Double-layer Space Research Articles

Special Forms Of Structural Systems ProposedFor Cable Domes

The paper presents two proposals of structural systems shaped for design of roof covers by means of so-called cable domes or suspend-domes. These both systems were worked-out by the author on the background of a chosen component part of a double-layer space structure and its suitable transformations. The proposed shapes of structural systems consist of a small number of rigid bars, creating separate sets, which are connected together by means of cables. All the structures are suitably pre-stressed. Membrane sheets, made of fabric, can be the component parts of these structural systems and they can be mounted to the appropriate cables, bars or nodes. The both proposed systems can be applied as lightweight structures for large span roofs. It can be expected that they could be assembled in relatively simple way and in short time at the building sites.

Experiments and analysis of the post-buckling behaviors of aluminum alloy double layer space grids applying ball joints

This study discusses on the experimental and analytical results of the global buckling tests, carried out on aluminum alloy double layer space grids composed of tubular members, ball joints and connecting bolts at the member ends, with the purpose of demonstrating the effectiveness of a simplified analysis method using an equivalent slenderness ratio for the members. Because very few experiments have been carried out on this type of aluminum space grids, the buckling behavior is investigated experimentally over the post buckling regions using several space grid specimen with various values for the member slenderness ratio. The observed behavior duping the experiments is compared with the analytically obtained results. The comparison is made based on two different schemes; one on the plastic hinge method considering a bending moment-axial force interaction for members and the other on a method using an equivalent slenderness ratio. It is confirmed that the equivalent slenderness method can be effectively applied, even in the post buckling regions, once the effects of the rotational rigidity at the ball joints are appropriately evaluated, because the rigidity controls the buckling behavior. The effectiveness of the equivalent slenderness method will be widely utilized for estimation of the ultimate strength, even in post buckling regions for large span aluminum space grids composed of an extreme large number of nodes and members.

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.

Non-linear analysis of double-layer Space grids

This paper is related to the topic developed in my RH.D. thesis. A new model is proposed to describe the non-linear behaviour of straight pin-jointed compression members. Sucti a method Is based upon obtaining the complete constitutive equations in the case of circular hollow sections. The stability functions of imperfect bars and the analytical formulation of the post-buckiing behaviour are obtained by taking the exact expression of the curvature in the integratlon of the differential equation of the elastic. The linearization of the constitutive relationships and the application of an incremental iterative model based upon the modification of the elasticity of the bars at critical point allows us to consider the non-linear analysis of the double layer space grids. The models of analysis proposed here have been applied to a wide variety of trusses with different characteristics and typologies, some examples of which accompany this paper.

崩壊問題の動的解析と静的解との比較 : 材料および幾何学的非線形を考慮した鋼構造骨組の動的崩壊解析 その2

There are many difficulties in the nonlinear statical analysis for the collapse of structures. In the case of considering the discontinuity of the mechanical behavior of a materials, further hardships will obstruct to obtain a good solution because of the abrupt dropping of the strength. All structural problems which many researchers had treated as statically should have a dynamic effect tacitly such as the inertia force of the own weight of deforming structural element. At the critical or limit point, the inertia term will help to solve the equlibrium eqations. In this paper, a comparison between statical analysis method and dynamic is done, and three numerical examples show the effectiveness of the dynamic method. 1. Yielding and breaking analysis of straight bar 2. Snap through problem of reticulated space truss 3. Material and geometrical nonlinear analysis of double-layered space frame

ヒューマンエラーが複層立体トラス構造の力学的性質に与える影響に関する研究

Human error is recognized as the major cause of structure failure. In this paper, the authors simulate human error in the process of structural design, manufacture, assembly and erection, and investigate statistically the influence they have on the structure's behavior. A 6×6 square plan double-layer space truss is designed and used as an example. A computer program is written to analyze the truss structure, with the ability to realistically simulate member buckling and to automatically adjust the displacement increment. The Monte Carlo method is used with trial number set to 100. The fully intact truss, and groups of trusses with either design errors, assembly errors, or variations in member strength, are analyzed and investigated statistically. It is found out that human error has a much bigger influence on the behavior of double-layer grids than member strength variation, and for the standard deviation of the structure strength, the influence of these two factors is shown to differ at least by a factor of 6.

Initial Bar Tensions in Pin-Jointed Assemblies

This paper is concerned with initial bar tensions in pin-jointed statically indeterminate assemblies, for example the grid shown in Fig. 1. Initial tensions are present in such assemblies on account of the lack-of-fit of the constituent bars and joints due to unavoidable inaccuracies in manufacture: and they may contribute to premature collapse of an assembly under increasing load, by predisposing particular bars to early failure by buckling. An algorithm for computing initial stresses due to given lack-of-fit is used to make statistical estimates of the magnitudes of initial bar tensions in a grid assembled from bars whose lengths are specified in the form of a mean and standard deviation. A scheme for computing the attenuation of these initial bar tensions by allowing for a limited amount of “backlash” at the bar-joint connections is also investigated. The theoretical and computational work is supported by a series of detailed experiments on a double-layer space grid of the type shown in Fig. 1, and built from standard MERO spherical bolted junctions: these experiments involve the measurement of initial bar tensions both with and without some deliberate loosening of bolts to produce limited “backlash” at the joints.

An Investigation into the Design Parameters of Double Layer Space Frame Grids

A parametric study of the various factors affecting the design of double layer space frame grids is presented. This parametric study was conducted with the help of example structures and covered the support arrangement, the grid depth, the grid module and the grid layouts. The intent is to give the designer an idea about the effects of the choice of any of these parameters on the grid's behaviour and design requirements. This information should serve as a means for developing successful preliminary designs and as such reduce the need for many trials before the design is finalised.

Optimum Geometry Design of Double‐Layer Space Trusses

In recent years, extensive and increasing use has been made of space trusses, especially in the form of double-layer space grids. In the design, almost unlimited possibilities exist in practice for the choice of geometry of space trusses. This forms the background for a research project, in which the optimum design of double-layer space trusses has been investigated. A literature study covering what has, until recently, been obtained as regards optimization of double-layer space grids has been carried out as part of the investigation. Furthermore, actual cases, including both square and rectangular double-layer space grids, simply supported along the entire edge or column-supported at the corners, have been analyzed to determine the optimum design. An account of the most important achievements is given.

Shear deformation plate continua of large double layered space structures

A simple method is presented to model large rigid-jointed lattice structures as continuous elastic media with couple stresses using energy equivalence. In our analysis the transition from the discrete system to the continuous media is achieved by expanding the displacements and the rotations of the nodal points in a Taylor series about a suitable chosen origin. The strain energy of the continuous media with couple stresses is then specialized to obtain shear deformation plate continua. Equivalent continua for single layered grids, double layered grids and three-dimensional lattices are then obtained.

Influence of joint eccentricity and rigidity on the load capacity of a space truss sub-assemblage

Abstract Experimental testing of bolted and welded space truss sub-assemblages with large joint eccentricities has displayed satisfactory performance. Tests have been carried out on five sub-assemblages from a double layer (plate-like) space truss configuration. The distinctive features of the configuration employed were chord member continuity and the resulting large joint eccentricities. The particular layout adopted furnished orthotropic behaviour for stiffness and strength, so two sub-assemblage configurations were adopted. To provide control and comparisons a welded concentrically jointed sub-assemblage was tested in addition to the bolted and welded sub-assemblages. Although the large joint eccentricities reduced sub-assemblages stiffness and peak load capacity, the continuity of chords largely offset these reductions even when bolted joint details were used; for the welded joint cases peak load capacities were at least 50 per cent higher again. The stiffness of such systems is seen to be sensitive to member and joint imperfections, and joint slip.

Limit analysis of space grids

The paper presents generalized, unique solutions for the limit design of pin-connected, double-layer space grids of regular construction, simply-supported along the sides of a rectangle and carrying a uniform concentration of normal nodal loading applied to the upper layer of the structure. The principal assumption upon which the foregoing results are obtained is that member forces increase monotonically with the applied loads, therefore insuring against the inducement of higher than ultimate loads in the compressive elements at anytime prior to structure failure. The virtual work method of the plastic analysis has been employed in conjunction with the techniques of the finite difference calculus to study the various collapse modes of the system. The work is concluded with an illustrative example to demonstrate the simplicity of the proposed solutions.

異方性合平版の応力解析理論とその応用 : その 1 : 基礎理論

In this paper, the theory of stress analysis of plates, composed of anisotropic layers, is established under the assumptions of Kirchhoff. And its applications to some space structures such as double layered space trusses and stiffened plates with grid ribs are described. In chapter I, general theory and their characters are discussed. Some characters of plates are clarified and classified according to the relations of stretching D^<ijkl>, bending K^<ijkl> and reciprocal S^<ijkl> rigidities, as follows. If the rigidities, whose superscripts i+j+k+l is odd, are zero, the plate is orthotropic, and adding the condition : R^<iiii>=R^<iijj>+2R^<ijij> (i&bne;j, R for D, K, S), the plate becomes isotropic. S^<ijkl>=0 is the condition of the separation of plate action (stretching) and disk action (bending) each other. The separation condition of tangential displacements from normal one in the differential equations is S^<iiii>=S^<ijjj>=0 and 2S^<ijij>+S^<iijj>=0 (i〓j). And if the plates are orthotropic or other special cases, the sine system and cosine system in Fourier series are separable. In chapter II, double layer plates and idealized sandwich plates are discussed. Even if both layers are isotropic, the plate and disk actions are not separable except the cases where both Poisson's ratios are equal. In chapter III, the analogy between sandwich plates and double layered space trusses is discussed. Plane trusses are firstly compared with homogeneous disks and their stretching rigidities in plane are derived, then the theory of anisotropic sandwich plates is applied to them. So the effective rigidities of double layered space trusses are derived and these trusses can be analized by the theory described in chapter I, II. In chapter IV, the grid systems composed of beams, which have bending and twisting elasticities, are discussed. On these systems, the character of bending rigidity tensor differs from that of homogeneous layered plates. But considering this character, it can be posible to analize the composit plates, some of whose layers are grid systems.