Single-layer Latticed Domes Research Articles

Numerical simulation and performance evaluation of compression members in long-span single-layer spatial grid structures constrained by steel bars

The collapse of long-span single-layer spatial grid structures can be triggered by the instability of compression members. To improve the stability of axially compressed members, this study proposes two novel compression members that are constrained using steel bars based on the design concept of existing constraint measures. A validated FE analysis is adopted to investigate the compressive mechanical behaviors, including parametric analysis. Members with different constraint measures are applied to single-layer latticed domes, and their feasibility in improving the progressive collapse resistance of the domes is evaluated. The results show that restraint measures using steel bars can significantly improve the stability of compression members, and when the ends of the restraint body are able to slide, the bearing capacity and ductility are greatly improved. The improvement can be maximized by reasonably designing various parameters of the constraint body. In addition, using different measures to constrain the compression members with higher key grades and thus improve the progressive collapse resistance of single-layer latticed domes is found to be feasible. However, the study finds that the failure mechanism of the constrained members sliding at the ends of the constraint body cannot be fully realized following dome collapse.

Progressive Collapse Analysis of Single-Layer Latticed Domes Under Seismic Loading Using Enhanced Fiber-Based Approach

This paper presents a novel computational framework based on the Finite Particle Method (FPM) for the progressive collapse analysis of single-layer latticed domes subjected to seismic loading. The framework integrates a fiber-based approach to simulate the nonlinear behavior of steel structural members, including yielding, cyclic buckling, and fracture. For structural seismic analysis, the fiber-based approach is enhanced by incorporating a dynamic increase factor, which accounts for the impact of high strain rates during seismic events. Furthermore, the framework extends the pseudo-dynamical stiffness of the particle to consider Rayleigh damping, surpassing the limitations of the original mass damping model. The computational efficiency of the proposed framework is optimized by implementing it on a generic parallelized GPU platform. The computational framework has the advantage of elaborately simulating the response of individual structural members while efficiently capturing the complex behavior of the overall structure. Subsequently, the effectiveness of the enhanced framework is demonstrated through the analysis of the collapse behavior of a representative single-layer latticed dome under seismic loading. The study conducts a parametric analysis to evaluate the influence of two key factors, namely, rise-to-span ratios and imperfections, on the collapse behaviors. The findings contribute to a better understanding of the complex behaviors of single-layer latticed domes during seismic events, providing knowledge for improving structural safety and resilience in public buildings.

Collapse-resisting mechanism and damage propagation pattern of suspended-domes following sudden cable loss

This paper aimed to reveal two important mechanisms that determine the survival of suspended-domes subjected to a sudden cable rupture scenario: the mechanism for the initial local damage to be arrested by the remaining structure, and, the mechanism for the local damage to propagate throughout the remaining structure in case it is not fully arrested. A test was performed on a scale-down suspended-dome model respecting all structural details. After one of the outer-ring hoop cables was suddenly ruptured by an innovative remotely-controlled cable-breaking device, the remaining structure established an alternative path at the outer ring, tying the remaining hoop cables, and thereby regained balance. Complementary finite-element analysis was performed and validated. Other cable rupture scenarios were investigated, for which the alternative path for hoop cables was also confirmed. The cable rupture-induced damage, characterised primarily by the relaxation of hoop cables, was able to transmit outwards and inwards to the other rings of the suspended-dome, during which the relaxation of diagonal cables was a critical step. The hoop cable relaxation propagated easier inwards than outwards, and the rupture of outer-ring hoop cable caused the most severe damage. The failure of a hoop cable and resultant relaxation of neighbouring cables would effectively turn the suspended-dome into a single-layer latticed dome within the local range of failure, and point buckling of the latticed dome may occur and even cause structural progressive collapse. The failure of one diagonal cable would hardly cause the hoop cable to relax and thus normally caused no further damage.

Fiber-based approach for seismic analysis of steel members using finite particle method

This paper presents an enhanced fiber-based approach for the seismic analyses of the behavior of steel structural members. This approach is built based on the framework of the finite particle method. Specifically, a fiber-beam element is developed to model the behaviors of structural members more elaborately. A cyclic constitutive model for fiber is proposed by enhancing a uniaxial steel hysteretic constitutive relationship to consider large strain amplitude and low cyclic fatigue. In addition, a fiber-based fracture model is proposed for modeling the progressive failure process of members. The proposed enhanced approach combines the finite particle method and fiber-beam element with more elaborated constitutive and fracture models, and it has the advantages in evaluating the cross-sectional plastic development and dealing with non-linear and non-continuum problems, which is suitable for analyzing the cyclic fatigue, buckling, and fracture of steel structural members. The analyses of steel plates and steel tube member specimens are performed to verify the effectiveness of the proposed approach. The proposed method is applied to analyze the collapse of a Kiwitt-8 single-layer latticed dome subjected to different seismic loads, which shows the feasibility of the fiber-based approach for seismic collapse analysis.

Study on the mechanical performances of single-layer latticed domes with SLO joints based on beam elements FE model

Single-Layer ORTZ (SLO) joint, as a kind of assembled joint, has been widely adopted in single-layer latticed shells. However, previous research on this subject has primarily focused on the mechanical properties of joint, and the mechanical performances of single-layer latticed shells with SLO joints have not been systematically studied. In this work, a modeling method based on beam elements is proposed to simulate the SLO joint, and the key parameters of the model is studied. According to the modeling method, a series of nonlinear stability analyses is performed to investigate the mechanical performances including static stabilities of single-layer latticed domes with different typical geometrical parameters, and the instability mechanisms and modes are found. The stability capacities of the structures with SLO joints are compared with those with rigid nodes. The results prove that the proposed beam elements FE model can well simulate the SLO joint, and the stability analyses results show the instability modes and stability capacities of single-layer latticed domes with SLO joint in different parameters. The results presented in this article can be used to aid engineers in the design of single-layer latticed shells with SLO joints.

Progressive Collapse Analysis of Single-Layer Latticed Domes With Fabricated Joints

Progressive collapse accidents of single-layer latticed domes seriously threaten public safety. The progressive collapse-resisting capacity (PCRC) is gradually becoming an essential requirement in the design of spatial structures. Currently, the joint system used in spatial structures can be divided into two categories: welded joints and fabricated joints. The semi-rigidity of fabricated joints may have a significant influence on the PCRC of single- layer latticed domes. In this study, the PCRCs of single-layer fabricated latticed domes with identical span and rise-to-span ratio are evaluated based on the critical progressive collapse load (CPCL). The collapse mechanism of single-layer latticed domes with different grid forms is revealed by progressive analysis. In addition, the effects of joint rigidity, grid form and type of initial failure are further evaluated. The results indicate that the collapse mechanism of single-layer latticed domes includes the radial propagation type and the circumferential propagation type. The latticed domes with quadrilateral grids have much lower PCRC than those with triangular grids. The CPCLs of weld-jointed latticed domes are 5% to 22% higher than those of the fabricated latticed domes with the same grid form. The above influence should be fully considered in the progressive collapse-resisting design of latticed domes with fabricated joints.

Wind-induced instability analysis of large-span single-layer lattice domes

This paper addresses the instability behaviour of single-layer lattice domes with a long span subjected to wind action. Two structural configurations with a span of 120 m and a rise-to-span ratio of 1:3 and 1:6 are analysed to compare critical dynamic loads to critical static loads. The Budiansky–Roth and phase-plane criteria are employed for estimating dynamic critical conditions. Wind fluctuation (Cpf) is simulated as a function of the average pressure coefficient (C¯p) over time, and the imperfections are set by means of the so-called “Conformable Imperfection Method”. The parameters considered in this research include the wind fluctuation, fluctuation period, geometric imperfection, and strengthening the members. It is found that the critical wind velocity reduces as the wind fluctuation increases. Furthermore, as the fluctuation period Tf increases, the difference between the static and the dynamic critical loads decreases. The use of Cpf=0.3C¯p and Tf/T1=1.0 (T1 being the fundamental period) produced the lowest amount of critical velocities of 50 and 43 m/s for D1:3 and D1:6 configurations, respectively. The corresponding critical dynamic loads were 29.27 and 15.15 kN giving the dynamic load ratio of 193%, the dynamic to static critical load ratios being 0.67 and 0.68 for these configurations. The D1:3 and D1:6 domes exhibited imperfection sensitivity by as much as about 17 and 82% load reduction, respectively, for an imperfection amplitude of Span/350. Strengthening the critical members of the D1:6 dome subjected to the wind action had the advantage of increasing the static instability load and the dynamic critical load bearing capacity by 20 and 30%, respectively. For estimating the equivalent static wind load, a reduction factor of 0.50 defined as the ratio of dynamic to static load was proposed.

A Hybrid Approach for the Dynamic Instability Analysis of Single-Layer Latticed Domes with Uncertainties

Currently, there is no unified criterion to evaluate the failure of single-layer latticed domes, and an accurate nonlinear time-history analysis (NTHA) is generally required; however, this does not consider the uncertainties found in practice. The seismic instability of domes subjected to earthquake ground motions has not been thoroughly investigated. In this paper, a new approach is developed to automatically capture the instability points in the incremental dynamic analysis (IDA) of single-layer lattice domes by integrating different efficient and robust methods. First, a seismic fragility analysis with instability parameters is performed using the bootstrap calibration method for the perfect dome. Second, based on the Sobol sequence, the quasi-Monte Carlo (QMC) sampling method is used to efficiently calculate the failure probability of the dome with uncertain parameters, in which the truncated distributions of random parameters are considered. Third, the maximum entropy principle (MEP) method is used to improve the computational efficiency in the analyses of structures with uncertainties. Last, the uncertain interval of the domes is determined based on the IDA method. The proposed method has been used to investigate the instability of single-layer lattice domes with uncertain parameters. The results show that it can determine the probability of structural failure with high efficiency and reliability. Additionally, the limitations of the proposed method for parallel computation are discussed.

Evaluation of equivalent friction damping ratios at bearings of welded large-scale domes subjected to earthquakes

The major sources of damping in steel structures are within the joints and the structural material. For welded large-scale single-layer lattice domes subjected to earthquake ground motions, the stick-slip phenomenon at the bearings is an important source of the energy dissipation. However, it has not been extensively investigated. In this study, the equivalent friction damping ratio (EFDR) at the bearings of a welded large-scale single-layer lattice dome subjected to earthquake ground motions is quantified using an approximate method based on the energy balance concept. The complex friction behavior and energy dissipation between contact surfaces are investigated by employing an equivalent modeling method. The proposed method uses the stick-slip-hook components with a pair of circular isotropic friction surfaces having a variable friction coefficient to model the energy loss at the bearings, and the effect of the normal force on the friction force is also considered. The results show that the EFDR is amplitude-dependent and is related to the intensity of the ground motions; it exhibits complex characteristics that cannot be described by the conventional models for damping ratios. A parametric analysis is performed to investigate in detail the effects of important factors on the EFDR. Finally, the friction damping mechanism at bearings is discussed. This study enables researchers and engineers to have a better understanding of the essential characteristics of friction damping under earthquake ground motions.

Progressive collapse resistance of single-layer latticed domes under different failure conditions at the same joint

A joint connecting multiple members is prone to failure under accidental loads such as blasting, impact, and ice-snow thick cover. A scaled Kiewitt-6 (K6) single-layer latticed dome with a rise-to-span ratio of 1/8 was tested to evaluate the collapse resistance. After three members of the same joint were abruptly removed in succession, the displacements and strains of the remaining structures were determined. The collapse-resistant performance of the identical dome under simultaneous failure (SIF) of the aforementioned three members was analyzed after developing and validating a finite element (FE) model. Finally, the dynamic performance of numerous full-scale K6 domes with different rise-to-span ratios under two failure conditions was investigated. The results indicate that the failure mode of the tested dome under the successive failure (SUF) condition is local collapse. The members connected to the failed joint and other members rely on the beam and compression mechanisms, respectively, to resist progressive collapse. The FE results are well validated by the test results, and the difference between the two conditions is examined via theoretical analysis. Compared with the SUF condition, K6 single-layer latticed domes are more prone to progressive collapse under the SIF condition. A novel collapse model related to the failure conditions, rise-to-span ratios, and loads of single-layer latticed domes is proposed in this work.

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.

Progressive collapse resistance of single-layer latticed domes subjected to non-uniform snow loads

Catastrophic progressive collapse of long-span spatial structures subjected to non-uniform snow loads is often reported; however, few studies have been performed in this field. In the present study, progressive collapse tests of a scaled single-layer latticed K6 dome subjected to the non-uniform load were conducted. The failure mode, dynamic response, and collapse mechanism of the tested dome were examined. After the FE model was validated, the effects of the degrees and distributions of non-uniformity and rise-to-span ratios on the progressive collapse resistance under non-uniform loads were examined by a series of full-scale models. The results indicate that the failure mode of the tested dome subjected to the non-uniform load is a global collapse. The members connected to the failed joint and other members demonstrate the beam and compression mechanisms, respectively. For K6 domes, under the same mean loading condition (the change of snow height due to wind), the higher non-uniform degree causes a bigger structural response and leads to a lower collapse resistance; under the same maximum loading condition (snow melts locally due to temperature), although the maximum load has not changed and the total load is smaller, the non-uniform load can still result in unfavorable collapse for domes when the maximum load increases to a certain value, meaning that a dome is also dangerous when snow melts locally. Domes are most prone to collapse when the load is distributed non-uniformly along the ring direction (the settlement of snow accumulation), followed by the load distributed non-uniformly about radial members (the change of wind direction). Additionally, a dome with a smaller rise-to-span ratio under non-uniform loads collapses earlier.

A comparative study on the effectiveness of bidirectional and tridirectional isolation systems used in large-scale single-layer lattice domes during earthquakes

To improve the structural seismic performance, structural vibration control technology is widely introduced into building structures. In terms of base isolation, both bidirectional and tridirectional isolation systems are usually used in large-scale domes. However, the difference in the isolation performance between the two systems needs to be evaluated and further understood. In this paper, large-scale single-layer lattice domes with bidirectional and tridirectional isolation systems are investigated and compared under near-field and far-field ground motions. The dynamic demands of isolated structures are quantified, and the isolation effectiveness of different isolation systems is evaluated. The effects of the near-field and far-field ground motions on isolated structures are compared. The seismic performance of isolated structures is analyzed based on incremental dynamic analysis (IDA). In addition, a parametric study is performed to discuss the effect of the damping coefficient of the damper in the tridirectional isolation system on the isolation effectiveness. It is found that from a statistical point of view, both the bidirectional and tridirectional isolation systems are able to reduce the dynamic demands of domes during earthquakes, while the tridirectional isolation system has better suppression effectiveness for dynamic demands; the near-field earthquake ground motions have a more obvious influence on isolated structures than the far-field earthquake ground motions. For the tridirectional isolation system, a larger damping coefficient may not necessarily be able to obtain better isolation effectiveness in structures. This study provides a basis for improving the understanding of the isolation effectiveness of different isolation systems used in large-scale domes.

Grid patterns optimization for single-layer latticed domes

In previous studies on optimized single-layer latticed domes, the inner space and external shape of the optimized dome is different from those of the initial dome. This difference may result in loss of structural functionality and aesthetics intended by the designers, making it difficult to separately evaluate the mechanical properties of the grid patterns and shape of the surface. In this study, 64 types of single-layer latticed domes having different geometric properties are optimized to obtain mechanically effective grid patterns. Six types of objective functions are employed. The nodal coordinates of the domes serve as the design variables under geometrical constraints, where the nodes of the domes can be shifted on the surface area. The geometric and mechanical properties of the optimized grid patterns are evaluated quantitatively against the objective functions. Moreover, interactions between the geometric and mechanical properties are investigated. The results show that the optimized grid pattern has superior mechanical properties and geometric imperfection sensitivity. This optimization scheme can be applied for designing mechanically effective grid patterns for single-layer latticed domes.

Initial stress state at installation of a single-layer lattice dome due to errors of its assembly

The paper presents the results of the numerical modeling of the assembly process of single-layer lattice domes with respect to random deviations in lengths of individual bars which was performed with a special purpose software SBORKA developed by the author. Modeling of the installation process of the dome frame was performed by sequential calculation of the coordinates of its nodes through simulation of the connection of individual bars in these nodes. The inaccuracies of the bar lengths used were random variables with a normal distribution law. Due to errors in the length of the bars, the actual geometric scheme of the dome frame is distorted in relation to the design scheme. To obtain objective data on such distortions, numerical computer modeling was performed repeatedly with statistical processing of the results obtained. The sequence of assembly of the dome frame was chosen such that the largest number of different types of rods were used. Distortions in the geometric scheme of a single-layer lattice dome do not allow its frame to be installed simultaneously on all support nodes. First, the dome frame is installed only on three support nodes, and then due to deformation under its own weight, the remaining support nodes are included in the work. This deformation of the dome frame leads to the appearance of initial stress state in the bars. In this research, computer static analysis of a single-layer lattice dome was performed for the action of the self-weight load of its frame. The analysis was made taking into account the sufficiency of the load to exhaust the existing gaps in the support nodes. Based on the results of these calculations, the initial stress state in the bars of the dome frame are obtained, which should be taken into account in the analysis and design of the structure.

Seismic performance analysis of a large-scale single-layer lattice dome with a hybrid three-directional seismic isolation system

A large number of studies and applications have been carried out on horizontal seismic isolation systems, and their effectiveness has been indicated. For long-span spatial structures, vertical seismic load plays an important role. However, vertical seismic isolation technology has not been extensively investigated. In this paper, a hybrid bearing with three-directional seismic isolation effects is proposed, in which the triple friction pendulum component and the viscous damping component are combined in series. Compared with other seismic isolation systems, the advantages of this hybrid seismic isolation system are that it can not only greatly lengthen the structural periods but also dissipate the seismic energy in all three directions. A hybrid numerical modeling method for this hybrid seismic isolation bearing is also developed. The seismic performance of a welded large-scale single-layer lattice dome with this hybrid seismic isolation system subjected to near-field ground motions is analyzed. The results show that the important dynamic demands in the dome are significantly suppressed compared with the base-fixed dome. The seismic isolation effects are evaluated in all three directions, and the effectiveness of the hybrid isolation system is verified. Finally, a comparative study is performed, and the mechanical parameters of this hybrid bearing are discussed. It is found that the damping energy dissipation in the seismic isolation bearings is not the most important factor in reducing structural dynamic demands. The proposed seismic isolation system and its numerical modeling method provide an attractive and effective alternative for the design of long-span spatial structures with hybrid seismic isolation systems.

Buckling characteristics of span 300m single-layer latticed dome using H-section

Buckling characteristics of span 300m single-layer latticed dome using H-section

Nonlinear dynamic analysis method for large-scale single-layer lattice domes with uncertain-but-bounded parameters

Currently, nonlinear dynamic analysis for large-scale single-layer domes is commonly performed using deterministic numerical methods. However, in practical engineering cases, complex large-scale single-layer domes have many uncertain parameters that cannot be considered using deterministic methods. Therefore, there is a growing awareness that classical deterministic methods need to be extended towards the introduction of the uncertain aspects in dynamic analysis, and a non-deterministic analysis method for large-scale spatial structures is required. In this paper, a new method is presented by introducing uncertainties into the nonlinear dynamic analysis for large-scale single-layer lattice domes. The method accounts for uncertainties in material properties, structural imperfections, loads, and damping with bounds. The focus is on the treatment of uncertainty in damping and the adopted geometric shape, which is different from that of conventional approaches. Finite element dynamic analyses for sample structures with multiple sources of uncertainty subjected to dynamic loads are performed. Results show that the variability of the variables with an associated uncertainty imposes significant negative effects on the dynamic properties, dynamic demands, and safety of a dome. Uncertain damping in a structure plays the most important role in determining structural performance. The numerical results reveal the differences between conventional analysis methods with deterministic parameters used in previous practical applications and the uncertain analysis method. Finally, a parametric study is performed, and the impacts of sample size on statistical dynamic demands, single uncertain source on structural failure, and single uncertain source on damping coefficients are discussed.

Effects of the rise-to-span ratio on the progressive collapse resistance of Kiewitt-6 single-layer latticed domes

Kiewitt-6 (K6) single-layer latticed dome scale models with rise-to-span ratios of 1/8 and 1/6 were developed to evaluate their progressive collapse dynamics. For each dome, the structural responses, including the joint displacement and member strain of the remaining components, were recorded after four key members were abruptly removed in succession. The effects of the rise-to-span ratio on the progressive collapse resistance of the K6 single-layer latticed domes were examined after constructing and validating finite element (FE) models. The experiments and FE analysis yielded the following results: 1) K6-6 and K6-8 domes have identical collapse modes; the joint loads were transferred via surrounding localised arch action, and the collapse of the arch following member failure led to the progressive collapse of the latticed domes. 2) Compression mechanisms served to inhibit progressive collapse of the K6-6 and K6-8 domes. 3) For the K6-6 dome, there was a 1-s transient equilibrium state following the structural vibration prior to the final collapse; this transient state was not observed in the K6-8 dome. 4) The K6-6 dome collapsed more slowly and demonstrated better progressive collapse resistance than the K6-8 dome. 5) The progressive collapse resistance and steel consumption were optimised under the condition of a rise-to-span ratio of 1/5.

Comparison of the progressive collapse resistances of different single-layer latticed domes

This study conducted progressive collapse tests of Keiwitt-6 (K6) and three-way diagonal grid (TD) single-layer latticed domes. Progressive collapse tests of single-layer latticed domes were performed to examine the dynamic responses, collapse mechanisms, and collapse modes of different structural types after the failure of multiple structural members. The results indicated the following: 1) Under the same test conditions, two types of structures exhibited the same collapse mode: local collapse occurred first at the destructive part of the structures; then, with increases in the number of failed members, the collapse range continuously expanded, and the structures ultimately exhibited complete collapse. Some of the members at the supports exhibited cracks or necking. 2) The K6 and TD single-layer latticed domes relied on the compression and beam mechanisms, respectively, to resist progressive collapse. 3) The K6 single-layer latticed dome exhibited better resistance to progressive collapse as compared to that of the TD single-layer latticed dome. 4) The progressive collapse resistances of K6 and TD single-layer latticed domes were significantly improved by increasing the bending stiffness of radial members.