• 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.

• 한국공간정보시스템학회:학술대회논문집
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• 2004.05a
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• pp.279-286
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• 2004

An accumulated crack damage which propagates progressively with time was frequently observed on several engineering structures, This paper numerically demonstrates this damage process on large cooling tower shells under thermal and wind loads. Damage states under varying loads are investigated and the influence of this progressive damage process on the life-cycle of cooling towers discussed. The paper presents briefly some fundamentals of the geometrically and physically non-linear numerical analysis employed for reinforced concrete, especially concerning the models used for concrete, steel reinforcement and the bond between them. As a numerical example an existing cooling tower with noticeable meridian crack damage is analysed. The existing damage state of the cooling tower is determined by quasi-static analyses for temperature, hygric and cyclic wind leading. The change in the dynamical behaviour of the structure as mirrored in its natural frequencies and mode shapes is presented and discussed. Finally, the example shows that such damage processes develop progressively over the life-time of the structures.

• Computational Structural Engineering : An International Journal
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• v.2 no.1
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• pp.25-32
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• 2002

Natural draught cooling towers often develop visible crack structures as consequences of progressive damage processes over their life-time. The aim of this paper is a numerical demonstration of the progressive damage process of cooling towers, representatively for the reinforced concrete structures, in order to improve the durability and extend the life-time of structures subjected to such damage processes. For the analyses, the applied material model for reinforced concrete will be briefly introduced. An existing natural draught cooling tower with a pronounced crack structure, in which this crack structure indicates the typical damage pattern of large cooling towers will be numerically simulated. The change of dynamical behavior of the structure with regard to natural frequencies, reflecting the global damage process due to the degrading stiffness of the structure in dependence of the load type and intensity, will be presented and discussed.

• 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 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.

• 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.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.12 no.4
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• pp.59-70
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• 1992

Inelastic nonlinear behavior of a hyperbolic cooling tower under wind loading is studied using a finite element program developed on a Cray Y-MP. Convergence studies for the elastic and inelastic analyses are performed using three mesh models. It is shown that the mesh convergence plays an important role in accurately predicting the inelastic behavior of a cooling tower. Even though the cooling tower resists the applied forces through membrane stresses, it is found that the bending stresses play an important role in the failure and behavior of the cooling tower. The present analysis gives a shape factor of 1.48, which indicates a significant redistribution of meridional stresses. It is further evidenced by the distribution of meridional reinforcement yielding which reaches up to $30^{\circ}$ from the windward meridian. The present practice of using elastic analysis for calculating the design stresses appears to be at least safe and conservative. A more comprehensive study should lead to conclusions that would allow use of a higher-than-one shape factor, thus requiring less meridional reinforcement than the present design method does.

• Computers and Concrete
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• v.20 no.1
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• pp.99-110
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• 2017

Service life assessments which do not include the synergy between mechanical and environmental loading are neglecting a factor that can have a significant impact on structural safety and durability assessment. The degradation of concrete structure is a result of the combined effect of environmental and mechanical factors. In order to make service life design realistic it is necessary to consider both of these factors acting simultaneously. This paper deals with the advanced modelling of concrete carbonation and chloride ingress into concrete using stochastic 1D and 2D models. Widely accepted models incorporated into the new fib Model Code 2010 are extended to include factors that reflect the coupled effects of mechanical and environmental loads on the durability and reliability of reinforced concrete structures. An example of cooling tower degradation by carbonation and an example of a bended reinforced concrete beam kept for several years in salt fog are numerically studied to show the capability of the stochastic approach. The modelled degradation measures are compared with experimental results, leading to good agreement.

• Structural Engineering and Mechanics
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• v.4 no.2
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• pp.139-148
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• 1996

Vector algorithms and the relative importance of the four basic modules (computation of element stiffness matrices, assembly of the global stiffness matrix, solution of the system of linear simultaneous equations, and calculation of stresses and strains) of a finite element computer program for inelastic analysis of reinforced concrete shells are presented. Performance of the vector program is compared with a scalar program. For a cooling tower problem, the speedup factor from the scalar to the vector program is 34 for the element stiffness matrices calculation, 25.3 for the assembly of global stiffness matrix, 27.5 for the equation solver, and 37.8 for stresses, strains and nodal forces computations on a Gray Y-MP. The overall speedup factor is 30.9. When the equation solver alone is vectorized, which is computationally the most intensive part of a finite element program, a speedup factor of only 1.9 is achieved. When the rest of the program is also vectorized, a large additional speedup factor of 15.9 is attained. Therefore, it is very important that all the modules in a nonlinear program are vectorized to gain the full potential of the supercomputers. The vector finite element computer program for inelastic analysis of RC shells with layered elements developed in the present study enabled us to perform mesh convergence studies. The vector program can be used for studying the ultimate behavior of RC shells and used as a design tool.