• Journal of Korean Association for Spatial Structures
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• v.17 no.1
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• pp.49-58
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• 2017

The result of the previous work leads to the idea that the inner area of the hyperbolic shell generator should be minimized for the cooling tower with higher first natural frequency. In this study the inner area of the hyperbolic shell generator was graphically established under varying height of the throat and angle of the base lintel. From the graph, several shell geometries were selected and analysed in the aspect of the natural frequency. Three representative towers reinforced differently due to different first natural frequencies were analysed non-linearly and evaluated using a damage indicator based on the change of natural frequencies. The results demonstrated that the damage behaviour of the tower reinforced higher due to a lower first natural frequency was not necessarily advantageous than the others.

• Structural Engineering and Mechanics
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• v.84 no.6
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• pp.707-722
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• 2022

In this study, a new refined hyperbolic shear deformation theory (RHSDT) is developed using an equivalent single-layer shell displacement model for the static bending and free vibration response of cross-ply laminated composite spherical shells. It is based on a new kinematic in which the transverse displacement is approximated as a sum of the bending and shear components, leading to a reduction of the number of unknown functions and governing equations. The proposed theory uses the hyperbolic shape function to account for an appropriate distribution of the transverse shear strains through the thickness and satisfies the boundary conditions on the shell surfaces without requiring any shear correction factors. The shell governing equations for this study are derived in terms of displacement from Hamilton's principle and solved via a Navier-type analytical procedure. The validity and high accuracy of the present theory are ascertained by comparing the obtained numerical results of displacements, stresses, and natural frequencies with their counterparts generated by some higher-order shear deformation theories. Further, a parametric study examines in detail the effect of both geometrical parameters (i.e., side-to-thickness ratio and curvature-radius-to-side ratio), on the bending and free vibration response of simply supported laminated spherical shells, which can be very useful for many modern engineering applications and their optimization design.

• Journal of Korean Association for Spatial Structures
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• v.12 no.3
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• pp.97-104
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• 2012

In the design procedure of the cooling tower the form-finding of the shell is the most important process, because the shape of the shell determines the sensitivity of dynamic behaviour of the whole tower against wind excitation. In engineering practice, geometric parameters of the shell are generally determined based on natural frequency analysis. 32 cooling tower shell geometries were selected through variation of the geometric parameters of an existing cooling tower shell. They were evaluated based on the first natural frequency. From the result three representative cooling towers are selected for the analysis of the structural behaviour by means of linear FE-method. As a result, a hyperbolic rotational shell with the small radius overall will yield the shell geometry with a higher first natural frequency and thus a wind-insensitive structure.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.14 no.4
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• pp.807-814
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• 1994

One case of pointwise limit design is performed for a hyperbolic paraboloid saddle shell(originally used by the Lin-Scordelis) to check the design strength against a consistent design loads, therefore, to verify the adequacy of current design practice for reinforced concrete shells. The design method which was based on stresses from membrane analysis in conjunction with pointwise limit state design equations shows a good performance, which means that the design method gives a lower bound on the ultimate load. This shows the adequacy of the current practice at least for this saddle shell case studied. To generalize the conclusion many more designs-analyses are performed with different shell configurations.

• Earthquakes and Structures
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• v.14 no.1
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• pp.85-94
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• 2018

The paper focuses on the seismic responses of a hyperbolic cooling tower resting on soil foundation represented by the three-parameter Vlasov elastic soil model. The three-parameter soil model eliminates the necessity of field testing to determine soil parameters such as reaction modulus and shear parameter. These parameters are calculated using an iterative procedure depending on the soil surface vertical deformation profile in the model. The soil and tower system are modeled in SAP2000 structural analysis program using a computing tool coded in MATLAB. The tool provides a two-way data transfer between SAP2000 and MATLAB with the help of Open Application Programming Interface (OAPI) feature of SAP2000. The response spectrum analyses of the tower system with circular V-shaped supporting columns and annular raft foundation on elastic soil are conducted thanks to the coded tool. The shell and column forces and displacements are presented for different soil conditions and fixed raft base condition to investigate the effects of soil-structure interaction. Numerical results indicate that the flexibility of soil foundation leads to an increase in displacements but a decrease in shell membrane and column forces. Therefore, it can be stated that the consideration of soil-structure interaction in the seismic response analysis of the cooling tower system provides an economical design process.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1995.10a
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• pp.207-214
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• 1995

Muller-Scordelis RC Gabled Hyperbolic Paraboloid (HP) shell is divided by 40 40 mesh and analyzed using a finite element computer program which was developed by Mahamoud and Gupta and migrated to a Cray Y-U 00 at SERI. The results are compared with membrane theory and Muller-Scordelis's results. Comparing with Muller-Scordelis's result it shows that good agreements between two analyses, except a discrepancy in the normal deflections of the crown beam. The behavior of the crown beam is quite sensitive and needs further study. The analysis shows that Gabled HP shells do not behave as the typical shells according to the membrane theory. To design such Gabled HP shells we rather use a finite element analysis which simulates realistically membrane and honing actions of the shells.

• Proceedings of the Korea Concrete Institute Conference
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• 1998.10a
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• pp.405-411
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• 1998

An iterative numerical computational algorithm is presented to design a plate of shell element subjected to membrane and flexural forces. Based on equilibrium consideration, equations for capacities of top and bottom reinforcements in two orthogonal directions have been derived. The amount of reinforcement is determined locally, i. e., for each sampling point, from the equilibrium between applied and internal forces. One case of design is performed for a hyperbolic paraboloid saddle shell (originally used by Lin and Scordelis) to check the design strength against a consistent design load, therefore, to verify the adequacy of design practice for reinforced concrete shells. Based on nonlinear analyses performed, the analytically calculated ultimate load exceeded the design ultimate load from 14-43% for an analysis with relatively low to high tension stiffening, ${\gamma}$ =5~20 cases. For these cases, the design method gives a lower bound on the ultimate load with respect to Lower bound theorem. This shows the adequacy of the current practice at least for this saddle shell case studied. To generalize the conclusion many more designs-analyses are performed with different shell configurations.

• Advances in materials Research
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• v.5 no.4
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• pp.205-221
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• 2016

In this article, the buckling responses of functionally graded curved (spherical, cylindrical, hyperbolic and elliptical) shell panels under elevated temperature load are investigated numerically using finite element steps. The effective material properties of the functionally graded shell panel are evaluated using Voigt's micromechanical model through the power-law distribution with and without temperature dependent properties. The mathematical model is developed using the higher-order shear deformation theory in conjunction with Green-Lagrange type nonlinear strain to consider large geometrical distortion under thermal load. The efficacy of the proposed model has been checked and the effects of various geometrical and material parameters on the buckling load are analysed in details.

• Earthquakes and Structures
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• v.20 no.4
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• pp.405-415
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• 2021

Following the dynamic property analysis and elaboration, linear response spectrum analysis (RSA) and response history analysis (RHA) were conducted on a representative hyperbolic cooling towers (HCT) in present study. The seismic responses in tower shell were illustrated in detail, including the internal force amplitude, modal contribution, influence from damping ratio, comparison of results got from RSA and RHA and especially the latitude distributions of internal forces. The results show that the eigenmodes could be classified in a new method into four types according to their mode shapes and only the lateral bending modes and vertical stretching modes are meaningful for horizontal and vertical earthquake correspondingly. The bending modes and seismic deformation display the same feature which is global lateral bending accompanied by minute circular flow displacement of section. This feature also decides the latitude distributions of internal forces as sine or cosine. Moreover, the following method is also proposed for approximate estimation of internal force amplitudes without time-consuming response history analysis: getting the response spectrums of the selected ground accelerations and then comparing values of response spectrums at the natural period of first lateral bending mode because it is always prime dominant for horizontal seismic responses.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.13 no.2
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• pp.11-20
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• 1993

Nonlinear inelastic behavior of an HP saddle shell has been examined by a finite element computer program developed on a Cray Y-MP. The mesh convergence is studied using three progressively refined finite element mesh models, $16{\times}16$, $32{\times}32$ and $64{\times}64$, for the elastic and inelastic analyses. It is shown that the $32{\times}32$ mesh model gives a solution that is very close to that given by the $64{\times}64$ mesh model, thus, showing a convergence. The inelastic analysis shows that the shell has a tremendous capacity to redistribute the stresses. At the ultimate, the concrete cracks and the reinforcement yieldings are spread out all over the shell, indicating that the stress distribution in the shell is approaching that given by the classical membrane theory. The present computer program provides a very useful tool for evaluating the nonlinear ultimate behavior of concrete shells during the design process.