Double-layer Space Trusses Research Articles

Progressive collapse demolition of double-layer space truss under different demolition load conditions

Two double-layer space trusses (DLSTs) under different demolition load conditions were tested for progressive collapse demolition. The primary load-carrying members of the tested DLSTs were removed one by one according to a pre-designed demolition process. The global structural responses, including the strains of the members on the main force transmission paths and the vertical displacements of representative joints, were measured. The structures' internal force redistributions and load-carrying mechanisms were investigated based on the experimental results and the corresponding FE analysis. The results show that both the tested DLSTs achieved progressive collapse demolition as expected. The two tested DLSTs under different demolition load conditions followed the same internal force redistribution patterns and exhibited three identical mechanical characteristics: arch action, catenary action, and beam action. The removal of specific members will change the load-carrying mechanism of the DLST and lead to local or global collapse.

PhloVer: A Modular and Integrated Tracking Photovoltaic Shading Device for Sustainable Large Urban Spaces—Preliminary Study and Prototyping

In this work, a flower-shaped shading system with integrated tracking photovoltaic, suitable for sustainable extensive urban coverages, is designed. Detailed photovoltaic energy yield simulations with a single-diode model approach are performed to disclose the potential of the proposed tracking photovoltaic shading device (PVSD). Simulations are performed with reference to a case study. A double-layer space truss is used to house the innovative modular photovoltaic tracking system, and the first application is envisaged for the coverage of a public market area of a sunny municipality in Southern Italy. By comparing it with the traditional photovoltaic fixed system, the results of the simulations show a steadier energy generation of the new PVSD, and it also provides better coverage with renewable energy during the hours of the day when the traditional system produces low electric energy. Lastly, an early interactive prototype of the PVSD system is presented. The tracking mechanism is carefully designed, 3D-printed at a small scale and tested with a motorized dynamic system controlled by a microcontroller board. The realization of the physical prototype and the engineering of the movement mechanism confirmed the feasibility and the correct functioning of the conceived system opening to real-scale applications.

Study on progressive collapse demolition method of double-layer space truss

This paper conducted a demolition test of a double-layer space truss (DLST) to investigate more efficient, safe and environmentally friendly demolition methods of truss systems. The high-speed 3D displacements of representative joints and the global dynamic strain response of the structure were well collected. The internal force redistribution and load-carrying mechanisms of DLST structures during demolition were explored. The results indicate that new equilibrium states were sought in the DLST through local and global internal force redistribution. When the main force transmission members were removed, the load-carrying mechanism of the DLST underwent sudden changed, which resulted in a snap-through in the structural load-carrying capacity. The test DLST exhibited three load-carrying mechanisms in time sequence during the proposed demolition: arch action, catenary action, and beam action. The theoretical vertical load-carrying capacity provided by each load-carrying mechanism was investigated separately. Finally, a progressive collapse demolition method was presented for the engineering DLST structures subjected to certain demolition external loads.

Estructura espacial con elementos a cortante desarrollables

En este artículo se revisita la clásica cercha espacial de doble pared reemplazando las diagonales por módulos poliédricos curvos de paredes delgadas. Las mejoras esperadas son tanto tecnológicas como mecánicas. Los nodos complejos de 8 ramas se dividen en una conexión de dos miembros continuos superpuestos y una conexión lineal entre las barras y los bordes del poliedro. La curvatura en las caras y bordes de los módulos introduce resistencia por forma y estabiliza los miembros frente al pandeo. La optimización global de la estructura se realiza mediante un proceso de búsqueda de forma basado en la parametrización individual de los módulos.Finalmente, se lleva a cabo una validación experimental mediante la fabricación y prueba de un prototipo a escala real (de 6 x 6 m aproximadamente).

Novel soft members in double-layer space trusses

Progressive collapse of space structures has received much attention in recent years due to the recent failure of a double-layer space truss (DLST) stadium in Terengganu, Malaysia which collapse twice in Year 2009 and 2013. There is a considerable interest in understanding the collapse behaviour of space structures and possibility of improving its collapse behaviour. This phenomenon was demonstrated by earlier researchers, such as Collins (1981) and Parke (1988) which investigated the collapse behaviour both theoretically and experimentally. In their study a carefully designed DLST structure may possess reserve of strength in excess of their elastic capacity. Although DLST have a high degree of statically degree of statically indeterminacy, not all of them are robust, as it has been found a loss of one critical member could trigger the collapse of the entire structure. Usually the collapse of the DLST is influenced by the ductility behaviour of the compression members. The aim of this study was to investigate the use of novel soft member to reduce the catastrophic progressive collapse behaviour of DLSTs. A novel soft member was constructed to measure its behaviour under tensile and compressive loads. The term novel soft member used in this study is referred to a combination of three circular tubes which is made into one component and is used to support compressive load. It was found that using a blend of three circular tubes significantly increase the ductility behaviour of the member. These test illustrates that while the inner and outer tube experience compressive forces, the middle tube will continue to increase linearly. This indicates that there is a possibility of improving the collapse behaviour of DLST by incorporating the novel soft member.

Improving double-layer space trusses collapse behavior by strengthening compression layer and weakening tension layer members

Progressive collapse is a chain of local failures leading to the collapse of either the entire or a part of the structure. The double-layer space trusses are susceptible to progressive collapse due to sudden buckling of compression members. The method of strengthening the compression layer members along with weakening the tension layer members is an effective method for retrofitting the double-layer space truss behavior against progressive collapse. In this study, the method is applied on offset double-layer space truss models with different support conditions, members’ geometrical imperfections, height, and shapes, and the effectiveness in increasing the structure’s ductility and load-bearing capacity is demonstrated. The results show that the method converted the sudden collapse of the structures into a beneficial gradual (progressive) collapse. More specifically, for double-layer space trusses comprising members with similar geometrical imperfection, strengthening the compression layer chords along with weakening the tension layer chords within 30%–40% will significantly improve the ductility and load-bearing capacity. In addition, the results show that the method can decrease the weight of the structures and consequently provide more economical structures.

Probing the Probabilistic Effects of Imperfections on the Load Carrying Capacity of Flat Double-Layer Space Structures

Load carrying capacity of flat double-layer space structures majorly depends on the structures' imperfections. Imperfections in initial curvature, length, and residual stress of members are all innately random and can affect the load-bearing capacity of the members and consequently that of the structure. The double-layer space trusses are susceptible to progressive collapse due to sudden buckling of compression members. Progressive collapse is a chain of local failures leading to the collapse of either the entire or a part of the structure. In this paper, the effects of the probabilistic distribution of initial curvature and length imperfections on the bearing capacity of flat double layer grid space structures for different member’s length and support conditions have been studied. First, equal to the number of the members of the structure, two sets of random numbers have been generated using the Gamma and Gaussian distributions to account for the initial curvature and the length imperfections, respectively. Thereupon, the amount of the imperfection randomly varies from one member to another. Afterward, based on the Push-Down analysis, the ultimate load-bearing capacity of the structure was determined through nonlinear analyzes performed through the OpenSees software and this procedure for certainty was repeated numerous times. Finally, based on the Monte Carlo simulation method, the structure’s reliability diagrams and tables were procured. The acquired results indicate that the behavior of flat double-layer space grids are sensitive to and can be affected by the random distribution of initial imperfections.

Collapse Modes of a Double-Layer Space Truss Subjected to Multi-Dimensional Earthquakes

In order to investigate the collapse mode of double-layer space trusses, the whole collapse process is simulated by the explicit finite element methods. The calculation results indicate that horizontal earthquake and vertical earthquake waves will lead to two typical collapse modes of the structure. The collapse mode of the structure under horizontal earthquake are mainly strength failure, which is characterized by the failure of members connected to the columns; the collapse mode of the structure under vertical earthquake are mainly dynamic instability, which is characterized by the V shape deformation. The analytical results agree with the experimental results.

超高強度繊維補強コンクリートを用いた複層立体トラスの開発

This study aims to develop a truss system by precast concrete members using Ultra High Strength Fiber Reinforced Concrete, UFC, which shows ductile behavior and high durability.A pyramid shaped truss with prestressed truss members were designed, and a constructional experiment was carried out. The result of cyclic loading test on the pyramid shaped truss demonstrated that this structure could be applied to an actual double layer space truss structure. Finally, the failure process of the structure was described in this paper.

Effects of support positioning on thermal behaviour of double layer space truss domes

This paper presents the follow-up of a study on the influence of the type and properties of support conditions on the thermal behaviour of spherical double layer space truss roofs. The earlier papers were about the effects of support flexibilities on the behaviour of space trusses subjected to uniform, gradient and partial loadings. In this paper, the effects of columns’ spacing and positioning on the thermal behaviour of space structures are considered. These parameters are defined by the distance between two opposite columns (radial distance), and the space between two adjacent columns (circumferential distance).

Effect of flexibility of substructures upon thermal behaviour of spherical double layer space truss domes. Part II: Gradient & partial loading

This paper presents the second part of a study on the influence of the type and properties of support conditions on the thermal behaviour of spherical double layer space truss roofs. Whereas the first part focused on the consequences of uniform thermal loadings, this paper studies the effects of support flexibilities on the behaviour of such structures subjected to gradient and partial loadings. It is observed that the thermal forces are very high and depend on the magnitude of temperature and the dome size. It is also pointed that the important point in partial loading is the unsymmetrical deformation and behaviour of the dome, while in gradient loading it is the rotational deformations. Finally, it is concluded that the use of rigid supports should be carefully examined.

Effect of flexibility of substructures upon thermal behaviour of spherical double layer space truss domes. Part I: Uniform thermal loading

Double layer space trusses are one of the most popular lightweight structures selected for covering large span roofs. These highly redundant and stiff structures, which consist of thousands of members and joints, are normally single structural assemblies, without expansion joints, and are thus required to be free to expand and contract without restraints. The type and properties of supports, which may permit or restrain radial movements of the structures, can greatly influence their behaviour. The aim of this study is to present an assessment of the influence of support flexibility on the behaviour of double layer space truss domes subjected to uniform thermal loading.

Configurations of double-layer space trusses

Space truss structures may be fabricated in any of several common grid configurations. With different configurations, the truss performance varies considerably affecting both its competitiveness and suitability for specific applications. The work presented in this paper is an assessment of the most commonly adopted truss configurations and their effect on truss characteristics such as the stiffness/weight value, member stress distribution, number of joints and members, degree of redundancy and cost. The study is parametric and covers wide variations of truss aspect ratios, boundary conditions and span/depth ratios. The results of this study could be of significant value to the design of space truss structures.

Static and dynamic post-buckling behavior of truss structures

This paper proposes a vibration model in which the lateral inertia force is considered in order to analyze the dynamic post-buckling behavior of truss members. The post-buckling behavior of perfectly symmetrical truss-structures and symmetrical truss-structures with a small imperfection are analyzed. The structures analyzed are a plane parallel chord truss structure and a double-layer space truss structure. The load-deformation relationships obtained by static and dynamic analyses are compared. It is found that the dynamic load-displacement relationship oscillates around the static relationship after buckling. Some examples show that the buckling mode and the post-buckling load-displacement relationship differ remarkably between static and dynamic analysis.

Shape Optimization of a Double-Layer Space Truss Described by a Parametric Surface

A method is presented for finding the optimal configuration of a double-layer space truss described by a parametric surface. The number of design variables is drastically reduced, without sacrificing the smoothness of the upper layer surface, by using the control net parameters as design variables. The coordinates of the lower nodes are defined by using a vertical or normal offset vectors from the upper surface. Curvatures of the curve associated with the lower polygon are calculated for evaluating feasibility and regularity of the a double-layer lattice space truss. In the examples, a feasible optimum design, which minimizes compliance under constraints on structural volume, are successfully found by using the proposed method. It is shown that the optimal solutions strongly depend on the specified ratios of the cross-sectional areas of the members.

Nonlinear Numerical Analysis of Composite Space Trusses

The composite action between an upper concrete slab and a double-layer space truss has been shown to have positive effects on the behaviour of such structures. Primarily, the prevention of the typical brittle behaviour of trusses and the introduction of appreciable ductility are among the important benefits. Substantial improvements have been achieved also in both stiffness and ultimate strength. The analysis of composite space trusses requires a careful study especially in the modelling of the shear connection between the concrete slab and the steel truss, involving shear studs mounted on both the nodes and the members of the top chord. Additionally, parts of the concrete slab may be projecting inside the top chord members, and therefore contribute to the shear interaction. This connection, being far from simple, could be modelled using various techniques. The present paper concentrates on these techniques, and numerical results are produced for each case (using a previously-developed and verified finite element program) and compared with the experimental results of a full-scale composite space truss tested earlier. As a conclusion of this work, two methods for preliminary and final design of composite space trusses are recommended for future use.

Sensitivity of Composite and Non-Composite Space Trusses to Member Loss

Since double layer space trusses have typically a large number of redundant members, it is frequently assumed that they are quite safe as the loss of one or more members can be accommodated without any noticeable effect on truss overall behaviour. The present study shows that every truss includes a number of critical members, the loss of any of which would cause force distributions that could lead to an overall premature collapse. The sensitivity of space trusses to member loss is clearly identified. The composite action between a top concrete slab and a space truss is also introduced as a means to control truss sensitivity to member loss. Factors that affect this sensitivity such as the truss supporting conditions are also investigated.

Discrete Multicriterion Optimization of a Space Truss

Final forming of a space truss used as roof in a sports or market hall is a result of searching for a solution which is the best one according to various criteria such as safety, reliability, economy, functionality and so forth. An illustration of this problem a numerical example of various optimizations of an orthogonal, double layer space truss of dimensions 24 × 24 m made of steel is shown in the paper. First, eight single-criterion objective functions such as: weight of members, weight of nodes, weight of columns, weight of whole truss, weight of walls and roofing elements made of steel, vertical displacements of a node in the middle of the truss, energy of deformation and a certain function of geometry of the truss were investigated assuming the number of divisions and the depth of the truss as decisive variables. The problems were formulated as discrete ones since the element cross-sections were selected from a finite catalogue. The All Variants Inspections Method was employed. For three among the aforementioned objective functions, describing weight of structure, displacement of the central node and the geometry of the truss, a discrete multicriterion optimization problem was formulated and solved. From the set of compromises a preferred sollution has been chosen by using the discrete functions and, the global criterion method.

Numerical Analysis of Space Trusses With Flexible Member-End Joints

The conventional procedure for the analysis of space trusses, lattice domes and similar structures, assumes that member-end joints behave as pure pins or, in some cases, as rigid joints. However, experimental studies have shown that these joints typically exhibit some level of flexural stiffness and are therefore flexible (semi-rigid). It was reported that the characteristics of the space truss jointing system play a major role in truss response (see Refs. 1,2,3). The results of experiments conducted on space trusses with rigid or flexible joints produced less brittle behaviour than that found for assemblies with nominally-pinned joints. A nonlinear beam-column element with end springs has been developed to model the actual rotational stiffness of truss member-node connections, and its stiffness expressions are presented in this paper. Incorporation of this element in the numerical analysis of space trusses has led to better predictions of behaviour and strength when compared to the commonly-used two-noded frictionless truss element. This new element was used successfully in the numerical analysis of two non-composite and one composite double-layer space truss, and the results are presented in this paper.

Influences of Uncertainties on Mechanical Behavior of a Double-Layer Space Truss

A space truss, as all other structures, is constantly subject to various types of uncertainties. For the purpose of estimating, and furthermore, ensuring the safety of a space truss, it is important to investigate its mechanical behavior with consideration of the influences of uncertainties. A 6 × 6 square-plan, double-layer space truss is designed in accordance with minimum weight design concept and used as an example to study. A computer program is written to analyze the truss structure, with an ability to simulate member buckling. The Monte Carlo method is applied for statistical studies with trial number of each study set to 100. The variation of member strength, initial imperfection of member length are chosen for component uncertainties, and the error in assembly process is chosen for human error. The mechanical behavior of the space truss influenced by these uncertainties is studied. A comparison between the influences of the component's uncertainties originating in human error, is made to determine where the most critical uncertainties lie.