RC Shell Research Articles

Robust design procedure for RC plates and shell structures using developed advanced sandwich model

In recent years, a notable increase in the number of complex concrete roofs has been observed. Simultaneously, the design codes lack design approaches for such structures in which the elements are subjected to combined forces (membrane and transverse) and moments (flexure and torsion). The finite element-based design (FEBD) has been provided for these structural elements; however, it is not widely adopted for the design. Hence, there is an urgent need to fill this gap. Therefore, an automatic FEBD procedure is developed in this study based on the equilibrium consideration, named the developed advanced sandwich model (DASM). The element cracking inspection was performed according to the multi-axial compression state of concrete. Subsequently, the DASM was developed to account for the effect of transverse shear forces. The proposed design algorithm was developed using a Python script linked with ABAQUS software to perform an automatic design for all elements and to be presented as a practical design tool. Additionally, the damage-based analysis was performed as an assessment tool to demonstrate the efficiency of the proposed design procedure. This study illustrated that using the DASM reduced the steel reinforcement by up to 40% and increased the ductility by 10–15%. Also, it is observed that the ultimate capacity of the considered examples, including the solid plate and flat plate, slightly decreased by 4.1% and 1.8% (less than 5%), respectively, which hardly affects the overall response of the designed structure. Indeed, these results demonstrate the efficiency of the developed procedure. In summary, the results of this study indicate that the proposed design framework (DASM) presents a highly accurate, relatively simple, and robust procedure for designing plate and shell structures with complex geometry, where the design process can be completed on a standard personal computer in a few seconds.

Inverted Umbrella-type Hyperbolic Paraboloid Reinforced Concrete Shell Structures (Inverted Umbrella HP RC Shells)

The inverted umbrella HP RC shells became a predominant type of single column structure during the 1950s and 1960s. The paper provides a historical overview of architecturally most attractive inverted umbrella HP structures made out of reinforced concrete. It starts in the second quarter of the 20th century with the world’s oldest umbrella structures, designed by three pioneers: F. Aimond, A. Williams and K. Hruban. The most notable master in designing was F. Candela, as he constructed a number of this structures in Mexico between 1953-68. During the 1960s this form became widely used all over the Western world but suddenly disappear after 1975. The results of the paper are presented in three figures where the inverted umbrella HP RC shells are analysed according to several criteria (number of built elements, roof dimensions with shapes, use of the structures in relationship to year of completion). The similarities and differences between elements of the analysed buildings are compared and discussed. In the conclusion, the advantages and disadvantages are briefly exposed.

On the form of the Musmeci’s bridge over the Basento river

The bridge over the Basento river in Potenza, Italy, designed by Sergio Musmeci, is supported by a continuous double-curvature RC shell optimized to reduce bending forces. This 300m long bridge can be considered as a unique representative example of pioneering research on the design and construction of optimized structures.First, the design process employed for determining the form of the shell and the relevant constructive issues are described. A refined 3D geometric model of the shell is then obtained through an aerial survey carried out by a commercial UAV and a photogrammetric image-based reconstruction. A recent formulation of the Force Density Method allowing for non-isotropic stress state is exploited to numerically derive the form of the supporting shell; it is validated versus the surveyed geometry of the shell by employing a nonlinear optimization procedure in order to identify forces and stresses to be used as input parameters. Finally, the derived form of the shell is tested by a Finite Element analysis to verify its funicular efficiency, i.e., whether it is capable to withstand design loads by pure membrane actions.

Unsteady interaction simulation of a large RC shell with heterogeneous soil milieu for a gradually increasing caisson structure

Prediction and simulation of large shells construction parameters in heterogeneous soil milieu provided considerable expansion of the rational use area of megapolices underground areas for deep transport facilities and engineering infrastructure. Mega sizes of an RC shell allow creating open underground areas, unique in volumes and deepness. The analysis of massive gravitational fencing shell behavior at its gradual increasing and driving into heterogenenous soil milieu allowed identifying the nature of their non-linear and unsteady one. Unsteadiness of the massive structure interaction processes and soil milieu causes the necessity to create methods for strain-stress behavior control of the system “gravitational large body – heterogeneous host medium” for decreasing aggravating influence of the unsteadiness effect on the lowering process. Due to joint step-by-step implementation of geotechnical and structural calculations a history of the shell-soil milieu interaction processes is modeled and the adaptive control parameters of strain-stress behavior are predicted, thus providing conditions of controlled lowering. The paper demonstrates results of the given concept implementation during the unique underground structures of St. Petersburg sewage system design and construction.

STRUCTURAL BEHAVIOR OF R/C SHELL CONSIDERING THE POSITION OF EDGE BEAM

Reinforced Concrete (R/C) shell has been constructed to cover large public spaces and large industrial buildings. RC shell is originally a continuous structure and shows the large load bearing capacity. To apply these structures to such purpose, the structure is cut at any particular portion and loses their continuum properties. Therefore, edge beams must be placed to avoid the stress concentration and a local failure. In this paper, R/C cylindrical shell with edge beam on meridional free edges was analyzed by use of FEM. RC shell had 960 x 960 mm plan and the thickness was 10 mm. The radius and the depth of the shell were 688 mm and 190 mm, respectively. As the edge beam, three kinds of rectangular beams, which had 2 cm width and 4 cm depth, were arranged. One was connected to the shell at the gravity center of the beam and the others were connected at the bottom or the top of the beam. From the numerical analyses, the deformation and the stress distribution of the shell mentioned above were analyzed precisely. The shell connected with the gravity center of the beam showed the smooth deformation and the stress distributions.

Capturing Out-of-Plane Shear Failures in the Analysis of Reinforced Concrete Shells

AbstractA procedure for nonlinear analysis of RC slabs and shell structures is presented. Cracked RC is treated as an orthotropic material governed by a smeared rotating crack procedure and the constitutive formulations of the disturbed stress field model. The analysis procedure is implemented within the framework of a finite-element program employing layered thick-shell elements that consider out-of-plane (through-thickness) shear deformations. A simple modification method employing an effective shear strain concept is introduced to improve the out-of-plane performance of the layered shell element for RC applications. The adequacy of the procedure is verified using test data of RC members controlled by out-of-plane shear failure mechanisms and elements under combined in-plane and out-of-plane loading scenarios. The nonlinear finite-element program is shown to be suitable for elements exhibiting ductile or brittle responses, and the shear modification method introduced is found to be capable of capturing ...

Viscous Dampers Utilized at an Operating Electronic Facility for Reducing Seismic Risk

Using supplemental energy dissipation devices into the structure to increase the damping ratio for reducing the responses of seismic activity has become more and more popular. This paper presents a case study of seismic retrofit strategy, utilizing a type of passive energy dissipation device, namely, the viscous damper, in order to make an ongoing chips produced facility resistant to seismic activity. The building in question was a chips produced facility belonging to a semiconductor manufacturing company. This was a double FAB where the structure system was divided into an island building and an RC shell. The retrofit involved installing 44 non-linear dampers between the island building and the RC shell. This was due to the significant differences in the fundamental vibration periods. This paper will present the rationale of making a decision on the parameters of the dampers to give the optimum retrofit strategy.

Solar updraft power plants: Engineering structures for sustainable energy generation

Solar updraft power technology will generate highly sustainable electricity in world-wide deserts in future. It will overcome certain deficits of present renewable energy technologies. In several countries, such power plants are in pre-design stage, forming an important contribution of structural engineering to future energy supply. The present manuscript starts with the working principles of solar updraft power plants, followed by explaining climatic and wind-technologic design assumptions. Then the central solar updraft chimney – the power tower – is treated in more detail: a thin ring-stiffened RC shell of extreme height, forming the utmost structural challenge of such plants. This part is followed by technical requirements for the collector constructions, by far the largest glass-covered areas ever built, and of the wind-loading on the glazing. Then, further design aspects are extracted by the durability requirements for at least 100years of operation in extreme desert climates. The paper closes with some cost estimates for the generated electricity.

A Proposal for 4000m-span Cable-stayed Suspension Bridge

This study proposed a compound bridge of suspension bridges and cable-stayed bridges with 4000 m super-long-span over the Tsugaru Strait, Japan. Near to the main towers, cable-stayed bridges and prestressed concrete decks are proposed. It is helpful to enhance rigidity and endure the great axial compression force. In the center of the span, suspension bridges and steel box decks are stiffened by trusses, it can reduce self-weigh and the space between girders, thus contribute to aero-elastic stability. RCFT main tower, RC shell pier and RCFT jacket foundation can enhance rigidity and reduce self-weigh. As a result, the live-dead load ratio of proposal is 0.05 and it is equivalent to 2500m-span suspension bridge.

Design aids for fixed support reinforced concrete cylindrical shells under uniformly distributed loads

Shells are objects considered as materialization of the curved surface. Despite structural advantages and architectural aesthetics possessed by shells, relative degree of unacquaintance with shell behavior and design is high. Thin shells are examples of strength through form as opposed to strength through mass; their thin cross-section makes them economical due to low consumption of cement and steel as compared to other roof coverings such as slabs. Current study presents design curves for reinforced concrete open barrel cylindrical shells for different geometric parameters. The analysis is done in two parts namely: i) RC shell subjected to uniformly distributed load that remain constant along its length and curvature of the shell surface; and ii) RC shell subjected to uniformly distributed load varying sinusoidally along its length in addition to different symmetric edge loads present along its longitudinal boundaries. Design charts are proposed for easier solution of shell constants after due verification of results obtained from finite element analysis. Expressions for stress resultants proposed in closed form make the design more simple and straightforward; stress resultants plotted at closer intervals of f can be useful for detailing of reinforcement layout in RC shells. Axial force-bending moment yield interaction studied on shells under uniformly distributed loads show compression failure, initiating crushing of concrete. Keywords: cylindrical shells; design curves; open barrel; reinforced concrete; stress resultants

Path-dependent failure analysis of RC shell structures using volume control technique

To overcome the drawbacks of conventional load control method and displacement control method, the so-called volume control method was developed by utilizing a pressure node added into a finite shell element. The pressure node has an increment of pressure as an additional degree of freedom of the shell element. In this study, the so-called path-dependent volume control method which improves the volume control method for the analysis of path-dependent behaviors of RC shell structures subjected to cyclic loading is proposed. The path-dependent volume control method is a technique which calculates control-volume change of the RC structure subjected to the cyclic loading conditions like loading, unloading, reloading for nonlinear failure analysis of RC structures and overcomes the limitation of controlling path-dependent volume change of the RC structure according to the deformational history. For the finite element failure analysis of RC shell structures using the technique, each structure is discretized with multi-layered shell elements and in-plane two-dimensional constitutive equations for concrete and reinforcements are implemented for each layer of the shell elements. The results of failure analysis for RC slab, RC tank, RC box culvert, and RC hollow columns subjected to cyclic loading as well as reversed cyclic loading using the path-dependent volume control method are verified with experimental results.

경로의존형 체적제어법을 이용한 철근콘크리트 중공 기둥의 유한요소해석

The volume control method which utilize a pressure node added into a finite shell element can overcome the drawbacks of conventional load control method and displacement control method. In this study, an improved volume control method is introduced for effective analysis of path-dependent behaviors of RC columns subjected to lateral cyclic loading or reversed cyclic loading along with compressive loading. RC shell structures and RC hollow columns are analyzed by discretizing the structures with layered shell elements and by applying in-plane two dimensional constitutive equations for concrete layers and reinforcement layers of the shell elements. The so-called path dependent volume control method as a finite element analysis technique is verified by comparing analysis results with other data including experimental results. The validity and applicability of the modeling technique is also confirmed by the comparison.

一葉双曲面RC造冷却塔の構造特性に及ぼす形状不整の影響の分析 : 実測された形状の再現モデルを用いた損傷・耐力評価

In the inland in Europe and America, construction case of many reinforced concrete cooling towers exists mainly on the power plant which is hard to utilize much cooling water. It is long in the history of such tower construction, and many towers constructed in 40〜70's are used at present. In China and India, the construction of towers in the power plants increases. In such situation, it is reoorted that the collapse accidents by the gust repeatedly arose in United Kingdom and France in a past. Investigation of the cause of those accidents and examination of the countermeasure are developing, and the evaluation of the safety of the existing facilities becomes important problem. On the thin RC shells for these towers, the much research analyzes buckling / vibration problem and effect of initial imperfection on structural properties, and the proposal of design guidelines has been made. To begin with, using the initial imperfection of the distribution idealized axisymmetrically and asymmetrically, a useful knowledge on fundamental phenomenon and analysis method were obtained, and the recommendations for the tolerance limit of the initial imperfection magnitude were proposed. It was analyzed that according to the many leading research results. the fluctuation of meridian direction in-plane stress by initial imperfection was inversely proportional to the shell thickness due to dead weight and wind load within elastic stress analysis, and that it largely affects meridian direction in-plane stress and circumferential direction bending stress for the circumferential curvature error. In addition. partial initial imperfections with small amplitudes play a major role in meridian and circumferential stresses. Concerning the characteristic of initial imperfection itself, the probability-statistical technique for simulating the spatial distribution property is examined, and the statistical analysis procedure to simulate the effect of imperfection on the stress and buckling load is proposed. Recently, the effect of material nonlinearity of RC members on the ultimate strength also became remarkable problem by some researches. In this study, the three-dimensional distribution of the geometric error based on the reported measured data in the shell surface is reproduced numerically in detail for the tower which caused the collapse accident in a past, and the spatial distribution characteristic is analyzed. Next, the effect of the geometric imperfection of reoroduced shape on elastic stress distribution due to dead weight is examined, and the effect on the wind resistance performance is examined by the elasto-plastic analysis. In addition, the evaluation on the performance of the tower by the thermal stress is made, and the numerical examination on the reinforcing method of the tower is tried. By this study, some results shown below were obtained. Reproduced geometric imperfection widely exists for the shell full face, and it becomes a waveform which recurs in circumferential and meridian direction, and the complicated distribution in which the component which recurs periodically overlaps with the local component is shown. The peak of the imperfection component exists from N=0(axisymmetric) to N=5 on the circumferential direction and from 0 to 10(cycle/100m)in the height direction. ・ The possibility of changing to tension from compression exists on hoop stress due to dead load within large area by the effect of the imperfection. ・Due to wind load, the bending cracks develop in the windward of the imperfect shell, and next, it leads to the failure of the tower by the tension which arises by the bending of the meridian direction. This situation is similar to the thing for the perfect shell. From the result shown in the model which reoroduced the imperfection, the turbulence of the remarkable section forces existed further than the case of the perfect shell, and the result of predicting the l

Design and ultimate behavior of RC plates and shells

An iterative numerical computational algorithm is developed to design a plate or shell element subjected to membrane and flexural forces, which is based on equilibrium considerations for the limited ultimate state of the reinforcement and cracked concrete. Equations for capacities of top and bottom reinforcements in two orthogonal directions have been derived. To verify the design algorithm on the element level several experimental examples are designed. Nonlinear inelastic analyses are performed with the designed examples using the Mahmoud-Gupta’s computer program to show the adequacy of the design equations. The calculated ultimate strengths are from 3 to 18% higher than the ultimate strength obtained from the test results, except in one example. On the global structural level, a design is performed for a hyperbolic cooling tower to check the design strength to verify the adequacy of the design algorithm. Based on the ultimate nonlinear analysis performed with the designed reinforcement, the analytically calculated ultimate loads exceed the design ultimate load from 26 to 63% for analyses with various amounts of tension stiffening effect. Even though the ultimate loads are dependent on the tensile properties of concrete, the calculated ultimate loads are higher than the design ultimate loads for the cases considered. This shows the adequacy of the design algorithm developed, at least for the structures studied. The presented design algorithm for combined membrane and flexural forces can be evolved as a general design equation for reinforced concrete plates and shells through further studies involving the performance of many more designs and analyses of different plate or shell configurations.

Design and ultimate behavior of RC plates and shells: two case studies

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.

上載圧を受ける鉄筋コンクリート球形シェルの非線形振動性状に関する検討 : 複合非線形性を考慮した数値解析手法と基本的な応答性状について

In this paper, earthquake response analysis technique considering geometric nonlinearity and material nonlinearity is presented for the purpose of making to be the aid of the evaluation of earthquake resistance by numerical analysis for RC shells. Next, the results of trying nonlinear seismic response analysis by the proposed technique are shown for the purpose of the evaluation of earthquake resistance of the spherical shells for roofs of the various underground container structures. The fundamental analysis on nonlinear vibration property of the RC spherical shell is tried, and the results of trying the evaluation of damage levels and collapse levels by numerical analysis in the time history are shown.

Computer-Aided Retrofitting of a Damaged RC Cooling Tower Shell

The role of numerical simulations in the design of the repair of damaged reinforced concrete structures is illustrated in the context of the retrofitting of a damaged RC cooling tower built in 1963. Nonlinear material behavior of concrete and steel as well as the state of damage, including the nonsymmetric spatial distribution of the cracks and the corrosion of the reinforcement at the end of the anticipated lifetime of the structure, are accounted for in the computational model. Two alternatives for the repair of the shell by means of stiffening rings are investigated. If the repair is based on the application of two cast in situ stiffening rings, structural failure of the RC shell is initiated by two failure zones located between the upper stiffening ring and the cornice. In these zones, the shell is severely weakened by the locally dense distribution of existing cracks and the corrosion of the reinforcement. The coefficient of structural safety of the retrofitted shell can be further increased if the existing cornice is strengthened. This coefficient is considerably larger than the one obtained for the uncracked shell.

Inelastic vector finite element analysis of RC shells

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.

Nonlinear Analysis of RC Shell Structures Using Laminated Element. I

An incremental variational formulation is presented for large deflection analysis of elastic‐plastic continuum by considering the energy consistency of a nonlinear multivariable discrete system based upon incompatible trial functions. The functional is given in orthogonal curvilinear coordinate system and the initial stress procedure has been introduced. Equilibrium imbalance correction is included to prevent drifting of the solution during the incremental process. As an initial application of the suggested formulation, a hybrid stress laminated shell element, in which an energy constraint is introduced to improve the element performance, has been developed to analyze the through‐thickness plastic behavior and the progressive cracking in RC plates and shells. It is of quadrilateral shape with only four corner nodes and can be used for both shallow and deep laminated shells with satisfactory numerical characteristics. Example problems are also included to illustrate the element performance.

On shape finding methods and ultimate load analyses of reinforced concrete shells

Due to considerable imperfection sensitivity the initial shape of a shell can play a dominant role for the quality of the load carrying behaviour. In particular, this is important if large deformation effects and material failure may interact unfavourably, as can be the case for thin reinforced concrete shells. The present contribution discusses different form-finding methods for the shape of free form shells. Among these are the well-known experiments with pressurized or dead-loaded membranes which can also be simulated by a nonlinear membrane analysis or the application of shape optimization schemes using stress levelling or strain energy minimization. The second part is devoted to ultimate load analyses of RC shells. After a brief review of the material models used, selected examples are described, for instance conical shaped cooling towers and a free form model shell which is also experimentally investigated.