrete shells especially at this time. The above mentionedtechnical innovation and scientific development met some immediate needs dictated by the general socialdevelopment of the end of the 19th century in Europe. Thus, a large urban developing was accompanied by

infrastructure constructions (water supply and sewing systems) requiring tanks and water towers of greatcapacity and good quality. The process has continued during the first decades of the 20 th century. At the sametime, an important industrial as well as social-cultural development took place, requiring new establishmentsassociated with large covered spaces like industrial halls, market halls, theaters, exhibition halls, gymnasiumsetc. Studying the further development of the shell structures during the second half of the 20th century, especiallyat fifties and sixties, one can find out an intense process of new form finding and researching of reinforcedconcrete shells. This period is marched by great achievements (Torroja, Nervi, Esquillan and others). The lastfew decades introduced the incisive concurrency of the lightweight structures in bridging large spans. Even so,the numerous varieties of structural form and large functional offers make to go successfully on with the thinshell structures.

2. HISTORICAL RETROSPECTIVE

The roots of the shell, respectively cupola building can be found in the ancient dwelling constructions. Theearliest ancient shell structures, dwellings and other buildings were put into evidence by archeologicaldiscoveries. Examples are comprised in the Table 1.The inhabitants of the oldest town of the world we know, Jericho (8th millenary BC), lived in houses of circular form [2]. Over the circular plane a cupola-form covering of clay-bricks was erected. This kind of house can beillustrated by a dwelling from Northern Cameroon. Remains of such constructions were discovered in many

points of the world (China, Egypt, Cyprus etc.). Architects of antique Egypt and Mesopotamia built dome andvaulted masonry structures of stone or brick. There are also exemplified.The cupola and vault building was improved by the Romans. Their domes and vaults were built of stone or/and

traditions another way of vaulting was developed in the New Persian Empire, the so-called Sassanide technique.Examples of these technical improvements are presented in the Table 2.Afterwards the vault and especially the cupola as structural form, accompanies the whole thread of architecturaldevelopment (Early Christian, Byzantine, Islamic, Roman, Gothic, Renaissance, Baroque and Eclecticarchitecture). Along this well-known historical period characterized by many new formal and technical

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mechanical behaviour of the structure, to take over the tensions respectively. Let see some examples (Table 3).

Table 1. Ancient dome and vaulted structuresCONSTRUCTION

DATE

REFERENCES

TECHNICALDATA

1. Type of ancientdwelling(North-Cameroon)[2]

Cupolas of clay- bricks

2. Vault of stoneDashur Egypt3504 BC[3]

Simple vault of stone

3. Forth of Babylon6th c. BC[2]

Row of brick vaults

Table 2. Technical improvements on ancient domes and vaultsCONSTRUCTION

DATEREFERENCES

TECHNICALPERFORMANCE

1. Theatre of Pompeius

Rome63 BC[4]

Vault of opus ceamentitium,opus reticulatum wall building technique

2. Tempio dellaTosseTivoli115-125[4]

Spherical dome of opusceamentitium caste on built instone shuttering; forerunner

of Pantheon

3. Reception hall

(Iwan) of Royal PalaceKtesiphon (New PersianEmpire)241-272[5]

Cylindrical masonry vault of brick and high quality mortar;Special technique of vaultingwith successively builtinclined arches;

L = 25 m

Giacomo della Porta, the last constructor of the cupola of Basilica S. Pietro in Rome, raised the profile of thedome in comparison with that designed by Michelangelo in order to decrease the horizontal thrusts. At the sametime, the tambour was strengthened with an iron ring. Later on (1743-1744) Vanvitelli built in the basic tambour another five metallic rings as a result of the mathematical analysis performed by three mathematicians,

-1710) is alate Baroque building with Eclectic singes. Also in this case metallic bars were built into the basic ring of the

cupola. The pilgrimage church Vierzehnheiligen (1743-1774), masterpiece of the Middle-European Baroque iscovered by flat elliptic cupolas intersecting each other. The whole vaulted ensemble consists of tuff-stone laid ona mortar bed with a regular steel reinforcement.

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Table 3 Reinforced stone cupolas and vaultsCONSTRUCTION

DATEAUTHOR(S)

REFERENCES

TECHNICALPERFORMANCE

1. Cupola of Basilica S.PietroRome1588-1593D. BramanteMichelangeloG. della Porta[1] [2] [6]

High cupola with basictambour;

Caisson structure of faced stone;

The originally provided profile was firstlyraised by Michelangeloand farther on by G.della Porta;

Strengthening of thetambour with iron rings

2. S. PaulCathedralLondon1675-1710Sir Ch. Wren[1] [2] [6]

High cupola with basictambour;Interior double cupolaof brick and mortar, anexternal cupola of timber;

Strengthening of the basic ring with iron bars

3. Pilgrimage ChurchVierzehnheiligen1743-1772J. B. Neumann[1] [2] [6]

Vaulted ensemble of flat cupolas supported

by a system of spatialarches; Built in tuff

stone and mortar withregular steelreinforcement

The new era of shell structures began with the appearance of reinforced concrete as new building material in thesecond half of the 19th century. The main advantage of the new material is its possibility to be cast in any formobtaining rigid and resistant carcasses. The presence of reinforcement assures the overtaking of the tensions.Therefore, based really on an ancient experience, a great perspective was opened in designing more and more

rational, economic and esthetic structures. Besides the classical dome and vault a series of new forms appeared.Some significant examples are presented in the Table 4. It is to be mentioned the apparition of the hyperbolicshells never met before.

3. PRINCIPLE OF EQUILIBRIUM

It is well known that besides functional and aesthetical qualities the thin shells presents also advantageousmechanical properties. They are mainly subjected by membrane forces. Bending moments are generally of smallaccount. So, like natural carcasses (shell, egg, nut), the mechanical equilibrium of a membrane structure meansthe minimum of the ststresses (membrane state) and those acted by two signed stresses (bending state) assuming an elastic behaviour and a certain resistance of the material (Figure 1). The computing shows that the included internal energy is three

case of the membrane state of stresses. In other words the section is able to support more loading, it has a greater loading capacity. Obviously it is advantageous to fulfill the main conditions of the membrane theory of the shellstructures.

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Table 4. Shell structures of reinforced concreteCONSTRUCTIONDATE, AUTHOR

REFERENCES

DESCRIPTION

1. Water reservoir of 500 m3

in Toulon1898E. Coignet[4]

cylindrical tanks (Fontenaible1870, BougivalSèvresreservoir is an ensemble of cylindrical, spherical andconical thin shells.

2. Summer Playhouse in Cluj-Kolozsvár (actually

HungarianTheatre)

1909-1910F. SpiegelG. Márkus[7]

The spherical dome with 28,50m span and 5,00 m rise is thevery first reinforced concretecupola of large span, with basicring, supported by masonry

piles. The reinforced concreteshell is two-layered.

3. Ball-playing hallMadrid1935E. Torroja[2]

Long cylindrical shell ensemblewith included lightening ;

Longitudinal span: 53mTransversal span: 32 mThickness of the shell: 8 cm.

4. RestaurantLos Manantiales

XochimilcoMexico1958F. Candela[2]

Intersection o of hyperbolicshells;

Diagonal span; 32,5 m

Thickness of the shell: 4 cm.

5. Palazetto delloSportRome1957P. L. Nervi[2]

Spherical dome of ribbedreinforced concrete shell built

by assembly of precastelements;

Supported by inclined columns;

Span: 80 m.

Figure 1. Comparison of the potential strain energy in the case of membrane and bending state of stresses

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4. RELATION BETWEEN FORM AND MECHANICAL BEHAVIOUR

The theory of shell structures demonstrates that is a strong relation between differential geometrical properties of second order (curvatures) of the middle surface of the shell and the mechanical behaviour, the state of stresses

when the normal plane is turning around the normal line to the surface. It divides the points on a surface,

respectively surfaces, in elliptic, hyperbolic and parabolic. Thus, a surface consisting of elliptic, hyperbolic or parabolic points is an elliptic, hyperbolic, respectively parabolic surface. The corresponding resolvingdifferential equations in the membrane theory are of elliptic, hyperbolic and respectively parabolic type. Thecharacteristic mode of discharging of the before mentioned types of shell are presented in the Figure 3.

Figure 2.

The characteristic mode of discharging of the before mentioned types of shell are presented in the Figure 3.

Figure 3. Characteristic discharging of different types of shell

From very practical functional or/and technical reason in many cases higher as two degree surfaces are adopted.In these situations the surfaces contains zones of both elliptic and hyperbolic type, separated each other by acurve of parabolic points.For example, in order to cover large square areas the velaroidal surface can be used (Figure 4). Described by aforth degree equation it is generated by a variable curve (1) which is translated on another curve (2) degeneratinginto straight lines on the boundaries. Thus, the edge elements become simpler, easy to prestressed if it isnecessary and certain structural arrangement (Figure 5) offers also a simple configuration for natural l ightening.In order to emphasize the influence of the geometry of the surface on the structural behaviour a comparative

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study was made [8] for velaroidal surfaces with parabolic, circular and elliptic directrix having the sameheight/span ratio (Figure 6). It put into evidence different trajectories of parabolic type of points (Figure 7). So,from structural point of view for the velaroidal shell supported on four columns, the proper geometry will be thatof velaroid with elliptic directrix assuring a reduced zone of hyperbolic points.

Figure 4. Generating of velaroidal shell Figure 5. Universal hall with velariodal shells

Figure 6. Velaroid of different directrixes Figure 7. Lines of parabolic points

Until the sixties the form finding was limited on thin shells working in a merely compressive membrane state,systems whose tensile element position are known or fixed. The spectacular hyperbolic paraboloid, or thefunctionally useful conoidal shells accompanies these structures. The basic theories of thin shell structures were

elaborated (F. Dischinger, W. Flügge, K. Girkmann, S. Timoshenko, W. H. Wlassow etc.) at this time.The last decades of the 20th century is characterized by searching for new forms and technologies. There are to

be mentioned the free forms. Some researchers instead rigorous calculus prefer experimentation like H. Isler whoworks on funicular forms, by the use of physical modeling leading to unique funicular equilibrium shape. Inother cases the form finding process was focused on tensioned elements when the position of every compressiveelement is known, fixed or prescribed by the designer. There are structures, including merely tensioned elementscomprises cable nets, fabric membranes, also funicular cables or thin steel sheets [9]. Finally, many researcheswere carried out on form finding of mixed systems. In other words, this problem consists in determining a stableequilibrated prestressed system. That is to say its geometry and stress distribution, while evaluating a possibleinstability because of compressive element presence. Such a system is the tensegrity system made up of cableand struts covered with plane panels (for instance, glass panel fixed on a prestressed bar-cable skeleton). Alsocabledomes are mixed systems composed generally of non-curved fabric strips. All these researches areaccompanied with different strategies in order to calculate the coupled parameter shape/stress (Force Density

method developed by K. Linkwitz during the Munich Olympic Roof project, different stress control methods,traditional Finite Elements method).

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5. CONCLUSIONS

Any prognosis in this domain should start from the retrospective analysis and a careful examination of the present tendencies. We should also take into account series of factors. The difficulty of this purpose consists inthe fact that these factors are changeable whereas their evolution lies under the sign of uncertainty and

probability. However, we may establish some criteria of influence based both on general or individual

determinations. Then, knowing the evolution of the tendencies in time (experiment) and estimating the presenttendencies, considering also the phenomena that guide these criteria, we may appreciate the future of reinforcedconcrete shells. Thus, based on the criteria systematized in Table 5, one could appreciate that the area of using of reinforced concrete shells will cover the domains foreseen in Table 6.

Table 5. Factors of influence on reliability of reinforced concrete shellsGENERAL FACTORS DETERMINE REAL CRITERIA

Socialcommand

Social-economicaldevelopment

Spiritual andmaterialresources

necessity

possibility

Urban development- space covering- public worksEnergetic development (conventional andunconventional)- deposits of energy-bearing materials

- art works- protection works

Building materials development- special concrete and reinforcement- appearance of new materialsDevelopment of execution technologyScience development- structural mechanics- calculation means (methods, software)

Table 6. Prospect of using reinforced concrete shellsDOMAIN OBJECTS

RoofsOptimized formsSculptural formsSecondary roof elements

Tanks, vessels, depositsWater tanks and towersSettling tanks, methane-tanksBunkers and silos

Art works DamsTunnels and pipes

Protective shellsReservoirs for oil productsReactor envelopesScreens

It could be estimated that there will not take place a narrowing of the domain but a better adequacy of using of reinforced concrete shells in accordance with their specific qualities.

REFERENCES

[1] Bucur-Horváth, I., Retrospect and Prospect of Reinforced Concrete Thin Shells. In: International Symposiumluj-Napoca, 15-16 Oct. 1993, Proceedings, vol.4, pp. 1414-1431.

[2] Hart, F., Kunst und Technik der Wölbung. Verlag Georg D. W. Vallwey, München, 1965.[3] Heinle, E., Schlaich, J., Kuppeln aller Zeiten aller Kulturen, Deutsche Verlags-Anstalt, Stuttgart, 1996.[4] Haegermann, G., Huberti, G., Möll, H., Von Caementum zum Spannbeton, Band I, Bauverlag GmbH,Wiesbaden-Berlin, 1964.[5] Bucur-Horváth, I., Építészet mérnökszemmel . Kriterion Könyvkiadó, Bukarest, 1995.[6] Kollár, L., Vámossy, F., Mérnöki alkotások esztétikája, Akadémiai Kiadó, Budapest, 1996.[7] Bucur-Horváth, I., Bacsó, Á., Popa, I., An Early Reinforced Concrete Cupola in the Context of Thin Shells

Evolution. In: Proceedings of the IASSIstanbul Turkey, May 29 June 2, 2000, pp.417-426.[8] Mihailescu, M., I. Bucur-Horvath, Velaroidal Shells for Covering Universal Industrial Halls. In: Acta

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Technica Academiae Scientiarum Humgaricae, Tomus 85 (1-2), 1977, pp. 135 145.[9] M. René, M. Bernard, The Development of Form: from Concrete Shells to Contemporary Lightweight Structures. In: 40th Anniversary Congress of the International Association for Shell and Spatial Structures(IASS), Madrid, 20-24 September 1999, Vol. II, pp.F51-F58.

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