Exploring the Design, Analysis, and Applications of Shell Structures

Exploring the Design, Analysis, and Applications of Shell Structures

Vidya Vijay K. P, Pooja S M, Gayathri S. Shivakumar

Assistant Professor , Associate Professor BMS School of Architecture

Bengaluru, Karnataka

Abstract The shell structure is a type of structure that consists of a shell and a concrete shell. It is characterized by a double-curved shape of the shell which enhances the load distribution and contributes to the stability of the structure. The study explains the use of lightweight material to create lightweight structures with larger spaces by optimizing the structural frame. The paper also discusses the structural awareness required in the alteration of design in the conceptual design stage and to have the software tools required for decision support and interact concurrently with the architect in the optimization process. The analysis of shell structures reveals a fascinating intersection of architectural ingenuity and engineering precision. Emerging technologies such as 3D printing and additive manufacturing offer new avenues for creating intricate and customized shell forms. Moreover, the exploration of hybrid construction methods, combining different materials to optimize strength and durability, exemplifies the dynamic nature of this architectural and engineering discipline. Whether in iconic landmarks, cultural institutions, or sustainable environments, shell structures stand as a testament to the creative synergy between architectural vision and engineering expertise.

Keywords Shell structures; Light weight aggregate; Structural efficiency; Constructional techniques; Thin shell concrete

INTRODUCTION

Shell structures, also known as shell roofs or shell forms, are architectural and engineering designs that utilize curved, thin, and lightweight structures to create a shell-like, curved surface that efficiently spans large spaces. These structures are often associated with elegant and innovative architectural designs. Shell structures are characterized by their curved and often domed shapes, which can range from simple cylindrical or spherical shells to more complex shapes like hyperbolic paraboloids. Shell structures are renowned for their structural efficiency. They distribute loads in a way that minimizes the need for internal support, allowing for large, open interior spaces. Shell structures are notable for their aesthetic appeal, as they often create iconic architectural landmarks. They offer architects and designers the opportunity to explore unique and visually striking forms. The design and analysis of shell structures involve complex mathematical calculations

and engineering principles to ensure stability and safety. Finite element analysis and computer-aided design software are often used in this process.

Types of shell structure

Shell structures are engineering and architectural form that derives their strength and stability from their curve shaped form. These structures are characterized based on their efficiency in utilizing the material as they distribute loads along the surface, making them structurally strong. Some of shell structures are:

Domes

A dome is a shell structure that takes the shape of an inverted bowl or hemisphere. A dome is a structural element or architectural feature that resembles the shape of an inverted bowl or hemisphere. Domes are known for their iconic and elegant architectural designs. They have been used in various architectural styles and cultures, from ancient Roman and Byzantine structures to Renaissance and modern buildings.

Barrel Vault

A barrel vault is a type of architectural element or structural design that consists of a series of arches or vaults placed end to end, creating a continuous, semi-cylindrical ceiling or roof structure. They have been used in various architectural styles, from ancient Roman and Byzantine structures to medieval cathedrals and Renaissance buildings. Barrel vaults are recognized for their simplicity and strength.

Hyperbolic paraboloids

Hyperbolic paraboloids, also known as hypars or saddle roofs, are a class of architectural shapes and structural forms characterized by their distinctive, doubly curved surface. These have a saddle-like shape with two opposing, hyperbolic curves along two perpendicular axes, often referred to as the "x-axis" and "y-axis." The surface can be described as a ruled surface, created by straight lines that intersect at right angles.

Saddle shells

Saddle shells refer to architectural structures that exhibit a saddle-like shape, often characterized by a double-curved surface. This form resembles an inverted saddle or the shape of a horse's back, with two opposing curves along different

axes. The design of saddle shells combines aesthetics with structural efficiency.

LITERATURE REVIEW

Historical and contemporary examples of shell structures Shell structures are engineering and architectural form that derives their strength and stability from their curve shaped form. These structures are characterized based on their efficiency in utilizing the material as they distribute loads along the surface, making them structurally strong. Some of the historical and contemporary examples of shell structures are:

The Pantheon's dome is still the world's largest unreinforced concrete dome. It was built in 126 AD. It is one of the massive concrete shell structures having an oculus at top, allowing natural light to enter. Another interesting feature about the Pantheon is the use of series of massive concentric stepped rings and the lightening of the dome by the coffering and gradated, light weight aggregates.[1]

Hagia Sophia in Istanbul Turkey was a cathedral built in 537AD. It was one of the architectural and engineering marvels at the time with a huge dome. The height of the dome is 55.60m and the diameter 31m. The large dome is a combination of pendentives and semi-domes, creating a shell structure. The four pendentives forms a square supported by four arches resting on four massive piers in the middle if the building. The heavy thrust of the dome is taken by two semi domes of which one end rests on the massive pier and other end on two minor pillars. The thrust of the semi dome is received by smaller domes and covey to the main walls. [2] The Trans World Airline Flight Centre (TWA Flight Centre) at John F. Kennedy International Airport (JFK Airport) in New York, is a pioneering example of thin- shell construction, consisting of a reinforced concrete shell roof supported at the corners.

The roof structure is expansive 310 ft x 220ft composed of four vaulted shells supported by four buttresses along the edges. [3] The roofing comprises four concrete shells, with two upward-slanting shells resembling wings at the edges, and two smaller shells slanting downward towards the front and back of the structure.

Kuwait Pavilion at Expo 67 in Montreal, which features a large-scale saddle-shaped roof.

Sydney Opera House has elements exhibit saddle shell characteristics. The shell consists of a series of parabolas supported by precast concrete ribs. The cost of employing in- situ concrete formwork would have been excessively high. However, opting for precast concrete construction for each unique roof section was likely deemed even more expensive due to the absence of repetitive forms. Sydney Opera House modern building in the world next to falling water.[4] Reyrey, 2022 [5] in his paper explained the appropriateness of using nature as an inspiration for numerous shell structures exemplified by Sydney Opera House as the world heritagebuilding.

1. Cassinello et al., 2010 [6] in their publication on thin concrete shells lightweight structures the author highlighted the influential work of the renowned architect Felix Candella who has worked on 800 and more thin shell structures. The

   paper explains about the utilization of light weight material to construct structures with larger interior space by optimizing the structural framework.

   Holzer et al., 2007 [7] in their paper formed a research team to address various issues on interconnecting design intelligence with the work methodologies adopted by the practitioners. The researchers from architecture and structural background ensure that integrated design information in the early stages is beneficial and agree on common goals and define suitability rules that guide optimization processes. The paper also discusses the structural awareness required in alteration of design in the conceptual design stage and to have the software tools required for decision support and interact concurrently with the architect in the optimization process.

   PRINCIPLES IN THE DESIGN OF SHELL STRUCTURES

   1. Architectural Characteristics:

      Shell structures are often chosen for their aesthetic appeal. The form and shape of a shell can create visually striking and iconic buildings. Architects consider how the shell interacts with light, the surrounding environment, and the overall design concept to achieve a harmonious and aesthetically pleasing structure.

      Domes are characterized by their curved, hemispherical, or elliptical shape, resembling the top half of a sphere. They are constructed by rotating a curved arch around a central vertical axis to create a continuous, self-supporting shell structure. Hyperbolic paraboloids are commonly used in architecture for their aesthetic appeal, structural efficiency, and versatility. Saddle shells have a distinctive shape characterized by two opposing curves along orthogonal axes. The form is similar to that of a saddle, hence the name. It combines elements of hyperbolic paraboloids and provides a visually dynamic and aesthetically pleasing appearance.

   2. Design and Form:

      Shell structures often begin with the process of "form finding," where architects and designers explore geometric shapes that naturally distribute loads and stresses. This process involves finding a form that minimizes material usage while maintaining structural integrity. The curvature of a shell is crucial for its structural performance. Shells are often designed with double-curvature surfaces, such as domes or hyperbolic paraboloids, to distribute forces more efficiently. The geometric shape of the shell influences how loads are transferred and resisted.

      There are various types of domes, including hemispherical domes, onion domes, saucer domes, and ribbed domes, each with its own structural and aesthetic characteristics.

      Hyperbolic paraboloids offer a wide range of design possibilities. They can be used to create complex and organic shapes, as well as more simple and practical structures.

   3. Materials:

      The choice of materials is crucial in shell construction. Materials such as reinforced concrete, steel, or lightweight

      materials like tensile fabrics are selected based on their strength, durability, and weight. The material must be able to withstand the forces and loads exerted on the shell.

      Domes and Hyperbolic paraboloids can be constructed using masonry (stone, brick, or concrete), metal, glass, wood, and more. For concrete structures, formwork and precise construction are vital. Hyperbolic paraboloid and Saddle shells can be constructed using light weight tensile fabric, for these structures tensioning systems and cable nets are used to maintain the shape.

   4. Structural Analysis and Structural Efficiency:

      The structural analysis of shell structures involves complex mathematical modelling to understand how forces, stresses, and deformations are distributed throughout the shell. Finite element analysis (FEA) is commonly used to simulate and optimize the structural behavior of shell forms. Designing and analyzing hyperbolic paraboloids can be complex. Foroughi Het al., [8] in their research the structural analysis of various types of shell can be done by mechanically modelled with one partial differential equation system. The equation obtained is solved by semi analytical solution. The material properties such as thickness and cross-sectional area on the strength of shell structure is studied. This research includes analysis of any shell structure with various kinds of geometric shapes. Nonlinear analysis has the major impact on the functional shell structures between three spherical, conical structures.

      Dastjerdi, S et al., 2021 [9] in their research the structural analysis of various types of shell can be done by mechanically modelled with one partial differential equation system. The equation obtained is solved by semi analytical solution. The material properties such as thickness and cross- sectional area on the strength of shell structure is studied. This research includes analysis of any shell structure with various kinds of geometric shapes. Nonlinear analysis has a major impact on the functional shell structures between three spherical, conical.

      Shell structures distribute loads through their curved surfaces, which helps minimize stress concentrations. The inherent curvature of the shell helps in efficiently transferring loads to the supports, reducing the need for internal columns or supports.

      Domes distribute loads efficiently, transferring the weight to the base of the structure or to supporting columns or walls. This design minimizes the need for interior support, creating open and unobstructed interior spaces. Hyperbolic paraboloids and Saddle shells are structurally efficient and can span large areas with minimal need for internal support. They distribute loads effectively, often making them suitable for roofing and canopy structures. The double-curved shape of saddle shell enhances load distribution and contributes to the stability of the structure.

   5. Applications:

      Domes are commonly found in churches, mosques, temples, as well as in government buildings. Hyperbolic paraboloids and Saddle shells are used in a variety of architectural applications, including roofs, canopies, shells, and pavilions.

      They can be found in both residential and commercial buildings, as well as in public spaces and cultural institutions. They are often employed in museums, sports arenas, exhibition halls, and other large-scale public spaces. They are also used in modern architecture to create unique and aesthetically pleasing interior and exterior designs.

   6. Construction techniques

      The construction of shell structures involves specialized techniques to achieve the desired curvature and structural integrity. The choice of construction method depends on factors such as the type of shell, materials used, and the overall design concept.

      Traditional Formwork: For concrete shell structures, traditional formwork may be used. Plywood or other materials are shaped to match the desired shell geometry, and concrete is poured and cured within the formwork.

      Pneumatic Forming: Inflatable forms can be used to shape the concrete. These forms are initially flat and are inflated to the desired shape, creating the shell geometry. After the concrete is set, the forms are deflated and removed.

      Thin-Shell Concrete: Thin-shell concrete construction involves casting relatively thin concrete sections to form shell structures. These shells can be precast and then assembled on-site or cast in place using appropriate formwork.

      Prestressed Concrete: Prestressed concrete shells involve reinforcing the concrete with tensioned cables or tendons before placing the concrete. This technique helps control cracking and enhances the structural performance of the shell. Steel Ribs and Panels: Steel shells may be constructed using a framework of steel ribs covered with steel panels. The ribs provide the necessary curvature, and the panels contribute to the structural stability. This method is common in the construction of geodesic domes.

      Membrane Structures: Tensile fabric structures, such as canopies or roofs, are often used for lightweight shell applications. High-strength fabrics are tensioned over a framework to create the shell shape. This method is common in sports stadiums, exhibition centers, and other large-span structures.

      Prefabricated Shell Elements: Some shell structures can be prefabricated off-site, with elements assembled on-site. This approach can enhance construction speed and quality control. Shotcrete: Shotcrete is a method where concrete is sprayed onto a formwork surface. It is often used for creating complex shapes, and the application can be controlled to achieve the desired curvature. This technique is suitable for both new construction and rehabilitation of existing shell structures.

      Combination of Materials: In some cases, a combination of materials may be used to achieve the desired shell structure. For example, a steel and concrete composite shell can provide both strength and durability.

      Additive Manufacturing: Emerging technologies like 3D printing are being explored for creating intricate shell structures. While still in the experimental stage, 3D printing offers the potential for efficient and customized construction.

   7. Support and Foundations

      Proper support and foundation design are critical for the stability of shell structures. The shape and geometry of the shell influence the distribution of loads to the foundation. Engineers must carefully consider the soil conditions and overall structural behavior to design effective supports.

   8. Environmental Considerations

Shell structures often incorporate sustainable design principles, considering factors such as energy efficiency, natural lighting, and ventilation. The geometry of the shell can be optimized to enhance environmental performance and reduce the need for artificial lighting or heating.

Adekunle P. et al., 2015 [10] studied the use of mollusc farming residue replacing coarse aggregate and ordinary Portland cement. The durability of the concrete produced from shell coarse aggregate is good to a maximum temperature of 300oC and the shell blended concrete under sulphate attack with least reduction in compressive strength. Shang et al., 2020 [11] Studied the use of artificial lightweight capsule aggregates (CAs) in place the concrete. Capsule Aggregate composed of a fly ash-cement inorganic shell and sodium alginate organic core. The study helped to learn about reusing industrial and biomass resources in construction of LWAs which has potential application in the preparation of light weight concrete.

CONCLUSION

The exploration of design, analysis, and application of shell structures reveals a fascinating intersection of architectural ingenuity and engineering precision. The historical and contemporary examples showcase the evolution of these structures, emphasizing their aesthetic appeal, structural efficiency, and diverse applications. Architectural principles such as form finding, curvature, and attention to visual impact converge with engineering principles like structural analysis, material selection, and construction techniques to bring these shell structures to life.

The integration of advanced construction methods, such as formwork construction, thin-shell techniques, and innovative materials like tensile fabrics or laminated timber, highlights the adaptability of shell structures to various design challenges. Additionally, the emphasis on sustainability and environmental considerations in contemporary shell architecture underscores the ongoing commitment to responsible and efficient design.

As technology continues to advance, the potential for pushing the boundaries of shell structure design becomes even more promising. Emerging techniques such as 3D printing and additive manufacturing offer new avenues for creating intricate and customized shell forms. Moreover, the exploration of hybrid construction methods, combining different materials to optimize strength and durability, exemplifies the dynamic nature of this architectural and engineering discipline.

In summary, the analysis, design, and application of shell structures reflect a continuous pursuit of innovation, efficiency, and aesthetic excellence. Whether in iconic landmarks, cultural institutions, or sustainable environments, shell structures stand as testament to the creative synergy between architectural vision and engineering expertise.

REFERENCES

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