Analysis Of Suspension Bridge Research Articles

A Simplified Approach for Dynamic Analysis of Suspension Bridges under Extreme Limit State

A Simplified Approach for Dynamic Analysis of Suspension Bridges under Extreme Limit State

Analytical model analysis of suspension bridges with tower-girder-connected dampers

Recently the tower-girder-connected damper has been utilized to suppress multi-mode vertical vortex-induced vibration (VIV) of long-span suspension bridges. In this paper, an analytical solution is proposed for the damping ratio of vertical bending modes of a single-span suspension bridge, with a vertical or/and a rotational damper mounted near the end of the stiffening girder, which significantly simplifies the design procedure for tower-girder-connected dampers on suspension bridges. The damping effect and the accuracy of the analytical solution are validated for Humen Bridge. It is found that both the vertical and rotational damper with an appropriate parameter selected can supply significantly additional damping ratio to multiple bending modes of the suspension bridge. The rotational and vertical dampers work in a similar way and provide nearly the same maximum additional damping ratio for each mode. In particular, for the first two symmetric modes, regions of reduced motion near the ends of the stiffening girder are developed due to the effects of cable geometry and elasticity, and this reduces the effect of the tower-girder-connected damper. Excluding these modes, the damper effect on a suspension bridge is similar to that on a tension beam with the same beam stiffness and horizontal tension forces.

Multimodal aeroelastic analysis of suspension bridges with aerostatic nonlinearities

Multimodal aeroelastic analysis of suspension bridges with aerostatic nonlinearities

FE Analysis of Suspension Bridges Based on Extended Deflection Theories with Extensible Hangers and Floating Girders

This paper presents extended deflection theories of multi-span continuous suspension bridges and their FE formulations using the energy method. The proposed deflection theories take into account effects of hanger extensibility, free sliding of main cables at the saddle, and floating girders. Suspension bridge elements consisting of main girder, main cable, and tower elements are then introduced and simplified FE formulations are rigorously proposed to solve the extended deflection theories. In order to demonstrate the validity and accuracy of the presented formulation, three/four-span suspension bridge models having regular and floating support conditions of the main girder are analyzed using the simplified FEMs, and the analysis results are compared with those by the unstrained length method, which is a sophisticated FEM. Finally, three virtual earth-anchored suspension bridge models are analyzed to explore the effects of hanger extensibility.

Numerical analysis of suspension bridges with box girders subjected to detonations

This paper focuses on the dynamic behavior of a typical three-span suspension bridge subjected to blast loads. Three-dimensional finite element models were established to simulate the blasting excavation of these structures using the explicit dynamic analysis code LS-DYNA. The explosive charge model was developed using the *LOAD_BLAST_ENHANCED tool in the LS-DYNA software. The accuracy of finite element models was validated against existing experimental and numerical results. The failure patterns and damage process of the bridge under explosive loading on the deck were analyzed, while the effects of mass and location of explosive charge were further explored. Dynamic responses such as displacement, stress, and strain were discussed and compared. Based on the computed results, the most critical location of the explosives was assessed. The results indicated the superior performance of the bridge against near-tower detonation over mid-span detonation. The deck exhibited disproportionate collapse due to very high charges of 5000 kg and 8000 kg TNT detonation at mid-span. The blast outcome generated on the bridge's components due to high charges from 1000 kg TNT to 2500 kg TNT at a standoff distance of 2 m was identified as partial collapse. Moderate charges of 250 kg TNT and 500 kg TNT at standoff distances of 2 m and 3 m led to plastic deformation without fracture of the bridge's component. Very high TNT charges at near-tower detonation caused only partial collapse. The severity of cable relaxation and detachment from the deck due to mid-span detonation exceeded the near-tower one.

Full long-term buffeting analysis of suspension bridges using Gaussian process surrogate modelling and importance sampling Monte Carlo simulations

Recent findings from full-scale measurements campaigns and analytical investigations of the design buffeting response of long-span bridges suggest that the assumptions adopted in most wind-resistant design guidelines are not strictly conservative. In such cases, a full long-term analysis is the most accurate alternative for reliability-based design. However, the application of such methodology becomes unfeasible due to the corresponding computational demand. Notably, many evaluations of the buffeting response are required, and time-consuming numerical integration is traditionally used to evaluate the long-term response. To overcome these drawbacks, this paper proposes a framework to increase the computational efficacy of long-term analyses for the wind-resistant design of long-span bridges by combining two strategies. First, the buffeting response is estimated with a Gaussian process regression that requires less time than the traditional multimodal buffeting response estimation. Then, long-term analysis is carried out using importance sampling Monte Carlo simulations that converge faster than the traditional analysis based on numerical integration. The computational framework is demonstrated in a case study of a proposed super-long suspension bridge subjected to loads induced by wind buffeting. The advantage of the proposed framework is verified, as it requires less than 1% of the computational demand of the traditional full long-term analysis.

Framework of vehicle-bridge coupled analysis for suspension bridges under refined vehicle modeling considering realistic traffic behavior

Long-span suspension bridges experience complex dynamic interactions with stochastic traffic, which has a critical impact on the design and safety assessment of bridges. In this study, a traffic-bridge interaction (TBI) framework is proposed for suspension bridge dynamics analysis by considering realistic traffic behavior and real vehicle characteristics. A stochastic traffic simulation model aiming to faithfully reproduce realistic traffic flow is developed by integrating the Monte Carlo approach and an intelligent driving model. The key parameters of the stochastic traffic model are input into the refined vehicle model established and the bridge model is built. The vehicle and bridge models are coupled by an interface contact method to obtain a complete TBI framework. The TBI framework is applied to a prototype long-span suspension bridge to fully investigate the effect of stochastic traffic flow loads on the vertical vibration of the bridge. Furthermore, the effect of stochastic traffic flow loads on the vertical displacement of a bridge is evaluated by varying key parameters in the TBI framework, such as traffic density and road roughness. The study provides a novel perspective on the refined dynamic analysis of suspension bridges under complex traffic conditions, which can further serve as a reference for the safety assessment of suspension bridges.

Response Spectrum Analysis of Suspension Cable Bridge and Tied Arch Bridge

Abstract—Bridges are recognition of a nation’s infrastructure. Bridges play an important role in connecting people, good and transports. A bridge’s close down can halt economic progress of any nation. Services those are no longer available can be simply completed with the help of bridges. Most advanced technology that are used for bridge design and construction are Building Information Modelling (BIM), Prefabrication and computer aided AI-based system. Various new construction materials are also being used as a replacement for traditional materials. A Tied-arch bridge is an arch bridge in which the outward-directed horizontal forces of the arch are borne as tension by a chord tying the arch ends, rather than by the ground or the bridge foundations. A Suspension bridge is a type of bridge in which deck is hung below suspension cables on vertical suspenders. Suspension Bridge consists of main span, side span, main cables, hanger ropes, pylons and deck. Tied arch bridge is type of bridge in which deck is below the arch and vertical suspender ropes. A tied-arch bridge is an arch bridge in which the outward horizontal forces of the arch caused by tension at the arch ends to a foundation are countered by equal tension of its own gravity plus any element of the total deck structure such great arch support. The arch have strengthened chord that run to a strong part of the deck structure or to independent tie-rods below the arch ends. This research presents the Response Spectrum analysis of Suspension Bridge and Tied-arch Bridge. The modelling is done using SAP 2000. Response Spectrum analysis is done and the deformation of both the bridges under dead load live load and earthquake load is studied. Axial force, Shear force Moment and Torsion values are observed and studied. Along with earthquake load vehicle load is also applied. According to IRC 006, vehicle loading of class 70R wheeled is applied. Keywords—Suspension Cable Bridge, Tied Arch Bridge, SAP 2000, Response Spectrum Analysis

Numerical Methods for Geometric Nonlinear Dynamic Analysis of Suspension Bridges Under Earthquake

ABSTRACT A reliable numerical procedure is proposed for the geometric nonlinear dynamic analysis of suspension bridges subjected to earthquake excitations. The geometric nonlinearities of cable members are captured by the catenary element derived from exact analytical expressions of elastic catenary, while the geometric nonlinearities of tower and girder members are predicted by nonlinear beam element which can undergo large deflections and rotations. An incremental-iterative solution based on Newmark-β direct integration and Newton–Raphson iteration is adopted for solving the nonlinear equation of motion. The results are compared with those generated by ANSYS to show the accuracy and efficiency of the proposed procedure.

Nonlinear torsional primary resonance analysis of suspension bridge with generalized configuration using mathematical model

Torsional vibration of long span suspension bridge can be commonly induced by various sources, and detailed investigation is required from both design and safety point of view. This study proposes a continuum model of the generalized suspension bridge using the Hamilton principle. This model can consider any inclination angle of main cables. The horizontal and vertical motions of main cables, and torsional motion of deck are considered individually in this model. The proposed model is verified by comparing its modal properties with those from a finite element model. The nonlinear primary resonances of the two lowest torsional modes are studied through multiple-scale method (MSM) under harmonic excitation. The effects of system parameters, such as inclination angle of hangers, sag-to-span ratio, tensile stiffness of main cable and torsional stiffness of deck, on the resonance responses are investigated in this study. Results show that, increasing inclination angle of main cable and torsional stiffness of deck can intensify the softening feature of the system. In contrast, increasing the sag-to-span ratio and tensile stiffness of main cable can strengthen the hardening feature.

Buffeting analysis of a suspension bridge under construction based on adjacent wind field data

Buffeting analysis of long-span suspension bridge has received considerable attention in the past decades. In current practice, it is challenging to determine the wind turbulence spectrum at bridge site accurately if the field measured wind data is insufficient. To address this issue, this paper proposes a novel framework for bridge buffeting responses evaluation. The framework first proposes an approach based on long short-term memory (LSTM) network to compose long term data on wind characteristics for estimating the wind turbulence spectrum at bridge site via leveraging the wind field data acquired from the long-term monitoring data at adjacent locations (e.g., nearby meteorological station and bridges). Afterwards, the obtained wind spectrum at bridge site will be utilized for the buffeting analysis. To demonstrate the usage and performance of the proposed framework, a long-span cross-sea suspension bridge under construction is used throughout the paper as an example to investigate the buffeting-induced responses. The analysis results show that buffeting responses are significantly affected by wind speed and the identified bridge frequencies are consistent with the design frequencies.

Modeling and modal analysis of suspension bridge based on continual formula method

A continnum model is developed for the dynamic analysis of a suspension bridge with inclined main cables and hangers, based on incremental Lagrangian formulation and kinematics theories. The static equilibrium equations are derived from a shape-finding method followed by the equations of motion. Comparison of modal analysis results of the proposed model and the finite element method demonstrates the accuracy of the proposed modelling technique.Modal analysis is further conducted with variations of the following system parameters, i.e. inclination angle of main cable, the ratio of flexural stiffness of deck in the vertical and lateral directions, the ratio of vertical flexural stiffness of deck and tensile stiffness of cable, and torsional moment of inertia of cross-section of deck. Results show that the difference of eigenfrequencies within the eigenfrequency cluster is smaller for a suspension bridge with vertical cables than that with inclined cables. Phenomena of crossover and veering of eigenfrequency loci of the bridge system are observed. The mechanism of such phenomena is further studied with the help of a sectional bridge model. The effect of variation of stiffness matrix of bridge system on the eigenfunction is studied. The condition for crossover and veering of the eigenfrequency loci of this bridge model is identified. It is noted that veering can affect the modal property of the system by coupling two involved modes. This effect should be carefully examined during the design of the suspension bridge.

Effect of the main cable bending stiffness on flexural and torsional vibrations of suspension bridges: Analytical approach

In the design and analysis of suspension bridges, the main cables are conventionally treated as flexible ropes transmitting only tensile loads. Large-span suspension bridges used in new railways require the main cables to be designed with larger cross-sections and higher bending stiffness. The latter can affect the dynamic behavior of the entire bridge. To this end, the analytical expression of the main cable's shape is established in this paper, considering the bending stiffness under the dead loads. According to the D'Alembert principle, the partial differential equations of vibration of the cable in the suspension bridge are derived and solved. Finally, frequencies and mode shapes of the flexural and torsional vibrations of the bridge are calculated considering the main cable bending stiffness. To verify the feasibility of the proposed method, a case study of the Wufengshan Yangtze River Bridge is investigated. The analytical results are compared with the finite element solutions obtained by the ANSYS software, with good agreement achieved. By using the proposed method, the effect of the main cable bending stiffness on the flexural and torsional vibrations of suspension bridges is analyzed. The results show that the cable bending stiffness has a larger effect on flexural vibrations than torsional vibrations. The bridge's frequencies become higher with the increase of cable bending stiffness. Besides, as the order of vibration mode or the ratio of the bending stiffness of cables to the beam increases, the effect of main cable bending stiffness gets greater.

Analysis of suspension bridges in construction and completed status considering the pylon saddles

A nonlinear analysis approach is newly proposed to obtain the configurations of suspension bridges in both construction and completed status, and the effects of the pylon saddles are considered in this algorithm. With the expression determining the position of the cable’s attachment point on the saddle, the approach can automatically take the saddle into account in the analysis process. In order to verify the accuracy, the analytical methods, which respectively describing the whole bridge completed status and the main cable completed status, are established to obtain the comparative results. Finally, a bridge case is adopted to illustrate the application of the proposed approach. The comparative analysis shows that the proposed algorithm and analytical method can obtain the results with high consistence. What is more, the results indicate that the saddles can significantly change the effective length of the cable, which can have a non-negligible effect on the bridge’s configuration. With the proposed scheme, the accuracy of the calculated parameters can be further improved for the suspension bridge.

Fragility surfaces for multi-hazard analysis of suspension bridges under earthquakes and microbursts

The flexible nature of long-span suspension bridges increases their vulnerability to dynamic excitations such as winds and earthquakes. Non-stationary and transient wind events such as microbursts have the potential to create even more damage to these flexible structures. The problem becomes even more apparent when a structure is expected to undergo multiple extreme events. This paper aims to present a multi-hazard framework that assesses the vulnerability of a suspension bridge to earthquake and extreme wind events. For this purpose, specific damage states for wind and earthquake have been defined. Then, fragility curves and surfaces are generated to estimate the exceedance probability of different damage states throughout the structure as it undergoes multiple extreme events. The probability convolution theory is then used to assess the annual probability of failure considering the likelihood of occurrence of damage and likelihood of occurrence of each of the extreme events. The proposed framework will provide a meaningful procedure to calculate and communicate the risks from multiple extreme events on suspension bridges.

Unstrained length-based methods determining an optimized initial shape of 3-dimensional self-anchored suspension bridges

Two robust methods, a Generalized Target Configuration Under Dead Loads (GTCUD) method and a simplified analytical method are developed for 3D analysis of suspension bridges. These methods provide an optimized initial state for 3D suspension bridges under dead loads. The current study makes application to 3D self-anchored suspension bridges with spatially curved main cables and initial cambers of the main girder. Furthermore, the unstrained length method (ULM) based on the unstrained lengths is applied to the bridge structure using two procedures. Finally, it is demonstrated through a bridge example having vertical cambers that the proposed analysis methods can indeed provide an optimized initial solution by showing that both schemes lead to practically identical initial configuration with localized small bending moment distributions.

悬索桥竖向自由振动的传递矩阵解

A transfer matrix algorithm was proposed for the solution of vertical free vibration of suspension bridges. First, a solution scheme was presented for the governing differential equation of vertical free vibration of suspension bridges, in which the analytic expression of structural free vibration was deduced directly. On this basis, the transfer matrix of the vertical free vibration was obtained. With this method, the problem of vertical free vibration of both the uniform-cross-section and the nonuniform-cross-section suspension bridges was studied. The research results indicate that the transfer matrix algorithm is efficient for the analysis of the vertical free vibration of suspension bridges, and has specific advantages in dealing with the nonuniform-cross-section problem. The work makes a good reference for the dynamic analysis of suspension bridges in the concept design stage.

Effects of aerodynamic interference on the iced straddling hangers of suspension bridges by wind tunnel tests

The wind-induced vibration of suspension bridge hangers may be ascribed to hanger icing. The aerodynamic characteristics of the iced straddling hangers of suspension bridges under various working conditions are analyzed in this paper via wind tunnel experiments. The analysis results show that the aerodynamic characteristics of leeward hangers are greatly influenced by the varying thicknesses of B- and D-shaped ice and suggest that lift force must be considered in the static analysis of suspension bridges. The hanger spacing of A × B = 8D × 4D, where the aerodynamic characteristics of leeward hangers with both B- and D-shaped ice are stable, can be used as reference for designers. The change in the aerodynamic coefficients of leeward hangers must also be considered when analyzing the stability of the straddling hangers of suspension bridges because iced hangers have different relative positions and the Strouhal number of leeward hangers rapidly fluctuate when the relative angle (β) is 4°. The shielding effect of windward hangers on leeward hangers with B- and D-shaped ice is most visible at a wind attack angle of −24°, and the drag coefficients of D-shaped iced hangers are obviously less than those of B-shaped iced hangers. The results of static analysis of suspension bridges are produce on non-conservative side results when hanger icing is disregarded. The findings of this study work can be used as references in the structural design and wind-resistance designs of suspension bridges with straddling hangers.

Flutter reliability analysis of suspension bridges based on multiplicative dimensional reduction method

A reliability analysis method is proposed in this paper based on the maximum entropy (MaxEnt) principle in which constraints are specified in terms of the fractional moments instead of integer moments. Then a multiplicative dimensional reduction method (M-DRM) is introduced to compute the fractional moments. The method is applicable for both explicit and implicit limit state functions of complex structures. After two examples illustrate the accuracy and efficiency of this method in comparison to the Monte Carlo simulation (MCS), the method is used to analyze the flutter reliability of suspension bridge. The results show that the empirical formula method in which the limit state function is explicitly represented as a function of variables is only a too conservative estimate for flutter reliability analysis but is not accurate adequately. So it is not suitable for reliability analysis of bridge flutter. The actual flutter reliability analysis should be conducted based on a finite element method in which limit state function is implicitly represented as a function of variables. The proposed M-DRM provide an alternate and efficient way to analyze a much more complicated flutter reliability of long span suspension bridge.

Continuum Model for Static and Dynamic Analysis of Suspension Bridges with a Floating Girder

Continuum Model for Static and Dynamic Analysis of Suspension Bridges with a Floating Girder