Multi-tower Suspension Research Articles

Deformation and internal force of multitower suspension bridges: Numerical modeling and analytical analysis

An analytical model for predicting the deformation and internal forces of multitower suspension bridges is proposed in this paper. Equilibrium differential equations and deformation coordination equations are established based on deflection theory and coupling analysis of bridge components, in which the vertical stiffness contribution of girders and the longitudinal stiffness of all towers are considered. The equations for the deformation and internal forces of the bridge components, including towers, hangers, cables, and girders, are derived taking into account the live loads to which the multitower suspension bridge is subjected. The equations capture the mechanical characteristics of the bridge components, and the results can be obtained explicitly with the proposed model, notably improving the calculation efficiency. The applicability and efficiency of the proposed model are verified by two finite element model examples featuring two and three towers. A parametric analysis is performed to investigate the impact of major bridge parameters using the proposed model. The analysis results indicate that the longitudinal stiffness ratio of the mid-tower to the main cable plays an important role in the key design indices, including girder deflection and safety factor of anti-slipping of the saddle. A suitable stiffness range for the mid-tower is obtained by the proposed model.

Simplified Calculation Method of Middle Tower Effect of Multi-tower Suspension Bridge

In accordance with the “middle tower effect” design problem of multi-tower suspension bridges, the finite element method is currently used to find the reasonable range of the longitudinal stiffness of the middle tower through trial calculations. This method has disadvantages such as complex modeling and large calculation workload. Based on the principle of stiffness distribution, a simplified analysis method of the mid-tower effect of the multi-tower suspension bridge is proposed with the coordination of unbalanced force at the tower top and tower offset as the convergence target. By this method, the mid-span deflection-span ratio parameter and the anti-slip safety factor of the main cable at the saddle under the most unfavorable vehicle live load can be quickly obtained. Relying on the Oujiang River North Estuary Bridge project, the applicability of the method is verified, and the result has a slight deviation from the finite element solution, and the calculation accuracy meets the requirements. The influence of the longitudinal stiffness of the center tower and the friction coefficient between the main cable saddle slots on the middle tower effect of multi-tower suspension bridge is studied. (1) For an 800 m main span multi-tower suspension bridge, when the longitudinal stiffness of the middle tower is greater than 4 MN.m-1, the structure can basically satisfy the requirements of the vertical rigidity of the specification, and the deflection-span ratio is greater than 1/300; when the longitudinal rigidity of the middle tower is greater than 20 MN.m-1, the structure can meet the design requirements of the deflection-span ratio of 1/400. (2) When the longitudinal tower stiffness of the middle tower is 4 MN.m-1, the maximum tower deflection reaches 0.95 m; when the stiffness of the middle tower is greater than 80 MN.m-1, the maximum tower deflection of the middle tower is less than 0.3 m, but the unbalanced force at the top of the tower is greater than 27000 kN, which is unfavorable for the anti-skid requirements of the main cable at the top of the middle tower. (3) Increasing the friction coefficient of the cable saddle from 0.15 to 0.3 can effectively reduce the limiting effect of the middle tower effect on the value of the longitudinal stiffness of the bridge tower. Finally, through the response surface analysis method, based on the independent variable parameters such as the span of the main span, the number of lanes, the friction coefficient of the saddle groove, etc., the recommended formula for the longitudinal stiffness of the middle tower is given, which provides a quick solution method and check basis for the preliminary design of the middle tower of a multi-tower suspension bridge.

Gradual Deterioration Behavior of the Load-Bearing Strength of Main Cable Wires in a Suspension Bridge

The main cable is the primary load-bearing component of a long-span multi-tower suspension bridge. The interaction between a dead load, vehicle load, wind load, and the corrosion environment leads the main cable wire to exhibit tribo-corrosion-fatigue behaviors. This behavior causes wire wear and deterioration, as well as a reduction in the effective cross-sectional area. This leads to the gradual deterioration of the wire’s load-bearing strength and seriously affects the load-bearing safety of the main cable. In order to ensure the safety of suspension bridges, it is critical to investigate the gradual deterioration behavior of the main cable wire’s load-bearing strength. A wire tribo-corrosion-fatigue test rig was established to test the wire under different friction pairs (saddle groove or parallel wires). The cross-sectional failure area of the wire with different pairs was obtained by super-depth electron microscopy and calculation. The damage degree evolution model and the deterioration model of the wire load-bearing strength were established by combining the theory of damage mechanics and the finite element method. The results show that, as contact and fatigue loads increase, so does the cross-sectional failure area of the fatigue steel wire. The fatigue wire’s damage degree has a good quadratic function relationship with fatigue cycles. The damage degree of the wire increases and the load-bearing strength decreases with increasing contact load and fatigue load. The load-bearing strength of the wire changes little at the beginning and decreases with increasing fatigue cycles. The results have fundamental significance for the life prediction of the main cable wires of suspension bridges.

Research on flutter-mode transition of a triple-tower suspension bridge based on structural nonlinearity

As the typical span of suspension bridge increases and multi-tower suspension bridges are developed, the linear flutter theory cannot meet the design requirements of modern flexible bridges, and the study of nonlinear flutter of bridges becomes necessary. The author discovered the flutter-mode transition phenomenon in a full-bridge aeroelastic model wind tunnel test of the Maanshan Bridge; that is, the bridge vibration was transformed from first-order anti-symmetric torsion mode (A-T-1) to first-order symmetric torsion mode (S-T-1) and diverged when the flutter critical wind speed was approached. A vertical bending mode acted as a medium for energy transfer between A-T-1 and S-T-1. This phenomenon greatly increased the critical wind speed of flutter, and therefore it is interesting to study its mechanism. Starting from the nonlinear nature of the bridge structure itself, this paper discusses the mechanism of the flutter-mode transition phenomenon, and analyzes the typical characteristics of flutter-mode transition of Maanshan Bridge in depth. A nonlinear discrete mathematical model of the Maanshan Bridge is built, and the transition between the vertical bending mode and torsional mode of the bridge is realized. Adopting the Mathieu function theory and based on the single-degree-of-freedom vibration equation of the Maanshan Bridge corresponding to each mode, the evolution between A-T-1 and S-T-1 is realized, the mechanism of which is also explained.

Review on the Service Safety Assessment of Main Cable of Long Span Multi-Tower Suspension Bridge

The long-span multi-tower suspension bridge is widely used in the construction of river and sea crossing bridges. The load-bearing safety and anti-sliding safety of its main cable are directly related to the structural safety of a suspension bridge. Failure mechanisms of the main cable of a long-span multi-tower suspension bridge are discussed. Meanwhile, the tribo-corrosion-fatigue of main cable, contact, and slip behaviors of the saddle and service safety assessment of the main cable are reviewed. Finally, research trends in service safety assessment of main cable are proposed. It is of great significance to improve the service safety of the main cable and thereby to ensure the structural safety of long-span multi-tower suspension bridges.

Strand element analysis method for interaction between cable and saddle in suspension bridges

A stable cable-saddle connection relying on the frictional resistance is essential for the safety of suspension bridges. However, the frictional resistance cannot be adequately quantified due to the unclear contact forces, giving rise to a thorny anti-slip problem that particularly troubles the design of multi-tower suspension bridges. In this paper, the cable-saddle interactions are therefore studied by means of theoretical modeling and experimental verification. First, the feasibility and strategy of analyzing the PPWS (prefabricated parallel-wire strand) cable from the perspective of strand are demonstrated. The geometric and mechanical models of 37-, 61-, 91- and 127-wire strands are created, and a strand element analysis (SEA) method with recursive algorithm is then developed. Large-scale model tests are further conducted to investigate the cable-saddle frictional mechanism and to verify the SEA method. Finally, a typical multi-tower suspension bridge is taken as an example for an extended case study. The results show that the proposed SEA method can offer reliable predictions for the contact behavior of multi-strand cables in the saddle. The strand tensions at the critical slip state are unevenly distributed, while slight changes are present on the average tensions of the strand on both sides of the saddle. The use of two vertical plates can improve the frictional resistance by about 30%, and adopting a fewer-wire strand specification and arranging the strands in a higher pattern is also beneficial to improve the cable-saddle frictional resistance.

Numerical Analysis on Buffeting Performance of a Long-Span Four-Tower Suspension Bridge Using the FEM Model

The multi-tower suspension bridge (MTSB), which is a considerable choice for the cross-river and even cross-sea bridges, has attracted intensive attentions by researchers in recent years. However, the static and dynamic performance of the MTSB becomes more complicated due to its super long spans and the multiple middle towers. The wind-induced vibration becomes the critical issue when constructs the MTSBs due to their low rigidity. In this work, a finite element model (FEM) of a MTSB with four towers and three spans is presented. Several major parameters such as the stiffness of the main girder and the middle towers, the sag-to-span ratios, the self-excited forces, and the spectral model of turbulence are selected to investigate their effects on buffeting performance of the MTSB. Results show that the rigid main girder can decrease the buffeting displacements in lateral and torsional directions, while the vertical buffeting displacement significantly decreases with the increasing stiffness of middle towers. In addition, the buffeting displacements of the main girder increase with the decreasing sag-to-span ratio. Besides, it can be concluded that the self-excited forces should be considered and the turbulent power spectrum should be carefully chosen in analyzing buffeting responses of the MTSB.

Dynamic Response of Multitower Suspension Bridge Deck Pavement under Random Vehicle Load

Recently, the multitower suspension bridge has been widely used in long‐span bridge construction. However, the dynamic response of the deck and pavement system of the multitower suspension bridge under random vehicle load is still not clear, which is of great significance to steel‐bridge deck pavement (SBDP) design and construction. To reveal the mechanical mechanism of the steel‐bridge deck pavement of the multitower suspension bridge under traffic load, this paper analyzed the mechanical response of the pavement based on case study through the multiscale numerical approach and experimental program. Firstly, considering the full‐bridge effect of the multitower suspension bridge, the finite element model (FEM) of the SBDP composite structure was established to obtain key girder segments. Secondly, the influences of pavement layer, bending moment and torque, random traffic flow, and bridge structure on the stress of the girder segment were analyzed. Thirdly, the mechanical response of the pavement layer to the orthotropic plate under random vehicle load was studied. Finally, a full‐scale model of the experimental program was established to verify the numerical results. Results show that (1) the pavement layer reduced the stress of the steel‐box girder roof by about 10%. In the case of adverse bending moment and torque, the longitudinal and transverse stresses of the pavement layer were mainly concentrated in the stress concentration area near the suspender. Under the action of the random vehicle flow, the stress response of the pavement layer was increased by 40% compared with that under standard load. (2) Three‐tower and two‐span bridge structures have a great influence on the vertical deformation of the pavement layer under the action of vehicle load. Thus, the pavement material needs to have great deformation capacity. (3) The full‐bridge effect has a significant influence on the longitudinal stress of the local orthotropic plate, but a small influence on the transverse stress. (4) There is a good correlation between the experimental measurement results of the full‐size model and that of the numerical model. The research results can provide guidance for SBDP design and construction of the multitower suspension bridge.

Parametric analysis on flutter performance of a long-span quadruple-tower suspension bridge

Flutter is a critical point of concern in the wind-resistant design of long-span suspension bridges. As a novel realization, the multi-tower suspension bridge is becoming more and more popular in engineering communities. The aeroelastic stability of this kind of bridge attracts intensive attentions. To better understand the flutter performance of multi-tower suspension bridges, a long-span quadruple-tower suspension bridge (QTSB) with three main spans is designed in this study by extension from Taizhou Bridge, which is a triple-tower suspension bridge (TTSB) with double main spans. Considering the role of some important structural parameters in flutter performance, a parametric analysis is carried out for the long-span QTSB with comparisons to the TTSB that has the same length in each main span. The parameters of focus include sag-to-span ratio of the main cable, vertical and torsional rigidities of the girder, mass of the girder as well as longitudinal rigidities of middle towers. The analytical results indicate that increasing the torsional rigidity of the girder and longitudinal rigidities of middle towers can effectively improve the critical wind velocities. Changing the sag-to-span ratio or the mass of girder would cause complicated results, in which the transition of the dominant mode is observed. The mode transition phenomenon can be reasonably utilized in the wind-resistant design of a long-span QTSB.

Discrete analytical model for lateral mechanical behavior of cable-saddle system in suspension bridges

AbstractFrictional resistance, typically provided by the bottom and sides of saddle, is essential for counterpoising unbalanced cable tension between adjacent spans. In most practices, however, the friction from the saddle sides is ignored due to the lack of an effective calculation method of lateral forces, giving rise to serious anti-slip issues, especially for multi-tower suspension bridges. For this reason, the lateral forces between the main cable and saddle are studied in this paper. A similar formula of lateral force in specification is first investigated to reveal its theoretical basis and limitations. Considering each cable wire as an individual discrete body, an analytical model with recursive algorithm is then developed, which allows to calculate the contact forces layer by layer. Based on this, the effects of possible errors are quantified, and the sensitivity of lateral forces to key parameters, such as friction coefficient, extra pressure, arrangement and diameter of the wires, is subsequently discussed in detail. The results show that the existing formula evolved from the Janssen theory is insufficient for anti-slip assessment of the main cable. The transverse gap of saddle trough has a limited increase effect on the lateral force. As the wire arrangement widens, the lateral force grows rapidly and then approaches a certain value. The lateral force is negatively related with the friction coefficient, and the extra pressure can create great yet regular influence on the distribution of lateral pressure. Finally, the Taizhou Yangtze River Bridge is taken as a case example for an application of the proposed model. It is found that 32.2% of the total friction comes from the lateral friction when two vertical friction plates are used, confirming that the anti-slip capacity of cable-saddle system can be greatly improved by adequately utilizing the lateral friction.

Study on midtower longitudinal stiffness of three-tower four-span suspension bridges with steel truss girders

The determination of midtower longitudinal stiffness has become an essential component in the preliminary design of multi-tower suspension bridges. For a specific multi-tower suspension bridge, the midtower longitudinal stiffness must be controlled within a certain range to meet the requirements of sliding resistance coefficient and deflection-to-span ratio. This study presents a numerical method to divide different types of midtower and determine rational range of longitudinal stiffness for rigid midtower. In this method, influence curves of midtower longitudinal stiffness on sliding resistance coefficient and maximum vertical deflection-to-span ratio are first obtained from the finite element analysis. Then, different types of midtower are divided based on the regression analysis of influence curves. Finally, rational range for longitudinal stiffness of rigid midtower is derived. The Oujiang River North Estuary Bridge which is a three-tower four-span suspension bridge with two main spans of 800m under construction in China is selected as the subject of this study. This will be the first three-tower four-span suspension bridge with steel truss girders and concrete midtower in the world. The proposed method provides an effective and feasible tool for engineers to design midtower of multi-tower suspension bridges.

Seismic Response of Long-Span Triple-Tower Suspension Bridge under Random Ground Motion

Multitower suspension bridge is of different style compared to the traditional suspension bridge with two towers, and consequently the dissimilarity of static and dynamic behaviors is distinct. As a special case of multitower suspension bridge, two long-span triple-tower suspension bridges have been constructed in China and the seismic random response of triple-tower suspension bridges is studied in this paper. A nonlinear dynamic analysis finite element model is established in ABAQUS and the Python language is utilized to facilitate the preprocess and postprocess during the finite element analysis. The procedure for random response calculation of structures based on the pseudoexcitation method is presented, with the initial equilibrium state of structure considered, which may be ignored for long-span bridges during calculating of stochastic response. The stationary seismic random responses of triple-tower suspension bridge under uniform excitation in firm, medium, and soft soil conditions and under spatially varying excitation in soft soil are investigated. The distribution of RMS of random responses of displacements and internal forces of the stiffening girder and towers is presented and discussed in detail. Results show that spatially variable ground motions should be considered in the stochastic analysis of triple-tower suspension bridge.

Approximate Calculation for Deformation of Multi-Tower Suspension Bridges

This paper presents a method for solving tower deformation and girder deflection in multi-tower suspension bridges. An equivalent model is proposed to simulate a multi-tower suspension bridge in which the towers and main cables are treated as a series of springs. This model can be used for cases of live load acting on one or more spans , and the simple explicit formulas can be used to resolve deformation of the towers and girders as well as for the increment of horizontal cable force in the loaded span. The superposition principle can be used for live loads acting on more than one main span. This paper also presents a finite element model (FEM) of a multi-span suspension bridge with five towers and six spans to verify the analytical formula. Results calculated with the FEM show good agreement with those of the proposed method. This indicates that the proposed method is effective for the preliminary analysis and design of multi-tower suspension bridges.

Impact Analysis of Tower Number on Automotive Live Load Effect in Suspension Bridge

As a bridge with a large span, suspension bridge has obvious advantage in the current cross-sea engineering. In order to achieve longer span capacity, long-span multi-tower suspension bridge programs were repeatedly proposed. Due to the increase in the number of tower, the mechanical behavior would be inevitably different with the ordinary two-tower suspension bridge. For better grasp the difference of the mechanical properties, Midas civil 2011 is used to model to analyze. Suspension bridge models whose spans are 1080m with different towers (two, three, four, five, six,) are established to analyze the change in the mechanical properties under the action of vehicle load. The results show that the mechanical properties of multi-tower suspension bridge are quietly different from two-tower suspension bridge and with the increase in the number of bridge tower, the displacements of main girder and main tower have large difference. When the number of tower is more than or equal to four, multi-tower suspension bridges have little difference in the mechanical properties and that means multi-tower effect is not obvious.

Improved Particle Swarm Optimization-Based Form-Finding Method for Suspension Bridge Installation Analysis

In this paper, an improved particle swarm optimization (IPSO) method, which is based on standard particle swarm optimization (PSO) and a changing range genetic algorithm (GA), is proposed, and it is applied in the form-finding analysis of a suspension bridge installation. The new method has been integrated into the successive iteration method of the form-finding analysis, and it transfers the usual iterative process of form-finding analysis into a single objective optimization problem. The computation formulation and computer code of the IPSO have been developed and implemented, and benchmark examples are studied to test the performance of the IPSO method through numerical experiments. The results show that IPSO can be used as a viable solution methodology for the form-finding analysis in various initial, boundary, and complicated load conditions to overcome the limitations of the conventional Newton-Raphson (N-R) iterative method. Furthermore, compared with GA, PSO, and GA-PSO, IPSO has greater accuracy and efficiency. Finally, the method is applied in an actual form-finding analysis of a multitower suspension bridge (Yingwuzhou Yangtze River Bridge) to validate the practicality and feasibility of the IPSO-based method in engineering design. The case study indicates that IPSO provides superior convergent solutions for the analysis considered here when compared to the N-R method, and the computation time is affordable for large-scale engineering bridge construction design and analysis.

Influence Law of Middle Tower on Mechanical Performance of Three-Tower Self-Anchored Suspension Bridge

To multi-tower suspension bridge, reasonable design of middle tower is very important. In this paper, a three-tower self-anchored suspension bridge (TSSB) was taken as research background. The effect of middle tower stiffness and mass on static and dynamic performance of TSSB was discussed. Through dynamic characteristic analysis, we got the modes whose nature frequencies were affected obviously by middle tower stiffness. The seismic parameter analysis showed that rigid and light weight middle tower was benefit to seismic performance of TSSB. At last, this paper concludes that designer should consider static and dynamic performance of TSSB comprehensively in the design of middle tower.

Research on Parametric Modeling and Computing of Multi-Tower Suspension Bridge Based on ANSYS

Based on FEM program ANSYS and the OpenGL graphics, this paper develops the parametric modeling module and the computing module of the multi-tower suspension bridge, this module being embedded into the ANSYS system, and the parametric modeling module parameters can be entered by way of interface, which establish fast a multi-tower suspension bridge model. Calculation module can establish load conditions for the features of road bridge and specifications, in which multiple conditions can be defined and solved automatically. Post-processing part of the solution also for the results of the subtotals and select the output, so that the results of the output and finishing work has become more convenient and easier, and also the results can also be saved in word, excel and other different file types.

Center Tower Stiffness Study in Multi-Tower Suspension Bridge

The existence of center towers is the origin of performance difference between multi-tower suspension bridge and the traditional one, and longitudinal stiffness of the center tower is a decisive factor. Based on the finite element theory, the paper establishes numerical calculation model of multi-tower suspension bridge, and analyzes it’s static and dynamic performance variation by using different longitudinal flexural stiffness. Moreover, the factors that affect center tower stiffness are determined. Referring to judgment standards about usability and structure security given by existing research, the reasonable range of center tower stiffness is established. Besides, the paper tries to ascertain reasonable center tower stiffness by using the static mechanic performance of service phase as judgment standards.

Multi-Tower Effect Analysis of Long-Span Suspension Bridge

As a new bridge system, mechanics behavior study on long-span multi-tower suspension is also very deficiency. The existence of center towers is the origin of performance difference between multi-tower suspension bridge and the traditional one. Based on the Midas/Civil platform, the paper takes a three tower suspension bridge as project reference, establishes finite element models of suspension bridge, which the main span is longer than one kilometer and towers from two to seven. Moreover, the structural property is analyzed separately, which bending moment and displacement effect of girder and tower along with the tower number changes is considered. Natural frequency differences of the model bridges are also paid attention on.