Lattice Domes Research Articles

Experimental investigation of reciprocally supported element (RSE) lattice honeycomb domes structural behaviour

The honeycomb configuration of the many Diamatic dome patterns available is particularly convenient for reciprocally supported element (RSE) transformation. This is due to there being only three lattice bar elements intersecting at any apex, irrespective of the number of the bar elements used to form the crown polygon. RSE transformation effort therefore is both reduced and simplified compared to some RSE forms. To inform the understanding of the structural behaviour of honeycomb RSE lattice domes, a study comparing structural modelling predicted behaviour with monitored behaviour in the laboratory was carried out. This investigation focused on the structural behaviour of a RSE lattice honeycomb dome structure under applied static loading. The first part of the study included configuration processing, structural modelling and analysis. The second part involved manufacture, construction and monitored behaviour of the dome in the laboratory. The creation of the selected RSE honeycomb lattice structure together with the structural modelling and experimental outputs are presented and discussed. Predicted displacements and stresses are compared under varying applied loading, boundary support conditions and connection stiffnesses. The locations of the onset of local yielding is considered and discussed. The applied loading did not exceed the tube yield stress according to the von Mises ductile material failure criterion indicating that the dome behaviour observed was elastic.

Seismic response and failure mechanism of single-layer latticed domes with steel columns and braces as substructures

Seismic response and failure mechanism of single-layer latticed domes with steel columns and braces as substructures are studied using incremental dynamic analysis in the paper. The member models considering cyclic buckling and low cycle fatigue of steel are used in the analyses. The results show that the seismic responses will be greatly influenced by the material low cycle fatigue under strong earthquakes in different ways for the domes with different parameters. Two typical failure modes are found for the structures: one is the failure of domes and the other is the failure of both the dome and the substructure. Influence of rise-span ratio of domes, brace sections and column sections in substructures on the ultimate PGA and yielding PGA are studied, and the optimized values of the parameters are suggested for structural designing.

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.

Behavior of the frames of large-span metal domes in the process of their installation

Goal. The goal of this paper is to characterize the process of forming the frames of large-span metal domes during assembly process. The load-bearing structural schemes during the assembly of frames differ from those, adopted for their analysis and design. Due to this fact, initial internal forces appear in the structural elements of frameworks that are called assembly forces. Geometric schemes of dome frameworks and the principles of their formation are described for ribbed domes, ribbed domes with annular rings and lattice domes. It is shown how lattice dome frameworks are formed and why they are considered as spatial bar systems. Specific features of the structural solutions for single-layer and double-layer frameworks are described. It is noted that the technological scheme for the assembly of structures of large-span metal domes depends on the structural systems of frameworks and on the methods of their erection. A brief description is given of differrent methods for erecting frameworks of large-span metal domes and of the number of temporary supports and mechanisms used in this process. Review. Different methods of erection are illustrated with the examples of several well-known dome structures built in the world. The evaluation of the influence of each process on the behavior of structures during the installation is given. The nature of the work of individual structures and a frame is described for the process of erecting large-span metal domes. The emphasis was made on the significant differences in the nature of work of structural systems of dome frame-works with different ways of their installation. Research. Computer models of the lattice metal domes are made of steel I-bars with rigid connections at the joints. Additional models were created for incomplete frameworks to study alternative ways of erection. For each assembly model of the dome framework, computer analysis was performed for the action of its self-weight. Stresses in the structural members, obtained as a result of the analysis, were compared with the stresses in the corresponding elements of the design model of the framework under the self-weight. Conclusions. The conclusion is made that the stresses in the elements of frameworks of the large-span metal domes are unavoidable when they are erected. The necessity of compulsory analysis of frameworks for erection conditions in the design of large-span metal domes was noted.

Impact of single-layer dome modelling on the critical load capacity

In the study an attempt was made to evaluate the effect produced by the modelling of the single-layer lattice dome on its critical load capacity. The modelling concerned the means of connecting bars in a node, bars of the lattice dome, and the effect of geometric imperfections. Taking steel covers, two basic means of modelling of how bars are connected in the node can be distinguished, namely pin and rigid joints. In the study, the pin joint was SBP-1 type connector, whereas the rigid joint - WABI-1 connector. In the description of bars, truss and frame elements were employed. Each element accounted for geometric nonlinearities in the Lagrange description. Regarding a frame element, the physical relationships represented the elastic behaviour of the structure with the use of the Hooke’s law. With respect to the compression truss elements, a nonlinear relationship resulting from experimental investigations was additionally employed. Stability analysis of the structure was performed by means of the Finite Element Method using Abaqus and Robot Structural Analysis software. In order to obtain the load-displacement relations, the Riks arc length method was used. The analysis was focused on global modes of stability loss due to snap-through and bifurcation.

Buckling characteristics according to the rise-span ratio of span 300m single-layer latticed dome

Buckling characteristics according to the rise-span ratio of span 300m single-layer latticed dome

Seismic Analysis of Single-Layer Latticed Domes Composed of Welded Round Pipes Considering Low Cycle Fatigue

Member failure due to low cycle fatigue may occur for steel structures under strong earthquakes. In this paper, the seismic response of single-layer latticed domes composed of welded round pipes is analyzed by the software Open System for Earthquake Engineering Simulation (OpenSees) incorporating low cyclic fatigue, in which the equations of initial camber for members are obtained from the buckling coefficient curve of compression members in Chinese codes. Single-layer latticed domes composed of welded round pipes with different parameters are modeled, and the seismic responses of the domes with and without material fatigue are compared by the incremental dynamic analysis. The results show that under strong earthquakes, the seismic responses including the maximum displacements and plastic development of the domes with fatigue are larger than those of the domes without fatigue. The collapsed PGAs decrease by 10–25% if low cycle fatigue is incorporated. Therefore, the low cycle fatigue of material should be taken into account in the seismic analyses of single-layer latticed domes under strong earthquakes.

Nonlinear Integrated Design of Lattice Domes with Supporting Substructures

This paper investigates the response interaction between reinforced concrete substructure and steel raised lattice roofing. The viewpoint of dynamic stability and nonlinear seismic behavior are considered as both geometrical and material nonlinearity. In particularly, dynamic stability performance of single layer Diamatic domes located on peripheral reinforced concrete columns is investigated under vertical loads and seismic excitation. Different supporting structures with rigidity and reinforcement detailing of the circular peripheral columns are considered in the integrated design. The vibration modes for the lattice dome with and without substructure effects are studied. Results show that high capacity substructure or fixed supporting assumption may lead to unsafe stability performance as well as uneconomical designs. The integrated design of composite system, RC supporting substructure and upper lattice roof could be provided superior dynamic stability performance when compared to the design without supporting substructure.

Reliability of lattice dome with and without the effect of using small number of ground motion records in seismic design

Linear and nonlinear seismic responses can be estimated using the time history analysis for given ground motion records. To reduce the computing time, design codes prescribe guidelines to select a small number of ground motion records to perform the analysis and to estimate the seismic design demand. However, the assessment of the statistics of the seismic design level by using a small number of record components and the evaluation of the failure probability of the designed structures in such a manner are unavailable. The assessment and evaluation focused on the lattice dome are presented in this study. The results indicate that the use of average response from seven ground motion record components for design can lead to over- or under-estimation of the seismic design effect, the frequency of underestimation is about 50%. The variability of the seismic design effect estimated by using seven selected record components is considerable. By carrying out simulation analysis with 1000 trials, the minimum underestimation and the maximum overestimation of the seismic design demand are 35% and 64%, respectively; the estimated failure probabilities of the dome designed by using average response from seven record components can be about half an order of magnitude greater or smaller than that of the dome designed without the effect of small sample size. This suggests that to reduce the observed relative differences in the failure probabilities, an increased number of ground motion record components needs to be used in seismic design.

Dynamic behaviour and seismic design method of a single-layer reticulated shell with semi-rigid joints

Most of the existing studies on reticulated shells with a semi-rigid joint system have been focused on the mechanical properties under static loads. Taking material and geometric nonlinearities into account, the finite element analysis (FEA) model of a single-layer reticulated shell with semi-rigid joints was established using the software ABAQUS and then validated through comparison with the experimental result. Based on the bending stiffness of a bolt-column (BC) joint obtained through experiments, the dynamic behaviour and a seismic design method for single-layer reticulated shells with semi-rigid joints were investigated in this paper. First, analysis of the free vibration frequency of the single-layer latticed domes with semi-rigid bolt-column (BC) joints was conducted based on several different parameters, including joint stiffness, ratio of rise to span, initial geometric imperfection. Second, the seismic internal force coefficient of the members of the semi-rigidly jointed spherical single-layer reticulated shells of different parameters was studied in detail. Finally, the seismic internal force coefficients for spherical single-layer reticulated shells with semi-rigid joints under a common earthquake were derived.

Experimental Study and Numerical Simulation of the Progressive Collapse Resistance of Single-Layer Latticed Domes

Progressive collapse accidents of single-layer latticed domes seriously threaten public safety and social security. Structural integrity and progressive collapse–resisting capacity are gradually becoming essential requirements in structural design. The Kiewitt Lamella and geodesic single-layer latticed domes are typical of domes used in large-scale public facilities. In this paper, an experimental study and a numerical simulation were carried out to understand the mechanism of internal force redistribution in the progressive collapse of domes. Three effective methods to evaluate progressive collapse resistance and critical displacement were determined and verified. The results indicate that both the Kiewitt Lamella dome and the geodesic dome exhibit undergo snap-through collapse. The collapse of the Kiewitt Lamella dome was induced by unexpected local instability around the initial failure members, whereas that of the geodesic dome was the result of a rapid change in nodal displacement and a sharp decline in structural stiffness.

Structural modelling investigation of reciprocally supported element lattice honeycomb domes

Reciprocally supported element (RSE) lattice honeycomb dome structures have the ability to support considerable loading via their composition of interconnected closed circuits of elements. Distinctively, these dome structures use only three elements in each circuit. To understand the structural behaviour of these RSE lattice domes, a structural modelling investigation was carried out. Global linear elas- tic analysis was considered where the behaviour of the structure under the application of loading on selected elements was monitored. The aim of the modelling was to investigate the influencing factors to monitor for model calibration as well as to compare predicted structural behaviour output with future monitored behaviour in laboratory experiments involving the manufacture and construction of an RSE lattice honeycomb dome structure. The creation of the selected RSE honeycomb lattice structures together with the structural modelling findings are presented and discussed. Predicted displacements and stresses were compared under varying boundary support conditions. The von Mises ductile material failure criterion showing the onset of local yielding is considered.

Effects of viscous damping models on a single-layer latticed dome during earthquakes

Rayleigh damping model is recommended in the recently developed Performance-Based Earthquake Engineering (PBEE) methodology, but this methodology does not provide sufficient information due to the complexity of the damping mechanism. Furthermore, each Rayleigh-type damping model may have its individual limitations. In this study, Rayleigh-type damping models that are used widely in engineering practice are discussed. The seismic performance of a large-span single-layer latticed dome subjected to earthquake ground motions is investigated using different Rayleigh damping models. Herein a simulation technique is developed considering low cycle fatigue (LCF) in steel material. In the simulation technique, Ramberg-Osgood steel material model with the low cycle fatigue effect is used to simulate the non-uniformly distributed material damping and low cycle fatigue damage in the structure. Subsequently, the damping forces of the structure generated by different damping models are compared and discussed; the effects of the damping ratio and roof load on the damping forces are evaluated. Finally, the low cycle fatigue damage values in sections of members are given using these damping models. Through a comparative analysis, an appropriate Rayleigh-type damping model used for a large span single-layer latticed dome subjected to earthquake ground motions is determined in terms of the existing damping models.

Reinforcement Effects of Buckling Member for Single-layer Latticed Dome

Reinforcement Effects of Buckling Member for Single-layer Latticed Dome

Comparison of progressive collapse resistance of single-layer latticed domes under different loadings

Progressive collapse tests of two single-layer latticed Kiewitt domes were conducted in this paper. In each dome, one meridian member was suddenly removed and the full field structural responses, including high-speed 3D joint displacements and high-frequency member strains, were collected. Results of the test program and the corresponding FE analysis show that: (1) The tested dome under smaller loads regained balance easily, while a snap-through collapse occurred for dome under larger loads. Hence, although a single-layer latticed dome is normally constructed with hundreds of structural members, progressive collapse of the whole structure can be caused merely by the loss of a single critical member; moreover, load-resistance redundancy of a single-layer latticed dome is crucially important in resisting progressive collapse. (2) The sudden removal of a member caused a non-significant impact on the overall compressive membrane force flow but resulted in severe structural damage at the end-joints of the removed member; if the local damage was not properly absorbed, point buckling would occur on one of these two joints and was regarded as the immediate cause of the progressive collapse. (3) The collapse mode of a single-layer latticed dome subjected to sudden member-loss was characterized by a totally snap-through collapse; the collapse started from the point-buckling joint and was caused by successive downward movements of the surrounding joints. (4) Finite-element analysis provides an efficient way for progressive collapse study of dome structures, but fracture criterion of constructional steel that considers the complex stress states during progressive collapse is still needed.

하부구조의 고유진동수비에 따른 래티스돔의 동적응답특성에 관한 연구

This study analyze the dynamic response property of latticed domes according to natural frequency ratio of substructure. Through eigenvalue analysis, it is was confirmed that the half-open angle <TEX>$30^{\circ}$</TEX> and <TEX>$45^{\circ}$</TEX> dominate vibration mode of the vertical direction and the half-open angle <TEX>$60^{\circ}$</TEX> and <TEX>$90^{\circ}$</TEX> dominate vibration mode of the horizontal direction. Through the dynamic response analysis, it is was confirmed that the first frequency about total structure largely appears about the vertical and the horizontal direction regardless of half-open angle.

Analysis of Lowering Effects in Aluminum Single-Layer Latticed Dome with Temcor Joints

The numerical analysis of a single-layer latticed dome has been carried out by using ANSYS, in order to evaluate the effect of influencing factors, like semi-rigidity of joint, buckling in compressed bars, load distribution and initial imperfections, which can produce important reductions of the load bearing capacity of these kind of structures. As a case study, the use of Temcor joint has been investigated. The characterization of the Temcor joint behavior to be introduced in the global model of the dome has been done by a FE model implemented on ABAQUS. The effects of the analyzed factors on the load-carrying capacity of the dome have been identified and useful suggestions for the design of this type of structures have been given.

Stiffness characteristics of joints and influence on the stability of single-layer latticed domes

In this paper, the theoretical and practical formulas of initial stiffness of welded hollow spherical joints were presented, and the elastic and elastoplastic critical displacements and rotations were obtained respectively. A mechanical model considering the stiffness characteristics of joints was proposed, the criterion of eccentric states and bearing stages was established to analyse the influence on the stability of single-layer latticed domes. Results indicate that the practical initial stiffness formulas proposed fit well with the theoretical solutions. The mechanical model can accurately simulate the stiffness characteristics and bearing stages of joints in the failure process of structure. Compared with the experimental results, the average error of mechanical model for the initial slope of load-rotation curve is 8%, and the average error for the ultimate bearing capacity is 7%. The stiffness degeneration of the joints in the plastic stage may cause a significant reduction in stability capacity of the structure. The stability reduction factors of K6 and Geodesic domes are between 0.7 and 1.0, and the stability reduction factors of K8-lamella domes are between 0.65 and 1.0.

The stability and stressed skin effect analyses of an 80 m diameter single-layer latticed dome with bolt-ball joints

Recent researches have demonstrated that bolt-ball joints have a certain amount of flexural stiffness, so they should be classified as semi-rigid joints and it is possible to apply them on single-layer latticed domes. In order to study the stability and stressed skin effect of the latticed domes with bolt-ball joints, a series of nonlinear full-produce analyses were conducted on the basis of the design of an 80 m diameter single-layer latticed dome with bolt-ball joints, which is the main structure of the Shenbei New District citizen fitness center in Shenyang, China. Above all, the moment-rotation relations for bolt-ball joints, which were established based on numerical results, were introduced into the latticed dome numerical model. Then, the nonlinear stability analyses for the latticed dome in different construction stages were carried out by the above-mentioned numerical model under vertical loads and horizontal wind loads. The mechanical behaviors discussed in this investigation including the stability and the ultimate bearing capacity of the latticed dome in different construction stages, and the influence of the stressed skin effect on the stability of the latticed dome with decorated plates. The result shows that: after being properly designed, the latticed dome with bolt-ball joints can exhibit a good mechanical performance, and this successful application of bolt-ball joints on the Shenbei New District citizen fitness center can set an example project for the design of single-layer latticed domes with semi-rigid joints; under vertical loads, it is more dangerous for the 75% complete latticed dome, while the dangerous construction stage for horizontal wind loads is the 50% completed latticed dome; the stressed skin effect can increase the stability of latticed domes.

Dynamic Collapse Analysis of Single-Layer Lattice Domes with Supporting Frames

Dynamic collapse analysis is an important research subject for large span single layer reticulated shell structures. In this paper, the dynamic collapse behavior of the single layer reticulated shell with substructure which support the reticulated shell are investigated under the earthquake actions. In the analysis, the geometric imperfections, the material and the geometric nonlinear of the structures are considered. The effects of different stiffness of substructure to the collapse earthquake accelerations and the plastic member distribution of the reticulated shell are investigated.