Stayed Columns Research Articles

A nonlinear FE formulation for elastic buckling and post-buckling analysis of pre-stressed stayed columns with bonded/un-bonded cable stays

This study intends to investigate elastic buckling and post-buckling behaviors of pre-stressed (PS) stayed columns with single and triple cross-arms using a nonlinear FEM. To achieve this, a two-node shear-rigid/shear-flexible beam element considering second-order effects and multi-node stay cable elements under bonded/un-bonded conditions with consistent consideration of their unstrained lengths are formulated using an energy method. After validity and accuracy of the present formulation under the bonded condition is demonstrated through comparison of analysis results by Abaqus, elastic buckling and post-buckling characteristics of two PS stayed column models with single and triple cross arms is rigorously examined, considering the stays under the bonded or un-bonded conditions.

Nonlinear stability and design of prestressed stayed columns in fire considering non-uniform temperature distribution

Prestressed stayed columns are vulnerable to fire due to material weakening. The fire behaviour of the stayed columns is investigated with non-uniform temperature distributions considered using steady state analysis within ABAQUS. This study aims to reveal the load-carrying capacity reduction of stayed columns in fire and propose a design method. Results show that ultimate loads decrease with temperature increasing, and the stayed columns approximate failure at the temperatures higher than 600°C. The failure deflected mode maintains similar to the dominant linear buckling mode for the uniform temperature distribution, and the sensitivity of ultimate loads to prestressing levels becomes less significant at higher temperatures. Moreover, compared to buckling and ultimate behaviour, initial post-buckling behaviour shows more significant sensitivity to temperature distributions. The non-uniform distribution can lead to asymmetric deflected mode due to stiffness re-distribution from the material weakening at elevated temperatures, and the post-buckling behaviour of the cases with rotational symmetric mode dominance is sensitive to prestressing levels. Finally, a fire design method is proposed based on the ultimate load reduction in fire.

Behavioral Analysis of a Mast with a Combined Prestressed Stayed Columns System and Core of a Spun Concrete Circular Cross-Section

Widely used telecommunication structures are usually of the tower or mast type. For medium and tall telecommunications structures, tower-type constructions become less efficient compared to mast-type structures. The goal of our article is to discover a new, efficient telecommunication structure. For relatively low heights, tower systems can be designed with a continuous cross-section, in most cases using reinforced concrete elements. Among them, efficient spun concrete elements, whose load-bearing capacity is higher than that of ordinary solid reinforced concrete elements due to the technological features of their production, should be mentioned. A significantly higher efficiency of masts can be achieved by employing various combined structural systems that utilize a prestressed stayed columns system. It should be noted that there are not many solutions for prestressed stayed columns systems with spun concrete core elements and that research into their design and behavior is not yet sufficiently developed. The behavior of this combined structure is analyzed with regard to the geometric and physical nonlinearity of its elements. The strength and stability of the spun concrete core of such a combined system are evaluated. The impact of the prestressing of this prestressed stayed column structure on the internal forces and displacements of the reinforced concrete core is analyzed. The performance of the new structure compared to conventional tower and mast structures is presented. In the article, it has been determined that by applying the prestressed stayed columns system to telecommunication structures, the innovative structural system becomes 2.5 times more efficient than the classic mast and 5 times more efficient than the typical tower system on the mass criterion.

Probing in situ capacities of prestressed stayed columns: towards a novel structural health monitoring technique.

Prestressed stayed columns (PSCs) are structural systems whose compressive load-carrying capacity is enhanced through pre-tensioned cable stays. Much research has demonstrated that PSCs buckle subcritically when their prestressing levels maximize the critical buckling load of the theoretically perfect arrangement. Erosion of the pre-tensioned cables' effectiveness (e.g. through creep or corrosion) can thus lead to sudden collapse. The present goal is to develop a structural health monitoring (SHM) technique for in-service PSCs that returns the current structural utilization factor based on selected probing measurements. Hence, PSCs with different cable erosion and varying compression levels are probed in the pre-buckling range within the numerical setting through a nonlinear finite element (FE) model. In contrast to the previous work, it is found presently that the initial lateral stiffness from probing a PSC provides a suitable health index for in-service structures. A machine learning-based surrogate is trained on simulated data of the loading factor, cable erosion and probing indices; it is then used as a predictive tool to return the current utilization factor for PSCs alongside the level of cable erosion given probing measurements, showing excellent accuracy and thus provides confidence that an SHM technique based on probing is indeed feasible. This article is part of the theme issue 'Probing and dynamics of shock sensitive shells'.

Probing the stability landscape of prestressed stayed columns susceptible to mode interaction

Prestressed stayed columns are structural systems where the compressive load-carrying capacity is enhanced through pre-tensioned external cable stays. Recent theoretical studies using analytical and nonlinear finite element models have shown that, under certain configurations, this enhancement leads to a sequence of closely spaced bifurcation points beyond the critical one. This undesirable characteristic can give rise to dangerously unstable interactive post-buckling behaviour including ‘mode jumping’ and ‘snaking’ phenomena. Even though these highly nonlinear behaviours can be readily modelled using numerical methods, they cannot be verified robustly using traditional quasi-static testing techniques based on force or displacement control at a single point. The current work explores a novel testing concept for potential experimental implementation, from the theoretical and numerical point of view. The concept allows the stability landscape of prestressed stayed columns to be ascertained by controlling the shape of the structure at multiple points. By controlling the mode shape of the structure, it is possible to traverse limit points, path-follow otherwise unstable equilibria, pinpoint bifurcation points and branch-switch between different post-critical segments of the equilibrium manifold. To explore the feasibility of the new testing method, we have created a virtual instantiation of the experiment in the commercial finite element package Abaqus, coupled to a control algorithm that coordinates the movements of the different control points. A number of different stability phenomena that have previously been identified analytically and numerically are reproduced successfully in the virtual test environment. Moreover, a noise sensitivity study is conducted to assess the robustness of the experimental technique proposed herein. The present work lays the foundation for physically assessing the stability landscape of prestressed stayed columns in a more comprehensive way.

Behaviour of eccentrically loaded prestressed stayed columns with circular hollow sections

The behaviour of axially loaded prestressed stayed columns is a commonly studied area. Despite the fact that load eccentricity in columns is commonplace in practice, the amount of investigation into these systems under eccentric loading is limited. This study employed finite element analysis to investigate the interactive post-buckling behaviour of prestressed stayed columns. Critical imperfection combination with respect to the load carrying capacity was established and a comparison of a planar and a three-dimensional model was carried out to investigate key differences in the models. In this work, it has been shown that the load carrying capacity of eccentrically loaded columns can be significantly reduced when buckling in interactive mode is observed. Furthermore, it was established that increase in eccentricity results in a decrease in load carrying capacity of columns for both planar and three-dimensional models. However, a major difference between the models is the twisting effect exhibited in the three-dimensional model under out-of-plane eccentric loading. This work highlights the importance of carefully designing prestressed stayed columns’ connections to minimise loading eccentricity as it has been shown that the benefit of employing these systems over unstayed columns reduces with increasing load eccentricity.

Buckling Behaviour of Three-Dimensional Prestressed Stayed Columns

Slender columns exhibit instability under compression, which causes buckling. Prestressed stayed system can be used to improve the load carrying capacity of these columns. In this study, three-dimensional prestressed stayed column was investigated through the use of commercially available finite element software-ABAQUS. Although many numerical studies into the buckling behavior of stayed columns exist, these have mainly focused on two-dimensional (2D) systems. In order to fully understand the behavior of these structural systems, three-dimensional (3D) numerical studies are essential. In this work, the buckling behavior of three-dimensional prestressed stayed columns was investigated through linear perturbation method. The critical buckling loads and modes of four-branch and three-branch columns were investigated. The effect of varying the cross-arm length on the buckling load of the four-branch column was also investigated and compared with the theoretical values. It was found that the theoretical buckling loads reported in previous research with 2D systems were conservative and largely underestimated the buckling capacities of prestressed stayed columns. Furthermore, it was observed that transition point from the symmetric to antisymmetric buckling mode occurs at a higher value of cross-arm to column length ratio for the 3D prestressed stayed columns compared to the 2D model.

Buckling and collapse capacity of prestressed steel tube stayed columns with one and two crossarms

Prestressed tube stayed columns with one and two crossarms are investigated. The analyses are performed using SCIA Engineer software and ANSYS package and validated by tests of four stayed columns. First, the investigations concern the ideal (perfect) columns and cover linear buckling analyses (LBA) and geometrically nonlinear analyses (GNIA) to obtain critical loads and buckling modes under various prestressing levels. Second, the collapse loadings of the imperfect columns with initial deflections required by Eurocode EN 1993-1-1 are analysed with respect to relevant initial deflection modes and material behaviour (elastic for mild steel, nonlinear for stainless steel). All the analyses are performed for geometrical characteristics of the tested columns and the results concerning both the column with one or two crossarms are set against each other to assess the respective effectivity. In addition, the geometrical analysis of the prestressed ideal column with two crossarms and respective formulas concerning optimal prestressing and maximal critical loading are presented. Finally some recommendations for practical use are suggested.

Stability of Multiple-crossarm Prestressed Stayed Columns With Additional Stay Systems

Prestressed stayed columns have an enhanced resistance to buckling through the effective use of crossarms and pretensioned stays when compared to conventional columns. An analytical derivation of the minimum, linear optimum and maximum initial pretension forces for configurations of prestressed stayed columns with multiple crossarms and additional stays is presented for the first time. The findings are validated through comparisons with finite element models developed in the commercial package ABAQUS. The influence of the initial pretension on the load-carrying capacity of the configurations considered is also analysed, providing insight into the actual optimum initial pretension force for the configurations accounting for the significance of geometric nonlinearities.

Optimal prestressing of triple-bay prestressed stayed columns

A nonlinear finite element model of a triple-bay prestressed stayed column is developed within the commercial package ABAQUS. A linearly obtained ‘optimal prestressing force’ that maximizes the critical buckling load is investigated since this quantity has been demonstrated in previous work on single-bay prestressed columns to provide a lower bound to the actual maximum load carrying capacity when compared to experimental results and nonlinear modelling. The ratio of the crossarm to the overall column length, the diameter of the cable stays, the relative lengths of the individual crossarms and the ratio of the initial prestressing force to the aforementioned linear optimal prestress are varied. Measures for the relative efficiency of the main column and the stays are defined and the objective of the optimization study is for the efficiency to be maximized. It is found that the true optimal prestress is generally higher than the equivalent, linearly obtained, quantity but by a significantly reduced factor when compared to an equivalent study for single-bay prestressed stayed columns.

05.22: Stainless steel prestressed stayed columns

ABSTRACTBehavior of stainless steel prestressed stayed columns with a central crossarm is investigated numerically in 3D, following 3 tests of a reasonable size. The paper discusses previous analyses concerning critical loading and strength capacity with respect to influence of geometrical and material properties, prestressing and boundary conditions. Critical buckling loads and post‐buckling paths with regards to 2D and 3D GMNIA (geometrically and materially nonlinear analysis with imperfections) are demonstrated using ANSYS software. The buckling of the main column in 3D is shown, resulting into deflection in between the arms of the central crossarm, while the value of critical loading is rather unaffected in comparison with 2D analysis. Other results cover influence of the imperfection level with both symmetrical and antisymmetrical imperfection mode, boundary conditions at central crossarm (fixed or sliding stays) and nonlinear stainless steel material.

05.23: Optimal prestressing of triple‐bay prestressed stayed columns

ABSTRACTA nonlinear finite element model of the triple‐bay prestressed stayed column is developed within the commercial software ABAQUS. A linearly obtained ‘optimal prestress’ that maximizes the critical buckling load is investigated since this quantity has been demonstrated in previous work on single‐bay prestressed columns to provide a lower bound to the actual maximum load carrying capacity when compared to results from physical experiments and nonlinear modelling. The ratio of the crossarm to column length, the diameter of the cable stays and the ratio of the prestressing force to the linear optimal prestress are varied. Measures for the relative cost of the main column and the stays are defined and it is determined that the true optimal prestress is generally higher than the linearly obtained quantity but by a reduced factor when compared to an equivalent study for the single‐bay column case.

Mode interaction in triple-bay prestressed stayed columns

Prestressed stayed columns are an innovative type of structural system where the compressive load-carrying capacity can be enhanced through prestressed external cable stays. A nonlinear analytical model for prestressed stayed columns with multiple crossarm systems along the column length, based on the Rayleigh–Ritz method, is presented that captures modal interactions for perfect geometries explicitly for the first time. It is demonstrated that the theoretical compressive strength enhancements under certain configurations can only be obtained at the expense of triggering a sequence of destabilizing bifurcations. This can give rise to dangerously unstable interactive post-buckling behaviour including so-called ‘mode jumping’ and ‘snaking’ phenomena. Parametric spaces where the system is most susceptible to the modal interactions are identified and it is for those configurations that the system is likely to be highly sensitive to initial imperfections. The model is validated using a nonlinear finite element model formulated within the commercial code ABAQUS and excellent comparisons are obtained.

Stability of prestressed stayed steel columns with a three branch crossarm system

Analytical and numerical investigations of the stability of prestressed stayed columns with three crossarms branching laterally and symmetrically are presented. It is shown that modal symmetry is broken automatically if the critical mode is antisymmetric, which distinguishes it from the stayed columns studied hitherto. The governing imperfection distribution that should be adopted within finite element analysis to capture the actual load-carrying capacity is also obtained. The findings suggest that when the critical buckling mode is symmetric, the governing imperfection distribution should also be symmetric. Conversely, if the critical buckling mode is antisymmetric, a symmetric imperfection distribution or an asymmetric imperfection distribution may be adopted as the most severe imperfection distribution depending on the system characteristics. This would enable designers to determine an accurate prediction of the actual strength through nonlinear finite element analysis.

Structural behaviour of prestressed stayed columns with single and double cross-arms using normal and high strength steel

One solution to improve load carrying capacity of slender columns is to add prestressed cables and cross-arms as they provide additional restraints along the length. Such columns are called prestressed stayed columns (PSSC). This solution is very effective, but there are no experimental results on long columns which is a practical case for such columns. This paper presents the results of an experimental study on 18m PSSC with single and double cross-arms along the length and using normal and high strength steel. In total, 77 tests were carried out to investigate the structural behaviour of such systems and improvements made by using high strength steel and stay systems. The results in this paper provide detailed data on the behaviour of realistic PSSC which was not available before and highlight the advantages of the using high strength steel in such systems.

A full scale experimental study of prestressed stayed columns

This paper presents the results of an experimental study on 12m prestressed stayed columns. In total, 44 tests were carried out to investigate the compressive strength and behaviour of such systems by varying column cross-section geometry, diameter of cables, initial pretension level of stays and steel grade. The details of material testing for both steel and cable, and the compressive strength of each specimen including a detailed analysis of results for further numerical and analytical investigations are presented. The applicability of available analytical and design methods for determining the elastic buckling load and the load carrying capacity of stayed columns was assessed. The results provide detailed data on the behaviour of realistic PSSC and highlight the importance of the imperfections and the benefits of such systems.

Buckling mode interaction in prestressed stayed columns

Prestressed stayed columns offer an innovative and aesthetically attractive solution where designs demand long and slender elements under compression. The addition of cross-arms and pretensioned cables to the columns provides significant lateral and rotational support that can result in a marked increase of the buckling capacity. The current work presents a simplified model, comprising discrete rigid links and springs with a mathematically exact formulation including the destabilising effect of cable slackening, which mimics the response of stayed columns and reveals the governing physical parameters that drive the behaviour. A recent finite-element study had indicated that these structural components are likely to exhibit interactive buckling phenomena, particularly if the critical buckling mode is antisymmetric, leading to highly unstable responses. However, by its very nature, that study could not reveal the bifurcational structure of the equilibrium response. The results from the present model reveal similar behaviour to that observed in the earlier finite-element study. A sequence of bifurcations is found that switch the post-buckling response from one mode to another by way of a path of interactive buckling.

Numerical Studies on the Buckling Resistance of Prestressed Stayed Columns

The structural behaviour of prestressed stayed columns is investigated through nonlinear finite element modelling. The models were developed using the commercial software ABAQUS and validated against a series of recently conducted experiments. The sensitivity of the load-carrying capacity to the geometry of the stayed column, the initially applied prestress level within the stays and the initial global imperfection is investigated through parametric studies. It is found that there is a substantial increase in load-carrying capacity with increasing cross-arm length, provided the critical buckling mode remains symmetric. Once the critical buckling mode becomes antisymmetric, mode interaction becomes significant and the load-carrying capacity reaches a plateau and the component generally becomes more sensitive to imperfections. It is also found that the relative level of initial prestress required to maximize the load-carrying capacity of a given stayed column tends to reduce with increasing cross-arm length.

Design of prestressed stayed columns

General design procedures for prestressed stayed columns with a single cross-arm system are presented. The accuracy of the proposed design expressions is confirmed by comparison with the results of physical experiments and validated finite element simulations. Reliability is assessed by following the approach set out in Annex D of EN 1990. The presented resistance expressions for prestressed stayed columns are a function of the system geometry, the level of initial prestress in the cables and the global imperfection level. Worked examples are also presented to illustrate the application of the developed design approach.

Experimental study of critical and post-buckling behaviour of prestressed stayed columns

A full scale experimental investigation into the strength and behaviour of prestressed steel stayed columns in compression has been conducted. Results, including full load versus end-shortening curves, for a total of 18 test specimens are presented. Two critical modes of buckling — symmetric and antisymmetric — with interactive post-buckling are demonstrated experimentally and the imperfection sensitivity of the stayed columns is investigated. Interactive buckling is observed primarily when the individual buckling loads of the antisymmetric and symmetric modes are close or when the antisymmetric mode is critical. Analysis of the results reveals that increased prestress leads to an increased load-carrying capacity when instability occurs in the symmetric mode, but the reverse trend is found when the antisymmetric mode is critical.