Double-layer Domes Research Articles

The effects of mechanical imperfections on the stability behavior of double-layer Scallop domes

Mechanical imperfections are almost inevitable in large-span spatial domes with hundreds of members and joints. The lack of fit in members is the most common form of imperfections in double-layer domes which influences the behavior of these structures under gravitational or seismic loads. In this study, the probabilistic effect of mechanical imperfections (lack of fit) on the stability behavior of double-layer Scallop domes with sinusoidal arching style under symmetric and asymmetric snow-loading is investigated. On some double-layer scallop domes, nonlinear static and dynamic analyses are carried out using Abaqus/CAE and MATLAB. The behavior of the structures with randomly distributed imperfect members is compared with those of the ideally perfect structures. A Monte Carlo simulation approach is used to statistically assess the effects of uncertainties on the response parameters and the ultimate capacity of the structures. In the first approach, named here as the “rigorous probabilistic approach”, the amount and the distribution of imperfect members are all treated as random variables, and in the second approach, named as “concise approach”, a fixed amount of imperfections are applied to a number of randomly selected critical members. No simplification method is used in the rigorous probabilistic approach to achieve a reliable assessment of the effect of uncertain parameters. Results show that the collapse behavior of double-layer Scallop domes is sensitive to random imperfections and a considerable decrease is seen in their load-bearing capacity.

Experimental study and numerical simulation of partial double-layer latticed domes against progressive collapse in member-removal scenarios

Experiments were conducted to evaluate the progressive collapse resistance of a scaled partial double-layer latticed Kiewitt-6 (K6) dome in member-removal scenarios. The test results were compared with results obtained previously for a single-layer latticed dome to demonstrate the advantages of the partial double-layer members for improving the collapse resistance. A finite element (FE) analysis was also executed to confirm the experimental observations and to evaluate that the collapse-resistant behavior of a full-scale partial double-layer latticed dome. The collapse-resistant mechanism of partial double-layer domes was examined via theoretical analysis. On the basis of these results, a novel cable-stiffened partial double-layer latticed dome was proposed. The results indicated that the tested dome did not completely collapse, but some of the upper chord members buckled. For the whole dome, the compression mechanism is regarded as the major load-carrying mechanism to resist progressive collapse. In terms of the local area around the failed members, the adjacent members initially rely on the beam and compression mechanisms to resist progressive collapse. As the number of the failed members increases, the adjacent members completely rely on the beam mechanism to resist progressive collapse. The FE results agree well with the experimental results. The progressive collapse-resistant behavior of partial double-layer domes is far superior to that of single-layer domes because of the better stiffness of the partial double-layer members. The cable-reinforced partial double-layer dome is a novel structural system that has significantly better progressive collapse-resistant behavior than traditional single/double-layer and partial double-layer domes.

Two subdivision methods based on the regular octahedron for single- and double-layer spherical geodesic domes

The paper presents the topological–geometric analysis of a selected number of space frames configurations for geodesic domes which are generated from the regular octahedron. Two subdivision methods for spherical triangles, proposed by Fuliński, were used to create two families of structures. The first family consists of six single-layer and six double-layer geodesic domes shaped on the basis of the first method of subdivision, while the second family contains six single-layer and six double-layer geodesic domes shaped on the basis of the second method of subdivision. The calculated results of the geometric parameters of the analyzed structures were used to create original formulas that allow for more advanced structures to be achieved, that is, with a larger number of nodes and struts. The geometric results were also used to create nomograms showing the range of struts of the same length for double-layer geodesic domes. In both single-layer and double-layer domes, the number of groups of struts of equal lengths and the number of faces with different areas are smaller for structures created according to the first method of subdivision. The comparison of the resulting element quantities of two methods shows that the largest differences appear between the domes with a larger number of struts (up to 67%). Here, the analysis might help the designer reach a final decision on the better choice of topology, in particular, when this aspect is combined with other design goals, such as efficiency, economy, utility, and elegance in the design of the structure and the cover of large areas.

Hyperboloid offset surface in the architecture and construction industry

Abstract In this paper the issue of approximation of the hyperboloid offset surface off(S(t, v); d) at distance d by the hyperboloid surface S 1(ϕ, v) is considered. The problem of determining various surfaces approximating the hyperboloid offset surface off (S(t, v); d) is important due to the applications of the hyperboloid as a mathematical model for miscellaneous objects in the architecture and construction industry. The paper presents the method of determining the angles and coordinates of points of various surfaces approximating the hyperboloid of revolution. A two-sheet hyperboloid offset surface can be used for modelling double-layer domes. A one-sheet hyperboloid offset surface was used to model the reinforced structure of the cooling tower.

Optimal Design of Double-Layer Domes Considering Different Mechanical Systems via ECBO

In this paper, a finite element model based on geometrical nonlinear analysis of large-scale double-layer domes and suspen-domes with pinned and rigid connections is presented. An optimal geometry and sizing design are performed using the enhanced colliding bodies optimization (ECBO) method. The length of the strut, the cable initial strain, the cross-sectional areas of the cables and steel elements, and height of domes are considered as design variables and the volume of each dome is taken as the objective function. A simple approach is defined to determine the configurations of the dome structures. This approach includes calculating the joint coordinates and formation of steel elements and cables. Numerical results show the robustness of ECBO algorithm. The efficiency of Lamella suspen-dome with pin-joint and rigid-joint connections is then explored and compared with double-layer Lamella dome to investigate the performance of these systems under dead and snow loading condition. Optimization process is performed via ECBO algorithm to demonstrate the effectiveness and robustness of the ECBO in finding optimal designs for different systems of domes.

Большепролетные металлические купольные покрытия и их возведение

The article presents the main types of geometrical and structural systems of steel frameworks of metal dome roofs. Based on the geometrical system, three main types of metal domes can be specified: ribbed domes, ribbed domes with rings, and lattice domes. Lattice domes can be cyclically symmetrical with repeating sectorial patterns, or geodesic, that are based on geodesic polyhedrons, inscribed in a sphere. Based on the structural system, the frameworks of ribbed domes can have single chord or dou- ble chord ribs. Geometric system of the framework of a large-span metal dome governs the method of its erection which in its turn defines the structural solutions for the elements of the framework and the sequence of their assembly. The paper describes the following methods of erection of large-span domes: erection by crane from the ground with temporary supports, placement of the complete structure or large elements of the dome, and cantilever erection. The examples of large-span metal domes built in different countries of the world are reviewed with respect to the method of construction used. General characteristics of the structural system of the framework of each dome are presented. The examples are used to demonstrate that the method of construction of a large-span metal dome roof is dependent on the geometric system of its framework. It is noted that metal domes are widely used as structural solutions for roofs of buildings of different types. It is noted that erection with temporary supports of different types, or ground assembly are mostly used for the construction of relatively low double layer domes, or high single-layer domes. For large-span double-layer metal domes of considerable high the method of cantilever erection is usually preferred.

Reliability analysis of double-layer domes with stochastic geometric imperfections

This study aimed to investigate the effect of initial member length an imperfection in the load carrying capacity of double-layer domes space structures. First, for the member length imperfection of each member, a random number is generated from a normal distribution. Thereupon, the amount of the imperfection randomly varies from one member to another. Afterwards, based on the Push Down analysis, the collapse behavior and the ultimate capacity of the considered structure is determined using nonlinear analysis performed by the OpenSees software and this procedure is repeated numerous times by Monte Carlo simulation method. Finally, the reliability of structures is determined. The results show that the collapse behavior of double-layer domes space structures is highly sensitive to the random distribution of initial imperfections.

Optimum Design of Geometrically Nonlinear Double-Layer Domes by Firefly Metaheuristic Algorithm

Size optimization of double-layer scallop domes subjected to static loading is focused in the present paper. As this type of space structures possesses a large number of the structural elements, optimum design of such structures results in efficient structural configurations. In this paper, optimization task is achieved using firefly algorithm (FA) by taking into account linear and nonlinear responses of the structure. In the nonlinear optimization process only the geometrical nonlinearity effects are included. The numerical results demonstrate that nonlinear optimization provides more efficient structures compared with the linear one.

Composite Polyhedra

The composite polyhedra constitute a group of regular solids which until recently had not been catalogued as geometrical objects. Some, being completely triangulated, make up isostatic compositions. Others, with valleys or undulations, can be used as lobed domes or as stalactitic vaults. These forms can be transformed into double layer domes connecting their external vertices.