• Structural Engineering and Mechanics
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• 제5권5호
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• pp.507-521
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• 1997

The ultimate behavior of a reinforced concrete hyperbolic paraboloid saddle shell under uniformly distributed vertical load is investigated using an inelastic, large displacement finite-element program originally developed at North Carolina State University. Unlike with the author's previous study which shows that the saddle shell possesses a tremendous capacity to redistribute the stresses, introducing tension stiffening in the model the cracks developed are no longer through cracks and formed as primarily bending cracks. Even though with small tension stiffening effect, the behavior of the shell is changed markedly from the one without tension stiffening effect. The load-deflection curves are straight and the slope of the curves is quite steep and remains unchanged with varying the tension stiffening parameters. The failure of the shell took place quite suddenly in a cantilever mode initiated by a formation of yield lines in a direction parallel to the support-to-support diagonal. The higher the tension stiffening parameters the higher is the ultimate load. The present study shows that the ultimate behavior of the shell primarily depends on the concrete tensile characteristics, such as tensile strength (before cracking) and the effective tension stiffening (after cracking). As the concrete characteristics would vary over the life of the shell, a degree of uncertainty is involved in deciding a specified ultimate strength of the saddle shell studied. By the present study, however, the overload factors based on ACI 318-95 are larger than unity for all the cases studied except that the tension stiffening parameter is weak by 3 with and without the large displacement effect, which shows that the Lin-Scordelis saddle shell studied here is at least safe.

• 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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• 제14권4호
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• pp.807-814
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• 1994

철근콘크리트 쉘구조물에 대한 현행 설계방법의 타당성을 증명하기 위한 시도로서 Lin과 Scordelis에 의해서 사용되었던 쌍곡 포물선 '안장' 쉘에 대한 설계를 막응력 해석(membrane analysis)에 의해서 구한 응력을 토대로 하여, 보강철근의 설계는 특정부분의 극한거동에 근거를 둔 설계방정식을 이용하여 수행하였다. 비탄성해석을 수행한 결과 행이 97%의 설계극한하중을 지지할 수 있음을 보여주었다. 이는 설계방법이 본 연구에서 해석한 특정 쉘의 실제 극한하중에 대해서 소성이론의 하계정리(Lower bound theorem)가 적용 될 수 있다는 가능성을 보여주고 있으며, 따라서 현행 설계방법의 타당성을 제공하고 있다고 볼 수 있다. 이러한 결론을 일반화하기 위해서는 여러 형태의 철근콘크리트 쉘구조물에 대해서 광범위한 설계와 해석이 행해져야 할 것이다.

• 한국콘크리트학회:학술대회논문집
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• 한국콘크리트학회 1998년도 가을 학술발표논문집(II)
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• pp.405-411
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• 1998

An iterative numerical computational algorithm is presented to design a plate of 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. One case of design is performed for a hyperbolic paraboloid saddle shell (originally used by Lin and Scordelis) to check the design strength against a consistent design load, therefore, to verify the adequacy of design practice for reinforced concrete shells. Based on nonlinear analyses performed, the analytically calculated ultimate load exceeded the design ultimate load from 14-43% for an analysis with relatively low to high tension stiffening, ${\gamma}$ =5~20 cases. 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 the current practice at least for this saddle shell case studied. To generalize the conclusion many more designs-analyses are performed with different shell configurations.

• 대한토목학회논문집
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• 제13권2호
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• pp.11-20
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• 1993

쌍곡 포물선 '안장' 쉘의 극한(極限) 거동(擧動)을 슈퍼 컴퓨터에 개발한 유한요소(有限要素) 컴퓨터 프로그램으로 연구(研究)하였다. 잘게 자른 3 모델을($16{\times}16$, $32{\times}32$과 $64{\times}64$) 이용하여 탄성(彈性)과 비탄성(非彈性) 해석으로 유한요소 망(mesh)의 수렴관계를 연구하였으며, 해석 결과 $32{\times}32$ 모델의 해(解)가 $64{\times}64$ 모델의 결과에 매우 가깝게 나타나서, 이 모델이 수렴하고 있음을 보여 주었다. 비탄성(非彈性) 해석 결과(結果) '안장' 쉘이 상당한 응력(應力)재분포 능력(能力)을 갖고 있었으며, 극한 상태에서 콘크리트의 균열과 철근의 항복이 전체 젤에 걸쳐서 나타났다. 이 현상에 따라 응력 분포가 고전적인 막이론(膜理論)(Membrane theory)의 결과에 접근하고 있음을 관찰할 수 있었다. 개발된 컴퓨터 프로그램은 설계시에 콘크리트 쉘구조물의 비선형 극한거동을 산정하는데 매우 유용하게 사용될 수 있을 것이다.