Stability Analysis and Comparison of Conventional Concrete and Expanded Polystyrene Concrete Spherical Shells

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1. Introduction 1.1. Buckling of spherical shells Several research works have been conducted on the stability issues of spherical shells. The theory of shell buckling has originated from Euler’s formula of critical load determination for a straight bar. Following this, a first theory of linear buckling of spherical shells was developed by Zoelly in 1915 where the elastic critical buckling load of complete spherical shells under external pressure was determined according to the formula [1]: where t - thickness of the shell, R - radius of curvature of the shell, E - modulus of elasticity, - Poisson’s ratio. In most codes of design equation (1) is commonly taken as a reference load of buckling for elastic spheres. However, most experimental studies reveal that the actual buckling capacity is a fraction of the amount obtained from equation (1). External disturbances and imperfections whose magnitude can not be predicted at the design stage, are the main factors for the decreased capacity of the buckling load. The load carrying capacity of perfect shells is greater than shells that show deviations in material behavior, geometry and boundary conditions [2-6]. Numerical concepts for load carrying capability of shells with imperfection are based on perfect shell models and on the postcritical equilibrium paths which are estimated analytically. This idea was established first by Koiter [7]. The post buckling theory of Koiter describes the static non-linear load carrying behavior of a structure at the buckling initial stages. The post buckling analysis gives information about the post buckling path at the initial stage, the stability of the corresponding equilibrium state and the way geometric imperfections influence the load bearing behavior of a structure. Thus, in the computation of buckling capacity of a structure, it is necessary to apply reduction factors in consideration to the influence of imperfections and effects from plastic behavior of a material. A wide research on the buckling behavior of spherical shells became possible with the enhancement of computer technologies and finite element method. In numerical simulation, a method of construction for the relationship between the worst imperfection with its amplitude and the limit load are applied [8]. In this paper, a numerical simulation of the elastic, perfectly plastic and imperfect spherical shells of conventional concrete and EPSC are presented. The results are compared each other for investigating the possible application of EPSC in spherical domes. 1.2. Cement concrete Cement concrete is one of the popular structural materials. Cement concrete is isotropic, homogeneous and elastic material of construction. The main ingredients of concrete are cement, sand, Coarse aggregate and water [9]. Concrete is strong in compression but weak in tension and in locations of a structure where there is tension, steel reinforcement is provided to give tensile strength to the structure. Strength of cement concrete increases with increasing hydration of cement. High strength concrete has a modulus of elasticity ranging from 14-41MPa [10] and generally a Poisson’s ratio varying between 0.15 for high strength concrete and 0.22 for low strength [11; 12]. Concrete structural members have big cross-sections resulting from the high self-weight of the material. Coarse aggregate and sand are the main ingredients for the increased weight of concrete. Concrete’s weight can be reduced by using lightweight aggregates such as cinders, pumice, shales, EPS… In this paper stability of a lightweight concrete, which is expanded polystyrene concrete (EPSC) is going to be investigated. It is produced by partially or totally replacing aggregates with expanded polystyrene (EPS) [13-16]. Expanded polystyrene concrete has a lesser density than conventional concrete with range of densities 800-200 kg/m3. The density and compressive strength of EPSC decrease with increasing amount of EPS used in the concrete mix [17-20]. EPSC has been utilized in several applications like curtain walls, pavements and load bearing blocks [21]. However, its application, stability and strength capacity in shell structures has not yet studied. Therefore, this research will focus on: ➢ Studying the properties of EPSC to be used for the current study ➢ Analyzing the stability of conventional concrete and EPSC spherical shells considering elastic critical buckling, plastic buckling and buckling with geometric imperfection and material non-linearity. Moreover, the shells’ displacements are also analyzed numerically in ABAQUS considering the same geometric data for both EPSC and concrete shells. . 2024;20(3):211-219 2. Methods 2.1. Experimental work In a 1:2:3 proportion by volume, 16.67 % of sand and 33.33 % of coarse aggregate were replaced by EPS to produce expanded polystyrene concrete. By using 0.6 water cement ratio, ingredients cement, sand, coarse aggregate water and EPS were thoroughly mixed. A flowing and homogeneous EPSC was then obtained and filled into three cubic molds of dimension 150 mm×150 mm×150 mm for testing at a laboratory. After demolding, curing and drying the specimens’ compressive strength testing was followed as shown in Figure 1. Figure 1. Testing for compressive strength The mass, compressive strength and density were S o u r c e : photo by I.A. Sereke recorded as shown in Table 1. Table 1 EPSC properties from experiment Cubic EPSC No. Measured mass, kg Density, kg/m3 Compressive force, kN Compressive strength, MPa 1 7.15 2120 235 10.44 2 6.948 2058.66 207 9.2 3 6.898 2043.85 198 88 S o u r c e: made by I.A. Sereke The computed average values of density and compressive strength are 2074.17 kg/m3 and 9.48 MPa respectively. The elastic modulus of EPSC is computed from the formula in equation (2), [22]: and obtained as 11.18GPa: Ec = wc1.5 0.043 (2) where wc - density ranging from 1440-22560 kg/m3, Ec - modulus of elasticity in MPa, fc' - compressive strength of a cylinder specimen in MPa. The cylinder compressive strength is computed from equation (3) [23]. Cylinder strength = 0.8×cube strength. (3) In the stability analysis, a cylinder strength of conventional concrete C20, unit weight of concrete 24 kN/m3, Poisson’s ratio 0.2 and corresponding modulus of elasticity 22.61 GPa are adopted. Similarly, for EPSC, a unit weight of 20.74 kN/m3 a cylinder strength of 7.58 MPa, modulus of elasticity 11.18 GPa and a Poisson’s ratio of 0.22 are used. 2.2. Numerical methods of analysis Application of finite element method with advanced computer programs accelerated research works, that shells of different material, geometry, loading or support condition were able to be analyzed with high ANALYSIS AND Сереке И.А., Рынковская М.И., Дамир Х.Ю. Строительная механика инженерных конструкций и сооружений. 2024. Т. 20. № 3. С. accuracy and reliability. In this study linear buckling analysis (LBA), material non-linear analysis (MNA) and geometric and material non-linear analysis with imperfection (GMNIA) are applied for both concrete and EPSC spherical shells. For analysis and comparison, a spherical shell with radius of curvature 35 m, half central angle 55o, base radius 28.67 m, thickness 0.15 m and rise of 14.92 m is considered as shown in Figure 2. The buckling pressures are compared to the external pressures coming from the respective selfweights and assumed snow load of 1.5 kN/m2. Figure 2. Shell geometric details S o u r c e: made by Sereke I.A. 2.2.1. Linear buckling analysis Elastic critical buckling load

About the authors

Issaias A. Sereke

RUDN University; Eritrea Institute of Technology

Author for correspondence.
Email: 1042195035@rudn.ru
ORCID iD: 0009-0003-4351-8205

PhD Student of the Department of Civil Engineering, Academy of Engineering, RUDN University

Moscow, Russia; Asmara, Eritrea

Marina I. Rynkovskaya

RUDN University

Email: rynkovskaya-mi@rudn.ru
ORCID iD: 0000-0003-2206-2563
SPIN-code: 9184-7432

Dr. of Structural Mechanics, Associate professor of the Department of Civil Engineering, Academy of Engineering, RUDN University

Moscow, Russia

Habte Y. Damir

RUDN University; Eritrea Institute of Technology

Email: khabte-y@rudn.ru
ORCID iD: 0000-0002-7275-6750

PhD Student of the Department of Civil Engineering, Academy of Engineering, RUDN University; Lecturer, Eritrea Institute of Technology

Moscow, Russia; Asmara, Eritrea

References