Cable Roof Research Articles

Optimal Design of Cable Structures with Genetic Algorithms

Genetic Algorithm is employed for cable structures subjected to large displacements, stress and diameter constraints. Design solution is governed by nonlinear interaction of cable sag, amount of pretension and stiffness of cable with deformations under transverse loads. Geometrical nonlinear finite element method with total Lagrangian approach is integrated in the present work with genetic algorithm to evaluate optimum values of design parameters, i.e. diameter of cable and amount of prestress. Study is performed on steel and carbon fibre cable stays, cable nets and cable roofs. Different types of crossover operators are applied along with single- and multi-level optimization techniques in order to obtain true optimum in the search space of global optimum.

Tension roofs and bridges

The term ‘Tension Structures’ is commonly used for those structures wherein one or more primary load bearing elements are in tension. Such structures include membrane roofs, cable roofs, cable bridges, guyed masts or towers, cooling towers though some of these are less common. The tension elements are strands, ropes or membranes, which have to combine with structural elements carrying compression, flexure or a combination thereof, such as, columns/towers/masts, arches, beams/girders/trusses. This review note confines itself to roofs and bridges, summarising the status of the various issues involved. The note covers a summary discussion on materials, analytical approach, illustration of forms, and the latest information and trends on cable technology and aerodynamics. Despite interesting developments that are taking place in the field of tension structures, this is not a subject of common attention. A brief historical perspective has therefore also been included in this note.

Utilization of Composite Materials in Saddle-Shaped Cable Roofs

A saddle-shaped cable roof formed by two orthogonal groups of cables joined with a compliant support contour is considered. The kinematic invariability of the roof obtained by prestabilizing the cables makes it possible to avoid heavy slabs of reinforced concrete in the construction of roofs and to use light composite materials. The main geometric characteristics for a cable roof with CFRP load-carrying and contour cables and steel stabilizing cables are determined by a numerical experiment.

Microcomputer-aided design of tensile roof structures

This paper presents interactive microcomputer-aided design of tensile roof structures. A highly interactive multi-window system has been developed on an IBM PS 2 Model 80 for the design of three different classes of cable roof structures: freely suspended synclastic-surface (dish-shaped) nets, prestressed flat nets, and prestressed anticlastic-surface (saddle-shaped) nets. Graphic displays of cable roof structures include various perspective views of the structure, deformed shape of the structure, and deformation of individual cables.

Aeroelastic model study of suspended cable roof

The aerodynamic response of a suspended-cable roof over a railway station is examined using a full aeroelastic model in a boundary-layer wind tunnel. The results of the wind-tunnel tests, conducted in thin and thick boundary-layer flow conditions, are presented and compared with those obtained for a section model in smooth and turbulent flow conditions. Vortex-induced oscillation at relatively low wind speed and flutter at high wind speeds were observed in a thin boundary-layer flow. Furthermore, it is shown that the presence of structures beneath the roof results in a sdecrease in the vertical oscillations of the roof. However, a train parked in the station on the upstream track caused an aerodynamic torsional instability for wind speed exceeding 70 mph (113 km/hr).

Discrete analysis method for random vibration of structures subjected to spatially correlated filtered white noises

Random vibration analysis of large-span space structures or high-rise structures which are subjected to spatially correlated filtered white noise excitations such as wind load and earthquake motion, has been a difficult problem in engineering computation. Based on the idea of the discrete analysis method of random vibration, this paper attempts to solve this problem. The formulae of calculating structural mean and mean square responses are given. As an example, the wind-induced vibration of a cable roof structure is analysed by using these formulae.

Self-excited oscillation of a pretensioned cable roof with single curvature in smoothflow

The characteristics of the dynamic response of a pretensioned cable roof with single curvature in smooth flow are investigated by model tests in a wind tunnel. A self-excited oscillation occurs in the anti-symmetric first mode. A hypothesis is proposed to explain its mechanism. It states that the oscillation occurs because vortices are formed through fluid-elastic interaction and because these vortices are converted downstream at about 0.9U 0 , where U 0 is the approach flow velocity at which the self-excited oscillation starts. In order to test the validity of this hypothesis, the characteristics of fluctuating velocities above a model are investigated. The results support the hypothesis.

Free Vibration of Light Roofs Backed by Cavities

Modal properties of light roofs such as cable roofs backed by cavities with openings are theoretically investigated. Taken into account are the interaction between the roof and the air enclosed by the cavity, the air outside the roof, and air leakage through the openings in the building walls. Both the structural and acoustical damping are considered for the roof as well as for the wall openings. The outside air is assumed to be still. An approximate formula for the evaluation of roof model damping is derived using an energy consideration, and its accuracy is assessed by comparison with complex eigenvalue analysis and an exact solution for the circular membrane backed by a cavity. Comparison with experimental data is made. The theoretical approaches are used in a parametric study of two roofs with prototype properties. The first roof has the basic parameters of the Calgary Olympic Coliseum. The second roof is similar but features lighter mass per unit area.

Numerical modelling of the non-linear static response of clad cable net structures

An efficient numerical approach is presented for the analysis of cladding-network interaction in pretensioned cable roof structures under static loads. The approach is based on the sub-region mixed energy principle, which allows for the linear and non-linear aspects of the behaviour of the structure to be treated separately. Membrane action of the cladding is represented by a five-force model calculated by the finite element method. The governing equilibrium and compatibility equations are solved using the dynamic relaxation technique with kinetic damping. Computations are carried out for an experimental model of a hyperbolic paraboloid net with a discrete membrane surface and the numerical and experimental results are compared.

Nonlinear finite element analysis of a frame stiffened with tension members

Finite element techniques were applied to the analysis of a general curved frame stiffened with tension members. Curved stiffened frames are found in a variety of structures such as space structures and cable roof structures. A tennis racket was used as a specific example problem. The model discussed here has the flexibility to deal with any frame shape and stringing pattern. The strings of the structure are modeled using nonlinear cable theory. The frame is modeled with linear isoparametric elements. Group iteration is used to analyze the two substructures, resulting in displacements, forces, and stresses for the entire structure.

On the mechanism of a self-excited oscillation of single curvature cable roofs

Cable roofs are light and flexible. They may exhibit self-excited oscillations under the action of wind. Here, studies on self-excited oscillations of single curvature cable roofs are surveyed. Recent studies indicate that single curvature cable roofs do exhibit a type of self-excited oscillation in the smooth flow. A hypothesis on its mechanism is proposed.

Interactive microcomputer-aided design of circular suspension cable roofs

This paper presents interactive computer-aided design of circular suspension cable roofs. A microcomputer program developed in Advanced BASIC and according to the principles of structured programming is presented. The program can display/plot the plan of cable roof, the elevation of the structure including the loading on the cables and the cross-section of the reinforced concrete compression ring. The interactive program helps the user to explore many design alternatives rapidly and arrive at a practically optimum design.

Boundary Effects in Suspended Cable Roofs

A formulation for analytical study of cable roof systems is presented wherein the flexibility of supports bounding the roofs is accounted for. The analytical work is based on the finite element method and accounts for nonlinearity of the cable assembly using the Newton‐Raphson method. The supporting structure is, however, treated as being linear. Using this approach, examples of bicycle wheel type cable roofs are analyzed and the results compared with those obtained on a laboratory model as well as on a prototype. A parametric study of the laboratory model is also made.

Dynamic relaxation analysis of the non-linear static response of pretensioned cable roofs

A summary of various existing methods of cable roof analysis is followed by a detailed description of a dynamic relaxation technique that can be applied for the solution of such structures. Theoretical analysis of static response of pretensioned cable networks is presented using a non-linear energy approach. Solutions are obtained by dynamic relaxation, a numerical finite difference technique. Detailed results are presented for a pretensioned cable truss. Comparisons are made with alternative numerical and experimental results. The extension of dynamic relaxation to more complex cable-cladding problems is outlined.

Cladding-network interaction in pretensioned cable roofs, studied by dynamic relaxation

Current methods of analysis and design of pretensioned cable roofs disregard the cladding contribution to the overall stiffness of the structure, and therefore full-scale constructions suffer from excessive pretensioning of the cables. This paper investigates cladding stiffening effects in pretensioned cable roof models, using a dynamic relaxation algorithm. A mathematical model of cladding-network interaction in combined response to static external loads is presented, developed on the assumption of a discrete membrane surface of the cladding attached to the cable network. Detailed results are presented for a partially and fully clad hyperbolic paraboloid model. Comparisons are made between the results from the analysis of the composite structure clad with panels of varying stiffness and the corresponding “bare” network analysis. Results show that the cladding makes a substantial contribution to the stiffness of the composite structure, and suggest that future design of foundations for the cable anchorage should take this into account.

Wind tunnel studies of cable roofs

Behaviour of large cable roofs in turbulent wind is studied in the wind tunnel using both rigid and aeroelastic models. The similarity requirements are reviewed with special attention being paid to the effect of the air enclosed under the roof. A similarity law for the modeling of this enclosure is presented and its role in free vibration as well as wind induced vibration is investigated. A wind tunnel study of a large tension roof is described.

Performance of Cable Trusses under Static Loads

Tensioned cable structures are becoming increasingly popular for covering large column free areas. Among the various forms of cable roof systems used, the truss form is the most popular because of its simplicity and versatility. These structures exhibit a non-linear structural response and thus pose a special problem of analysis. A study of the comparative behaviour of different types of cable truss configurations is presented. The influence of design parameters, such as sag to span ratio, cable sizes and prestressing forces, upon the response of the structure has been investigated for various truss forms with unyielding supports subjected to both symmetrical and unsymmetrical loading conditions.

Analysis of cable structures

A numerical procedure has been developed to analyze complex 3-dimensional assemblies of substructures and cables. The procedure is applicable to guyed towers, flexible transmission lines, cable roofs or mooring networks. The computer program, which has been developed to analyze these composite structures, accepts arbitrary loads on the substructures but restricts the loads on the cable elements to gravity, thermal, or fluid drag effects. The algorithm is built around an efficient cable element subprogram. From given loads and given positions of the ends of a cable, the subprogram determines the complete geometry of the cable, its end forces, and its tangent stiffness matrix. The cable elements are connected together or to substructures nodes. The equilibrium configuration of the assembly is approached by successive iterations which decrease the imbalance of forces which still exist at each node at the end of the previous iteration. Special numerical schemes, which insure rapid convergence of the analysis, are presented. The computer algorithm is discussed in detail, and the simplicity and efficiency of the formulation is demonstrated by several examples. Very large displacements of the nodes and associated second order effects on the substructures do not present any difficulty as the imbalances and stiffnesses at each iteration are based on the geometry of the system at the end of the previous iteration.

Analysis of cable net-panel roof system

The study presented in this paper deals with the analysis of a cable net roof system with precast panels which are prestressed to increase the stiffness of the system. The roof structure can be stiffened by applying a temporary load to the structure after the precast panels are hung in place on the cable net, filling the space between the panels with concrete, and. after the concrete has cured sufficiently, removing the temporary load. This in effect, prestresses the monolithic roof structure. A computer program was developed to analyze a cable net roof structure and an experimental investigation was carried out to verify the theoretical analysis performed by the computer program and to study the response of a cable net-panel system during the prestressing of the panels. The model used in the experimental study was a 4 × 4 cable net with nine panels.

Interdisciplinary design optimization: A search method

The design of architectural structures frequently involves interdisciplinary aspects and aesthetic considerations which, being of subjective nature, are difficult to quantify. The computer-aided design optimization model presented here, therefore, is an attempt to optimize, in an interdisciplinary context, quantifiable parameters only. The objective function is graphically illustrated to give the designer a means to evaluate the impact of esoteric design decisions on performance variables, such as costs. A search method is used, i.e., evaluation of a discrete number of designs and nonlinear interpolation. The model's system of computer programs is demonstrated on the sample of an anticlastic cable roof structure.