Four-span Suspension Bridge Research Articles

Nonlinear static solution of suspension bridge formulated from a surrogate model with secant stiffness of suspension cables

Explicit analytical solution may offer great convenience for the design and parametric study of suspension bridges. However, the nonlinear behavior of suspension cable exacerbates the difficulty of such theoretical derivation. Adopting secant stiffness is an effective way to deal with the nonlinearity of the cable, but the crux is how to find its deformed state under external loading. The strategy of this study is primarily targeted at a typically arranged three-span suspension bridge. It starts from formulating the basic form of nonlinear stiffness of suspension cables by setting the elastic stiffness and geometric stiffness in series, then a surrogate model is accordingly established with the nonlinear springs to replace the mid-span and side-span cables. The deformed state of the surrogate model subjected to the specified external load cases will be found by restricting and releasing its tower tops, and thus the analytical formula of the secant stiffness can be obtained. Consequently, the nonlinear static solution of suspension bridge, including force and deformation changes in the cables and towers, can be explicitly expressed with the secant stiffness. The general solution procedure can also be extended to multi-span suspension bridges. Finally, the nonlinear static solution is verified by numerical examples of a three-span suspension bridge and a four-span suspension bridge. The parametric analysis reveals that the nonlinearity of suspension bridge will become significant as the side-span to mid-span ratio increases, or when the side-span cables are hung with hangers.

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.

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.

Mechanical performance analysis and parametric study of double-deck plate-truss composite steel girders of a three-tower four-span suspension bridge

A sufficient understanding of the mechanical performance of plate-truss composite steel girders is essential for practical design as such girders are utilized widely in long-span bridges worldwide. Using the Oujiang River North Estuary Bridge which is a three-tower four-span suspension bridge under construction in China as an example, this paper investigates the mechanical performance of two sub-systems Ⅰ and Ⅱ of double-deck plate-truss composite steel girders. System Ⅰ is the main bridge system, with the steel plate deck and the longitudinal ribs acting as a part of the main carrying members of the bridge. System Ⅱ is the stiffened steel plate deck consisting of the longitudinal ribs, diaphragms and the deck plate as their common upper flange, acting as a bridge floor. Three-dimensional finite element models (FEM) are developed and different load cases are considered for System Ⅰ and System Ⅱ in the analysis. The results show that 60–80% of total load is carried by the deck plate and longitudinal ribs in System Ⅰ, and the mechanical response of System Ⅱ is susceptible to live load. Finally, a parametric study is conducted to investigate the influences of various structural parameters on the mechanical performance of double-deck plate-truss composite steel girders. The obtained analytical results lead to a better understanding of the complex mechanical performance of steel deck-truss composite system, particularly with respect to stress distribution and load carrying mechanism.

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.

Parameter effects on the mechanical performance of triple-tower four-span suspension bridges

Given the ineffective anchorage of the middle tower, a triple-tower suspension bridge shows a different mechanical behavior when compared with a traditional suspension bridge. Accordingly, this work investigates the mechanical performance of triple-tower suspension bridges. First, theoretical analysis was performed while considering the top displacement of the side tower and the stiffness of the middle tower. And the analytical solutions to live load of cable force, girder deflection, and anti-slip coefficient between the cable and saddle were obtained. Second, finite element models were established to perform a parametric analysis on tower stiffness, sag–span ratio, and side–main span ratio. These parameters influence the mechanical behaviors of bridges in different ways, and determining these parameters at the conceptual design stage should fulfill the requirements of mechanical performance of these structures while comprehensively considering their economic performance.

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.

Effects of Flexural Rigidity of Center Tower in Four-Span Suspension Bridges

해협횡단 교량으로서 적용사례가 증가될 것으로 예상되는 다경간 현수교에 대한 거동을 간략하면서도 정확히 해석하기 위하여, 현수교에 대한 고유의 해석이론인 처짐이론 해석방법을 사용할 수 있다. 본 연구에서는 처짐이론 방법을 이용한 4경간 현수교의 구조해석을 수행하였다. 거더를 축인장력을 받는 단순보로 고려하였고, 연직방향 하중 및 지점부 모멘트에 의한 단순보의 수직변위를 산정하여, 이 변위가 케이블의 적합방정식을 만족할 때까지 반복해석을 수행하였다. 유한요소해석의 결과와 비교하여 모든 주탑의 휨강성을 고려하는 처짐이론 해석의 결과를 검증하고, 주케이블과 탑정부 간의 구속조건 변화에 따른 다양한 케이블 적합방정식을 이용하여, 4경간 현수교에서의 주탑 휨강성의 중요성을 확인하였다. 또한 중앙주탑 휨강성의 변화에 따른 간단한 변수해석을 수행하여 그에 따른 거동을 파악하였다. For simple and accurate analysis for behaviors of multi-span suspension bridges which are expected to be frequently constructed as strait-crossing bridges, the deflection theory as the peculiar theory of a suspension bridge can be applied. This paper performs a structural analysis for four-span suspension bridges using the deflection theory. Simply-supported beams with tension are used for girders and the deflections of the beams due to the vertical loads and moments at supports are calculated. The calculation is performed iteratively until the deflections satisfy the compatibility equations of cables. The results of the deflection theory analysis considering tower rigidity are compared with those of the finite element analysis for verification. Importance of the tower rigidity for four-span suspension bridges is confirmed using various compatibility equations of the cable due to variation of the constraint conditions between main cable and top of towers. In addition, the simple parametric analysis for variation of the center tower rigidity is performed.

Simplified Analysis for Preliminary Design of Towers in Suspension Bridges

This paper proposes an equivalent suspension bridge model for the preliminary design of support towers of suspension bridges. In this simplified model, the bridge is composed of its support towers, with equivalent springs replacing suspension cables and girders. An explicit formula for the spring stiffness was derived for the horizontal stiffness at the end of an inclined main cable and compared with Ernst’s formula as well as finite-element analysis results. For the analysis of the model, dead and live loads acting on the girders of each span were replaced with horizontal and vertical forces calculated using the deflection theory and placed on the tops of the support towers. Equilibrium equations were derived from free-body diagrams for each tower and their solutions were obtained from boundary conditions at the ends of the towers. This resulted in the formulation of nonlinear load-displacement equations in matrix form for the simplified bridge model. An example four-span suspension bridge was analyzed for displacements at the tops of the towers and moment reactions at the bottoms of the towers under six live-load cases. A comparison of the model predictions with a FEM analysis showed excellent agreement. The results prove that the proposed analysis method can be a useful alternative for the preliminary analysis and design of suspension bridge towers.

Advanced analysis of multi-span suspension bridges

In this paper, an efficient analysis method considering both geometric and material nonlinearities is proposed for predicting the ultimate strength and behavior of multi-span suspension bridges. The geometric nonlinearities of the cable members due to sag effects are captured using the catenary element, while the geometric nonlinearities of the beam-column members due to second-order effects are captured using the stability functions. The material nonlinearities of the cable and beam-column members are considered using elastic–plastic hinge and refined plastic hinge models, respectively. A simple initial shape analysis method is presented to determine the deformed shape and initial cable tension of the bridge under dead loads. Numerical examples are presented to verify the accuracy and efficiency of the proposed method. In addition, a case study on a four-span suspension bridge is carried out to show the capability of the proposed method in estimating the strength and behavior of very large scale structures.

Numerical Simulation of Ultimate of Slings for Three-Tower and Four-Span Suspension Bridge under Tanker Fire

Three-dimensional finite element model of Yingwuzhou Yangtze river bridge was established by using the finite element software ANSYS. Since the characteristics of bridge fire differed much from that of buildings, Heating curve HCinc was selected as heating curve caused by tanker fire. Heat loading was imposed on the middle of main span where the tanker fire had taken place of three-tower and four-span suspension bridge . The temperature field and stress, modulus of elasticity, strength of sling changing with time caused by tanker burning in midspan were systematically investigated to obtain the failure time of the sling. The calculation also compared the above results of HCinc curve with that of ISO834 curve. This research can provide some references to fire risk prevention measures of bridge during its service life.

Structural Characteristics and Applicability of Four-Span Suspension Bridge

A four-span suspension bridge which has two main 2,000 m spans is investigated with respect to the deformation characteristics. Generally, deformation behavior of the four-span suspension bridge is mainly influenced by rigidity of the center tower. This study is focused on properties such as bending and torsional rigidity of the girder, sag ratio, and dead load. The result of this investigation clarified that the lower rigidity under live load than the three-span bridge is caused by the smaller cable spring coefficient of the main span, which is 1/6 of the side span. Nevertheless, the tendency is stable and can be assisted by stiffened rigidity of the center tower. Live load deflection of the girder can be reduced to less than 1/200 of the main span length, which is useful and economical, by stiffening the bending coefficient of the center tower. Moreover, relatively lower rigidity of the center tower is sufficient for the 2,000 m span suspension bridge than for the 1,000 m span case, keeping the same deflection ratio. Three-dimensional sag geometry of the main cable is effective in limiting the torsional deformation, which is an especially important issue for the four-span suspension bridge caused by twist of the center tower.