Analyzing the Form-Finding of a Large-Span Transversely Stiffened Suspended Cable System: A Method Considering Construction Processes

The precise control of the shape of transversely stiffened suspended cable systems is crucial. However, existing form-finding methods primarily rely on iterative calculations that treat loads as fixed known conditions. These methods are inefficient and fail to accurately control shape results. In this study, we propose a form-finding method that analyzes the load response of models under different sag and stress levels, taking into account the construction process. To analyze the system, a structural finite element model was established in ANSYS, and geometric nonlinear analysis was conducted using the Newton-Raphson method. The form-finding analysis results demonstrate that the proposed method achieves precise control of shape, with a maximum shape error ranging from 0.33% to 0.98%. Furthermore, the relationships between loads and tension forces are influenced by the deformed shape of the structures, exhibiting significant geometric nonlinear characteristics. Meanwhile, the load response analysis reveals that the stress level of the self-equilibrium state in the transversely stiffened suspended cable system is primarily governed by strength criteria, while shape is predominantly controlled by stiffness criteria. Importantly, by simulating the initial tensioning process as an initial condition, this method solves for a counterweight that satisfies the requirements and achieves a self-equilibrium state with the desired shape. The shape of the self-equilibrium state is precisely controlled by simulating the construction process. Overall, this work presents a new method for analyzing the form-finding process of large-span transversely stiffened suspended cable system, considering the construction process which was often overlooked in previous studies.

Random vortex induced vibration response of suspended flexible cable to fluctuating wind

A popular dynamical model for the vortex induced vibration(VIV)of a suspended flexible cable consists of two coupled equations.The first equation is a partial differential equation governing the cable vibration.The second equation is a wake oscillator that models the lift coefficient acting on the cable.The incoming wind acting on the cable is usually assumed as the uniform wind with a constant velocity,which makes the VIV model be a deterministic one.In the real world,however,the wind velocity is randomly fluctuant and makes the VIV of a suspended flexible cable be treated as a random vibration.In the present paper,the deterministic VIV model of a suspended flexible cable is modified to a random one by introducing the fluctuating wind.Using the normal mode approach,the random VIV system is transformed into an infinite-dimensional modal vibration system.Depending on whether a modal frequency is close to the aeolian frequency or not,the corresponding modal vibration is characterized as a resonant vibration or a non-resonant vibration.By applying the stochastic averaging method of quasi Hamiltonian systems,the response of modal vibrations in the case of resonance or non-resonance can be analytically predicted.Then,the random VIV response of the whole cable can be approximately calculated by superimposing the response of the most influential modal vibrations.Some numerical simulation results confirm the obtained analytical results.It is found that the intensity of the resonant modal vibration is much higher than that of the non-resonant modal vibration.Thus,the analytical results of the resonant modal vibration can be used as a rough estimation for the whole response of a cable.

Analysis of tensioned membrane structures considering cable sliding

In routine design of tensioned membrane structures, the membrane is generally modeled using space membrane elements and the cables by space cable elements, with no sliding allowed between the membrane and the cables. On the other hand, large deflections are expected and sliding between the membrane and the cables is inevitable. In the present paper, the general finite element code ABAQUS was employed to investigate the influence of cable sliding on membrane surface on the structural behavior. Three analysis models were devised to fulfill this purpose: (1) The membrane element shares nodes with the cable element; (2) The cable can slide on the membrane surface freely (without friction) and (3) The cable can slide on the membrane surface, but with friction between the cable and the membrane. The sliding problem is modeled using a surface - based contact algorithm. The results from three analysis models are compared, showing that cable sliding has only little influence on the structure shape and on the stress distributions in the membrane. The main influence of cable sliding may be its effect on the dynamic behavior of tensioned membrane structures.

EIGENFREQUENCY ANALYSIS OF CABLE STRUCTURES WITH INCLINED CABLES

The approximate eigenfrequencies for the in-plane vibrations of a cable structure consisting of inclined cables, together with point masses at various points were computed. It was discovered that the classical transfer matrix method was inadequate for this task, and hence the larger exterior matrices were used to determine the eigenfrequency equation. Then predictions of the dynamics of the general cable structure based on the asymptotic estimates of the exterior matrices were made.

SVD Approach for Actuator and Sensor Placement in Active Vibration Control of Large Cable Net Structures

The actuator and sensor placement problem for active vibration control of large cable net structures is investigated in this paper.Since the structures exhibit closely spaced modes in the range of low frequencies,the number of modes to be considered is quite large after modal truncation,while only a limited number of actuators and sensors are to be placed.This makes it hard to determine the actuator and sensor locations with the existing placement methods in the literature such as the methods based on the controllability/observability grammian.To deal with this issue,an actuator and sensor placement method based on singular value decompositions(SVD)of the input and output matrices is proposed,which guarantees the modal controllability and observability of the system.The effectiveness of the SVD based method is verified through numerical simulations in which comparisons are conducted between randomly-chosen locations and the optimal ones obtained by a genetic algorithm.

Design and application of structural health monitoring system in long-span cable-membrane structure

Cable-membrane structures have small rigidity and are highly sensitive to wind. Structural health monitoring is necessary to ensure the serviceability and safety of the structure. In this research, the design method of a structural health monitoring system is using the characteristics of a cable-membrane structure. Taking the Yueyang Sanhe Airport Terminal as an example, a finite element model is established to determine the critical structural components. Next, the engineering requirements and the framework of the monitoring system are studied based on the results of numerical analysis. The specific implementation of the structural health monitoring is then carried out, which includes sensor selection, installation and wiring. The proposed framework is successfully applied to the monitoring system for the Yueyang Airport terminal building, and the synchronous acquisition of fiber Bragg grating and acceleration sensor signals is implemented in an innovative way. The successful implementation and operation of structural health monitoring will help to guarantee the safety of the cablemembrane structure during its service life.

Numerical and experimental research on annular crossed cable-truss structure under cable rupture

The Annular Crossed Cable-Truss Structure（ACCTS） is a new type of Tensile Spatial Structure with a configuration suitable to cover large-span stadiums. Its configuration has potential to perform well in resisting disproportionate collapse. However, its disproportionate collapse resistance hasn＇t yet been analyzed in depth. In this study, numerical and experimental research was carried out to investigate the performance of ACCTS under cable rupture. The numerical analysis was done for ten cable-rupture plans using LS-DYNA（explicit method） and the experimental test on an ACCTS with a diameter of 17.15 m was performed for three cable-rupture plans. It is concluded that, while deflections increase with the number of removed cables, an ACCTS does not undergo a disproportionate collapse and it provides a promising structural concept for tensile spatial structures.

STATIC ANALYSIS OF CABLE STRUCTURE

Based on the nonlinear geometric relation between strain and displacement for flexible cable, the equilibrium equation under self-weight and influence of temperature was established and an analytical solution of displacement and tension distribution defined in Eulerian coordinate system was accurately obtained. The nonlinear algebraic equations caused by cable structure were solved directly using the modified Powell hybrid algorithm with high precision routine DNEQNE of Fortran. For example, a cable structure consisting of three cables jointly supported by a vertical spring and all the other ends fixed was calculated and compared with various methods by other scholars.

A CATENARY ELEMENT FOR THE ANALYSIS OF CABLE STRUCTURES

Based on analytical equations, a cat ena ry element is presented for the finite element analysis of cable structures. Com pared with usually used element(3_node element, 5_node element), a program with the proposed element is of less computer time and better accuracy.

Internal Force Distribution in Steel-Concrete Composite Structure for Pylon of Cable-Stayed Bridge

Adopting a steel-anchor beam and steel corbel composite structure in the anchor zone on pylon is one of the key techniques for the design of Jintang bridge, a cable-stayed bridge in Zhoushan, China. In order to ensure the safety of the steel-concrete composite structure, a stud connector model for the joint section was put forward. Experiments were conducted to obtain the relation between load and slip of specimen, the failure pattern of stud connector, the yield bearing capacity and ultimate bearing capacity of a single stud, etc. The whole process of the structural behavior of the specimen was comprehensively analyzed. The features of the internal force distribution in the steel-concrete composite structure and the strain distribution of stud connector under different loads were emphatically studied. The test results show that the stud connector is applicable for the steel-concrete composite structure for pylon of Jintang bridge. The stud has a good ductility performance and a obvious yield process before its destruction. The stud connector basically works in a state of elasticity under a load less than the yield load.

The Coupling Effect of Spatial Reticulated Shell Structure with Cables

The spatial reticulated shell structure with cables (RSC) is a kind of coupling working system, which consists of flexible cables, reticulated shell structure (RS) and tower columns. The dynamic analysis of RSC based on the coupling model was carried out. Three kinds of elements such as the spatial bar element, cable element and beam element were introduced to analyze the reticulated shell, cable and tower column respectively. Furthermore, such parameter influences as structural boundary conditions, grid configuration, the span-to-depth ratio and the arrangement of cable system upon structural dynamics were analyzed. The structural vibration modes can be divided into four groups based on some numerical examples. And the frequencies in the same group are very close while the frequencies in different groups are different from each other obviously. It is clear that the sequence of the appearance of the each mode group heavily depends on the comparative stiffness of the tower column system, RS and cables.

Dynamic behaviors of pretensioned cable AERORail structure

The AERORail, a new aerial transport platform, was chosen as the object of this work. Following a review of the literature on static behaviors, model tests on the basic dynamic mechanical characteristics were conducted. A series of 90 tests were completed with different factors, including tension force, vehicle load and vehicle speed. With regard to the proper tension and vehicle load, at a certain speed range, the tension increments of the rail's cable were proved relatively small. It can be assumed that the change of tension is small and can be reasonably ignored when the tension of an entire span is under a dynamic load. When the tension reaches a certain range, the calculation of the cable track structure using classical cable theory is acceptable. The tests prove that the average maximum dynamic amplification factor of the deflection is small, generally no more than 1.2. However, when the vehicle speed reaches a certain value, the amplified factor will reach 2.0. If the moving loads increase, the dynamic amplification factor of dynamic deflection will also increase. The tension will change the rigidity of the structure and the vibration frequency; furthermore, the resonance speed will change at a certain tension. The vibration is noticeable when vehicles pass through at the resonance speed, and this negative impact on driving comfort requires the right velocity to avoid the resonance. The results demonstrate that more design details are required for the AERORail structure.

Practical Aspects of the Design and Construction of a Small Cable Roof Structure

Cable roof structures?have?only become widespread in large span structures in the latter part of the twentieth century. However,?they?still represent a relatively new form of roof construction, especially as in the present case of a small span innovative structural solution. The contribution of this text to the structural engineering community lies in the increased interest in building simple cable roof structures. Since its completion in September 1996, this small cable roof structure has been recognized as an interesting architectural and structural example. The text describes aspects of the design and construction of a small cable roof that was designed as a roof for an open-air theater stage for the city of Sao Jose do Rio Pardo, Sao Paulo, Brazil. A cable network, in the shape of a hyperbolic paraboloid surface, is anchored in a reinforced concrete edge ring. The projection of the ring’s axis onto the ground plane is an ellipse. Workers with specialized training were employed in the various stages of the construction, which was completed in September 1996.

Studying solutions for the fatigue of the FAST cable-net structure caused by the process of changing shape

The Five-hundred-meter Aperture Spherical Radio Telescope （FAST） is supported by a cable-net structure, whose change in shape leads to a stress range of approximately 500 MPa. This stress range is more than twice the standard recom- mended value. The cable-net structure is thus the most critical and fragile part of the FAST reflector system. In this study, we first search for a more appropriate deforma- tion strategy that reduces the stress amplitude generated by the process of changing shape. Second, we roughly estimate the tracking trajectory of the telescope during its service life, and conduct an extensive numerical investigation to assess the require- ments for fatigue resistance. Finally, we develop a new type of steel cable system that satisfies the cable requirements for construction of FAST.

Tensile Structures of Cables Net, Guidelines to Design and Applications

The structural engineering design of not conventional typologies imposes a complex path that begins evaluating procedures of a preliminary design and ends with complex procedures to validate the analysis response. Any guide lines to follow are often available. About complex shapes, in particular, any details are presented in the codes to evaluate wind action and so wind tunnel experiments are necessary to valuate this. The evaluation of wind tunnel data is a complex process that often needs new and specific subroutines programmed by researchers. The difficult increases when the objective is to study a not specific building but general aspects as for examples the dependence of a generic phenomenon by a geometric sample;in this case it is necessary to design and to program numerical subroutines before and then the wind tunnel experiments. Often, these subroutines are left detached and are non-generalizable process. Purpose of this paper is to describe a complete procedure to pre- and post-process wind tunnel data with the objective to design a not convectional structure as a tensile structure. In this particular case the research aim is a parametrization of the aerodynamic behavior of Hyperbolic Paraboloid roofs, shape used for cables net. The reason of the experiments is the absence in the international codes of the pressure coefficients for these geometries. The paper describes the numerical procedure evaluated to choose a sufficient representative geometric sample, the numerical procedure evaluated to design and to construct the wind tunnel models and FE models, the numerical procedure to evaluate and to use for FEM analyses of the wind tunnel data, the numerical procedure to calculate nonlinear structural analysis, and, finally some applications. All these numerical procedures use basic theory derived for example by the cable theory, the fluid mechanic, the nonlinear geometric analysis and other. However specific codes were necessary and were programmed to apply the theories on the specific case of study;the complete methodology followed is presented. The goal is to create a free open domain where the numerical procedures evaluated are merged, added, modified by researchers with the aim to obtain a common space of use for wind engineering of not conventional structure.

Aerodynamic unstable critical wind velocity for three-dimensionalopen cable-membrane structures

The aerodynamic unstable critical wind velocity for three-dimensional open cable-membrane structures is investigated. The geometric nonlinearity is introduced into the dynamic equilibrium equations of structures. The disturbances on the structural surface caused by the air flow are simulated by a vortex layer with infinite thickness in the structures. The unsteady Bernoulli equation and the circulation theorem are applied in order to express the aerodynamic pressure as the function of the vortex density. The vortex density is then obtained with the vortex lattice method considering the coupling boundary condition. From the analytical expressions of the unstable critical wind velocities, numerical results and some useful conclusions are obtained. It is found that the initial curvature of open cable-membrane structures has clear influence on the critical wind velocities of the structures.

Unconventional Hamilton-type variational principles for nonlinear elastodynamics of orthogonal cable-net structures

According to the basic idea of classical yin-yang complementarity and modem dual-complementarity, in a simple and unified new way proposed by Luo, the unconventional Hamilton-type variational principles for geometrically nonlinear elastodynamics of orthogonal cable-net structures are established systematically, which can fully characterize the initial-boundary-value problem of this kind of dynamics. An ifnportant integral relation is made, which can be considered as the generalized principle of virtual work for geometrically nonlinear dynamics of orthogonal cable-net structures in mechanics. Based on such relationship, it is possible not only to obtain the principle of virtual work for geometrically nonlinear dynamics of orthogonal cable-net structures, but also to derive systematically the complementary functionals for five-field, four-field, three-field and two-field unconventional Hamilton-type variational principles, and the functional for the unconventional Hamilton-type variational principle in phase space and the potential energy functional for one-field unconventional Hamilton-type variational principle for geometrically nonlinear elastodynamics of orthogonal cable-net structures by the generalized Legendre transformation given in this paper, Furthermore, the intrinsic relationship among various principles can be explained clearly with this approach.

Spatial structural analysis of main saddle for single tower spatial cable self-anchored suspension bridge

Based on the engineering background of the Jiangxinzhou Bridge in Nanjing, issues related to the spatial main saddle of the self-anchored suspension bridge are studied. The refinement finite element model is established by the secondary development technology based on the platform of the general finite element program, and a reasonable load pattern is used in its spatial structural analysis, by which its path of force transference and stress distribution are obtained. Matched with the spatial main cable, the tangency point correction method is also discussed. The results show that the lateral wall stress of the saddle groove is higher than the stress within the wall due to the role of lateral forces in the finished bridge state; the horizontal volume force of the main cable can generate a gradient distributed vertical extrusion pressure on the saddle clamping device and the main saddle body; the geometric nonlinear effect of the self- anchored suspension bridge cable system in the construction process is significant, which can be reflected in the spatial tangent point position of the main cable with the main saddle changes a lot from free cable to finished cable.

New algorithm of shape-finding of suspension bridge with spatial cables

A new algorithm is proposed to solve the problems of shape-finding of suspension bridge with spatial cables what include tedious iteration,slow convergence speed and even no convergent under some circumstances.In this paper,the stress analysis of the main cable is carried out,and the relationship between the slope change and the coordinate change is found.This paper also discussed how to find the minimum slope point of symmetrical or asymmetric main cable,and the deformation compatibility equation is established and solved to obtain the shape of main cable.The algorithm in this paper can ensure the convergence of the solution for the suspension bridge with spatial cables.The calculation accuracy is high through the demonstration of the calculation examples.