Long-span Roof Structures Research Articles

An efficient method for universal equivalent static wind loads on long-span roof structures

Wind-induced response behavior of long-span roof structures is very complicated, showing significant contributions of multiple vibration modes. The largest load effects in a huge number of members should be considered for the sake of the equivalent static wind loads (ESWLs). Studies on essential matters and necessary conditions of the universal ESWLs are discussed. An efficient method for universal ESWLs on long-span roof structures is proposed. The generalized resuming forces including both the external wind loads and inertial forces are defined. Then, the universal ESWLs are given by a combination of eigenmodes calculated by proper orthogonal decomposition (POD) analysis. Firstly, the least squares method is applied to a matrix of eigenmodes by using the influence function. Then, the universal ESWLs distribution is obtained which reproduces the largest load effects simultaneously. Secondly, by choosing the eigenmodes of generalized resuming forces as the basic loading distribution vectors, this method becomes efficient. Meanwhile, by using the constraint equations, the universal ESWLs becomes reasonable. Finally, reproduced largest load effects by load-response-correlation (LRC) ESWLs and universal ESWLs are compared with the actual largest load effects obtained by the time domain response analysis for a long-span roof structure. The results demonstrate the feasibility and usefulness of the proposed universal ESWLs method.

Coupled wind-induced responses and equivalent static wind loads on long-span roof structures with the consistent load–response–correlation method

Long-span roof structures with multiple vibration modes may undergo coupled motions when exposed to spatiotemporally varying dynamic wind loads. This article presents a framework for the analysis of coupled wind-induced responses and equivalent static wind loads on long-span roof structures. This framework takes into account the inter-modal coupling of modal response components and cross correlation between the background and resonance. The load–response–correlation method is widely used for the background equivalent static wind loads of rigid structures. Also, the concept of load–response–correlation was extended for the correct estimation of equivalent static wind loads by considering the correlation between the load and exact total responses. However, there is no detailed study for the correct estimation of equivalent static wind loads on the component of background, resonance, and their cross response using load–response–correlation method. In this article, a consistent load–response–correlation method for equivalent static wind loads is presented in a unified framework which contains the background, resonance, and modal coupling. First, the accuracy of wind-induced responses is ensured by considering the modal coupling. Meanwhile, the efficiency is improved by decomposing the covariance matrix of the generalized resuming forces. Second, several effects of the wind-induced responses are discussed in detail, such as the effect of the modal coupling, the effect of the modal participations to resonant responses, and the effect of the cross correlation between the background and resonance. Finally, the proposed equivalent static wind loads are represented by the composition of the external wind loads and inertial forces, which are both the most probable load distributions. Accordingly, the equivalent static wind load distribution and the responses by equivalent static wind loads are reasonable.

The Performance of Cold-formed Steel Long-span Roof Structure Combined with Laminated Timber: Cold-formed Steel – Laminated Timber Composite

This paper presents analytical observation results on the performance of CFS-laminated timber composite long-span roof structure attached by laminated timber composite, named as CFS–laminated timber composite. Two dimensional models of a 25 m CFS Vaulted Parallel Chord truss were analyzed separately. One of them was thoroughly assembled using CFS members only and the other one was assembled from composite members. Based on analytical results, the CFS-laminated timber roof truss has a better performance than the CFS roof truss in resisting the external load.

Estimation of wind-induced extreme responses with various mean recurrence intervals considering model uncertainty due to limited data

The wind-induced extreme responses with various mean recurrence intervals (MRIs) can be estimated by accounting for the aleatory uncertainties in wind speed and extreme response coefficient in terms of their probability distributions. These distribution models when determined from limited samples of data also have uncertainties, referred to as epistemic uncertainties. This study addresses the epistemic uncertainties in probability distributions of wind speed and extreme response coefficient, and their influence on the estimated extreme responses with various MRIs. Closed-form expressions for quantifying the epistemic uncertainties in terms of coefficients of variation of the distribution model parameters are presented as functions of sample size. The influence of epistemic uncertainties on the predicted extreme responses with various MRIs is also estimated using closed-form expression in terms of confidence intervals. Based on the proposed formulations, a parametric study is carried out to shed light on the importance of consideration of various epistemic uncertainties. The results show that the epistemic uncertainty of wind speed generally predominates the predicted extreme response, while the epistemic uncertainty in the extreme response coefficient can also have considerable effect when the aleatory uncertainty in wind speed is low and that in extreme response coefficient is high. The proposed method is then applied to a long-span roof structure using wind loads determined from a wind tunnel test.

Dominant mode selection and modal coupling analysis for wind-induced response of long-span roofs

Mode selection and modal coupling analysis are important to estimate wind-induced structural response of long-span roof structures. This article presents a framework for predicting wind-induced structural response of long-span roof structures based on modal analysis. This framework first identifies the dominant modes according to the correlation between the mode shape and the wind load spatial distribution on the structure as well as a proposed “modal participation coefficient.” Second, the concept of modal strain energy is introduced and a modal coupling coefficient is defined, based on which the dominant coupling modes are determined. A modified square root of the sum of the squares methodology is then developed to account for the modal coupling effects of the background and the resonant response components. The total responses can be obtained by combining the contributions of the dominant coupling modes and the square root of the sum of the squares results from the dominant modes. This avoids the use of the computation expensive complete quadratic combination method. Finally, an illustrative example of wind-induced response analysis of the China National Stadium roof structure is provided to demonstrate the effectiveness of the proposed framework.

Integral lifting simulation of long-span spatial steel structures during construction

Abstract This paper presents an analysis of the synchronous and asynchronous integral lifting of a China Eastern Airline hanger's steel roof. A novel asynchronous analysis method known as single and interlaced points is proposed. The results showed that setting up the lifting points according to Scheme 1 and multiplying the design strength by the reduction factor of 0.95 is a reasonable solution. Including the horizontal elastic stiffness in the multi-particle model was confirmed to improve the computational accuracy. The structural safety was ensured for synchronous lifting. The displacement difference of the lifting points was less than 15 mm. Thus, the method of single and interlaced points is appropriate for analyzing the asynchronous lifting of long-span steel roof structures. Replacing out-of-code members is feasible and has little effect on the overall structure under the design conditions, and the lifting trestles, lifting points, and concrete columns are reliable.

Topology Optimization and Advanced Manufacturing as a Means for the Design of Sustainable Building Components

This paper presents research exploring the potential of topology optimization as a means for the design of sustainable building components. Topology optimization is a mathematical, gradient-based design procedure that can be used to determine the distribution of required material within a design domain based upon defined loads and boundary conditions while meeting a prescribed target objective, such as minimizing deflection. The concept of topology optimization has been utilized by the automotive and aerospace industry for almost thirty years now, since its early development, where problems associated with solutions meant to satisfy maximum stiffness with minimum weight are of the utmost importance.The recent saturation of digital design tools and techniques within the architecture industry have led more and more architects to seek computationally driven, data-centric, methodologies to assist in the design process. Topology optimization is well suited as a methodology to assist in the development of form that is rooted in sound structural logic while striving for material efficiency. This paper presents case studies of recent architectural projects that utilize topology optimization for projects ranging from long-span roof structures to high-rise buildings. Advances in advanced manufacturing are also examined as a means of more easily realizing sustainable building systems through this use of topology optimization.

Optimum topology design of geometrically nonlinear suspended domes using ECBO

The suspended dome system is a new structural form that has become popular in the construction of long-span roof structures. Suspended dome is a kind of new pre-stressed space grid structure that has complex mechanical characteristics. In this paper, an optimum topology design algorithm is performed using the enhanced colliding bodies optimization (ECBO) method. The length of the strut, the cable initial strain, the cross-sectional area of the cables and the cross-sectional size of steel elements are adopted as design variables and the minimum volume of each dome is taken as the objective function. The topology optimization on lamella dome is performed by considering the type of the joint connections to determine the optimum number of rings, the optimum number of joints in each ring, the optimum height of crown and tubular sections of these domes. A simple procedure is provided to determine the configuration of the dome. This procedure includes calculating the joint coordinates and steel elements and cables constructions. The design constraints are implemented according to the provision of LRFD-AISC (Load and Resistance Factor Design-American Institute of Steel Constitution). This paper explores the efficiency of lamella dome with pin-joint and rigid-joint connections and compares them to investigate the performance of these domes under wind (according to the ASCE 7-05), dead and snow loading conditions. Then, a suspended dome with pin-joint single-layer reticulated shell and a suspended dome with rigid-joint single-layer reticulated shell are discussed. Optimization is performed via ECBO algorithm to demonstrate the effectiveness and robustness of the ECBO in creating optimal design for suspended domes.

Full-scale tests of wind effects on a long span roof structure

Full-scale measurements are regarded as the most reliable method to evaluate wind effects on large buildings and structures. Some selected results are presented in this paper from the full-scale measurement of wind effects on a long-span steel roof structure during the passage of Typhoon Fanapi. Some field data, including wind speed and direction, acceleration responses, etc., were continuously and simultaneously recorded during the passage of the typhoon. Comprehensive analysis of the measured data is conducted to evaluate the typhoon-generated wind characteristics and its effects on a long-span steel roof. The first four natural frequencies and their vibration mode shapes of the Guangzhou International Sports Arena (GISA) roof are evaluated by the stochastic subspace identification (SSI) method and comparisons with those from finite element (FE) analysis are made. Meanwhile, damping ratios of the roof are also identified by the SSI method and compared with those identified by the random decrement method; the amplitude-dependent damping behaviors are also discussed. The fullscale measurement results are further compared with the corresponding wind tunnel test results to evaluate its reliability. The results obtained from this study are valuable for academic and professional engineers involved in the design of large-span roof structures.

Estimation of internal forces in cladding support components due to wind-induced overall behaviors of long-span roof structure

Wind-induced internal forces in cladding support components of a long-span roof structure depend on local behaviors caused by local wind loads and wind-induced overall behaviors of the main structural frame. Based on the pioneering work of Ding and Tamura (2013); Ding et al. (2012), a new method is proposed to estimate internal forces in cladding support components due to wind-induced overall behaviors directly. A detailed investigation on the contributions of wind-induced overall and local behaviors for internal forces in cladding support components of a space truss structure is performed. The results demonstrate that the bending moments and shear forces in cladding support components are dominated by local wind loads acting on the corresponding tributary areas, and the axial forces are caused by the overall displacements of the main structural frame. Considering only the local behavior will underestimate the axial forces in cladding support components significantly, which may lead to buckling failure.

Wind Load Characteristics of a Long-Span Retractable Roof Structure

Taking a long-span retractable roof structure, which locates in a coastal city of China, as an example, a wind tunnel test on a rigid model was carried out. This paper analyzes the wind load characteristics of this structure under three conditions: open, closed and closed with damage in small area of windows. The block shape coefficients as well as its variation with wind direction are given; meanwhile, this paper analyzes the fluctuation characteristics of wind load, obtaining the gust coefficient as well as the variation of fluctuation coefficients with wind direction, which can be applied to the design of coating members in this structure. By comparing the analysis results under three conditions, the following conclusion can be reached: the long-span structure is more resistant against mean wind load when the roof is open than when it is closed. There is no decrease in fluctuating wind load and in some wind directions; the fluctuating wind load will be even larger. Additionally, the damage in small area of windows does not much affect the wind load characteristics on structure.

Development and analysis of a long-span retractable roof structure

A long-span retractable roof structure based on the beam string structure (BSS) and scissor mechanisms was presented in this paper. The BSS are placed parallel to each other and they are connected with the linear scissor mechanism. During the folding or unfolding, the structure just has one degree of freedom. The geometry of the retractable roof structure was firstly given. Then structural analysis of an integrated model of the unfolded configuration was conducted. Furthermore, the structural behavior of the structure in the semi-open configuration is also investigated. Finally, using the translational and rotational springs to model the elastic support of the strut, an analytical model for the lateral buckling of the BSS during the motion is developed. Based on the virtual work principle, the formulation of the critical load is obtained. Then a detailed parameter analysis of the BSS with a straight beam is undertaken.

Potential collapse of a roof structure averted by quick repair

The paper describes the analysis and repair of an accidentally damaged long-span roof structure in a large storage warehouse; these were successfully performed in order to avert potential progressive collapse. The damage was caused by the impact of the open bed of a moving truck against one of the exposed primary load-carrying steel girders of the gable roof of the building. The impact caused serious dislocation and cross-sectional deformation of the girder, as well as rupturing several purlin-to-girder connections. As a result, the girder was not only damaged in itself, but its lateral-torsional stability was also compromised. The structural analysis of the damaged roof structure is reviewed, and two versions of repair of the damaged elements are described, including temporary support by three-dimensional modern shoring towers for both gravity and wind loads. It is demonstrated that, at least in this case, the damage – however serious – to a single structural element does not necessarily impact the global safety and result in immediate failure of the entire structure. Prudent timely repair can avert a disaster.

Investigation of the Static and Dynamic Behavior of a Deployable Hybrid Grid Shell

The deployable hybrid grid shell, which can be deformed elastically by bending until the desired form is obtained, is an attractive structural form in the design and construction of long-span transparent glass roof structures. These hybrid structures are very slender and lightweight. Therefore, the structural behavior of the hybrid grid shell needs to be well understood. The mechanical characteristic, static and dynamic behaviors of the grid shell have been investigated in this paper. The effect of the structural parameters, such as rise-to-span ratios, cross-sections of steel beams, areas and pre-stress of cables, on the structural behavior has been studied in detail. Results show that the hybrid grid shell with a good translucence is more efficient than the general single-layer reticulated shell structure. The vertical structural stiffness initially increases with the increase of the rise-to-span ratio and then decreases afterwards. There exists an optimum rise-to-span ratio resulting in an optimum stiffness for the specified span. The optimum value of the ratio is found between 0.15 and 0.20 from the simulation study presented in this paper. Given a specific height-to-span ratio, the increase of the beam section greatly reduces the nodal displacement and member forces and increases the natural frequency. However, it can be found that increasing the areas and pre-stress of cables is not an economical way to improve the structural behavior.

Wind-Induced Response and Equivalent Static Wind Load of Long-Span Roof Structures by Combined Ritz-Proper Orthogonal Decomposition Method

AbstractThe contribution of higher vibration modes is important to the wind-induced response of long-span roofs, which makes it difficult to estimate the wind-induced response and equivalent static wind loads accurately. The authors have studied this topic for a number of years, and some research results are presented. The Ritz-proper orthogonal decomposition method for choosing dominant modes of the wind-induced response is proposed. Eigenvectors of fluctuating wind pressure obtained from the proper orthogonal decomposition are regarded as the spatial distribution of the load to generate Ritz vectors. The background and resonant response are redefined on the basis of the modal acceleration method, and a method is proposed to calculate the correlation coefficient between the background and the resonant responses. Target responses are expressed as the linear combination of basis vectors, which are the dominant eigenmodes of wind pressure and structural vibration modes representing the background and the re...

Characteristics of Wind Loads Acting on Complex Long-Span Roof Structure

The Shenzhen New Railway Station (SNRS) has roof dimensions of 450 m long and 408 m wide. This paper presents the results of wind loads acting on the large-span roof structure. In the wind tunnel test, wind-induced pressures including mean and fluctuating components were measured from the roof of a 1:200 scale SNRS model under suburban boundary layer wind flow configuration in a boundary layer wind tunnel of HD-2 at Hunan University. Based on the data obtained simultaneously from the wind tunnel tests, the distributions of the mean and fluctuating wind pressure coefficients and the characteristics of probability density functions of wind pressures of typical pressure taps were analyzed in detailed. The outcomes of the experimental study indicate that: (1) The maximum mean negative wind pressure coefficients on the roof occur at the windward leading edge region, where the maximum fluctuating wind pressure coefficients occur also in this region; (2) There are some differences of the maximum mean negative wind pressure coefficients and RMS wind pressure coefficients under conditions with different number of trains inside the station, but such effects on the overall pressure distributions on the whole roof are negligible; (3) There are clearly negative skewed distributions for some pressure taps at the windward leading roof edge and much longer negative tails are observed, which follow Non-Gaussian distributions. The results presented in this paper are expected to be of considerable interest and of use to researchers and professionals involved in designing complex long-span roof structures.

Characteristics of Wind Loads on Long-Span Roof

In recent years, many large span roofs of airport waiting room and garage were destructed in the tropic storm, which have the characteristics of light mass, high flexibility, slight damping and low natural frequency. Wind loads general control the design of such structures. Thus, the tests of wind pressure with the rigid scale model in boundary layer wind tunnel were conducted in the structural design stage. This paper presents the results of characteristics of wind loads on large-span roof structure of the Guangzhou International Convention & Exhibition Center (GICEC) in frequency domain. The power spectrum densities, correlation coefficients, coherence functions and probability density function (PDF) were analyzed in detail. The results can be summarized as follows: (1)The power spectrum densities of fluctuating wind loads have the characteristics of vortex shedding and the Strouhal number is about 0.295; (2)The coherence coefficients decrease with the frequency and the spatial distance increase at both the along-wind and across-wind direction; (3)There are clearly negative skewed distributions for some pressure taps at the windward leading roof edge and much longer negative tails are observed, which follow Non-Gaussian distributions. The results presented in this paper are expected to be of considerable interest and of use to researchers and professionals involved in designing complex long-span roof structures.

Large eddy simulation of wind effects on a long-span complex roof structure

This paper presents a combined study of numerical simulations and wind tunnel tests for the determinations of wind effects on a long-span complex roof of the Shenzhen New Railway Station Building. The main objective of this study is to present an effective approach for the estimations of wind effects on a complex roof by computational fluid dynamics (CFD) techniques. A new inflow turbulence generator called the discretizing and synthesizing random flow generation (DSRFG) approach was applied to simulate inflow boundary conditions of a turbulent flow field. A new one-equation dynamic subgrid scale (SGS) model was adopted for the large eddy simulations (LES) of wind effects on the station building. The wind-induced pressures on the roof and turbulent flow fields around the station building were thus calculated based upon the DSRFG approach and the new SGS model integrated with the FLUENT software. In parallel with the numerical investigation, simultaneous pressure measurements on the entire station building were made in a boundary layer wind tunnel to determine the mean, fluctuating, and peak pressure coefficient distributions. The numerically predicted results were found to be consistent with the wind tunnel test data. The comparative study demonstrated that the recommended inflow turbulence generation technique and the new SGS model as well as the associated numerical treatments are useful tools for structural engineers to assess wind effects on long-span complex roofs and irregularly shaped buildings at the design stage.

Buckling Analysis of a Long-Span Roof Structure Collapsed during Construction

AbstractNumerical simulation of damage and collapse mechanisms suffered by engineering structures can be an effective tool for a quantitative assessment of their causes. Large displacement inelastic analysis may be required in the case of highly flexible structures, such as steel roofs, which frequently experience large failures or even collapse because of buckling. This paper discusses the collapse of a long-span steel roof structure, which fell down suddenly during construction as a result of an out-of-plane buckling phenomenon induced by a gust of wind. Forensic investigations were carried out on behalf of the judicial authority to identify the causes of the accident. Based on detailed information gathered from site surveys and project documents, a three-dimensional numerical model of the as-built structure was created, and buckling analyses were performed to assess the safety level at the moment of the collapse. The as-built structure was braced through some purlins and steel cables fixed at the groun...

Wind effects on a long-span beam string roof structure: Wind tunnel test, field measurement and numerical analysis

The Guangzhou International Convention & Exhibition Center (GICEC) with roof dimensions of 210 m wide and 457 m long is the largest exhibition center in Asia and the 2nd largest of this kind in the world. This paper presents results from a combined study of wind tunnel test, full-scale measurement, and numerical analysis of wind effects on the long-span beam string roof structure. In the wind tunnel test, wind-induced pressures including mean and fluctuating components were measured from the roof of a 1:300 scale GICEC model under suburban boundary layer wind flow configuration. The Proper Orthogonal Decomposition (POD) method and the quasi-steady approach as well as probability analysis were adopted to estimate the characteristics of the fluctuating wind pressures on the roof. On the other hand, full-scale measurements of wind actions and wind-induced structural responses of the roof were conducted during the passage of Typhoon Nuri. The field data such as wind speed, wind direction, and acceleration responses, etc., were continuously and simultaneously monitored from a wind and structural response monitoring system installed on the roof structure during the typhoon. Detailed analysis of the field data was performed to investigate the characteristics of the typhoon-generated wind and the wind-induced vibration of the long-span roof structure under typhoon condition. The dynamic characteristics of the roof were determined from the field measurements and comparisons with those calculated from the finite element model (FEM) of the structure were made. The damping ratios of the roof structure were estimated by means of the random decrement method and the amplitude-dependent damping characteristics were presented and discussed. Finally, the full-scale measurements were compared with the model test results to examine the accuracy of the wind tunnel test results and to identify possible modelling errors in the numerical study. The results presented in this paper are expected to be of considerable interest and of use to researchers and professionals involved in designing long-span roof structures.