Hyperbolic Cooling Tower Shells Research Articles

A Simplified Procedure for the Structural Reinforcement Design of Hyperbolic Cooling Tower Shells

A Simplified Procedure for the Structural Reinforcement Design of Hyperbolic Cooling Tower Shells

Studies on the influence factors of wind dynamic responses on hyperbolic cooling tower shells

Wind induced dynamic responses on hyperbolic cooling tower (HCT) shells are complicated functions of structure and wind properties, such as the fundamental frequency fmin, damping ratio zeta wind velocity V, correlationship in meridian direction and so on, but comprehensions on the sensitivities of the dynamic responses to these four factors are still limited and disagree from each other. Following the dynamic calculation in time domain, features of dynamic effects were elaborated, focusing on the background and resonant components SigmaB and SigmaR, and their contributions to the total rms value SigmaT. The SigmaR is always less than SigmaB when only the maximum SigmaT along latitude is concerned and the contribution of SigmaR to SigmaT varies with responses and locations, but the SigmaR couldn\'t be neglected for structural design. Then, parameters of the above four factors were artificially adjusted respectively and their influences on the gust responses were illustrated. The relationships of SigmaR and the former three factors were expressed by fitted equations which shows certain differences from the existing equations. Moreover, a new strategy for wind tunnel tests aiming at surface pressures and the following dynamic calculations, which demands less experiment equipment, was proposed according to the influence from meridian correlationship.

Wind induced dynamic responses on hyperbolic cooling tower shells and the equivalent static wind load

Wind induced dynamic responses on hyperbolic cooling tower (HCT) shells and the equivalent static wind load (ESWL) are prime concerns for structural designers and researchers. Followed the dynamic calculation in time domain, using the wind pressure got from wind tunnel tests, the dynamic effects of internal forces and displacement of HCT shell were illustrated through the peak factor g and gust response factor G. The original 2-D distribution of G along latitude and meridian directions was degenerated reasonably to 1-D distribution just along meridian direction and the 2-D distribution of g to a single value, according to the structure behaviors, characteristics of dynamic responses and structural design principles of HCT shell. Based on these features of HCT shell and degenerations of g and G, a new approach pursuing ESWL was proposed whose objective is the reinforcement amount but not the internal forces. The ESWL is got by simple amplification of the mean wind load with a single parameter γ, but the γ used for the latitude and meridian directions are independent and the former is much larger. This is the actual reflection of the independent structural design and different dynamic effects of internal forces in latitude and meridian directions.

Vibration analysis of free-fixed hyperbolic cooling tower shells

Vibration analysis of free-fixed hyperbolic cooling tower shells

Free and Forced Vibration Analyses of Hyperbolic Cooling Tower Shell Using Harmonic Solid Ring Finite Elements

This paper discusses free and forced vibration responses of hyperbolic cooling tower shell which is one of the complex real life applications of axisymmetric structures. 9-noded harmonic solid ring finite element is used in the numerical model of the cooling tower. Physically a three-dimensional cooling tower problem is reduced to a two dimensional one by expressing earthquake loading in the form of Fourier series for a single harmonic with the help of harmonic elements. Therefore, the complete solution for the problem is obtained simply for a single load component that makes the model computationally much more efficient. A computer program is coded in Matlab for the purpose and the results obtained in the study are verified with the results available in the literature. A parametric study is also performed for the variations in shell curvature of the tower. The time history analysis method is used for the dynamic response of the cooling tower shell. Acceleration records of Duzce earthquake is used in the study and the results are presented in tabular and graphical formats comparatively for varying shell curvature. It can be concluded that circumferential mode number and shell curvature have significant effects on the dynamic responses of cooling towers.

Ultimate strength of large scale reinforced concrete thin shell structures

This paper presents ultimate behavior of large scale reinforced concrete shell structures: hyperbolic cooling tower shell and hyperbolic paraboloid (HP) saddle shell. Both geometrical and material nonlinearities were considered in the analysis. To investigate the influence of concrete tension cracks on the structural behavior, the smeared crack model having the capability of representing double crack and crack rotation was used in the analysis. The biaxial stress state in shells is represented by the improved work-hardening plasticity concrete model, where the ductility increase phenomenon can be depicted. The load-displacement relationship, stress fields, occurrence and propagation of cracks in concrete and steel yield patterns are presented. Due to the factors such as modification in plasticity model, stiffness contribution in the doubly cracked elements, the model predicts a more ductile behavior than the results reported in the current literature. The failure of cooling tower shell seems to occur due to local yielding of meridional reinforcement in the windward meridian. In the case of HP saddle shell, structural instability occurs due to severe tension cracks in the shell part before yielding of reinforcement could occur.

Significance of mesh-fineness in accuracy of finite element analysis of hyperbolic cooling tower shells

Increased dependence on finite element modelling of structures in practice has made awareness of error potential of these analyses essential. This concern is even more pertinent in case of shell structures, since finite element analysis results of these structures is more error-prone. In reported research, the effect of mesh-fineness of finite element models on accuracy of finite element analysis solutions is investigated for hyperbolic cooling tower shells. The sensitivity of the errors to geometry of the shell is also examined. Elastic material model and static gravity loading is used. The study findings indicate that under symmetric state of stress, inadequate mesh-fineness may cause significant error in the shell force estimate from finite element analysis. The accuracy of longitudinal shell force estimate is fairly insensitive to the geometry of the shell. However, even small changes in the shape may drastically affect the accuracy of meridional shell force estimates.

Buckling of cooling tower shells with ring-stiffeners

With the stability analysis of hyperbolic cooling tower shells with ring-stiffeners, our paper proposes the linear pre-buckling consistent theory. The numerical result shows that this linear analysis method is very effective and practical in engineering, for its precision of computation is up to the level of the nonlinear analysis when it is used for the study of critical loads of the hyperbolic cooling tower which is mainly governed by wind pressure and for the study of the effect of some other factors concerned in design on the buckling of shells. Based on that, we have obtained a series of conclusions which will greatly benefits the engineering design when discussing the effect on the critical wind loading of the shell which is caused by the following factors such as the position of rings, the number of rings and the dead weight.

Nonlinear buckling analysis of hyperbolic cooling tower shell with ring-stiffeners

This paper is concerned with a numerical solution of hyperbolic cooling tower shell, a class of full nonlinear problems in solid mechanics of considerable interest in engineering applications. In this analysis, the post-buckling analysis of cooling tower shell with discrete fixed support and under the action of wind loads and dead load is studied. The influences of ring-stiffener on instability load are also discussed. In addition, a new solution procedure for nonlinear problems which is the combination of load increment iteration with modified R-C are- length method is suggested. Finally, some conclusions having important significance for practice engineering are given.

Asymptotic analyses of dynamic response of hyperbolic cooling tower shells with ring-stiffeners perturbation finite element solution

In this paper, a new analysing method called perturbational finite element is suggested, by means of which we calculate the dynamic behaviour and response to turbulent wind of hyperbolic cooling tower shell with ring-stiffeners. The results are compared with those of finite element numerical method and show that the method has the advantages of clear physical idea and convenience of calculation and the accuracy of results is assured.

Stress analysis of hyperbolic shells of revolution with non-axisymmetrical geometric imperfections

In analyzing hyperbolic shells of revolution with non-axisymmeteric imperfections, an approximate method based on simulating the effect of imperfections by the application of fictitious normal pressure loading on the perfect shell is investigated. In the analysis of a shell of revolution with a bulge-type imperfection under non-axisymmetric loads, an efficient algorithm of applying the method is developed: the effect of individual curvature errors on stress resultants and couples are separately considered, while the interactions among various curvature errors are properly treated in the analysis by an iterative procedure. This algorithm avoids repeated analyses for non-axisymmetric loads and may be implemented with a purely axisymmetric analysis capability. A hyperbolic cooling tower shell with a bulge-type imperfection is analyzed under dead load and wind load conditions by the equivalent load method. A direct analysis of the imperfect shell is also made by a specialized finite element program. Through numerical studies, the accuracy and applicability of the equivalent load method are examined.

Free Vibration of Hyperbolic Cooling Towers

A modified finite difference technique is used to determine the natural frequencies and mode shapes of hyperbolic cooling tower shells. The influence of the meridional curvature and the boundary conditions on the vibration characteristics of the tower is investigated. In all cases, changes in frequency are found to be essentially due to changes in membrane energy. It is shown that, for a fixed-free shell, the increased meridional curvature leads to an increase in the natural frequency. The lack of axial restraint results in a large reduction in the membrane energy and consequently the natural frequency. For simply-supported shells, a critical meridional curvature at which the membrane energy effectively vanishes is shown to exist.

Natural frequencies of cooling tower shells

A theoretical determination of the lowest natural frequencies of inextensional vibrations of hyperbolic cooling tower shells is first presented. It is shown that inextensional behaviour is only possible for certain types of support condition at the base, one of which consists of four pairs of inclined columns evenly spaced round the circumference which, at their points of attachment, only permit displacements normal to the plane of the shell. Experiments to determine the natural frequencies and modes of vibration of a model shell are then described. This model, which was made by the electro-deposition of copper on a Perspex mould, could be supported at its base by up to forty pairs of inclined columns. Using only four evenly spaced pairs of columns the lowest natural frequencies of inextensional vibrations were first determined, and found to agree well with the theoretical values. The natural frequencies and modes of the extensional vibrations which occurred when the shell was supported by forty pairs of columns were then explored. Finally, the effect of removing some of the supports, thereby simulating a horizontal fracture in part of the shell, was studied. The possibility of wind-induced vibrations occurring in practice is then considered. It is concluded that these are unlikely to occur unless the shell has already suffered damage, as for example by experiencing a horizontal fracture over part of its circumference near the base.