Long-span Roof Structures Research Articles

The prediction on non-Gaussian characteristics of wind pressure for the long-span roof in the mountainous area using proper orthogonal decomposition–deep learning framework

To make an accurate prediction of the non-Gaussian characteristics of wind pressure for the long-span roof, this study combines the proper orthogonal decomposition (POD) technique, convolutional neural network (CNN), and long short-term memory (LSTM) network to propose a novel POD-CNN-LSTM framework. Then, the proposed framework was well validated based on the wind tunnel testing of a long-span roof structure, and some error criteria, such as mean square root error and correlation coefficient, were adopted to evaluate the prediction accuracy of the non-Gaussian characteristics. Furthermore, two other methods, POD-CNN and POD-LSTM, were also used to conduct a comparative study. The obtained results illustrate that compared to POD-CNN and POD-LSTM, the proposed framework can achieve better performance on the pulsating wind pressure coefficient. For predictions of non-Gaussian characteristics, the output results of the proposed POD-CNN-LSTM show fewer errors, which means the predictions are close to the measured results, including skewness, kurtosis, and wind pressure probability density distributions. To summarize, the proposed POD-CNN-LSTM framework shows superiority over others, which means the proposed framework has good potential for the practical application of non-Gaussian prediction of the engineering structure.

Wind-induced interference effect of complex building clusters on long-span roof structures

The presence of complex buildings introduces interference effects and complicates the wind field around the long-span roof structure. The complexity of the problem makes it challenging to predict wind load of long-span roof structures, resulting in a scarcity of design data available to engineers and designers. Thus, the influence of interference effect on mean and peak pressure coefficients of a long-span tri-centered cylindrical roof structure was investigated through wind tunnel tests conducted in an atmospheric boundary layer wind tunnel. The study focused on the interference effects caused by two cooling towers, chimney, and some low-rise buildings, considering all wind directions. The results show that the interference effects are the result of a combination of amplification effects from the adjacent cooling towers and chimney and shielding effects from the surrounding low-rise buildings. Due to the shielding effect of low-rise buildings, the wind suction on the roof is mitigated compared to that of a single building, while at the end of the roof, wind suction is amplified by cooling tower effects. The interference effect of the building clusters, however, amplifies the fluctuating wind pressure coefficient and the peak pressure coefficient on the roof. To accurately estimate the wind load of building components and envelopes, furthermore, this study investigates the influence mechanism of interference effect on non-Gaussian characteristics of wind pressure combining with fluctuating wind pressure spectrum, spatial correlation of fluctuating wind pressure, and probability distribution characteristics of standardized wind pressure coefficient. The spatial correlation of wind pressure in the roof interference area exhibits a strong association, and the probability density distribution characteristics of the standardized wind pressure coefficient significantly deviate from the Gaussian curve, with a peak factor exceeding 3.5. Thus, it can be concluded that the wind pressure within this region demonstrates significant non-Gaussian characteristics. Hence, the zone values of peak pressure coefficients are determined using the peak factor approach to inform the wind resistance design of the envelope structure.

Simplified calculation method of non-Gaussian wind pressure peak factor for large-span spatial roof structures

Based on the wind tunnel test data of a long-span spatial roof structure, the correlation between higher-order statistics and peak factors was obtained according to the time and frequency domain characteristics of wind pressure-time history, as well as the coincidence condition between wind pressure power spectra of measurement points and wind speed power spectra. A simplified peak factor calculation formula was proposed based on the moment-based Hermite polynomial model. The Gaussian part of the peak factor was calculated through the wind speed spectrum based on the zero-crossing theory, and the parameters related to higher-order statistics were considered as the non-Gaussian part of the peak factor. The simplified method was verified through the instantaneous extreme value method based on a coal shed structure with available long-term wind pressure-time history. It revealed that the results of the proposed simplified method correlate well with that of the instantaneous extreme value method, indicating its accuracy and potential value for engineering practice.

A comprehensive review on estimation of equivalent static wind loads on long-span roofs

Equivalent static wind load (ESWL) is helpful information for designing wind-sensitive structures since it converts complex wind-induced structural dynamic analysis into a simplified static analysis and facilitates combination of other loads or actions in structural designs. In recent years, there have been a growing number of long-span roof structures, most of which are sensitive to wind actions. Indeed, the accurate determination of ESWLs has been a primary concern in their wind-resistant design. Although some significant progress has been made on this topic, there are various issues to be addressed or improved due to a variety of reasons. With the further development of long-span roofs, there will be higher requirements for their ESWLs. This paper first combs through the existing representative methods depending on wind-induced structural responses (WISRs) and wind-induced structural stability (WISS), where the ESWLs linked with the former are the mainstream and the ones concerned with the latter are still somewhat in their initial stages of development. In each broad category, some momentous tactics of mathematics and mechanics are utilized to derive different methods. In the conclusion, this paper finally summarizes the existing achievements, highlights the technical challenges that hinder the current methods from being widely adopted and proposes some latent solutions for the future research. This review paper is anticipated to be a comprehensive reference for researchers and professionals in this field of study.

Reliability assessment and performance improvement of long-span roof structure subjected to coupled wind-snow multi-hazard

Sensitivity to wind and snow loads has been the focus of reliability analysis and safety design of long-span roof structures in cold regions. In this study, the reliability assessment and performance improvement of a long-span roof structure subjected to coupled wind-snow multi-hazard are addressed. To this end, the average wind pressure coefficients of roof surface are first derived from wind tunnel tests, and the two-dimensional wind velocity field simulation is carried out by using the refined spectral representation scheme based on joint wavenumber-frequency power spectrum and stochastic harmonic function. The snow pressure coefficients of structural roof considering wind-induced snow drift effects are obtained by conducting computational fluid dynamics simulation. Then the global reliability of the structure subjected to coupled wind-snow multi-hazard with 100-yr return period is assessed using the probability density evolution method (PDEM). To improve structural performance, a control scheme of distributed tuned mass dampers (d-TMDs) is designed according to the structural dynamics of their deployment positions. Numerical results show that the fluctuating wind is a critical factor resulting in deformation failure of the long-span roof structure, and the proposed control scheme has sound effectiveness and robustness to mitigate the fluctuating wind effect and thus improve the structural performance.

Non-Gaussian characteristics and extreme wind pressure of long-span roof under various approaching flow turbulences

This study investigates the effects of different turbulences on the non-Gaussian characteristics of wind loads on a long-span roof. Wind tunnel tests of the long-span roof under different turbulences were carried out. The wind pressure characteristics, non-Gaussian characteristics and formation mechanism of wind loads were analyzed in detail. The Sadek-Simiu method was used to calculate and analyze the peak factor of the fluctuating wind pressures. The results indicated that the wind pressure characteristics of the long-span roof presented non-Gaussian characteristics that are mainly influenced by turbulence. With the increasing of turbulence, the non-Gaussian characteristics of wind loads become more and more obvious. Furthermore, the criteria for the division of Gaussian and non-Gaussian zones under six different turbulence levels are identified considering that the constraint of the Skewness-Kurtosis of the long-span roof as Ku >|Sk|2 +2. It was found that the peak factor increases with the increase of turbulences and its value ranges from 4.56 to 7.03, which is about 82.4%–181.2% higher than the stipulated value of 2.5 specified in the design code. Therefore, the value of the peak factor in the specification should be appropriately increased to ensure the safety of the long-span roof structure

Effect of the MHS on Earthquake Response of Space Truss Structures under Horizontal Earthquake Motion

Space truss structures are commonly used in long-span roof structures. Recently, middle-hung scoreboards (MHS), a kind of large-scale display device flexibly suspended in the center of the roof, have been widely used in gymnasiums. However, the effect of the MHS on dynamic characteristics and earthquake response of space truss structures needs to be investigated. In this paper, the effect on the MHS under horizontal earthquake motion is studied. The simplified model, where the MHS is simplified to four fixed masses on a structure, and the flexibly suspended model are established with Abaqus software, and the earthquake response is analyzed by the time-history method with the dynamic explicit method. The influence laws of the wire extent and the MHS weight are discussed. Compared with the simplified model, the nodal acceleration and the axial force rise up to 2.123 times and 1.575 times, respectively, in the flexibly suspended model, indicating that the amplification effect of the MHS acts significantly under horizontal earthquake motion. It turns out that the earthquake response of a space truss structure could be underestimated if a simplified model is used. The crest acceleration of both top chord nodes and bottom chords nodes are greatly influenced by the MHS weight but little affected by the wire extent. The influence laws of the MHS weight and the wire extent on crest axial forces of structural members are very complicated. The central regions of both the top chords and the bottom chords are the most affected regions, and the boundary regions parallel to the direction of the earthquake motion are the least affected regions. It is suggested that the envelope value under the conditions of different wire extent and MHS weight are used for structural design.

Effects of free-stream turbulence on motion-induced aerodynamic forces of a long-span flexible flat roof using LES simulations

This study aims to investigate the effects of free-stream turbulence on motion-induced aerodynamic forces of a long-span flexible flat roof. Large-eddy simulations (LES) of both rigid and forced vibrating roofs under different free-stream turbulence conditions are performed to obtain the aerodynamic forces and flow field data simultaneously. Firstly, the LES simulations of the rigid and vibrating roofs are validated against the reference experiments. And then, characteristics of the distributed pressures on vibrating roofs under free-stream flow turbulence conditions with different turbulence intensities are elucidated. Moreover, the motion-induced forces acting on the vibrating roof under different turbulence conditions are identified and compared, in which the power spectra of wind forces and aerodynamic damping and stiffness are examined. Furthermore, the underlying flow mechanism of the turbulence effects on the motion-induced forces is investigated based on POD analysis of the flow around the vibrating roof. It is found that dual effects exist between the influences of free-stream turbulence and roof motion on the aerodynamic forces, the motion-induced aerodynamic forces on the roof would be greatly decreased with the increase of free-stream turbulence, and the motion-induced effects become less dominant under high free-stream turbulence. The outcomes of this study would facilitate our understanding of the role played by the motion-induced aerodynamic forces and improve the wind-resistant design of long-span roof structures for engineering practices.

Downburst-Induced Vibration Coefficient of Long-Span Roof Structures

Long-span roof structures are vulnerable to being damaged by downbursts due to the sensitivity of such structures to wind loads. However, there is still no simple and practical method for the downburst-resistant design of such structures to date. Inspired by the wind-induced vibration coefficient (WVC) frequently used by engineers, this paper proposes a downburst-induced vibration coefficient (DVC) to evaluate the response of a roof structure subjected to downbursts. The proposed DVC is defined as the ratio of the total response to the mean response of the structure due to the action of downburst wind loads. The influences of different parameters on the downburst-induced vibration response of a long-span single-layer spherical reticulated structure are first analyzed in detail. Then, using a statistical approach, a design DVC, which can be practically adopted for civil engineers to evaluate the total structural response, is proposed to facilitate the structural downburst-resistant design. With the influences of different structural parameters fully taken into consideration, the design DVCs of displacement and internal force are studied through orthogonal analysis. Finally, regression models of the design DVCs are presented, and their reliability is verified via the application to a case study. The verification results indicate that the proposed regression models of the design DVCs are reliable and can be utilized to simply calculate the structural downburst-induced vibration response. The results obtained can serve as a reference for the downburst-resistant design of long-span roof structures.

Reliability assessment of a building complex with four long-span roof structures based on wind tunnel experiments

Reliability assessment of a building complex with four long-span roof structures based on wind tunnel experiments

Computational Design of Indoor Arenas (CDIA): Integrating multi-functional spaces and long-span roof structures

Indoor arenas are important public buildings catering for various activities (e.g., sports events, stage performances, assemblies, exhibitions, and daily sports for the public) and serving as landmarks in urban contexts. The multi-functional space and long-span roof structure of an indoor arena are highly interrelated, which impact the multi-functionality and structural performance and mainly define the overall form of the building. Therefore, it is crucial to integrate the multi-functional space and long-span roof structure to formulate proper forms for indoor arenas, in order to satisfy various design requirements during the conceptual design. This thesis aims at formulating a computational design method, ‘Computational Design of Indoor Arena (CDIA)’, to support the conceptual design of indoor arenas by using the computational techniques of parametric modelling, Building Performance Simulations (BPSs), Multi-Objective Optimizations (MOOs), surrogate models based on Multi-Layer Perceptron Neural Network (MLPNN), and clustering based on Self-Organizing Map (SOM clustering). In the formulation of CDIA, these techniques are modified, improved and organized into five components and three workflows, to satisfy the demands of the conceptual design of indoor arenas.

Nonlinear analytical modelling of flat and hyperbolic paraboloidal panels under shear

The hyperbolic paraboloid (hypar) form has been widely used in long-span roof structures and is the subject of much research under out-of-plane loading. However, the behaviour of hypars under in-plane loading has been less keenly studied, and there is no suitable guidance for their design in current codes of practice. A nonlinear analytical model treating the hypar as a deliberate imperfection applied to a flat plate is presented. A Rayleigh–Ritz formulation using appropriate shape functions is developed and the resulting equations are solved using numerical continuation techniques. The results are verified with nonlinear finite-element models, showing good correlation across a range of thicknesses and degrees of initial curvature. Key modal contributions that influence the behaviour of the hypar are identified, providing insight into the nonlinear behaviour of hypars subject to in-plane shear. The main differences in behaviour between the flat plate and the hypar panel are shown to be most prevalent in the early stages of loading, where the influence of the initial geometry is at its greatest.

Development and evaluation of novel modules for deployable tension-strut structures

There is a growing need for new alternatives of long-span roof structures with high level of transformability and structural robustness. This led to the development of deployable cable-strut structures, which are composed of a continuous net of struts and another continuous net of cables. Subsequently, a special type of these systems was pioneered and given the term deployable tension-strut structures (DTSSs). The motivation beyond this new concept was the lack of structural efficiency and form flexibility of conventional space trusses that are usually employed for covering large spaces. Typically, DTSSs are roof structures consisting of multiple modules put together to form the roof system. This paper is mainly concerned with developing new robust modules for DTSSs. The technique that was adopted for this purpose is a form-creation methodology previously introduced in the literature. A few modules were already developed based on this shape grammar. However, its potential to develop multiple efficient modules has not been sufficiently investigated. In this current work, the afore-mentioned algorithm was utilized to form 16 new modules. A comparative study based on a nonlinear finite element technique was conducted to investigate the efficiency of the novel modules as compared to that of the previously proposed in the literature. The results show that some of the new proposed modules are far more efficient than those presented in previous researches. Based on this comparative study, the most two efficient modules among the novel ones were picked for further study. Parametric studies were conducted on these two systems under gravity loads and wind loads considering the following parameters: no. of modules, span/depth ratio, and cables’ pre-stress level. For each parameter, the optimal range of values were determined to be used as a guide for the design of such systems.

FATIGUE LIFE ANALYSIS OF PANELS UNDER WIND LOAD BASED ON NON-PROBABILISTIC SET THEORY

In the existing fatigue analysis methods, structural material parameters and geometric dimensions are usually considered to be deterministic variables. For real structures, however, the structural parameters are bounded but uncertain. It is unsafe to estimate the fatigue life of a structure according to the nominal values. In this paper, we apply the interval analysis method based on non-probabilistic set theory to estimating the roof fatigue life under fluctuation wind load. Considering the thickness and elastic modulus of large-span roofs under bounded-but-uncertain circumstances, we calculate the dynamic response range of long-span roof structures under fluctuating wind load by the interval finite element method and interval dynamic response analysis method. The time history curve of the interval stress of large-span roofs is obtained through the constitutive equation and stress. The amplitudes of the interval stress are calculated by the rain-flow counting method. Considering the S-N curve of the roof material, we estimate the fatigue life interval of large-span roofs by Miner's law.

Computational Design of Indoor Arenas (CDIA)

Indoor arenas are important public buildings catering for various activities (e.g., sports events, stage performances, assemblies, exhibitions, and daily sports for the public) and serving as landmarks in urban contexts. The multi-functional space and long-span roof structure of an indoor arena are highly interrelated, which impact the multi-functionality and structural performance and mainly define the overall form of the building. Therefore, it is crucial to integrate the multi-functional space and long-span roof structure to formulate proper forms for indoor arenas, in order to satisfy various design requirements during the conceptual design. This thesis aims at formulating a computational design method, ‘Computational Design of Indoor Arena (CDIA)’, to support the conceptual design of indoor arenas by using the computational techniques of parametric modelling, Building Performance Simulations (BPSs), Multi-Objective Optimizations (MOOs), surrogate models based on Multi-Layer Perceptron Neural Network (MLPNN), and clustering based on Self-Organizing Map (SOM clustering). In the formulation of CDIA, these techniques are modified, improved and organized into five components and three workflows, to satisfy the demands of the conceptual design of indoor arenas.

Computational Design of Indoor Arenas (CDIA)

Indoor arenas are important public buildings catering for various activities (e.g., sports events, stage performances, assemblies, exhibitions, and daily sports for the public) and serving as landmarks in urban contexts. The multi-functional space and long-span roof structure of an indoor arena are highly interrelated, which impact the multi-functionality and structural performance and mainly define the overall form of the building. Therefore, it is crucial to integrate the multi-functional space and long-span roof structure to formulate proper forms for indoor arenas, in order to satisfy various design requirements during the conceptual design. This thesis aims at formulating a computational design method, ‘Computational Design of Indoor Arena (CDIA)’, to support the conceptual design of indoor arenas by using the computational techniques of parametric modelling, Building Performance Simulations (BPSs), Multi-Objective Optimizations (MOOs), surrogate models based on Multi-Layer Perceptron Neural Network (MLPNN), and clustering based on Self-Organizing Map (SOM clustering). In the formulation of CDIA, these techniques are modified, improved and organized into five components and three workflows, to satisfy the demands of the conceptual design of indoor arenas.

Experimental Study of Wind Pressure on a Long-Span Canopy Roof Structure Using a Wind Tunnel

The wind pressure characteristics of the surface of a long-span canopy roof structure were investigated in detail using synchronized pressure measurement tests on a rigid model in an atmospheric boundary layer wind tunnel. The mean and fluctuating wind pressure distribution characteristics, power spectral density and coherence of the fluctuating wind pressure between different measurement points were analyzed. The results showed that the wind direction had a significant impact on the wind load distribution across the surface of the long-span canopy roof structure. When the short axis of the roof structure faced the wind, a positive pressure area was formed under the impact of the incoming flow, with the resulting turbulence being the main cause of excitation. When the long axis of the roof structure faced the wind (wind directions of 0° and 180°), a columnar vortex was formed on the windward side of the front edge of the roof structure and a suction force was created at the separation points, with the main excitation of the wind load being intermittent vortex shedding. The resulting spectral content was complex. The coherence of the measurement points on the roof structure surface decreased continuously as the distance between them increased. The correlation between the same two measurement points obviously also differed according to the wind direction. However, the coherence between measurement points aligned to the wind direction was stronger than it was in a cross-wind direction.

Rapid algorithm to find optimal step excitations for modal testing of long-span roof structures

A rapid algorithm is proposed to obtain optimal step excitations for the modal testing of long-span roof structures (LRS). Step excitations of LRS are realized by suddenly removing gravity loads. The optimization of step excitations aims to strengthen the contribution of a target mode to the structural free vibration and to suppress the participation of its adjacent modes at the same time. In this way, the target mode can be well triggered without the disturbances of its adjacent modes. The simplified mathematical relationship between the objective indicator vector and the load distribution is established. By solving a bounded-variable least square problem, the optimal step excitations are rapidly acquired. The numerical study of a Geiger cable dome and both numerical and experimental studies of a spatial truss are carried out. The results show that the rapid algorithm can quickly complete the optimization of step excitations, and help the classic Ibrahim Time Domain method greatly improve the identification accuracy of closely spaced modes of LRS.

Mechanical Properties and Design Method of Aluminum Alloy Bolt-sphere Joints

Aluminum alloy materials have been extensively used in long-span roof structures, especially in coastal and industrial buildings containing corrosive matters. In this study, new-type aluminum alloy bolt-sphere joints were taken as research objects and evaluated through tensile test and numerical simulation. The tensile properties and failure mechanism of the aluminum alloy bolt-sphere joints were explored. A calculation formula for the tension capacity of aluminum alloy bolt-sphere joints was proposed. The following conclusions were drawn based on the test data and the numerical simulation results: (1) the tension capacity of aluminum alloy bolt-sphere joints is controlled by the tensile properties of seal plates and the uplift-resistant properties of stainless steel bolts; (2) as the thickness of the seal plate increases, its main tensile failure modes are the combined tensile and shear failures at the ring crush part of the aluminum pipe, the tensile failure at the ring crush part of the aluminum pipe, and the tensile failure of the stainless steel bolt; (3) the tensile failure modes of the bolts are mainly the rupture failure of the bolt member and the shear failure of the thread according to the different screwing depths of the bolts into the sphere; and (4) the screwing depth of the bolt into the sphere should be more than 1.6d (d is the diameter of the stainless steel bolt); (5) the proposed calculation formula is accurate and effective.

Coupled Finite Volume and Finite Element Method Analysis of a Complex Large-Span Roof Structure

The main goal of this paper is to present coupled Computational Fluid Dynamics and structural analysis for the precise determination of wind impact on internal forces and deformations of structural elements of a longspan roof structure. The Finite Volume Method (FVM) serves for a solution of the fluid flow problem to model the air flow around the structure, whose results are applied in turn as the boundary tractions in the Finite Element Method problem structural solution for the linear elastostatics with small deformations. The first part is carried out with the use of ANSYS 15.0 computer system, whereas the FEM system Robot supports stress analysis in particular roof members. A comparison of the wind pressure distribution throughout the roof surface shows some differences with respect to that available in the engineering designing codes like Eurocode, which deserves separate further numerical studies. Coupling of these two separate numerical techniques appears to be promising in view of future computational models of stochastic nature in large scale structural systems due to the stochastic perturbation method.