• 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.

• Structural Engineering and Mechanics
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• v.14 no.2
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• pp.171-190
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• 2002

Two cases of design are performed for the hyperbolic paraboloid saddle shell (Lin-Scordelis saddle shell) and the hyperbolic cooling tower (Grand Gulf cooling tower) to check the design strength against a consistent design load, therefore to verify the adequacy of the design algorithm. An iterative numerical computational algorithm is developed for combined membrane and flexural forces, which is based on equilibrium consideration for the limit state of reinforcement and cracked concrete. The design algorithm is implemented in a finite element analysis computer program developed by Mahmoud and Gupta. The amount of reinforcement is then determined at the center of each element by an elastic finite element analysis with the design ultimate load. Based on ultimate nonlinear analyses performed with designed saddle shell, the analytically calculated ultimate load exceeded the design ultimate load from 7% to 34% for analyses with various magnitude of tension stiffening. For the cooling tower problem the calculated ultimate load exceeded the design ultimate load from 26% to 63% with similar types of analyses. Since the effective tension stiffening would vary over the life of the shells due to environmental factors, a degree of uncertainty seems inevitable in calculating the actual failure load by means of numerical analysis. Even though the ultimate loads are strongly dependent on the tensile properties of concrete, the calculated ultimate loads are higher than the design ultimate loads for both design cases. For the cases designed, the design algorithm gives a lower bound on the design ultimate load with respect to the lower bound theorem. This shows the adequacy of the design algorithm developed, at least for the shells studied. The presented design algorithm for the combined membrane and flexural forces can be evolved as a general design method for reinforced concrete plates and shells through further studies involving the performance of multiple designs and the analyses of differing shell configurations.

• Wind and Structures
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• v.16 no.6
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• pp.579-601
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• 2013

Interference effects are of considerable concern for group hyperboloidal cooling towers, but evaluation methods and results are different from each other because of the insufficient understanding on the structure behavior. Therefore, the mechanical performance of hyperboloidal cooling tower shell under wind loads was illustrated according to some basic properties drawn from horizontal rings and cantilever beams. The hyperboloidal cooling tower shell can be regarded as the coupling of horizontal rings and meridian cantilever beams, and this perception is beneficial for understanding the mechanical performance under wind loads. Afterwards, the mean external latitude wind pressure distribution, CP(${\theta}$), was artificially adjusted to pursue the relationship between different CP(${\theta}$) and wind-induced responses. It was found that the maximum responses in hyperboloidal cooling tower shell are primarily dominated by the non-uniformity of CP(${\theta}$) but not the local pressure amplitude CP or overall resistance/drag coefficient CD. In all the internal forces, the maximum amplitude of meridian axial tension shows remarkable sensitivity to the variation of CP(${\theta}$) and it's also the controlling force in structure design, so it was selected as an indicator to evaluate the influence of CP(${\theta}$) on responses. Based on its sensitivity to different adjustment parameters of CP(${\theta}$), an comprehensive response influence factor, RIF, was deduced to assess the meridian axial tension for arbitrary CP(${\theta}$).

• Structural Engineering and Mechanics
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• v.15 no.1
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• pp.53-70
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• 2003

The motivation of this paper is to introduce the modern technology of large-scale cooling tower design. Thereby the innovative design concept for the world's largest cooling tower with a height of 200 m is briefly presented (Harte & Kr$\ddot{a}$tzig 2002, Bush et al. 2002). The new concept was considered not only for safety, but also for preservation of the durability of the structure, because cracking damage in large cooling towers in general cause extremely high cost of maintenance and repair. The paper demonstrates numerically the damage process in large cooling towers (Kr$\ddot{a}$tzig et al. 2001), and describes some basics of the numerical finite element approach for damage propagation modelling of shell structure. A prototype is analysed to trace the progressive damage process, whereby the changes in the dynamical behaviour of the structure, as mirrored in its natural frequencies and the corresponding mode shapes, are presented and discussed. Finally, the example shows that such damage processes develop progressively over the life-time of the shell structure.

• Structural Engineering and Mechanics
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• v.22 no.2
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• pp.223-240
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• 2006

Taking into account the geometrical and material nonlinearities, an ultimate behavior of reinforced concrete cooling tower shell in hyperbolic configuration is presented. The design wind pressures suggested in the guidelines of the US (ACI) and Germany (VGB), with or without the effect of internal suction, are employed in the analysis to examine the qualitative and quantitative characteristics of each design wind pressure. The geometrical nonlinearity is incorporated by the Green-Lagrange strain tensor. The nonlinear features of concrete, such as the nonlinear stress-strain relation in compression, the tensile cracking with the smeared crack model, an effect of tension stiffening, are taken into account. The biaxial stress state in concrete is represented by an improved work-hardening plasticity model. From the perspective of quality of wind pressures, the two guidelines are determined as highly correlated each other. Through the extensive analysis on the Niederaussem cooling tower in Germany, not only the ultimate load is determined but also the mechanism of failure, distribution of cracks, damage processes, stress redistributions, and mean crack width are examined.

• Computers and Concrete
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• v.8 no.1
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• pp.97-110
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• 2011

In this paper, FEM procedure is applied to the static and dynamic analyses of R/C structures. Simple R/C shell structure is solved by using FEM procedures and the experimental evaluations are performed to represent the applicability of FEM procedure to R/C structures. Also, R/C columns are analyzed numerically and experimentally. On the basis of these results, FEM procedures are applied to the R/C cooling tower structures assembled by huge R/C shell structure and a lot of discrete R/C columns. In this analysis, the parallel computing procedures are introduced into these analyses to reduce the computational effort. The dynamic performances of R/C cooling tower are also solved by the application of parallel computations as well. From the numerical analyses, the conventional FEM procedures combined with computational technologies enables us to design the huge R/C structures statically and dynamically.

• Wind and Structures
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• v.20 no.3
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• pp.449-468
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• 2015

Current wind-resistance designs of large-scale indirect dry cooling towers (IDCTs) exclude an important factor: the influence of the ventilation rate for radiator shutter on wind loads on the outer surfaces of the tower shell. More seemingly overlooked aspects are the effects of various ventilation rates on the wind pressure distribution on the tower surfaces of two IDCTs, and the feature of the flow field around them. In order to investigate the effects of the radiator shutter ventilation rates on the aerodynamic interference between IDCTs, this paper established the numerical wind tunnel model based on the Computational Fluid Dynamic (CFD) technology, and analyzed the influences of various radiator shutter ventilation rates on the aerodynamic loads acting upon a single and two extra-large IDCTs during building, installation, and operation stages. Through the comparison with the results of physical wind tunnel test and different design codes, the results indicated that: the influence of the ventilation rate on the flow field and shape coefficients on the outer surface of a single IDCT is weak, and the curve of mean shape coefficients is close to the reference curve provided by the current design code. In a two-tower combination, the ventilation rate significantly affects the downwind surface of the front tower and the upwind surface of the back tower, and the larger positive pressure shifts down along the upwind surface of the back tower as the ventilation rate increases. The ventilation rate significantly influences the drag force coefficient of the back tower in a two-tower combination, the drag force coefficient increases with the ventilation rate and reaches the maximum in a building status of full ventilation, and the maximum drag coefficient is 11% greater than that with complete closure.

• Wind and Structures
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• v.19 no.4
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• pp.443-465
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• 2014

Hyperbolic thin-shell cooling towers have complicated vibration modes, and are very sensitive to the effects of group towers and wind-induced vibrations. Traditional aero-elastic models of cooling towers are usually designed based on the method of stiffness simulation by continuous medium thin shell materials. However, the method has some shortages in actual engineering applications, so the so-called "equivalent beam-net design method" of aero-elastic models of cooling towers is proposed in the paper and an aero-elastic model with a proportion of 1: 200 based on the method above with integrated pressure measurements and vibration measurements has been designed and carried out in TJ-3 wind tunnel of Tongji university. According to the wind tunnel test, this paper discusses the impacts of self-excited force effect on the surface wind pressure of a large-scale cooling tower and the results show that the impact of self-excited force on the distribution characteristics of average surface wind pressure is very small, but the impact on the form of distribution and numerical value of fluctuating wind pressure is relatively large. Combing with the Complete Quadratic Combination method (hereafter referred to as CQC method), the paper further studies the numerical sizes and distribution characteristics of background components, resonant components, cross-term components and total fluctuating wind-induced vibration responses of some typical nodes which indicate that the resonance response is dominant in the fluctuating wind-induced vibration response and cross-term components are not negligible for wind-induced vibration responses of super-large cooling towers.

• 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.

• Journal of The Korean Society of Agricultural Engineers
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• v.55 no.5
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• pp.17-23
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• 2013

Six-valent chromium ($Cr^{6+}$) is a highly toxic pollutant, supplied in a variety of industrial activities such as leather tanning, cooling tower blowdown, and plating. Herein, we investigated the removal of $Cr^{6+}$ from aqueous phase using low-cost adsorbents. Steel slag, montmorillonite, illite, kaolinite, red mud, and acid treated red mud with 0.5, 1.0, and 2.0 M HCl were used as adsorbent for the removal of $Cr^{6+}$ and the results showed that acid treated red mud with 2.0 M HCl (ATRM-2.0 M) had higher adsorption capacity of $Cr^{6+}$ than other adsorbents used. Accordingly, $Cr^{6+}$ removal by ATRM-2.0 M were studied in a batch system with respect to changes in initial concentration of $Cr^{6+}$, initial solution pH, adsorbent dose, adsorbent mixture, and seawater. Equilibrium sorption data were described well by Freundlich isotherm model. The influence of initial solution pH on $Cr^{6+}$ adsorption was insignificant. The use of the ATRM-2.0 M alone was more effective than mixing it with other adsorbents including red mud, zeolite, oyster shell, lime stone, and montmorillonite for the removal of $Cr^{6+}$. The $Cr^{6+}$ removal of the ATRM-2.0 M was slightly less in seawater than deionized water, resulting from the presence of anions in seawater competing for the favorable adsorption site on the surface of ATRM-2.0 M. It was concluded that the ATRM-2.0 M can be used as a potential adsorbent for the removal of $Cr^{6+}$ from the aqueous solutions.