Deck Section Research Articles

An enhanced forced vibration rig for wind tunnel testing of bridge deck section models in arbitrary motion

This paper presents a new experimental setup for the aerodynamic section model testing of bridge decks. The rig is designed to move a section model in arbitrary motion in a wind tunnel to imitate the motions of such scaled real bridge motion, step motion or random motion histories to be close to white noise. The proposed setup enables the forces acting on the section model to be measured directly while considering motions that resemble actual bridge motion and still fully utilizing the benefits of the forced vibration testing technique. The excellent performance of the system and testing procedure is proved by performing state-of-the-art forced vibration tests to extract 18 flutter derivatives of the Hardanger Bridge cross-section. The new experimental setup is further used to simulate a three-degree-of-freedom dynamic system driven by white noise to investigate whether the estimates of the aerodynamic derivatives are sensitive to the motion considered. The experimental results demonstrate that the estimates of the aerodynamic derivatives are not sensitive to the motion considered; these results indicate that the principle of superposition is fully applicable for the cross section as long as the motions are within the range considered.

Impact response of pedestrian bridge multicellular pultruded GFRP deck panels

The impact behaviour of pultruded glass fibre reinforced polymer (GFRP) multicellular footbridge deck panels was investigated via instrumented drop weight testing. Force-displacement history, maximum force, and displacement and absorbed energy at perforation were recorded. The effects of two damage protections (a resin-sand surface coating, and polyurethane foam-filled sections) and of alternative target specimen geometries (3-cells, 1-cell and single laminated flange) were investigated. Previous quasi-static test results were successfully used to estimate the impact incident energies required for perforation, thus saving material resources. The impact force-displacement behaviour was of a similar form to that of the quasi-static tests. Before damage, coated deck sections alone exhibited a strain rate effect, with the impact response stiffer than the quasi-static response. However, a similar stiffening strain rate effect was seen for all specimens after the onset of damage, which is believed to be due to rate sensitive damage propagation. The surface coating increased the perforation energy by 25%, but foam-filled sections gave no significant impact resistance improvement. Alternative geometries could be used in specific cases, but a 3-cell wide target was found to be preferable. It was shown that even relatively mild impact events such as tool drops could result in damage, or even perforation.

Experimental investigations on VIV of bridge deck sections: A case study

In this paper, the Vortex Induced Vibrations (VIVs) of bridge deck sections of the Hong Kong-Zhuhai-Macao Bridge were investigated experimentally. Aeroelastic tests for the bridge deck of two scale ratios (1:20 model and 1:50 model) under different wind attack angles, wind speeds, and damping ratios were performed. Accessory and windbreak effects on the VIVs of the bridge deck were also carried out. The experimental results show that the accessory and windbreak tend to enlarge the VIVs of the bridge deck. Furthermore, the most unfavorable wind attack angle is 5°. At this attack angle and low damping ratios, the VIVs of the bridge deck are significant and much larger than the allowable value. In addition, the VIVs of the bridge deck decrease with increasing the damping ratios (Particularly, at large damping ratios, the VIVs were well suppressed). This study provides a guideline for the designs of long span flexible bridges on suppressing the VIVs of the bridges.

On the importance of cross-sectional details in the wind tunnel testing of bridge deck section models

Experimentally derived aerodynamic derivatives are used to predict and prevent undesirable aeroelastic behavior of bridges and are currently considered indispensable in the design of long-span bridges. The aerodynamic derivatives are functions of the reduced frequency of motion and depend strongly on the shape of the cross-section. Therefore, the experimental results are sensitive to the degree of detail of the section model of the bridge deck, the precise modelling of the bridge railings and the testing method applied. This paper investigates how differences in the aerodynamic derivatives caused by the listed factors influence the buffeting response and critical flutter speed of a long-span suspension bridge.

Numerical analysis on the difference of drag force coefficients of bridge deck sections between the global force and pressure distribution methods

To analyze the difference of drag force coefficients of bridge sections obtained by the global force and pressure distribution methods, three-dimensional numerical simulations on the drag force coefficients of three typical sections are carried out. Firstly, after the numerical simulation method is validated, the percentage contribution of the friction drag force coefficient of the three sections under varying wind attack angles are investigated. Furthermore, the effect of the Reynolds number and handrails on the percentage contribution of the friction drag force coefficient is analyzed, and the results show that while the Reynolds number has an insignificant effect, the handrails’ effect is significant. Due to the importance of the contribution of the friction drag force for streamlined sections, more cases are simulated to investigate the percentage contribution of the friction drag force coefficient by varying the aspect ratio and fairing angle using the Sutong Bridge’s cross section as an example. The correction coefficients of the drag force coefficients obtained by the pressure distribution method for streamlined sections are obtained by the least square principle. The research conclusions can provide a reference for the differences of the drag force coefficient measured by the global force and pressure distribution methods for engineering practice.

Optimum design of steel floor system: effect of floor division number, deck thickness and castellated beams

Decks, interior beams, edge beams and girders are the parts of a steel floor system. If the deck is optimized without considering beam optimization, finding best result is simple. However, a deck with higher cost may increase the composite action of the beams and decrease the beam cost reducing the total cost. Also different number of floor divisions can improve the total floor cost. Increasing beam capacity by using castellated beams is other efficient method to save the costs. In this study, floor optimization is performed and these three issues are discussed. Floor division number and deck sections are some of the variables. Also for each beam, profile section of the beam, beam cutting depth, cutting angle, spacing between holes and number of filled holes at the ends of castellated beams are other variables. Constraints include the application of stress, stability, deflection and vibration limitations according to the load and resistance factor (LRFD) design. Objective function is the total cost of the floor consisting of the steel profile cost, cutting and welding cost, concrete cost, steel deck cost, shear stud cost and construction costs. Optimization is performed by enhanced colliding body optimization (ECBO), Results show that using castellated beams, selecting a deck with higher price and considering different number of floor divisions can decrease the total cost of the floor.

Numerical wind tunnel for aerodynamic and aeroelastic characterization of bridge deck sections

The aim of the present study is to propose a reliable engineering procedure to analyze bridges subjected to wind loads by-passing the expensive wind tunnel tests thanks to numerical simulations. These exploit Kratos, a free multi-physic FEM code developed by the Kratos Team at CIMNE in Barcelona, and, specifically, an adaptation to the long-span bridge case of its numerical tool for simulation of in-wind ultra-lightweight structures developed within the uLites project (supported by the Research Executive Agency in the Seventh Framework Programme of the European Union, SP4-Capacities, Research for the benefit of SMEs, FP7-SME-2012 GA-314891, see http://www.cimne.com/websasp/ulites/). Time histories of the forces induced by the flow around the sections are used to calculate aerodynamic and aeroelastic parameters through statistical, frequencies extraction and fitting algorithms. Several analyses have been performed to derive rules for a reliable and stable evaluation of these aggregated parameters for engineering purposes. Results obtained for the sections of Great Belt Bridge (Denmark) and of the bridge on A31 highway over Adige river (Italy) are shown. Both static analyses (CFD procedure with fix boundaries) and imposed-displacements analyses (CFD with ALE) give results that are comparable with those coming from wind tunnel testing and from literature; evaluated parameters also manifest regular trends and values little influenced by CFD setting. These facts represent proofs of the reliability of the proposed procedure.

Numerical simulation of a 5:1 rectangular cylinder at non-null angles of attack

In this paper, the flow around a rectangular cylinder with aspect ratio 5:1 is studied at three attack angles by means of both LES and URANS simulations. Despite its geometric simplicity, such a rectangular shape is characterized by many aerodynamic phenomena typical of reattached flows around bluff bodies and has been recently widely studied as a prototype of flows encountered around shapes of technical interest like, for example, bridge deck sections. The present study is aimed at providing insight in the modifications occurring in the flow at small incidence angles, by comparing the accuracy of the two aforementioned simulation strategies in reproducing them. Some recurring biases observed in URANS simulations are illustrated and their origin discussed. Results are presented in terms of flow bulk parameters and pressure distributions and systematic comparison with available experimental data is provided. Finally, the effects of small incidence angles on along span flow correlations are investigated and Covariance Proper Transformation is used in order to further characterize the flow dynamic behavior.

Effects of Exponentially Modified Sinusoidal Oscillation and Amplitude on Bridge Deck Flutter Derivatives

With the use of a computational fluid dynamics (CFD) numerical simulation, in this study an unusual exponentially modified sinusoidal (EMS) oscillation was forcibly imposed on deck section to simulate amplitude-varying self-excited forces. This approach facilitated the investigation of the influence of EMS transient oscillation and amplitude on self-excited forces and flutter derivatives. Study results show that for an ideal thin plate, the sensitivities of H2*, H4*, A2*, and A4* to oscillation decaying/diverging ratio (ξ) were higher than those of H1*, H3*, A1*, and A3*. With different amplitudes, ξ, and reduced wind velocities, the self-excited forces of one flat plate and two bluff bridge decks were numerically calculated and the flutter derivatives were extracted and compared with the theoretical and experimental results. If |ξ| < 0.1, its influence was almost negligible, by which the traditional sinusoidal oscillation technique was validated. The heaving and torsional amplitudes had different influences on each flutter derivative. The influences were also related to deck cross sections and reduced wind velocities. The proposed numerical simulation of EMS oscillation enables a better understanding of the influence of oscillation amplitude and ξ on bridge deck flutter derivatives.

Flutter Derivatives Identification and Aerodynamic Performance of an Optimized Multibox Bridge Deck

The bridge deck sections used for long-span suspension bridges have evolved through the years, from the compact box deck girders geometrical configurations to twin-box and three-box bridge decks sections. The latest generation of split and multiple-box bridge decks proved to have better aerodynamic behavior; thus further optimization methods are sought for such geometrical configurations. A new type of multibox bridge deck, consisting of four aerodynamically shaped deck boxes, two side decks for the traffic lanes and two middle decks for the railway traffic, connected between them by stabilizing beams, was tested in the wind tunnel for identifying the flutter derivatives and to verify the aerodynamic performance of the proposed multibox deck. Aerodynamic static force coefficients were measured for the multibox bridge deck model, scaled 1 : 80, for Reynolds numbers up to 5.1 × 105, under angles of attack between −8° and 8°. Iterative Least Squares (ILS) method was employed for identifying the flutter derivatives of the multibox bridge deck model, based on the results obtained from the free vibration tests and based on the frequency analysis the critical flutter wind speed for the corresponding prototype of the multibox bridge was estimated at 188 m/s.

Higher-Order Self-Excited Drag Forces on Bridge Decks

AbstractNonlinear features concerning self-excited drag forces induced by the vertical and torsional motions for typical deck sections are investigated comprehensively in this study. The self-excited drag forces are calculated using computational fluid dynamics (CFD)-based numerical simulations. In a conventional analysis framework, the self-excited drag force is modeled as a linear function of the structural motions. However, the simulation results from CFD indicate that in many instances, the second-order (nonlinear) component of the self-excited drag force is more significant than the first-order (linear) component. To enhance the modeling fidelity of a conventional aeroelastic analysis framework on the basis of the semiempirical flutter derivative concept, a nonlinear mathematical model for characterizing both the first- and second-order components is developed to better quantify the self-excited forces and more accurately extract the flutter derivatives. Its efficacy and superiority compared with the...

Numerical simulations and experimental validations of force coefficients and flutter derivatives of a bridge deck

This paper presents the results of the application of the large eddy simulation (LES) numerical method with the aim of investigating static coefficients and nonstationary flutter derivatives for a common symmetric bridge deck section. The results are compared with those of the unsteady Reynolds-averaged Navier–Stokes (URANS) study. The results of the investigated numerical simulations are validated by force and pressure measurements from wind tunnel experiments. In addition to the commonly used representation of flutter derivatives based on the integrated forces, the paper uses cross-sectional representation by tracking the contributions of nonstationary coefficients around the bridge deck section. Besides providing a better insight into the physical mechanism, the cross-sectional representation seems to be a powerful tool for identifying deficiencies in visualizing the impact of flow separations on flutter derivatives.

Aerodynamic instability performance of twin box girders for long-span bridges

Twin box girders are a popular choice among long-span bridge engineers, and the aerodynamic performance of such a system is critical to the stability of a bridge under wind excitation. Two groups of twin-box girders with six representative slot width ratios varying from 0% to 100% were utilised to investigate the influence of different wind fairing shapes on aerodynamic instability performance for both torsional divergence and flutter of the girders. The girders with two wind fairing shapes for various slot ratios were investigated by wind tunnel tests and theoretical analyses. Based on the experimental results of static wind loads and critical flutter wind velocities, the symmetry of wind fairing only showed an influence on the development pattern of drag force coefficients and the flutter performance was only significantly affected when the slot width ratio was over 40%. It is also shown that the effect of structural stiffness variation caused by the change of slot width ratio cannot be neglected in stationary torsional divergence analysis. The flutter performance of twin box girders with asymmetric wind fairing is sensitive to slot width ratio due to the existence of optimal slot width, which is opposite to the case with symmetric wind fairing, especially when this ratio is over 40%. Different aerodynamic damping parts contributing to the torsional aerodynamic damping and the participation level of each degree of freedom (DOF) were analysed through a two-dimensional three degree of freedom (2D-3DOF) method, and the results indicate that the improvement in flutter performance can be mainly attributed to the decrease in aerodynamic negative damping Part F (caused by the couple effect of the torsional and vertical motion) and the increase of participation level in heaving motion at the flutter onset. Particle Image Velocimetry (PIV) techniques were further employed to reveal that the change in central slot width ratio and the symmetry of wind fairing have a great influence on the vortices’ characteristics, especially in the central slot region when the slot ratio is over 40%. This was determined by observing the flow structures around the deck sections in terms of wind velocity field and vortex characteristics.

Transient flutter analysis of bluff bodies

This paper deals with the flutter theory for bridge decks and presents a new approach for the determination of 27 time domain dynamic force coefficients using forced motion of the deck section at either constant absolute speed (triangular wave form) or constant absolute acceleration (parabolic wave form). These coefficients are then introduced in a transient nonlinear flutter analysis where the wind speed is varied in order to predict the stability curve of a 3 degrees of freedom deck sections. This allows for considering the nonlinear nature of the flutter phenomenon, i.e. its variation according to multiple quantities (wind speed, frequency of motion, amplitude of motion, angle of attack, etc.), when predicting flutter amplitude at any wind speed. Results show good agreement with predictions from complex eigenvalue analysis and the stabilization of flutter was observed at different levels of vibration according to the wind speed. The effect of the aerodynamic mass is also studied and its non-inclusion is shown to lead to possible non-conservative results.

Numerical study of a twin box bridge deck with increasing gap ratio by using RANS and LES approaches

Twin box decks are becoming increasingly adopted in long span bridges due to their good aerodynamic performance with respect to the flutter instability. For small gaps between the decks they behave as a whole continuous body while, increasing the gap, strong dynamic interaction between the two occurs: the windward deck causes a turbulent wake that impinges on the leeward girder inducing unsteady aerodynamic forces. This complex behaviour makes the simulation of the aerodynamics of these structures a challenging task from the Computational Fluid Dynamic point of view. In this context, the present paper aims at investigating the capabilities and limitations of RANS and LES based simulations in reproducing the flow field organization around a twin box deck section. Different configurations, with increasing separation gap, are studied and compared with experimental data. Finally, the effects induced by the presence of barriers is investigated for the largest separation gap.

Application of Snapshot POD Analysis in Extracting Flow Structures around Bridge Decks

The long span bridges have been much more flexible and vulnerable to wind induced vibrations due to their continuing increase of span length. To understand the mechanism of wind induced vibrations and achieve better vibration mitigation methods, the complex flow around the bridge decks have been carefully studied using advanced numerical simulations or advanced experimental techniques. In the present paper, the snapshot proper orthogonal decomposition (SSPOD) is used to analyze flow structures obtained from numerical simulations and fluid visualization techniques. The results from numerical simulations based on computational fluid dynamics (CFD) are compared with those from numerical simulations and experiments in the literature and Particle Image Velocimetry (PIV) experiments in the present study. For a demonstration purpose, flow structures around a square cylinder and a twin box bridge deck section were analyzed using the SSPOD. Periodical flow patterns were found in the downstream of the bluff body sections. The revised frozen turbulence hypothesis is used in the present study to analyze the vortex evolution in four phase angles when taking the lift coefficient as a reference signal. Vortex structures are successfully extracted and the vortices are found moving at a constant speed, while the non-dimensional frequency of the vortex moving is the same as the Strouhal number. For the twin-box girders, periodical flow pattern changes are found in the downstream of the twin-box girders, as well.

Analysis and design procedure of hybrid long-span cable-stayed bridge using advanced composite material

An innovative solution is proposed in this paper by introducing a hybrid-type cable stayed bridge as a competent system to safely bridge very long spans. The new system leads into huge reduction in deck weight and its critical stresses in the pylon zones by using hybrid advanced composite deck. It also reduces the stiffness losses of the stay-cables due to the catenary’s action by using carbon fiber reinforced polymer cables. The paper proposes a proper consistent and systematic analysis and design procedure that optimize and precisely simulate the proposed bridge system. It recognizes the changes in structural behavior of the cable-stayed system, accordingly it clearly defines the ultimate and serviceability limit states for such new structural system in consistence with the limit state design philosophy. The design steps of the ADP represent a multi-scale design technique while the analysis steps characterize a multi-scale modeling technique. They represent the material design in the micro/macro-level, and accurate homogenization of the advanced composite components properties and evaluation of the resulting anisotropic characteristics and then, three-dimensionally simulate the hybrid bridge system involving all its nonlinearities. This paper investigates the performance of a new hybrid long-span cable-stayed bridge, which engages the use of advanced composite materials for the deck and the stay-cables, applying the analysis and design procedure. This design is scaled to match the general geometrical shapes, structural and aerodynamic characteristics of three of the world-longest cable-stayed bridges. What’s more, four advanced composite deck section models are proposed in this research. In order to study the performance of the referenced bridges, such as the natural frequencies, the deck top surface maximum vertical displacement, maximum Tsai-Hill failure function and the critical flutter velocity, three sets of parameters are investigated. The parameters include: (i) the micro level parameters-fiber fraction, (ii) the macro level parameters-Laminas Dominant Fiber Alignment and Laminate Thickness and (iii) the structure level parameters- cable radius.

Reynolds number effects on twin box girder long span bridge aerodynamics

This paper investigates the effects of Reynolds number (Re) on the aerodynamic characteristics of a twin-deck bridge. A 1:36 scale sectional model of a twin girder bridge was tested using the Wall of Wind (WOW) open jet wind tunnel facility at Florida International University (FIU). Static tests were performed on the model, instrumented with pressure taps and load cells, at high wind speeds with Re ranging from <TEX>$1.3{\times}10^6$</TEX> to <TEX>$6.1{\times}10^6$</TEX> based on the section width. Results show that the section was almost insensitive to Re when pitched to negative angles of attack. However, mean and fluctuating pressure distributions changed noticeably for zero and positive wind angles of attack while testing at different Re regimes. The pressure results suggested that with the Re increase, a larger separation bubble formed on the bottom surface of the upstream girder accompanied with a narrower wake region. As a result, drag coefficient decreased mildly and negative lift coefficient increased. Flow modification due to the Re increase also helped in distributing forces more equally between the two girders. The bare deck section was found to be prone to vortex shedding with limited dependence on the Re. Based on the observations, vortex mitigation devices attached to the bottom surface were effective in inhibiting vortex shedding, particularly at lower Re regime.

Accuracy of numerically evaluated flutter derivatives of bridge deck sections using RANS: Effects on the flutter onset velocity

In this article, the accuracy of standard computational fluid dynamics techniques and turbulence models in predicting the critical flutter speed of streamlined and bluff deck sections is investigated. It is well known that such numerical tools can provide inaccurate prediction of the flow field around bluff bodies which reflects in biases in their aeroelastic behavior. Aiming at systematically study the effects of such inaccuracies, in this article, six deck sections are analyzed by numerically extracting flutter derivatives and calculating the critical flutter speed for a set of representative test structures. It is shown that the flutter onset velocity is mainly underestimated but cases showing opposite behavior are identified and discussed. Two simulation strategies are adopted: the differences in the flutter mechanism between such two approaches are taken as an indicator of possible strong inaccuracies.

On the applicability of 2D URANS and SST k - ω turbulence model to the fluid-structure interaction of rectangular cylinders

In this work the practical applicability of a 2D URANS approach adopting a block structured mesh and Menter's SST k-ω turbulence model in fluid-structure interaction (FSI) problems is studied using as a test case a ratio B/H = 4 rectangular cylinder. The vortex-induced vibration (VIV) and torsional flutter phenomena are analyzed based on the computation of the out-of-phase and in-phase components of the forced frequency component of lift and moment coefficients when the section is forced to periodically oscillate both in heave and pitch degrees of freedom. Also the flutter derivatives are evaluated numerically from the same forced oscillation simulations. A good general agreement has been found with both experimental and numerical data reported in the literature. This highlights the benefits of this relatively simple and straightforward approach. These methods, once their feasibility has been checked, are ready to use in parametric design of bridge deck sections and, at a later stage, in the shape optimization of deck girders considering aeroelastic constraints.