Sensitivity study of load-dependent Ritz vectors on modal and seismic responses of cable stayed bridges

In the present article, 3D Finite Element Model (FEM) of a bridge structure under load dynamics is performed in order to assess the sensitivity study of Load-Dependant Ritz vectors (LDR) on modal and seismic responses of cable stayed bridges. In this context, two techniques are examined in the present study for solving structural dynamics problems; the Traditional Modal Superposition (TMS) technique and that of Load-Dependent Ritz orthogonal vectors (LDR). The latter is based on a very efficient algorithm allowing the systematic generation of Load-Dependent Ritz orthogonal vectors (LDR), the accuracy of this method is significantly influenced by the selection of LDR vectors used for the modeling of the structural behavior. The cable-stayed bridge connecting two districts in eastern Algeria, characterized by an expected Peak Ground Acceleration (PGA) equal to 0.275g in accordance with Algerian seismic design code is selected in order to perform critical modal properties such as, frequencies, shapes of the required vibration modes and effective mass participation as well as the dynamic response of the cable stayed bridge under earthquake loadings in three orthogonal directions (longitudinal, transversal and vertical). The results of this study reveal that the LDR vectors method which has the important advantages of short Central Processing Unit (CPU) time as compared to traditional modal method is very efficient for modal and seismic analyses of cable stayed bridges

A mathematical model for assessment of material requirements for cable supported bridges: implications for conceptual design

Recent technological developments have led to improvements in the strengths of materials, such as the steel and wire ropes used in the construction of cable supported bridges. This, combined with technological advancements in construction, has encouraged the design of structures with increasing spans, leaving the question of material and environmental costs behind. This paper presents a refined mathematical model for the assessment of relative material costs of the supporting structures for cable-stayed and cable suspension bridges. The proposed model is more accurate than the ones published to date in that it includes the self weight of the cables and the pylons. Comparisons of material requirements for each type of bridge are carried out across a range of span/dip ratios. The basis of comparison is the assumption that each structure is made of the same material (steel) and carries an identical design load, q, exerted by the deck. Calculations are confined to a centre span of a three-span bridge, with the size of the span ranging from 500 m to 3000 m. Results show that the optimum span/dip ratio, which minimises material usage, is 3 for a cable-stayed (harp type) bridge, and 5 for a suspension structure. The inclusion of the self weight of cable in the analysis imposes limits on either the span, or span/dip ratio. This effect is quantified and discussed with reference to the longest cable-supported bridges in the world completed to date and planned in the future

Effects Of Cable Diameter Reduction And Snapping On The Behavior Of Cable-Stayed Bridges

Cable–stayed bridges are usually constructed in coastal area in which the surrounding atmospheric is considered as severe environmental condition. This atmosphere helps in building up quickly the corrosion of steel cables with time. Visual inspection of cable-stayed bridges built up worldwide shows that the bridge cables suffer from serious corrosion although the cables are protected using different techniques. There is a considerable reduction in cable diameter due to corrosion, which depends on the severity of the environmental condition. There is no sufficient information regarding the effect of reduction in cable diameter on the structural response of cable-stayed bridge. Furthermore, snapping of cables due to accidental and /or corrosion is another important issue which affecting the structural response and safety of cable stayed bridges and need to be addressed for safe design.In this research, the effect of reducing cables diameter, cables layout and snapping of individual cables on the structural behavior and safety of cable-stayed bridge are presented. Three cable layouts are analyzed in this study i.e. harp, semi harp and fan layouts. In each layout, five different reductions in cables diameters are considered i.e 12.50%, 25.00%, 37.50%, and 50.00%. To address snapping of cable, harp bridge layout is considered and the structural behavior of the bridge due to snapping individual cables in the bridge are presented and discussed. The analysis starts with initial shape analysis to stress the cables to minimize the deformation under self-weight of the structure. The analysis was carried out using stiffness method considering the geometrical nonlinearities. The results of initial shape analysis show that in all bridge layouts reflect comparable behavior. The cable forces were found to be the lowest in fan layout cable bridge compared to harp and semi harp layouts. Reducing cables diameter will lead to a redistribution of forces and moment in different components of the bridge and alter the structural behavior in a nonlinear fashion. Reducing cables diameter by 25% will compromise the bridge safety as the stresses in cables, deformation, and bending moment will be increased significantly. The bridge cable layouts have little effect on the structure response of the cable-stayed bridge with reduced cables diameter. The fan layout shows better structural response compared to harp and semi harp layout, especially in term of cable forces and deformation profile. Notwithstanding this fact, 25% of cables reduction diameter will significantly affect the moment in girder of fan bridge layout compared to other layouts of cables Snapping the individual cable in the bridge has a significant effect on the cable force and bending moment distribution in the girder, tower and will cause bridge failure

Cable-stayed pedestrian bridge

Cílem práce je návrh lávky, která převádí odděleně pěší a cyklistickou dopravu nad rychlostní silnicí a místním potokem. Ze dvou variant byla vybrána lávka tvořena monolitickou mostovkou zavěšenou na pylonu ve tvaru písmene V. Práce obsahuje statický výpočet konstrukce modelované v programu ANSYS. Návrh a posouzení bylo provedeno dle aktuálně platných evropských norem.The aim of this master’s thesis is a design of the footbridge that transfers separately pedestrian and bicycle traffic over the expressway and the local creek. Chosen footbridge, which were one of two possible designs, consists of a monolithic bridge deck suspended on the V-shaped pylon. Thesis contains a static calculation of the structure modeled in ANSYS software. Design and assessment are according to the current European standards

Time-dependent effects on dynamic properties of cable-stayed bridges

Structural health monitoring systems are often installed on bridges to provide assessments of the need for structural maintenance and repair. Damage or deterioration may be detected by observation of changes in bridge characteristics evaluated from measured structural responses. However, construction materials such as concrete and steel cables exhibit certain time-dependent behaviour, which also results in changes in structural characteristics. If these are not accounted for properly, false alarms may arise. This paper proposes a systematic and efficient method to study the time-dependent effects on the dynamic properties of cable-stayed bridges. After establishing the finite element model of a cable-stayed bridge taking into account geometric nonlinearities and time-dependent behaviour, long-term time-dependent analysis is carried out by time integration. Then the dynamic properties of the bridge after a certain period can be obtained. The effects of time-dependent behaviour of construction materials on the dynamic properties of typical cable-stayed bridges are investigated in detail.link_to_subscribed_fulltex

Analysis of the performance of cable-stayed bridges under extreme events

University of Technology Sydney. Faculty of Engineering and Information Technology.In bridge structures, loss of critical members (e.g. cables or piers) and associated collapse may occur due to several reasons, such as wind (e.g. Tacoma narrow bridge), earthquakes (e.g. Hanshin highway) traffic loads (e.g. I-35W Mississippi River Bridge) and potentially some blast loadings. One of the most infamous bridge collapses is the Tacoma Narrow Bridge in United States. This suspension bridge collapsed into the Tacoma Narrow due to excessive vibration of the deck induced by the wind. The collapse mechanism of this bridge is called "zipper-type collapse", in which the first stay snapped due excessive wind-induced distortional vibration of the deck and subsequently the entire girder peeled off from the stays and suspension cables. The zipper-type collapse initiated by rupture of cable(s) also may occur in cable-stayed bridges and accordingly guideline, such as PTI, recommends considering the probable cable loss scenarios during design phase. Moreover, the possible extreme scenario which can trigger the progressive collapse of a cable-stayed bridge should be studied. Thus, there are three main objectives for this research, which are the effect of sudden loss of critical cable(s), cable loss due to blast loadings and progressive collapse triggered by the earthquake. A finite element (FE) model for a cable-stayed bridge designed according to Australian standards is developed and analysed statically and dynamically for this research purpose. It is noted that an existing bridge drawing in Australia cannot be used due to a confidential reason. The bridge model has steel deck which is supported by total of 120 stays. Total length of this bridge is 1070m with 600m mid-span. This thesis contains 8 chapters starting with the introduction as chapter 1. In chapter 2, comprehensive literature review is presented regarding three main objectives. In chapter 3 to 5, results of the cable loss analyses are presented. In chapter 3, the dynamic amplification factor (DAF) for sudden loss of cable and demand-to-capacity ratio (DCR), which indicate the potential progressive collapse, in different structural components including cables, towers and the deck are calculated corresponding with the most critical cable. The 2D linear-elastic FE model with/without geometrical nonlinearity is used for this analysis. It is shown that DCR usually remains below one (no material nonlinearity occurs) in the scenarios studied for the bridge under investigation, however, DAF can take values larger than 2 which is higher than the values recommended in several standards. Moreover, effects of location, duration and number of cable(s) loss as well as effect of damping level on the progressive collapse resistance of the bridge are studied and importance of each factor on the potential progressive collapse response of the bridges investigated. As it was shown in chapter 3, a 2D linear-elastic model is used commonly to determine the loss of cable. However, there is a need to study the accuracy and reliability of commonly-used linear elastic models compared with detailed nonlinear finite element (FE) models, since cable loss scenarios are associated with material as well as geometrical nonlinearities which may trigger progressive collapse of the entire bridge. In chapter 4, 2D and 3D finite element models of a cable-stayed bridge with and without considering material and geometrical nonlinearities are developed and analysed. The progressive collapse response of the bridge subjected to two different cable loss scenarios at global and local levels are investigated. It is shown that the linear elastic 2D FE models can adequately predict the dynamic response (i.e. deflections and main stresses within the deck, tower and cables) of the bridge subject to cable loss. Material nonlinearities, which occurred at different locations, were found to be localized and did not trigger progressive collapse of the entire bridge. In chapter 5, using a detailed 3D model developed in the previous chapter, a parametric study is undertaken and effect of cable loss scenarios (symmetric and un-symmetric) and two different deck configurations, i.e. steel box girder and open orthotropic deck on the progressive collapse response of the bridge at global and local level is investigated. With regard to the results of FE analysis, it is concluded that deck configuration can affect the potential progressive collapse response of cable-stayed bridges and the stress levels in orthotropic open decks are higher than box girders. Material nonlinearities occurred at different locations were found to be localized and therefore cannot trigger progressive collapse of the entire bridge. Furthermore, effect of geometrical nonlinearities within cables (partly reflected in Ernst’s modulus) is demonstrated to have some effect on the progressive collapse response of the cable-stayed bridges and accordingly should be considered. In chapter 6, the blast loads are applied on the bridge model and determined the bridge responses, since the blast load is one of the most concerned situations after 911 terrorist attacks. The effect of blast loadings with different amount of explosive materials and locations along the deck is investigated to determine the local deck damage corresponding to the number of cable loss. Moreover, the results obtained from the cable loss due to blast loadings are compared with simple cable loss scenarios (which are shown in chapter 3 to 5). In addition, the potential of the progressive collapse response of the bridge at global and local level is investigated. With regard to the results of FE analysis, it is concluded that the maximum 3 cables would be lost by the large amount of TNT equivalent material due to damage of the anchorage zone. Simple cable loss analysis can capture the results of loss of cable due to blast loadings including with local damages adequately. Short cables near the tower are affected by blast loadings, while they are not sensitive for the loss of cables. Furthermore, loss of three cables with damaged area did not lead progressive collapses. Finally, in chapter 7, dynamic behaviour of cable-stayed bridges subjected to seismic loadings is researched using 3D finite element models, because large earthquakes can lead to significant damages or even fully collapse of the bridge structures. Effects of the type (far- or near-field) and directions of seismic loadings are studied in several scenarios on the potential progressive collapse response of the bridge at global and local level. According to the case studies in this chapter, it is shown that near filed earthquakes applied along the bridge affected to deck and cables significantly. Moreover, the mechanism of bridge collapsed due to longitudinal excitation is analysed by an explicit analysis, which showed the high plastic strain occurring around the pin support created the permanent damage. The summary and suggestions for this research are shown in final chapter 8

The Effect of Seismic Isolation on the Dynamic Behavior of Cable-Stayed Bridges

The earthquake effects on cable-stayed bridges isolated by single concave friction pendulum (SCFP) are investigated in this study. Reducing ways of the destructive earthquake effects are getting vital important for researchers and engineers. One of the most accepted ways for reducing the effects of earthquake is using seismic isolation systems. The result obtained from an analytical study on the seismic responses of Manavgat Cable-Stayed Bridge with and without seismic isolation system are compared each other. The selected bridge is the first cable-stayed bridge of Turkey and has 202m length between its side supports. In order to determine the contributions of isolation systems to the bridge dynamic behavior, 3D finite element model (FEM) of the bridge is created in Sap2000 [1]. Time history analysis is performed for 3D FEM. Three different earthquake ground motions having transverse and longitudinal directions are used in analyses. Comparison of dynamic behavior of the bridge with and without the SCFP systems under three different earthquake motions has been conducted. The results obtained from analyses of the bridge are presented by graphics and tables in detail. It is seen that using of isolation system reduces the destructive effects of earthquakes on the bridge

Fundamental mode estimation for modern cable-stayed bridges considering the tower flexibility

The design of cable-stayed bridges is typically governed by the dynamic response. This work provides designers with essential information about the fundamental vibration modes, proposing analytical expressions based on the mechanical and geometrical properties of the structure. Different bridge geometries are usually considered in the early design stages until the optimum solution is defined. In these design stages, the analytical formulation is advantageous, because finite-element models are not required and modifying the bridge characteristics is straightforward. The influence of the tower flexibility is included in this study, unlike in previous attempts on mode estimation. The dimensions and proportions of the canonical models proposed in the analytical study stem from the previous compilation of the dimensions of a large number of constructed cable-stayed bridges. Five tower shapes, central or lateral cable-system layouts and box- or U-shaped deck sections, have been considered. The vibration properties of more than 1,000 cable-stayed bridges with main spans ranging from 200 to 800 m long were extracted within an extensive parametric analysis. The Vaschy-Buckingham theorem of dimensional analysis was applied to the numerical results to propose the formulation for period estimation. Finally, the formulas were validated with the vibration properties of 17 real cable-stayed bridges constructed in different countries. The importance of the tower flexibility is verified, and the errors observed are typically below 15%, significantly improving the estimations obtained by previous research works. © 2014 American Society of Civil Engineers

Vibration assessment of the International Guadiana Bridge

The paper describes the development of a monitoring program for a cable-stayed bridge and resumes the major dynamic properties identified from a series of test campaigns conducted on the bridge, which are also correlated with results from a numerical analysis. Some aspects of the current dynamic behavior of the bridge under ambient excitation are discussed, considering in particular the large cable vibrations that are frequently observed

Tension estimates in cable stayed bridges

A benchmark problem on an existing cable-stayed bridge was recently proposed. Recorded signals are available for standard working conditions and for special events (typhoons!). In this contribution, the authors report their attempt to detect significant variations in the cable tension during these extreme events