• Structural Engineering and Mechanics
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• 제22권2호
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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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• 한국공간정보시스템학회 2004년도 춘계 학술발표회 논문집 제1권1호(통권1호)
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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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• 제2권1호
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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.

• 한국콘크리트학회:학술대회논문집
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• 한국콘크리트학회 2000년도 봄 학술발표회 논문집
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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.

• 한국전산구조공학회논문집
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• 제13권1호
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• pp.147-158
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• 2000

철근콘크리트 냉각탑은 대형의 구조물로서 건설과정중의 오류와 콘크리트의 장기 거동에 의하여 기하학적 형상이 설계에서 목적하는 형상에서 벗어난 형상불완전을 가질 수 있다. 형상불완전의 구조거동에의 영향은 완전쉘에 나타나는 응력 이외에 추가적인 응력의 발생을 들 수 있다. 본 논문에서는 몬테카를로 방법을 사용하여 냉각탑 쉘의 형상불완전에 의한 확률론적 거동에 대하여 고찰하였다. 냉각탑에 형상불완전을 유발하는 기하인수로는 냉각탑의 반지름과 쉘의 두께를 택하였다. 이들 기하인수는 기존에 사용되던 모델인 축대칭 모델과 볼록형상의 모델과는 달리 특정 통계특성치를 가지는 추계장으로 가정하였다. 해석 결과는 냉각탑의 반지름에 나타나는 불확실성은 쉘의 두께에서의 불확실성보다 구조거동의 반응변화도에 매우 큰 영향을 미친다는 사실을 보여주었다. 기하학적 인수의 불확실성에 더하여 재료탄성계수의 공간적 불확실성에 의한 구조 반응변화도를 고찰하여 비교하였다.

• Structural Engineering and Mechanics
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• 제14권2호
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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.

• 대한토목학회논문집
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• 제12권4호
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• pp.59-70
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• 1992

풍하중(風荷重)을 받는 쌍곡 냉각탑의 비탄성(非彈性), 비선형(非線型) 극한(極限) 거동(擧動)을 Cray Y-MP 슈퍼 컴퓨터에 개발(開發)한 유한요소(有限要素)컴퓨터 프로그램으로 연구(研究)하였다. 유한요소 망(mesh)을 각각 잘게 잘라서 3모델을 만들고, 이 모델들을 이용하여 탄성과 비탄성 해석으로 유한요소 망의 수렴관계(mesh convergence)를 연구하였다. 연구결과 유한요소의 크기가 냉각탑의 극한거동을 예측하는데 매우 중요한 역할을 하고있음을 볼 수 있었다. 비록 쌍곡 냉각탑이 풍하중(風荷重)에 대해서 막응력(膜應力)(membrane stress)으로 저항하나, 본 연구(研究) 결과(結果) 휨응력(應力)(bending stress)도 냉각탑의 파괴와 거동(擧動)에 매우 중요한 역할을 하고 있음을 알아 내었다. 해석(解析)한 냉각탑은 형성값(Shape factor)이 1.48에 이르렀고, 이는 냉각탑의 자오선 응력(meridional stress)이 원둘레방향으로 상당히 재분배 되고 있음을 보여주는 것이다. 이러한 재분배에 대한 사실은 배치된 철근의 항복이 바람방향 자오선으로부터 $30^{\circ}C$에 까지 나타난 것으로 더욱더 뚜렷하였다. 현재의 탄성해석을 이용하는 냉각탑 설계(設計) 방법은 안전(安全)측에 있음을 보여 주었으며, 1보다 큰 형상값을 설계시에 활용하기 위해서는 더욱더 많은 연구가 선행되어야 할 것이다.

• Computers and Concrete
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• 제20권1호
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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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• 제4권2호
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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.