Three-tower Suspension Bridge Research Articles

Large deformation assessment of three-tower suspension bridges: An enhanced analytical model and solution algorithm

An enhanced nonlinear approach is proposed in this study to address the limitations of traditional deflection theory in analyzing large deformations of three-tower suspension bridges. In this approach, the three-tower suspension bridge is simplified as two quasi-independent bridges for analysis, and detailed considerations are given to the vertical and longitudinal deformations of the main cable, which produce the expression for the relationship between the cable's internal force and deformations. By employing the complementary energy principle and variational calculus, the nonlinear differential equations describing bridge deformations are then established. To ensure the displacement continuity at the middle tower, this paper proposes the use of Chebyshev polynomials to approximate the solutions of the differential equations, and the weighted residual method is then used to transform these differential equations into algebraic equations. On this basis, the developed nonlinear adjustment optimization algorithm enables efficient solving of the nonlinear equation and thus determination of bridge deformation under various load conditions. The accuracy and effectiveness of the proposed scheme are validated through the analysis of two suspension bridges with equal and unequal spans. Finally, the extended applications of the proposed scheme on the other type of multi-span suspension bridges are introduced for further applications.

Study on tension control method of anchor span for three tower suspension bridge

The traditional method of adjusting cable force doesn't effectively address the coupling relationship between the splay saddle's deflection angle and the anchor span's tension. To safely and efficiently adjust the tension of the anchor span and the deflection angle of the splay saddle on suspension bridges, this study examines the effects of temperature variations and side span sag deviation on the splay saddle's deflection angle, considering the rotation stiffness of the splay saddle. On this basis, combined with the engineering practice of a three-tower suspension bridge, a simplified method of cable force adjustment considering the rotation effect of the splay saddle is proposed. Practical results indicate that temperature fluctuations are the primary cause of splay saddle deflection. A relationship has been derived between temperature changes, side span sag deviation, and the deflection angle of the splay saddle. This relationship has been validated for its accuracy and correctness in real-world engineering scenarios. The introduced simplified method for adjusting anchor span tension can notably decrease the number of required adjustments, offers precise cable tensioning, and effectively prevents cable strand slippage. This method is advantageous due to its straightforward application, time-saving nature, and enhanced safety.

Reliability-based assessment of reasonable mid-tower lateral stiffness for a three-tower suspension bridge

A reasonable lateral stiffness of the bridge mid-tower should ensure that the deflection-to-span ratio and sliding resistance coefficient satisfy the design requirements. However, if this stiffness is determined by the deterministic parametric analysis, the above two verification indices may exceed the threshold due to the randomness of the high-dimensional structure and load parameters. To satisfy the structural safety requirements of a three-tower suspension bridge during its design life, this study proposes a method to quickly and accurately evaluate the reliability indices of the deflection-to-span ratio and sliding resistance coefficient of the three-tower suspension bridge. Based on advanced first-order second-moment, the proposed method transforms the reliability problem into an optimization problem with constraint functions, uses the single-cable theory to establish the limit state function, and combines the manta ray foraging optimization algorithm and penalty function to derive the reliability index. The effectiveness of the proposed method is verified by performing Latin hypercube sampling for an examplary three-tower suspension bridge. These results prove that the new technique avoids tedious finite element simulation and surrogate model fitting, ensuring the accuracy of the reliability index while improving the calculation efficiency. The study further identifies critical structural parameters by parametric analysis. Based on the inverse reliability, the dimensionless stiffness range for the mid-tower with the randomness of the parameters is derived, and the preliminary design method of the lateral stiffness of the mid-tower based on the reliability is established.

Energy-based analysis of 3D wind-induced-flutter mechanism of a three-tower suspension structure

Three-tower suspension bridges have broad application prospects in water-crossing and island-linking projects. The large span, flexibility, and slight rigidity of the central tower of three-tower suspension bridges make them extremely sensitive to wind action and wind-induced flutter, which mechanisms have not been clarified yet. In this paper, the Ma’anshan Yangtze River Bridge in China was taken as an example, and the mechanism of its flutter instability was analyzed from the flutter energy standpoint. Upon formulating the main principles of the three-dimensional (3D) flutter analysis of bridges, the respective method was proposed and applied to the bridge under study, yielding the main vibration modes and the movement decoupling in the time domain analysis. The relevant energy calculation was programmed for the 3D flutter energy analysis of the bridge under study. At the flutter onset, the energies of the torsional and heaving movement systems slightly increased and decreased, respectively, the latter being converted into the former and resulting in its divergence. Aerodynamic damping was the main factor in the system stability, while aerodynamic stiffness slightly influenced its flutter instability pattern.

Predicting the maximum deflection and girder-end rotation of a three-tower suspension bridge under live load: An analytical algorithm

The maximum deflection and girder-end rotation of the stiffening girder for a suspension bridge are key stiffness indicators that need to be verified to secure the structure's performance during the operation. The overall vertical stiffness of a three-tower suspension bridge is significantly reduced due to the mid-tower being constrained in the horizontal direction of the main cable in the main spans with large sag-to-span ratios. Therefore, rapid and accurate evaluation of the vertical stiffness of the three-tower suspension bridge is quite problematic. Based on the deflection theory, this study proposed an analytical expression of the deflection and girder-end rotation of a three-tower suspension bridge. The deflection and girder-end rotation were used as the optimization objectives. Combining the harmony search algorithm with the “death-penalty” function approach, the most unfavorable loading conditions and corresponding maximum values were obtained. The effectiveness of the proposed method was verified by finite element modeling of an exemplary-three-tower suspension bridge. The proposed method had high accuracy, improved calculation efficiency, and wide applicability, which made it lucrative for selecting the optimal structural parameters in the preliminary design of suspension bridges. The dead-to-live load ratio, cable sag-to-span ratio, mid-tower lateral stiffness, side-to-main span ratios, cable’s axial stiffness, and deck’s flexural rigidity were further analyzed. The results indicated that increasing the dead-to-live load ratio and mid-tower stiffness was the most effective method to control maximum deflection and girder-end rotation of stiffening girders.

Main Cable Shape of Short Span in Three-Tower Suspension Bridge

The main cable is one of the essential components of the suspension bridge; accurate calculation of the main cable shape is crucial in constructing a suspension bridge. This paper solves the challenge of the main cable shape for a “short span” in a three-tower suspension bridge by the analytical method of the ideal bridge shape and empty cable shape of the main cable. Feng Chu suspension bridge Xiangyang is taken as a prototype. This paper discusses the main cable shape and anchor-span tension control method in the construction stage of the main cable analyzes the deflection and stress characteristics of the main tower in the hoisting stage of the stiffening beam. The influence of pushing the cable saddle on the main tower provides accurate control of the main cable shape. Design sag and span of the main cable were taken as the known quantities. The sectional catenary equation is used to deduce and iteratively calculate the completed bridge alignment. The completed bridge alignment was taken as the target, the iterative calculation method of main cable bridge alignment and empty cable alignment compiles the corresponding program with MATLAB software. The calculation values of the unstressed length of the main cable, the pre-deflection of the saddle, and the mid-span sag of the empty cable are compared with the design values. The results show that the calculation accuracy of the program is high.

Study of seismic-responses and semi-active control of Taizhou Bridge under multi-support excitation

PurposeIn order to make sure of the safety of a long-span suspension bridge under earthquake action, this paper aims to study the traveling wave effect of the bridge under multi-support excitation and optimize the semi-active control schemes based on magneto-rheological (MR) dampers considering reference index as well as economical efficiency.Design/methodology/approachThe finite element model of the long-span suspension bridge is established in MATLAB and ANSYS software, which includes different input currents and semi-active control conditions. Six apparent wave velocities are used to conduct non-linear time history analysis in order to consider the seismic response influence in primary members under traveling wave effect. The parameters α and β, which are key parameters of classical linear optimal control algorithm, are optimized and analyzed taking into account five different combinations to obtain the optimal control scheme.FindingsWhen the apparent wave velocity is relatively small, the influence on the structural response is oscillatory. Along with the increase of the apparent wave velocity, the structural response is gradually approaching the response under uniform excitation. Semi-active control strategy based on MR dampers not only restrains the top displacement of main towers and relative displacement between towers and girders, but also affects the control effect of internal forces. For classical linear optimal control algorithm, the values of two parameters (α and β) are 100 and 8 × 10–6 considering the optimal control effect and economical efficiency.Originality/valueThe emphasis of this study is the traveling wave effect of the triple-tower suspension bridge under multi-support excitation. Meanwhile, the optimized parameters of semi-active control schemes using MR dampers have been obtained, providing relevant references in improving the seismic performance of three-tower suspension bridge.

Static characteristics analysis of three-tower suspension bridges with central buckle using a simplified model

Compared with traditional two-tower suspension bridges, three-tower suspension bridges have to face challenges caused by the mid-tower effect, which requires the stiffness of the mid-tower satisfying two contradictory parameters, the deflection-to-span and the saddle sliding resistance coefficient, simultaneously. Meanwhile, the central buckles are often utilized to reduce the live load deflection and the torsional vibration caused by wind in two-tower suspension bridges. This study proposes an analytical model for predicting the structural responses of three-tower suspension bridges with central buckle under vehicle loads and examines the effect of the central buckle on suppressing the mid-tower effect. The analytical model simplifies the bridge as a series of cables with horizontal spring constraints. The validation analysis based on the structural parameters of the Yingwuzhou Yangtze River Bridge using the nonlinear finite element method demonstrates that the error of the proposed model does not exceed 5%. The parametric investigations show that the central buckle can significantly improve the performance of three-tower suspension bridges by enhancing their stiffness and reducing the unbalanced tension of the main cable on both sides of the mid-tower. Three-tower suspension bridge with central buckle has a much wider feasible mid-tower stiffness range than that of the traditional three-tower suspension bridges, and the critical dead-to-live load ratio for the feasible dimensionless stiffness range has decreased from 6.7 to 4.4.

Gravity stiffness of a three-tower suspension bridge: Analytical solution via double-span bridge reduction to a single-span one with elastic constraints

Suspension bridge’s main cable under live load undergoes deformation depending on its gravity stiffness, i.e., work done against gravity under the initial dead load. In three-tower suspension bridges (3TSB), the middle tower's effect on the main cable's gravity stiffness is crucial but hard to assess. In this paper, the 3TSB model was simplified to the 2TSB with elastic constraints. The main cable shape was then calculated via the ratio between the simply supported beam's bending moment and the horizontal force component. The 2TSB model results were used to derive the 3TSB main cable's deflection using the middle tower's stiffness under vertical load. The analytical formula for gravity stiffness of 3TSB was derived by matching the latter with the simply supported beam's deflection formula. For a case-study 3TSB with main spans of 248 m + 1060 m + 1360 m + 380 m, analytical predictions were verified by FEM numerical results obtained via ANSYS. Linear relationships between live load and increments of the main cable's deflection and horizontal force component were derived. Besides, the main cable's deflection under live load can be reduced by increasing its sag-to-span ratio and cross-sectional area.

Fatigue reliability assessment of a three-tower four-spansuspension bridge under stochastic traffic loads

This paper aims to study the fatigue performance of three-tower four-span suspension bridges. For this purpose, 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 taken as an example in this study. This will be the first three-tower suspension bridge with steel truss girders in the world. This paper uses a random traffic load model to evaluate the fatigue reliability of the orthotropic steel bridge decks of three-tower four-span suspension bridges. In the study traffic load is simulated by random variables, and Monte Carlo simulation method is used to calculate the fatigue reliability index of the steel bridge deck. The parametric analysis is also carried out to clarify the influence of traffic growth rate, target reliability index and axle lateral distribution coefficient. It is found that the growth of traffic volume has the greatest impact on the evaluation results of the fatigue life, and the growth of traffic volume can result in a decrease of fatigue reliability of orthotropic steel bridge decks. The research results can provide a reference for the fatigue life and reliability assessment of three-tower four-span suspension bridge.

Cable spring effect and its longitudinal restraint stiffness on towers

On cable-stayed or suspension bridges, the cable spring concept is used to describe the influence of the main cable on the deflection of the towers. A formula for the longitudinal constraint stiffness of a cable spring was derived based on the catenary equation and two examples (construction stage and completion stage) were assessed introduced for verification. The results showed that the proposed catenary stiffness formula provides satisfactory accuracy. The stiffness value is related to the horizontal and vertical components at one end of the main cable and the weight of the cable when the unstressed length is an invariant constant. Furthermore, the stiffness value is closely related to the sag–span ratio of one span. Thus, in a two-tower suspension bridge, the longitudinal restraint stiffness of a side-span cable to the tower is much larger than the corresponding stiffness of the mid-span. In a three-tower suspension bridge, with two main spans and two side-spans, the cable spring effect plays an important role in the total stiffness of the mid-tower. The developed equations can be used for preliminary estimates of longitudinal displacement.

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.

Aerostatic instability mode analysis of three-tower suspension bridges via strain energy and dynamic characteristics

Multispan suspension bridges make a good alternative to single-span ones if the crossed strait or river width exceeds 2-3 km. However, multispan three-tower suspension bridges are found to be very sensitive to the wind load due to the lack of effective longitudinal constraint at their central tower. Moreover, at certain critical wind speed values, the aerostatic instability with sharply deteriorating dynamic characteristics may occur with catastrophic consequences. An attempt of an in-depth study on the aerostatic stability mode and damage mechanism of three-tower suspension bridges is made in this paper based on the assessment of strain energy and dynamic characteristics of three particular three-tower suspension bridges in China under different wind speeds and their further integration into the aerostatic stability analysis. The results obtained on the three bridges under study strongly suggest that their aerostatic instability mode is controlled by the coupled action of the anti-symmetric torsion and vertical bending of the two main-spans\' deck, together with the longitudinal bending of the towers, which can be regarded as the first-order torsion vibration mode coupled with the first-order vertical bending vibration mode. The growth rates of the torsional and vertical bending strain energy of the deck after the aerostatic instability are higher than those of the lateral bending. The bending and torsion frequencies decrease rapidly when the wind speed approaches the critical value, while the frequencies of the anti-symmetric vibration modes drop more sharply than those of the symmetric ones. The obtained dependences between the critical wind speed, strain energy, and dynamic characteristics of the bridge components under the aerostatic instability modes are considered instrumental in strength and integrity calculation of three-tower suspension bridges.

An analytical algorithm for reasonable central tower stiffness in the three-tower suspension bridge with unequal-length main spans

Three-tower suspension bridges with unequal-length main spans more easily adapt to different terrain features and therefore, have broader application prospects. However, due to the unique “central tower effect” of the three-tower suspension bridge, it is required that the lateral stiffness of the central tower in the longitudinal direction of the bridge girder should be neither too large nor too small. To calculate the reasonable range for the central tower stiffness in the three-tower suspension bridge with unequal-length main spans, this study proposes an analytical algorithm based on the segmental catenary theory. Firstly, hanger tensile forces under the joint action of dead and live loads are calculated. Next, the governing equations for the main cable shape of each span are constructed for the following conditions: closure of elevation difference, closure of span length, moment balance of splay saddle, and conservation of unstrained length of the main cable. The solutions of the derived set of simultaneous equations are obtained for (i) deflection-to-span ratio limit of the stiffening girder and (ii) anti-slip control between the main cable and saddle conditions, which yield the lower and upper limits of reasonable stiffness of the central tower, respectively. This study discusses a three-tower suspension bridge spanned as 248 m + 1060 m + 1360 m + 380 m. The calculation is performed for the two cases of the live load application: (i) to the longer main span and (ii) to the shorter main span. The results obtained proved the feasibility and effectiveness of the proposed algorithm. The following findings are reported: The upper and lower limits of reasonable central tower stiffness are derived from the above two cases, respectively. Therefore, it is not sufficient to consider only the former case when calculating the central tower stiffness of the three-tower suspension bridge with equal-length main spans. The dead-to-live load ratio and friction coefficient between the main cable and saddle also strongly influence the central tower stiffness: their increase can expand the reasonable range of the latter but if they are too small, no such optimization can be provided.

Mechanical performance study and parametric analysis of three-tower four-span suspension bridges with steel truss girders

This paper aims to study the mechanical performance of three-tower four-span suspension bridges with steel truss girders, including the static and dynamic characteristics of the bridge system, and more importantly, the influence of structural parameters including the side-main span ratio, sag-to-span ratio and the girder stiffness on key mechanical indices. For this purpose, 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 taken as an example in this study. This will be the first three-tower suspension bridge with steel truss girders in the world. The mechanical performance study and parametric analysis are conducted based on a validated three-dimensional spatial truss finite element model established for the Oujiang River North Estuary Bridge using MIDAS Civil. It is found that a relatively small side-main span ratio seems to be quite appropriate from the perspective of mechanical performance. And decreasing the sag-to-span ratio is an effective way to reduce the horizontal force subjected to the midtower and improve the antiskid safety of the main cable, while the vertical stiffness of the bridge will be reduced. However, the girder stiffness is shown to be of minimal significance on the mechanical performance. The findings from this paper can be used for design of three-tower suspension bridges with steel truss girders.

Feasible Range for Midtower Lateral Stiffness in Three-Tower Suspension Bridges

Feasible Range for Midtower Lateral Stiffness in Three-Tower Suspension Bridges

Wind tunnel investigation on flutter and buffeting of a three-tower suspension bridge

The Maanshan Bridge over Yangtze River in China is a new long-span suspension bridge with double main spans of 2x1080 m and a closed streamline cross-section of single box deck. The flutter and buffeting performances were investigated via wind tunnel tests of a full bridge aeroelastic model at a geometric scale of 1:211. The tests were conducted in both smooth wind and simulated boundary layer wind fields. Emphasis is placed on studying the interference effect of adjacent span via installing a wind deflector and a wind separating board to shelter one span of the bridge model from incoming flow. Issues related to effects of mid-tower stiffness and deck supporting conditions are also discussed. The testing results show that flutter critical wind velocities in smooth flow, with a wind deflector, are remarkably lower than those without. In turbulent wind, torsional and vertical standard deviations for the deck responses at midspan in testing cases without wind deflector are generally less than those at the midspan exposed to wind in testing cases with wind deflector, respectively. When double main spans are exposed to turbulent wind, the existence of either span is a mass damper to the other. Furthermore, both effects of mid-tower stiffness and deck supporting conditions at the middle tower on the flutter and buffeting performances of the Maanshan Bridge are unremarkable.

Seismic performance and its favorable structural system of three-tower suspension bridge

Due to the lack of effective longitudinal constraint for center tower, structural stiffness of three-tower suspension bridge becomes less than that of two-tower suspension bridge, and therefore it becomes more susceptible to the seismic action. By taking a three-tower suspension bridge-the Taizhou Highway Bridge over the Yangtze River with two main spans of 1080 m as example, structural dynamic characteristics and seismic performance of the bridge is investigated, and the effects of cable\'s sag to span ratio, structural stiffness of the center tower, and longitudinal constraint of the girder on seismic response of the bridge are also investigated, and the favorable structural system is discussed with respect to seismic performance. The results show that structural response under lateral seismic action is more remarkable, especially for the side towers, and therefore more attentions should be paid to the lateral seismic performance and also the side towers. Large cable\'s sag, flexible center tower and the longitudinal elastic cable between the center tower and the girder are favorable to improve structural seismic performance of long-span three-tower suspension bridges.

Risk Prevention Measures for Three-Tower and Four-Span Suspension Bridge under Vehicle Fire

Risk prevention measures were put forward about vehicle burning in operating periods for three-tower and four-span suspension bridge, combining with the characteristics of bridge vehicle burning accident. The article set up a traffic reporting system of the tankers for a bridge, and determined the report system of tankers across the bridge. Tankers should passed in the middle of the lane near the median under the guidance of bridge manager. Significant indicators were set on both ends of the bridge, so that vehicles could shunt rapidly in extreme fire conditions. Department of public security, fire control, transportation, bridges management center should get together to establish accident emergency rescue leading group, and formulated the security system of fire resistance and rescue organization for YingWuzhou Yangtze river bridge. Video monitoring alarm system and fire control facilities were set up in side pier, side tower, middle of the main span and the middle tower, which provided reliable and prevention measures for bridge operation.

Aerodynamic Stability of a Three-Tower Suspension Bridge during Erection via Aeroelastic Model Test

As a new long-span suspension bridge with double main spans and a typical closed streamline cross-section of single box deck, the flutter performance of the Maanshan Bridge during erection was investigated via a full bridge aeroelastic model test. Critical flutter wind speeds of 13 testing cases with different percentage of deck completion are much higher than the flutter checking wind speeds, and the bridge is hence proven to be stable enough during erection in aerodynamics. The case with the percentage of deck completion of 86.4% gets the lowest flutter critical wind speed, perhaps because frequency ratio gets the minimum value at this case.