• Structural Engineering and Mechanics
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• v.50 no.6
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• pp.797-816
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• 2014

Cooling tower is analyzed as an assembly of layered nonlinear shell elements. Geometric representation of the shell is enabled through layered nonlinear shell elements to define the different layers of reinforcements and concrete by considering the material nonlinearity of each layer for the cooling tower shell. Modal analysis using Ritz vector analysis and nonlinear time history analysis by direct integration method have been carried out to study the effects of the inclination of the supporting columns of the cooling tower shell on its dynamic characteristics. The cooling tower is supported by I-type columns and ${\Lambda}$-type columns supports having the different inclination angles. Relevant comparisons of the dynamic response of the structural system at the base level (at the junction of the column and shell), throat level and at the top of the tower have been made. Dynamic response of the cooling tower is found to be significantly sensitive to the change of the inclination of the supporting columns. It is also found that the stiffness of the structure system increases with increase in inclination angle of the supporting columns, resulting in decrease of the period of the structural system. The participation of the stiffness of the tower in structural response of the cooling tower is fund to be dependent of the change in the inclination angle and even in the types of the supporting columns.

• Wind and Structures
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• v.2 no.2
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• pp.105-117
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• 1999

The various spectral density functions of wind are applied in the wind process simulation by the spectral representation method. In view of the spectral density functions, the characteristics of the simulated processes are compared. The ensemble spectral density functions constructed from the simulated sample processes are revealed to have the similarity not only in global shape but also in the maximum values with the target spectral density functions with a high accuracy. For the correlation structure to be satisfied in the circumferential direction on the cooling tower shell, a new formula is suggested based on the mathematical expression representing the circumferential distribution of the wind pressure on the cooling tower shell. The simulated wind processes are applied in the dynamic analysis of cooling tower shell in the time domain and the fluctuating stochastic behavior of the cooling tower shell is investigated.

• Journal of Korean Association for Spatial Structures
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• v.16 no.3
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• pp.67-78
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• 2016

Determining of the shape in the process of design for natural draught cooling tower is very important, because the shape of hyperbolic shell is respond sensitively to dynamic behavior of the whole cooling tower against wind load. In engineering practice, the geometric parameters have been determining based on the natural frequency. This study analyses influence of the tower shell geometric parameters on the structural behavior. For three representative models were selected, they were analyzed based on evaluation of damage by means of nonlinear FE-method. As a result, a hyperbolic rotational shell with the small radius overall was the lowest damage index induced by sufficient capacity of the stress redistribution and thus a wind-insensitive structure.

• Structural Engineering and Mechanics
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• v.5 no.5
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• pp.541-552
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• 1997

In this paper the ultimate strength of the R/C cooling towers, which have initial imperfection and pre-cracked elements, is analyzed. The initial geometric imperfections arise from the unavoidable inaccuracies under the construction and the pre-cracks are assumed to be produced by the temperature stress gradients or cyclic loading under wind pressure and/or earthquake load. Both effects are strongly influenced on the strength of the R/C cooling tower shell structures. The reinforcing ratio is also the important factor to evaluate the ultimate strength of the R/C cooling tower shells. However we could not analyze these structures experimentally because of their large, analyses are the powerful schemes to evaluate the safety and reliability of these structures. The analyzed model is Port Gibson cooling tower shell. In the numerical analysis the geometric and material nonlinearities are taken into account.

• 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.

• Wind and Structures
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• v.11 no.6
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• pp.479-496
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• 2008

In this paper, computer simulation of wind flow around a single cooling tower with louver support at the base in the KAZERUN power station in south part of IRAN is presented as a case study. ANSYS FLOTRAN, an unstructured finite element incompressible flow solver, is used for numerical investigation of wind induced pressure load on a single cooling tower. Since the effects of the wind ribs on external surface of the cooling tower shell which plays important role in formation of turbulent flow field, an innovative relation is introduced for modeling the effects of wind ribs on computation of wind pressure on cooling tower's shell. The introduced relation which follows the concept of equivalent sand roughness for the wall function is used in conjunction with two equations ${\kappa}-{\varepsilon}$ turbulent model. In this work, the effects of variation in the height/spacing ratio of external wind ribs are numerically investigated. Conclusions are made by comparison between computed pressure loads on external surface of cooling tower and the VGB (German guideline for cooling tower design) suggestions.

• Proceedings of the Korea Concrete Institute Conference
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• 2000.04a
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• pp.501-506
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• 2000

An iterative numerical computational algorithm is presented to design a plate or 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. Based on nonlinear analyses performed in a hyperbolic cooling tower, the analytically calculated ultimate load exceeded the design ultimate load from 50% to 55% for an analysis with relatively low to high tension stiffening, cases $\gamma$=10 and 15. 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 th current practice at least for this cooling tower shell case studied. To generalize the conclusion more designs - analyses should be reformed with different shell configurations.

• 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.55 no.4
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• pp.785-799
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• 2015

A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies of hyperboloidal shells free at the top edge and clamped at the bottom edge like a hyperboloidal cooling tower by the Ritz method based upon the circular cylindrical coordinate system instead of related 3-D shell coordinates which are normal and tangent to the shell midsurface. The Legendre polynomials are used as admissible displacements. Convergence to four-digit exactitude is demonstrated. Natural frequencies from the present 3-D analysis are also compared with those of straight beams with circular cross section, complete (not truncated) conical shells, and circular cylindrical shells as special cases of hyperboloidal shells from the classical beam theory, 2-D thin shell theory, and other 3-D methods.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.13 no.1
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• pp.147-158
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• 2000

For the large scale reinforced concrete cooling tower shells, the shape imperfection can be introduced due not only to mistakes in the process of construction but also to the long term behavior of concrete. The shape imperfection evokes the additional responses such as displacements and stresses in addition to the design values. In this study, the statistical behavior of the RC cooling tower shell due to the shape imperfection is investigated using the Monte Carlo simulation. The radius of cooling tower and the shell thickness are adopted as the parameters which cause the shape imperfection. The shape imperfection is modeled as a stochastic field rather than the local one of axisymmetric or bulge type of imperfection. The randomness in the radius is shown to be more affecting the structural responses than the randomness in the shell thickness. In addition to the geometrical randomness, the effect of randomness in the modulus of elasticity on the structural response is also investigated and compared with that of the geometrical ones.