International Research Journal of Engineering and Technology (IRJET)
e-ISSN: 2395-0056
Volume: 12 Issue: 07 | Jul 2025
p-ISSN: 2395-0072
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A Study on Funicular Shell Structure with various rise and thickness Saravanan. M1, Dr. D. Shoba Rajkumar2 1PG Student, Department of Civil Engineering, Government College of Engineering, Salem, Tamil Nadu, India
2Professor & HOD, Department of Civil Engineering, Government College of Engineering, Salem, Tamil Nadu, India
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Abstract - Shell structures are characterized as stressed
complex shell roofs can be difficult, leading to the continued use of physical models as design tools.
skin systems due to their geometric form and minimal flexural rigidity, which enable them to primarily carry loads through in-plane direct stresses. In their ideal membrane state, concrete shells sustain external forces predominantly through compressive stresses, eliminating the need for reinforcement except for secondary effects such as bending or shrinkage. In most shell roof structures, the self-weight is the dominant load and selecting a shell geometry that facilitates compressive loading without inducing bending is beneficial. This study explores how the thickness and rise of funicular shells constructed on a square base affect their ultimate load capacity. Using ABAQUS Finite Element Analysis software, the impact of rise and thickness on displacements, maximum absolute stresses and membrane stresses are examined. Results indicate that increasing the rise reduces displacements and stress levels. The influence of thickness on membrane stress becomes less significant at higher rises, confirming the importance of shell rise in minimizing stress concentrations.
Certain secondary effects, like those caused by temperature fluctuations or material shrinkage, are difficult to calculate accurately, especially in tropical climates where temperature-induced stresses can exceed those from loading. Fine, closely spaced reinforcement is crucial in such situations to prevent cracking and increase ductility. This principle is applied in ferrocement, which involves embedding multiple layers of fine wire mesh in rich mortar to achieve the desired thickness and ductility. Although numerous shell geometries are possible, only a few standard forms are commonly used in construction, often individually or in combination. These combinations are referred to as composite shells. Shell surfaces can be categorized based on curvature (single or double) or generation method (translational or rotational). However, these classifications are not always precise and may overlap.
Key Words: Funicular Shell, Rise, Thickness, Displacement, Stresses
Additionally, shell like structures made from flat plates connected along straight edges often termed folded plates are widely used due to ease of construction. Finite element methods are a standard approach for analyzing such structures. Plate and shell elements in FEM can be triangular or quadrilateral and their thickness can vary across nodes. When quadrilateral elements are not planar, it is advisable to model them as triangles for better accuracy.
1. INTRODUCTION Shell structures are a category of load-bearing systems that primarily depend on direct in-plane stresses for structural integrity, made possible by their curved geometries and low bending stiffness. These thin, curved elements, typically constructed from concrete reinforced with a steel mesh, resist applied loads via combinations of tensile, compressive and shear stresses distributed across their surface. The goal in shell design is to make the structure as thin as practical constraints allow, thereby reducing dead load and allowing it to behave like a membrane, free from significant bending effects. This strategy promotes material efficiency while enabling strong and elegant structural forms. Natural shell forms are mostly doubly curved, offering advantages in both aesthetics and structural performance.
Software tools such as ABAQUS, ANSYS, STAAD.Pro, SAP2000 and STRAP offer strong capabilities for analyzing shell behavior under varied support conditions. In this investigation, ABAQUS is utilized for the modeling and analysis of funicular shell structures.
2. OBJECTIVES AND SCOPE This study investigates the structural response of funicular concrete shells with a square base, focusing on variations in shell rise and thickness. Using the finite element platform ABAQUS, the analysis evaluates displacement (y), maximum absolute stress and membrane stresses (S11 & S22) using the Finite Element Software ABAQUS. The Funicular shells with five different rises and three different thicknesses (40mm, 50mm and 65mm) are considered for this study and are designated as follows,
Particularly, funicular shells exhibit higher ultimate load capacity compared to singly curved shells such as cylindrical ones. In structural analysis, shell elements are often assumed to be isotropic and homogeneous. However, when designing reinforcement, concrete is typically treated as cracked and steel is introduced to resist direct and diagonal tensile forces. This distinction remains necessary as long as elastic theory governs shell stress analysis. The analytical modeling of
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1. FS-I - Funicular shell with rise, r1 (125mm)
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