• Structural Engineering and Mechanics
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• 제80권6호
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• pp.749-765
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• 2021

Suspension bridges bear large eccentric live loads in rush hours when most vehicles travel in one direction on the left or right side of the bridge. With the increasing number and weight of vehicles and the girder widening, the eccentric live load effect on the bridge behavior, including bending and distortion of the main girder, gets more pronounced, even jeopardizing bridge safety. This study proposes an analytical algorithm based on multi-catenary theory for predicting the suspension bridge responses to eccentric live load via the nonlinear generalized reduced gradient method. A set of governing equations is derived to solve the following unknown values: the girder rigid-body displacement in the longitudinal direction; the horizontal projection lengths of main cable's segments; the parameters of catenary equations and horizontal forces of the side span cable segments and the leftmost segments of middle span cables; the suspender tensions and the bearing reactions. Then girder's responses, including rigid-body displacement in the longitudinal direction, deflections, and torsion angles; suspenders' responses, including the suspender tensions and the hanging point displacements; main cables' responses, including the horizontal forces of each segment; and the longitudinal displacement of the pylons' tower top under eccentric load can be calculated. The response of an exemplar suspension bridge with three spans of 168, 548, and 168 m is calculated by the proposed analytical method and the finite element method in two eccentric live load cases, and their results prove the former's feasibility. The nonuniform distribution of the live load in the lateral direction is shown to impose a greater threat to suspension bridge safety than that in the longitudinal direction, while some other specific features revealed by the proposed method are discussed in detail.

• Earthquakes and Structures
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• 제3권5호
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• pp.767-781
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• 2012

The residual capacity against collapse of a main shock-damaged bridge can be coupled with the aftershock ground motion hazard to make an objective decision on its probability of collapse in aftershocks. In this paper, a steel tower suspension bridge with a main span of 2000 m is adopted for a case-study. Seismic responses of the bridge in longitudinal and transversal directions are analyzed using dynamic elasto-plastic finite displacement theory. The analysis is conducted in two stages: main shock and aftershocks. The ability of the main shock-damaged bridge to resist aftershocks is discussed. Results show that the damage caused by accumulated plastic strain can be ignored in the long-span suspension bridge. And under longitudinal and transversal seismic excitations, the damage is prone to occur at higher positions of the tower and the shaft-beam junctions. When aftershocks are not large enough to cause plastic strain in the structure, the aftershock excitation can be ignored in the seismic damage analysis of the bridge. It is also found that the assessment of seismic damage can be determined by superposition of damage under independent action of seismic excitations.

• Structural Engineering and Mechanics
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• 제42권4호
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• pp.489-505
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• 2012

In this study, it is aim to perform the construction stage analysis of suspension bridges using time dependent material properties. Fatih Sultan Mehmet Suspension Bridge connecting the Europe and Asia in Istanbul is selected as an example. Finite element models of the bridge are modelled using SAP2000 program considering project drawing. Geometric nonlinearities are taken into consideration in the analysis using P-Delta large displacement criterion. The time dependent material strength variations and geometric variations are included in the analysis. Because of the fact that the bridge has steel structural system, only prestressing steel relaxation is considered as time dependent material properties. The structural behaviour of the bridge at different construction stages has been examined. Two different finite element analyses with and without construction stages are carried out and results are compared with each other. As analyses result, variation of the displacement and internal forces such as bending moment, axial forces and shear forces for bridge deck and towers are given with detail. It is seen that construction stage analysis has remarkable effect on the structural behaviour of the bridge.

• Corrosion Science and Technology
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• 제10권3호
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• pp.87-94
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• 2011

The typical corrosion prevention method inside the steel upper box girder in a suspension bridge involves the use of paints. However, in an effort to reduce environmental impact and cost, the suspension portion of the Yeongjong Bridge, Korea utilizes dehumidification systems to control humidity and prevent corrosion inside its box girder. Maintaining a uniform humidity distribution at the proper level inside the box girder is critical to the successful corrosion control. In this study, the humidity and the resultant atmospheric corrosivity inside the box girder of the Yeongjong Bridge was monitored. The corrosion rate of the steel inside the box girder was obtained using thin-film electrical resistance (TFER) corrosion sensors. Time-of-wetness (TOW) measurements and the deposition rates of atmospheric pollutants such as $Cl^{-}$ and $SO_{x}$ were also obtained. Classification of the atmospheric corrosivity inside the box girder was evaluated according to ISO 9223. As a result, no corrosion was found in the upper box girder, indicating that the dehumidification system used in the Yeongjong Bridge is an effective corrosion control method.

• Structural Engineering and Mechanics
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• 제87권3호
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• pp.255-272
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• 2023

Spatial cable systems can provide more transverse stiffness and torsional stiffness without sacrificing the vertical bearing capacity compared with conventional vertical cable systems, which is quite lucrative for long-span earth-anchored suspension bridges' development. Higher economy highlights the importance of refined form-finding analysis. Meanwhile, the internal connection between the lateral and vertical sags has not yet been specified. Given this, an analytic algorithm of form-finding for the earth-anchored suspension bridge with spatial cables is proposed in this paper. Through the geometric compatibility condition and mechanical equilibrium condition, the expressions for cable segment, the recurrence relationship between catenary parameters and control equations of spatial cable are established. Additionally, the nonlinear general reduced gradient method is introduced into fast and high-precision numerical analysis. Furthermore, the analytic expression of the lateral and vertical sags is deduced and discussed. This is very significant for the space design above the bridge deck and the optimization of the sag-to-span ratio in the preliminary design stage of the bridge. Finally, the proposed method is verified with the aid of two examples, one being an operational self-anchored suspension bridge (with spatial cables and a 260 m main span), and the other being an earth-anchored suspension bridge under design (with spatial cables and a 500 m main span). The necessity of an iterative calculation for hanger tensions on earth-anchored suspension bridges is confirmed. It is further concluded that the main cable and their connected hangers are in very close inclined planes.

• Structural Engineering and Mechanics
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• 제90권4호
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• pp.325-343
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• 2024

Triple-tower double-cable suspension bridges have increased confinement stiffness imposed by the main cable on the middle tower, which has bright application prospects. However, vertical bending and torsional vibrations of the double-cable and the girder are coupled in such bridges due to the hangers. In particular, the bending vibration of the towers in the longitudinal direction and torsional vibrations about the vertical axis influence the vertical bending and torsional vibrations of the stiffening girders, respectively. The conventional analytical algorithm for assessing the dynamic features of the suspension bridge is not directly applicable to this type of bridge. This study attempts to mitigate this problem by introducing an analytical algorithm for solving the triple-tower double-cable suspension bridge's natural frequencies and mode shapes. D'Alembert's principle is employed to construct the differential equations of the vertical bending and torsional vibrations of the stiffening girder continuum in each span. Vibrations of stiffening girders in each span are interrelated via the vibrations of the main cables and the bridge towers. On this basis, the natural frequencies and mode shapes are derived by separating variables. The proposed algorithm is then applied to an engineering example. The natural frequencies and mode shapes of vertical bending and torsional vibrations derived by the analytical algorithm agreed well with calculations via the finite element method. The fundamental frequency of vertical bending and first- and second-order torsion frequencies of double-cable suspension bridges are much higher than those of single-cable suspension bridges. The analytical algorithm has high computational efficiency and calculation accuracy, which can provide a reference for selecting appropriate structural parameters to meet the requirements of dynamics during the preliminary design.

• Wind and Structures
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• 제23권5호
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• pp.405-420
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• 2016

Section model wind tunnel test is currently the main technique to investigate the flutter performance of long-span bridges. Further study about applying the wind tunnel test results to the aerodynamic optimization is still needed. Systematical parameters and test principle of the bridge section model are determined by using three long-span steel truss suspension bridges. The flutter critical wind at different attack angles is obtained through section model flutter test. Under the most unfavorable working condition, tests to investigate the effects that upper central stabilized plate, lower central stabilized plate and horizontal stabilized plate have on the flutter performance of the main beam were conducted. According to the test results, the optimal aerodynamic measure was chosen to meet the requirements of the bridge wind resistance in consideration of safety, economy and aesthetics. At last the credibility of the results is confirmed by full bridge aerodynamic elastic model test. That the flutter reduced wind speed of long-span steel truss suspension bridges stays approximately between 4 to 5 is concluded as a reference for the investigation of the flutter performance of future similar steel truss girder suspension bridges.

• 한국지진공학회논문집
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• 제8권6호통권40호
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• pp.1-11
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• 2004

이전의 연구(1)에서는 해석적 및 수치적 방법을 사용하여 전단변형 및 회전관성효과를 고려하는 현수교의 수직진동에 대하여 유한요소법을 이용하여 이동하중 해석을 수행하였다. 본 연구에서는 전단변형 및 회전관성 효과가 고려된 Hermitian 다항식을 사용하는 현수교요소를 이용하여 현수교의 수직진동에 대한 고유치 해석을 수행하고 이를 이용한 현수교요소와 차량 및 열차와의 상호작용을 고려한 운동방정식을 유도한다. 이와 같이 모드중첩법을 이용하여 유도된 운동방정식을 수치적분방법으로 Newmark $\beta$ Method를 사용하여 동적해석을 수행하였다.

• Korean Journal of Mathematics
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• 제19권2호
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• pp.233-242
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• 2011

We get a theorem that there exist at least two solutions for the piecewise linear suspension bridge equation with variable coefficient jumping nonlinearity and Dirichlet boundary condition when the variable coefficient of the nonlinear term crosses first two successive negative eigenvalues. We obtain this multiplicity result by applying Leray-Schauder degree theory.

• Korean Journal of Mathematics
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• 제16권1호
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• pp.1-24
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• 2008

Let $Lu=u_{tt}+u_{xxxx}$ and E be the complete normed space spanned by the eigenfunctions of L. We reveal the existence of six nontrivial solutions of a nonlinear suspension bridge equation $Lu+bu^+=1+{\epsilon}h(x,t)$ in E when the nonlinearity crosses three eigenvalues. It is shown by the critical point theory induced from the limit relative category of the torus with three holes and finite dimensional reduction method.