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SHELL STRUCTURES

R. Sundaram

Chairman & Managing Director, Sundaram Architects Pvt. Ltd.

# 19, Kumara Krupa Road, Bangalore 560 001, India

edp@sundaramarchitects.com

Abstract

In any structure, designers always aim at achieving economy by minimizing costs within the constraints of functional and aesthetic requirements. Thus, for providing a roof over a large area - a requirement of most clients - conventional structures will be uneconomical and aesthetically unpleasing. Hence, new forms were attempted that resist the loads more efficiently than when the structure is designed in a conventional form. This has resulted in the design and construction of innumerable outstanding large span structures including concrete shell roofs in the world. Efficiency of a long span structure depends upon the various parameters such as location, utility, structural economy and innovative design. There is a need for unique synthesis between architecture and structural systems to produce exciting and outstanding structures.

In India, prior to second World War large span structures were constructed with light weight material like steel. In the past two decades precast prestressed concrete structures are quite popular because of: Concrete shell roofs have been in existence for many years now. They are thin members. They are used for many purposes. They cover industries, auditoriums, food courts etc. They are cylindrical, hypars, folded plates and are thin. The author has executed a number of shell structures from 1963. The paper discusses a few of them. Some comparison made between shell structures in India and in other countries is presented.

INTRODUCTION

Concrete shells are aesthetically pleasing, structurally efficient, construction-wise challenging, and are optimized structures. Shells derive their structural action through their form and are unique in their behaviour and many other ways. Hence, shells are used in multi-various situations as coverings of convention centres, exhibition places, industrial buildings, etc. They look light and beautiful.

• Perfect quality control standards ensured
• Economical due to cost effectiveness
• Architectural beauty
• Ease of construction and simplicity of erection.
• Speed of construction. Extensive construction of folded plate structure is one example because of :
• Well known structural efficiency
• Simple method of fabrication
• Actual and theoretical deflection correlation.
• Optimum material consumption.

Extensive construction of hyperbolic paraboloid, conoidal shells with collapsible type of shuttering is another example in vogue since 1960. With the availability of user friendly finite element software along with high speed personal computers, it is now possible even for a small design office to perform 3D- Analysis of any type of structure. Also, with the availability of heavy duty cranes, derricks and with the analysis of structure at every stage of erection, it is now possible to go in comfortably for long span structures to commensurate with the requirements of the industry using concrete. The industries for both process and general purposes have taken advantage of the availability of long span structures so that they can have a large column free space which gives them immense flexibility for planning their machinery layout and services.

This paper presents a few such concrete shell structures. This paper also presents a few features of the comparative study made by a Master's Degree student at Princeton University, USA titled "R. Sundaram and Modern Thin Shell Concrete Structures".

ANALYSIS AND DESIGN OF SHELLS

• Opens up our minds for better understanding of the structural behaviours
• General ideas of aesthetics
• Synthesis of form and function
• May not build and yet study is very interesting.

A few examples are:

Projects approved and not yet commenced:

International Convention Centre, Mysore

INDOOR MULTIPURPOSE HALL FOR AN UNIVERSITY IN THE CITY OF FATEGRAH NEAR CHANDIGARH

An Institution in Northern part of India is developing a campus for "World University" in an area of 80 Acres.

It was required to design a building, which should be the focus of the University. This building should be a multi-purpose hall and also to house facilities for a multi-religious building dealing with subjects like Hinduism, Christianity, Sikhism, Buddhism, Islam, etc. It was also desired to have a unique roof covering this multi-purpose hall, preferably one of its kind. The author’s office has done different types of roof structures for various activities. After studying alternatives, it was decided to go ahead with a hyperbolic paraboloid shell roof. Multi–purpose hall The shell is supported at 2 points near the end and the clear span is 60 metres. Aesthetics is very important and therefore the shape is very pleasing especially since this is the focus for the Campus. A three-storeyed building is located under the shell roof near the periphery, which houses schools for various religions.

Section The height of the shell at the center is 34 mtrs. And there are 12 shells in plan. Image of the Multipurpose Hall Inside image of the Multipurpose Hall Span 95 m. Height 25mm. Seating capacity 5000. Concrete shell roof [Hyperbolic paraboloid shell].

The structure is composed of 12 petal-shaped roof elements. Recently a Masters thesis by Meggie June Betancourt was accepted by Princeton University and the title is "R. Sundaram and Modern Thin Shell Concrete Structures". She compares two of my projects namely, Kanteerava Indoor Stadium, Bangalore, and the Food Court at Infosys, Bangalore, with similar ones by two highly reputed designers. A brief note on the two structures is as follows:

KANTEERAVA INDOOR STADIUM, BANGALORE

Inspired by their predecessors, who have converted rock into architectural masterpieces like Taj Mahal etc., modern architects & engineers in India especially the author has created many architectural masterpieces using the material concrete. The thread of Indian traditions lingers on in our buildings. Painstaking attention to detail has taken the place once held by ornamentation. With this, we try to lend some order to this chaotic urban landscape. The Indoor Stadium is a classic example in this case. The Indoor Stadium of 4000 members capacity is located in the close vicinity of the rich green Cubbon Park in Bangalore.

The Stadium has an elliptical dome consisting of 120 folded plates [ precast M-40 grade concrete] of varying cross section [ average 2m ] with the plate thickness of 40mm and series of interconnected ribs. The lower end of the dome is supported on the elliptical ring beam at 8m level which in turn is supported on 24 equally spaced arch columns. The top end of the dome is supported on elliptical ring of 16m]. A small elliptical paraboloid in situ dome of 4m height and having a series of interconnected stiffeners is resting on the top ring. The folded plate spans about 40m between the two rings. The seating galleries are precast while the other cubicles are in situ.

STRUCTURAL SYSTEM

Individual Model analysis: The folded plates are individually modelled using the finite element method. Appropriate boundary conditions are applied (Hinged at base and fixed at top except for vertical deflections) and the structure is analysed. In the finite element model the longitudinal and transverse ribs are represented through beam elements and the diaphragm, the flange and web of T-section and the folded plates are represented through shell elements. Full Model Analysis: The entire frame is modeled using the software. All elements are represented as equivalent beams. The lateral stiffness of piles are also considered through lateral spring elements. The stiffness of these elements are arrived at based on the actual pile groups considered in design. Two different pile stiffnesses are considered in each analysis. The boundary conditions are: - all columns are vertically supported at the base, laterally and rotationally supported through piles. The connection between the equivalent beams representing the folded plates and the tension ring beam is considered to be a hinge.A three dimensional finite element multistage analysis was performed considering the various staging of construction. Each elements are designed to withstand the critical forces as per the analysis output.

Each folded plate of 42 metres in length and weighing 55 tonnes is placed elliptical in plan. A lot of details have been gone in to for both Kanteerava Indoor Stadium and Sundome stadium. The comparison with Sundome is based on 3 criteria of structural art - efficiency, economy and elegance. Kanteerava indoor stadium was constructed using precast methods. The stadium is in elliptical in plan with long and short axes of 390 feet [ 119m ] and 299 feet [91m] respectively. 119 m (390.4 ft) Plan drawing The Kanteerava dome is easier to see from the exterior due to its lower span-to-rise ratio and its nearness to ground level. It is also more expressive of its structural functioning.

Meggie concludes that:

"The Kanteerava dome is more successful in expressing its structure from the exterior. she mentions that Sundaram's attention to the aesthetic of his structure is apparent, and for this reason, combined with its achievement in efficiency and economy, the Kanteerava indoor stadium can be classified as a modern work of structural art".

FOOD COURT AT THE INFOSYS CAMPUS, BANGALORE, INDIA - 2000

Hypar shells for Infosys as Food Court. The most aesthetically pleasing, functionally satisfying shell structure has been done for the Infosys Food Court in Bangalore, Infosys Campus is located in Electronic City of Bangalore South City. This Technology Park houses Software blocks, Education and Research Center and Food Courts etc. While all other buildings are normal reinforced concrete framed structures, the Food Court has a unique Groined Vault roof accommodating 250 persons under each shell. There are three such shells of 20m x 20m. The height of the shell at the central portion is 7.5m and at the entry 10 to 12.5m on the four sides. Each shell is separated by a distance of 10m, which also can be used for dining on occasions.

All the three shells are located on an elevated podium of 2.50m high. Vast podium is housing in the basement, a well equipped gymnasium, kitchen, medical, aerobics, meditation, banking, AHU’s, steam bath, change rooms and toilets and so on. The geometry of the shell is a hyperbolic parabola. While overall shell thickness is 75mm, the main diagonal arch elements have 200mm thick over 3m wide tapered to 75mm. This means a compression arch in one direction and tension cable form in a perpendicular direction.

Meggie states “both Candela and Sundaram thought about the construction of their shells, and devised ways to cut time and cost from the process. Candela used the straight-board formwork method possible with the hypar shape, and Sundaram used repeated formwork possible due to the repeated shape of the structure. Both Sundaram and Candela had the advantage of working in countries (India and Mexico, respectively) where labor is not costly, making the construction of cast-in-place shells financially viable. The two structures are very similar visually. While Sundaram's design has the benefit of zero visible stiffeners on the shell surface, Candela’s shells have added elegance due to their elevation on thin ‘legs’. Both shells are extremely light and graceful, and create a visual effect that basic frame structures cannot achieve. By imitating a structural artist whom he admired, Sundaram designed and built a structure than can be classified comfortably as structural art".

INVERTED UMBRELLA - FOR MICO-BOSCH CANTEEN IN BANGALORE

This consists of cluster of shells of shape of hyperbolic paraboloid in the form of inverted umbrella. Size of each shell is 6.0m x 6.0 and diameter of the column is 350mm. The thickness of the shell is 50mm and edge beam of size 150mm x 150mm is provided at the edge of the shell. The spring level is 4.0m and depth of shell itself is 1.6m. The indirect lighting from the shell provides average illumination level of 120 lux and looks pleasing aesthetically. The gap of 1.0m between adjoining shells is covered with aluminium sheet on top and hit and miss ventilator arrangement on sides provides natural light and ventilation.

FOOD COURT, INFOSYS CAMPUS IN HYDERABAD

The Infosys campus, Hyderabad is about 4km from Hi-Tech City. The rectangular shaped site measure 270m x 450m. A number of Buildings in the campus have been built. 4 Software blocks, Food court, Swimming Pool, Amphi Theatre, Power Block, Chiller block, UGR and ETP. This phase is under construction and is nearing completion. One of the most interesting buildings in the campus is the Food Court it is planned with a dining capacity of 800. This is a unique column free space shell structure of 46m diameter. The shell structure is divided into 16 units. The entire roof sits on a series of columns, which are 5m high. The building is designed with flexibility to convert it into an auditorium with a seating capacity of about 1000-1200 people.

This food court itself sits on a podium of approximately 4 m above ground level. In this podium, services like kitchen, Gymnasium, aerobics, general store room, health club, bank ATM Kiosks and Medical Center etc are provided. Amphi Theatre flanks the podium on one side and Swimming Pool on the other side. Some of the salient features of the food court are given below:

Food Court

1. No. of floors 2 levels
2. Total Area 6266 m2
3. Area at each floor level Basement - 4605 m2 G.Floor - 1661 m2
4. Number of entrances Two to podium, Two to kitchen and One to service
5. Number of stairs, lifts and emergency exits  Two main stairs and One service stair
6. Special Feature Unique structure with column free space of 46 m dia.

Structural analysis and design details

The Dome consists of 16 segments of Paraboloidal shell, resting on 16 columns raised above podium. The dome is 54m in diameter at outer edge and 46m in diameter at column edge. The dome consists of lower ring beam and a top ring beam and shells. The thickness of shell is 75mm, increases to 150mm at valley beam location. The geometry of the structure may be visualized as a translational surface generated by a concave parabola moving over a concave parabola. The Cartesian co-ordinates of the shell element at every 1m are calculated. The co-ordinates are fed into the EMRC NISA software and the FEM model is generated. The stress results are obtained from the analysis. 3- Principal Stresses are considered in the design of the shell proper. The design of the beams and columns are done using the output results of EMRC NISA.

DR. T.M.A. PAI INTERNATIONAL CONVENTION CENTRE, MANGALORE

Geometry of Shell: KMC Auditorium at Mangalore has two multipurpose halls of octagonal shape in plan, The size of each side is 21m c/c and of 14.262 m c/c respectively. The two halls have a doubly curved circular conical shell roof. Any section cut horizontally is circular in plan; the roof surface is obtained when all concentric circles will move on another doubly curved radial beams. The shell emerges from a stiff tie beam over the columns on the periphery. The total height of the shell is 12.42m & 12.27m. The diameters of the shells are 54.876m & 37.284m. Generally the thickness of the shell is 75mm. The radial ribs are supported over columns at the bottom periphery and the central ring beam with skylight dome at top. There are transverse concentric circular ring beams. The geometry is maintained by these radial beams and transverse circular beams under the action of forces. A view

CONCLUSIONS

Architecture dominates, structure dominates, services dominate. Over all the synthesis is important resulting in intelligent structures with aesthetics and strength and durability.

REFERENCES

1. From the thesis presented to the Faculty of Princeton University, USA in candidacy for the Degree of Master of Science in Engineering by Meggie June Betancourt on "R. Sundaram and Modern Thin Shell Concrete Structures".
2. From the Keynote paper presented by R. Sundaram, the author on the subject "From Antiquity to Modern Shell Roofs" based on author’s design in the International Symposium by International Association for Shell and Spatial Structures [IASS] in Seoul, during May 21-24, 2012.