• Earthquakes and Structures
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• 제14권6호
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• pp.493-503
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• 2018

With the further increase of span length, the cable-stayed bridge tends to be more slender, and becomes more susceptible to the seismic action. By taking a super long-span cable-stayed bridge with main span of 1400m as example, structural response of the bridge under the E1 horizontal and vertical seismic excitations is investigated numerically by the multimode seismic response spectrum and time-history analysis respectively, the seismic behavior and also the effect of structural nonlinearity on the seismic response of super long-span cable-stayed bridge are revealed. Furthermore, the effect of structural parameters including the girder depth and width, the tower structural style, the tower height-to-span ratio, the side-tomain span ratio, the auxiliary piers in side spans and the anchorage system of stay cables etc on the seismic performance of super long-span cable-stayed bridge is investigated numerically by the multimode seismic response spectrum analysis, and the favorable earthquake-resistant structural system of super long-span cable-stayed bridge is proposed.

• Smart Structures and Systems
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• 제17권3호
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• pp.363-389
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• 2016

Deficient modes that cannot be always identified from different sets of measurement data may exist in the application of operational modal analysis such as the stochastic subspace identification techniques in large-scale civil structures. Based on a recent work using the long-term ambient vibration measurements from an instrumented cable-stayed bridge under different wind excitation conditions, a benchmark problem is launched by taking the same bridge as a test bed to further intensify the exploration of mode identifiability. For systematically assessing this benchmark problem, a recently developed SSI algorithm based on an alternative stabilization diagram and a hierarchical sifting process is extended and applied in this research to investigate several sets of known and blind monitoring data. The evaluation of delicately selected cases clearly distinguishes the effect of traffic excitation on the identifiability of the targeted deficient mode from the effect of wind excitation. An additional upper limit for the vertical acceleration amplitude at deck, mainly induced by the passing traffic, is subsequently suggested to supplement the previously determined lower limit for the wind speed. Careful inspection on the shape vector of the deficient mode under different excitation conditions leads to the postulation that this mode is actually induced by the motion of the central tower. The analysis incorporating the tower measurements solidly verifies this postulation by yielding the prevailing components at the tower locations in the extended mode shape vector. Moreover, it is also confirmed that this mode can be stably identified under all the circumstances with the addition of tower measurements. An important lesson learned from this discovery is that the problem of mode identifiability usually comes from the lack of proper measurements at the right locations.

• Structural Engineering and Mechanics
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• 제34권6호
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• pp.719-738
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• 2010

The aim of this paper concerns with the nonlinear analysis of cable-stayed bridges including the vibration effect of cable stays. Two models for the cable stay system are built up in the study. One is the OECS (one element cable system) model in which one single element per cable stay is used and the other is MECS (multi-elements cable system) model, where multi-elements per cable stay are used. A finite element computation procedure has been set up for the nonlinear analysis of such kind of structures. For shape finding of the cable-stayed bridge with MECS model, an efficient computation procedure is presented by using the two-loop iteration method (equilibrium iteration and shape iteration) with help of the catenary function method to discretize each single cable stay. After the convergent initial shape of the bridge is found, further analysis can then be performed. The structural behaviors of cable-stayed bridges influenced by the cable lateral motion will be examined here detailedly, such as the static deflection, the natural frequencies and modes, and the dynamic responses induced by seismic loading. The results show that the MECS model offers the real shape of cable stays in the initial shape, and all the natural frequencies and modes of the bridge including global modes and local modes. The global mode of the bridge consists of coupled girder, tower and cable stays motion and is a coupled mode, while the local mode exhibits only the motion of cable stays and is uncoupled with girder and tower. The OECS model can only offers global mode of tower and girder without any motion of cable stays, because each cable stay is represented by a single straight cable (or truss) element. In the nonlinear seismic analysis, only the MECS model can offer the lateral displacement response of cable stays and the axial force variation in cable stays. The responses of towers and girders of the bridge determined by both OECS- and MECS-models have no great difference.

• Wind and Structures
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• 제29권3호
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• pp.163-175
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• 2019

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.

• 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.

• Structural Engineering and Mechanics
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• 제43권5호
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• pp.691-709
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• 2012

This paper provides a variety of viewpoints to illustrate the mechanism of the deck-stay interaction with the appropriate initial shapes of cable-stayed bridges. Based on the smooth and convergent bridge shapes obtained by the initial shape analysis, the one-element cable system (OECS) and multi-element cable system (MECS) models of the Kao Ping Hsi Bridge in Taiwan are developed to verify the applicability of the analytical model and numerical formulation from the field observations in the authors' previous work. For this purpose, the modal analysis of the two finite element models are conducted to calculate the natural frequency and normalized mode shape of the individual modes of the bridge. The modal coupling assessment is also performed to obtain the generalized mass ratios among the structural components for each mode of the bridge. The findings indicate that the coupled modes are attributed to the frequency loci veering and mode localization when the "pure" deck-tower frequency and the "pure" stay cable frequency approach one another, implying that the mode shapes of such coupled modes are simply different from those of the deck-tower system or stay cables alone. The distribution of the generalized mass ratios between the deck-tower system and stay cables are useful indices for quantitatively assessing the degree of coupling for each mode. These results are demonstrated to fully understand the mechanism of the deck-stay interaction with the appropriate initial shapes of cable-stayed bridges.

• 대한토목학회논문집
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• 제30권2A호
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• pp.137-148
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• 2010

본 연구에서는 기존 엑스트라도즈드교와 PSC 사장교 사이의 영역인 주탑고비 1/6~1/7의 고주탑을 적용하여 엑스트라도즈드교의 구조적, 경제적 특성을 평가하였다. 주탑고가 증가함에 따라 사재의 연직하중 분담율의 증가와 함께 변동응력도 증가하여 사재의 피로안정성이 주요 설계변수임을 알 수 있었다. 국내에서는 엑스트라도즈드교의 설계기준 부재로 인하여 일본 설계기준을 준용하고 있다. 또한, 피로 검토하중도 정립되지 않고 있어 본 연구에서는 일본 피로 검토하중에 대응하는 국내 활하중을 적용 검토하여 DL24 하중이 피로 검토하중으로 적정함을 알 수 있었다. 제시된 피로 검토하중을 적용하여 주탑고, 주거더의 강성, 케이블 면수 등을 매개변수로 엑스트라도즈드교의 구조적, 경제적 특성을 검토하였다. 본 연구의 결과로써 일면 케이블 배치가 이면 케이블 배치보다 경제적임을 알 수 있었다. 또한, 주탑고비가 1/6의 변단면 고주탑 엑스트라도즈교에서 연직 하중분담율이 30~50% 이내로 모든 사재가 허용변동응력 이내로 들어와 사재를 효율적으로 사용할 수 있어 가장 경제적임을 알 수 있었다. 본 연구를 통해 기존의 엑스트라도즈드교보다 높은 주탑고를 적용함에 따라 구조적, 경제적으로 효율성을 높일 수 있음을 확인하였다.

• 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.

• Wind and Structures
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• 제21권4호
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• pp.407-424
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• 2015

To explore the favorable structural system of cable-stayed bridges with ultra-kilometer main span, based on a fully self-anchored cable-stayed bridge with 1400 m main span, a partially earth-anchored cable-stayed bridge scheme with the same main span is designed. Numerical investigation on the dynamic characteristics, aerostatic and aerodynamic stability of both two bridge schemes is conducted, and the results are compared to those of a suspension bridge with similar main span, and considering from the aspect of wind stability, the feasibility of using partially earth-anchored cable-stayed bridge in super long-span bridges with ultra-kilometer main span is discussed. Moreover, the effects of structural design parameters including the length of earth-anchored girder, the number of auxiliary piers in side span, the height and width of girder, the tower height etc on the dynamic characteristics, aerostatic and aerodynamic stability of a partially earth-anchored cable-stayed bridge are analyzed, and their reasonable values are proposed. The results show that as compared to fully self-anchored cable-stayed bridge and suspension bridge with similar main span, the partially earth-anchored cable-stayed bridge has greater structural stiffness and better aerostatic and aerodynamic stability, and consequently becomes a favorable structural system for super long-span bridges with ultra-kilometer main span. The partially earth-anchored cable-stayed bridge can achieve greater stiffness and better wind stability under the cases of increasing the earth-anchored girder length, increasing the height and width of girder, setting several auxiliary piers in side span and increasing the tower height.

• Smart Structures and Systems
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• 제26권5호
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• pp.619-629
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• 2020

Solar towers, which often has a large aspect ratio and low fundamental natural frequency, were extremely prone to large amplitude of wind-induced vibrations, especially Vortex-Induced Vibration (VIV). A tiny Tuned Mass Damper (TMD) with conveniently adjustable eddy current damping was specially designed and manufactured for elastic wind tunnel tests of a solar tower. A series of numerical simulations by using the COMSOL software were conducted to determine three key parameters, including the thickness of the back iron plate and the conductive plate (T_b and T_c), the distance between the magnet and the conductive plate (T_d). Based on the results of numerical simulations, a tiny TMD was manufactured and its structural parameters were experimentally identified. The optimized values of the tiny TMD can be conveniently realized. The tiny TMD was installed at the top of the elastic test model of a 243-meter-high solar tower, and a series of wind tunnel tests were carried out to examine the effectiveness of the TMD in suppressing wind-induced responses of the test model. The results showed that the wind-induced responses could be obviously reduced by the TMD, especially in the cross-wind direction. The cross-wind RMS and peak responses at the critical wind velocity can be reduced by about 86% and 75%, respectively. However, the maximum reduction of the responses at the design wind velocity is about 45%, obviously less than that at the critical wind velocity.