• Structural Engineering and Mechanics
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• 제43권1호
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• pp.71-87
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• 2012

This paper extends a single equation, semi-analytical approach for three-span bridges to multi-span ones for the rapid and precise determination of natural frequencies and natural mode shapes of an orthotropic, multi-span plate. This method can be used to study the dynamic interaction between bridges and vehicles. It is based on the modal superposition method taking into account intermodal coupling to determine natural frequencies and mode shapes of a bridge deck. In this paper, a four- and a five-span orthotropic roadway bridge deck are compared in the first 10 modes with a finite element method analysis using ANSYS software. This simplified implementation matches numerical modeling within 2% in all cases. This paper verifies that applicability of a single formula approach as a simpler alternative to finite element modeling.

• 산업기술연구
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• 제24권A호
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• pp.195-204
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• 2004

To evaluate inelastic seismic responses of multi-span bridge structures, the capacity spectrum method(CSM) incorporating the equivalent single-degree-of freedom(ESDOF) method is presented. Application of the CSM incorporating the ESDOF method is illustrated by example analysis for symmetric and asymmetric bridge structures. To investigate an accuracy of the CSM, the maximum displacements estimated by the CSM are compared to those by inelastic time history analysis for several artificial earthquakes. The results show that the CSM provided conservative estimates of the maximum displacements for the symmetric and asymmetric bridge structures, and the trend of conservative estimates of the asymmetric bridge structures was significantly larger than that of the symmetric bridge structure.

• Structural Engineering and Mechanics
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• 제52권1호
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• pp.51-73
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• 2014

A three-dimensional finite element model for the Jiashao Bridge, the longest multi-span cable-stayed bridge in the world, is established using the commercial software package ANSYS. Dynamic characteristics of the bridge are analyzed and the effects of structural system measures including the rigid hinge, auxiliary piers and longitudinal constraints between the girders and side towers on the dynamic properties including modal frequency, mode shape and effective mass are studied by referring to the Jiashao Bridge. The analysis results reveal that: (i) the installation of the rigid hinge significantly reduces the modal frequency of the first symmetric lateral bending mode of bridge deck. Moreover, the rigid hinge significantly changes the mode shape and effective mass of the first symmetric torsional mode of bridge deck; (ii) the layout of the auxiliary piers in the side-spans has a limited effect on changing the modal frequencies, mode shapes and effective masses of global vibration modes; (iii) the employment of the longitudinal constraints significantly increases the modal frequencies of the vertical bending modes and lateral bending modes of bridge deck and have significant effects on changing the mode shapes of vertical bending modes and lateral bending modes of bridge deck. Moreover, the effective mass of the first anti-symmetric vertical bending of bridge deck in the longitudinal direction of the fully floating system is significantly larger than that of the partially constrained system and fully constrained system. The results obtained indicate that the structural system measures of the multi-span cable-stayed bridge have a great effect on the dynamic properties, which deserves special attention for seismic design and wind-resistant design of the multi-span cable-stayed bridge.

• Structural Engineering and Mechanics
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• 제90권2호
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• pp.159-175
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• 2024

In order to solve the problem of calculating the reasonable completed bridge state of a self-anchored hybrid cable-stayed suspension bridge (SA-HCSB), this paper proposes an analytical method. This method simplifies the main beam into a continuous beam with multi-point rigid supports and solves the support reaction forces. According to the segmented catenary theory, it simultaneously solves the horizontal forces of the main span main cables and the stay cables and iteratively calculates the equilibrium force system on the main beam in the collaborative system bridge state while completing the shape finding of the main span main cable and stay cables. Then, the horizontal forces of the side span main cables and stay cables are obtained based on the balance of horizontal forces on the bridge towers, and the shape finding of the side spans are completed according to the segmented catenary theory. Next, the difference between the support reaction forces of the continuous beam with multiple rigid supports obtained from the initial and final iterations is used to calculate the load of ballast on the side span main beam. Finally, the axial forces and strains of each segment of the main beam and bridge tower are obtained based on the loads applied by the main cable and stay cables on the main beam and bridge tower, thereby obtaining analytical data for the bridge in the reasonable completed state. In this paper, the rationality and effectiveness of this analytical method are verified through a case study of a SA-HCSB with a main span of 720m in finite element analysis. At the same time, it is also verified that the equilibrium force of the main beam under the reasonably completed bridge state can be obtained through iterative calculation. The analytical algorithm in this paper has clear physical significance, strong applicability, and high accuracy of calculation results, enriching the shape-finding method of this bridge type.

• Earthquakes and Structures
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• 제12권3호
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• pp.375-388
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• 2017

Prior to modern seismic provisions, several bridges were not designed for seismic actions in moderate seismic areas. Precast multi-girder and slab bridges are typical highway overpass structures; they have a significant contribution to national bridge stocks. Since the seismic behavior is questionable, a preliminary parametric study is conducted to determine critical configurations and components. The results indicate that the behavior of the abutments, backfill soil, superstructure and foundation is normally satisfactory; however, the superstructure-abutment joints are critical for both single- and multi-span bridges, while the piers are also critical for longer multi-span configurations. The parametric results provide a solid basis both for detailed seismic assessment and development of design concepts of newly built structures in moderate seismic zones.

• Structural Engineering and Mechanics
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• 제33권2호
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• pp.239-255
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• 2009

In the companion paper, a simple but effective analysis procedure termed an Improved Modal Pushover Analysis (IMPA) is proposed to estimate the seismic capacities of multi-span continuous bridge structures on the basis of the modal pushover analysis, which considers all the dynamic modes of a structure. In contrast to previous studies, the IMPA maintains the simplicity of the capacity-demand curve method and gives a better estimation of the maximum dynamic response in a bridge structure. Nevertheless, to verify its applicability, additional parametric studies for multi-span continuous bridges with large differences in the length of adjacent piers are required. This paper, accordingly, concentrates on a parametric study to review the efficiency and limitation in the application of IMPA to bridge structures through a correlation study between various analytical models including the equivalent single-degree-of-freedom method (ESDOF) and modal pushover analysis (MPA) that are usually used in the seismic design of bridge structures. Based on the obtained numerical results, this paper offers practical guidance and/or limitations when using IMPA to predict the seismic response of a bridge effectively.

• 복합신소재구조학회 논문집
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• 제4권4호
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• pp.30-36
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• 2013

Partially earth anchored (PEA) can improve the structural safety and economic feasibility of multiple span cable stayed bridge (CSB). The PEA-CSB can restrain axial compressive load acting on a tower and reduce the global buckling length of a stiffened girder. For these reasons, structural members subject to axial forces can be effectively utilized and material quantity required for a steel deck can be reduced to save construction cost. In this study, the PEA system was verified for its application on a multiple span CSB. The CSB is a four-tower multi-span bridge which has a main span length of 500 m. As high tensile stress was generated at the top of the bridge decks at the mid-span between two main columns, a hybrid deck system for enhancing the bridge deck sections was proposed. While the composite sections made of concrete and steel were used near to the main columns, steel sections were used at the mid-span between two main columns.

• Structural Engineering and Mechanics
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• 제63권6호
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• pp.713-723
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• 2017

As a new type of ballastless track, longitudinal continuous slab track (CST) has been widely used in China. It can partly isolate the interaction between the ballastless track and the bridge and thus the rail expansion device would be unnecessary. Compared with the traditional track, CST is composed of multi layers of continuous structures and various connecting components. In order to investigate the performance of CST on a long-span bridge, the spatial finite element model considering each layer of the CST structure, connecting components, bridge, and subgrade is established and verified according to the theory of beam-rail interaction. The nonlinear resistance of materials between multilayer track structures is measured by experiments, while the temperature gradients of the bridge and CST are based on the long-term measured data. This study compares the force distribution rules of ballasted track and CST as respectively applied to a long span bridge. The effects of different damage conditions on CST structures are also discussed. The results show that the additional rail stress is small and the CST structure has a high safety factor under the measured temperature load. The rail expansion device can be cancelled when CST is adopted on the long span bridge. Beam end rotation caused by temperature gradient and vertical load will have a significant effect on the rail stress of CST. The additional flexure stress should be considered with the additional expansion stress simultaneously when the rail stress of CST requires to be checked. Both the maximum sliding friction coefficient of sliding layer and cracking condition of concrete plate should be considered to decide the arrangement of connecting components and the ultimate expansion span of the bridge when adopting CST.

• 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.

• Smart Structures and Systems
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• 제17권3호
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• pp.391-411
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• 2016

This study investigates the mode identifiability of a multi-span cable-stayed bridge in terms of a benchmark study using stabilization diagrams of a system model identified using stochastic subspace identification (SSI). Cumulative contribution ratios (CCRs) estimated from singular values of system models under different wind conditions were also considered. Observations revealed that wind speed might influence the mode identifiability of a specific mode of a cable-stayed bridge. Moreover the cumulative contribution ratio showed that the time histories monitored during strong winds, such as those of a typhoon, can be modeled with less system order than under weak winds. The blind data Acc 1 and Acc 2 were categorized as data obtained under a typhoon. Blind data Acc 3 and Acc 4 were categorized as data obtained under wind conditions of critical wind speeds around 7.5 m/s. Finally, blind data Acc 5 and Acc 6 were categorized as data measured under weak wind conditions.