A novel numerical approach and experimental study to evaluate the effect of component failure on spoke-wheel cable structure
Introduction
The spoke-wheel cable structure is similar to a bicycle wheel, consisting of inner tensile rings, outer compressive rings, spoke cables, poles, and lanyards. Its structural form can be classified into three main types according to the number of compressive and tensile rings: one compressive ring and one tensile ring, two compressive rings and one tensile ring, and one compressive ring and two tensile rings [1], as shown in Fig. 1.
This paper focuses on the spoke-wheel cable structure with one compressive ring and two tensile rings (Fig. 1c). This structural form has a radial arrangement of spoke cables, which connect the single outer compressive ring and two inner tensile rings. The inclined spoke cables are connected with poles and lanyards. The inner rings, spoke cables, and poles are the basic components of the structure. These basic components may fail under unexpected conditions which will reduce the structural reliability. As a result, the whole structure may collapse and cause significant property loss and severe casualties.
The research and application of spoke-wheel cable structures began in the 1980s. Schlaich et al. [1] successfully transferred the spoke-wheel principle to the roof structures, classified the spoke-wheel cable structures and introduced a variety of design methodologies for this structure. A series of studies have been conducted on the mechanical properties of spoke-wheel cable structures. Majowiecki et al. [2] designed the spoke-wheel cable roof for the Olympic Stadium in Rome and performed the dynamic analysis of the structure with a wind tunnel test and numerical simulation. The result showed that the major part of the dynamic load is due to vortices formed in the wake of the upstream sector of the roof. Bergermann and Göppert [3] investigated the influence of the inner ring’s shape on the structural performance of spoke-wheel cable structures and found that the structural internal force and steel consumption gradually increase when the inner ring changes from perfectly circular to oval and to almost rectangular. Wu et al. [4] investigated the mechanical performance of the spoke-wheel cable structure with large height difference. The results indicated that the large height difference of the structure may cause some spoke cables under compression, which should be replaced with rigid rods. Zhang et al. [5] conducted a detailed parametric analysis on the spoke-wheel cable structure and investigated the mechanical properties of the structure with different plane geometries and pole heights and concluded that the ratio of the short axis to the long axis of the spoke-wheel would better be greater than 0.8 to achieve a good internal force state. Schlaich et al. [6] investigated the composition of structural stiffness of spoke-wheel cable structures and found that their structural stiffness is mainly comprised of the geometric stiffness controlled by the pretension force of cables rather than the elastic stiffness controlled by the elastic modulus of cables. Park et al. [7] analysed the mechanical characteristics of large span spoke-wheel cable structures and pointed out that the sag ratio and pre-tension force are two important design parameters; increasing the sag ratio contributes to decreasing the pretension force and vice versa. Efforts have also been made to study the form-finding method of spoke-wheel cable structures. Guo et al. [8] introduced the force-density method for the form-finding of spoke-wheel cable structures and proposed a new form-finding process, i.e. from shape to force and then back to shape, which can effectively avoid convergence difficulties. Tamai [9] introduced a geometric approach for the form-finding of spoke-wheel cable structures and derived the mathematical explanations. Shang et al. [10] established a form-finding method based on nonlinear finite element (FE) analysis and applied it to the spoke-wheel cable roof of Bao’an Stadium in Shenzhen, which was completed in the general FE software ANSYS [11]. Li et al. [12] developed a novel form-finding method for the spoke-wheel cable structure, namely the cable length iteration method, which takes the cable length as the only iterative parameter to solve the coordinates of free nodes in the structure and can greatly improve the speed of convergence. The results showed that these form-finding methods all achieved satisfactory accuracy. Zhao et al. [13] took the roof of Bao’an Stadium in Shenzhen as the research object and carried out the cable failure simulation analysis in the FE software ANSYS [11]. The result indicated that the breaking of a spoke cable would result in the large deformation of the local structure but not the failure of the entire structure, while the breaking of a ring cable would cause the collapse of the entire structure. In summary, the existing studies mainly focus on the structural forms and mechanical characteristics of the spoke-wheel cable structure. Moreover, the theoretical analysis and numerical calculation dominate the existing studies, whereas the experimental research on the spoke-wheel cable structure remains insufficient.
Furthermore, the failure mechanism and reliability of large-span spatial steel structures have been gaining increasing attention of the civil engineering community in recent years. These structures are usually large-scale public buildings, whose collapse can cause severe property loss and casualties. Han et al. [14] studied the failure mechanism of the steel arch truss structure under earthquakes with the shaking table test and numerical analysis. The result showed that the structure lost its bearing capacity when the PGA (peak ground acceleration) reached 0.8 – 1.0g and the main trusses had an in-plane anti-symmetric deformation after the seismic loading. Nie et al. [15] investigated the collapse mechanism of the single-layer cylinder shell with a model experimental study and concluded that the whole shell collapses because of local instability, and the dynamic strain response of the structure behaves elastically during the collapse process. Liu et al. [16] conducted experimental and numerical research on the annular crossed cable-truss structure under cable rupture and reported that this structure does not undergo a disproportionate collapse after the rupture of a majority of cables. Tian et al. [17,18] studied the anti-progressive collapse mechanism of single-layer spatial grid structures and proposed using kinked steel pipe and extra member reinforcements to avoid stability failure and potential progressive collapse. Jiang and Chen [19] studied the failure process of a steel truss roof and proposed a safety assessment method for steel truss structures based on linear static analysis procedure. Foraboschi [20] performed the quantitative safety assessment of steel components under combined axial force and lateral load in terms of a simple analytical formulation. The comparison to the non-linear finite element analysis result confirmed that the formulation is equally accurate and less labour-intensive. Çeribaşı [21] investigated the reliability of steel truss roof systems under snow loads through probabilistic analysis and the results indicated that the effect of the standard deviation of snow load on failure probability is much more than the effect of the intensity of nominal snow load. Commonly used methods in the reliability analysis of steel structures include artificial neural network (ANN) [22], Monte Carlo simulation (MCS) [23], first order reliability method (FORM) [24] and response surface method (RSM) [25], which were summarized and compared by Chojaczyk et al. in Ref. [26]. The reliability assessment process of large span steel structures, such as steel truss structure and steel grid structure, were reviewed in Ref. [27]. However, there is a paucity of studies on the failure and reliability of spoke-wheel cable structures.
In light of the aforementioned research gap, the component failure of a typical spoke-wheel cable structure was investigated in this paper through the experiment and numerical simulation. Firstly, a newly developed technology called building information modelling (BIM) + three-dimensional laser scanning (3DLS) was introduced, which can modify the simulation model and significantly increase the accuracy of the numerical calculation. Then, the scale model test and the FE simulation of an actual spoke-wheel cable structure with one outer-ring and two inner-rings were carried out. The FE model was modified with BIM + 3DLS. Breakages of the spoke cable, the ring cable and the pole were considered and their influences on the structural reliability was investigated. The simulation results before or after the modification were compared with the experimental result.
Section snippets
Research significance
This research proposed a simulation modification method based on building information modelling (BIM) and three-dimensional laser scanning (3DLS) technologies, which is able to modify the finite element (FE) model considering the spatial coordinate change of the physical model. This method can effectively improve the information technology (IT) level of traditional structural analysis, solve the problem that the spatial coordinate of the FE model cannot be updated according to the real test
Simulation modification method based on BIM and 3DLS
Building information modelling, abbreviated as BIM, was first proposed by Autodesk at the beginning of the 21st century [28]. The core of BIM is to establish a virtual building engineering model and use digital technology to provide a complete and consistent information database for this model [29]. Three-dimensional laser scanning (3DLS) is also called teal scene reproduction technology. It saves the relative spatial position of each point of the object as a three-dimensional (3D) point cloud
Simulation and model test of component failure
An actual spoke-wheel cable structure with a circular shape was taken as the research object. This cable structure had one outer-ring, two inner-rings, ten pairs of upper and lower spoke cables, and three poles at each cable truss. The diameters of the outer-ring and inner-ring are 60 m and 15 m, respectively. Due to the restriction of test site, a scale model with the geometric scale ratio 1:10 has substituted the actual structure, whose geometry is shown in Fig. 3.
The same materials were used
Structural reliability analysis after the component failure
The mechanical behaviours of the structure after the failures of various components were clearly illustrated in Section 3. However, the failure of a single component does not necessarily mean the failure of the whole structure. The engineering community is usually more concerned about whether the structure is still reliable or not after the failure of a certain component. In view of this, the reliability of the spoke-wheel cable structure after the component failure was investigated. According
Conclusions
In the present study, the 6-m diameter scale model of an actual spoke-wheel cable structure was constructed. The numerical simulation and scale model testing on the impact of various component failures of the structure were performed. A newly developed technology, i.e. BIM combined with 3DLS, was used to modify the simulation model and increase the accuracy. Furthermore, based on the RSM and MCS, the reliability analysis was conducted to explore the structural reliability and failure
CRediT authorship contribution statement
Zhansheng Liu: Investigation, Supervision, Conceptualization, Project administration, Writing – original draft. Hang Li: Investigation, Writing – original draft. Yue Liu: Supervision, Conceptualization, Writing – original draft, Writing – review & editing. Jingchao Wang: Investigation. T. Tafsirojjaman: Writing – review & editing. Guoliang Shi: Writing – review & editing.
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
The authors gratefully acknowledge the financial support provided by the National Key Research and Development Program of China (No. 2018YFF0300300) and the National Natural Science Foundation of China Youth Science Foundation Project (NSFC 51908012).
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