• Structural Engineering and Mechanics
• /
• v.90 no.4
• /
• pp.325-343
• /
• 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.

• Journal of Ocean Engineering and Technology
• /
• v.23 no.3
• /
• pp.59-64
• /
• 2009

Bridge types such as the suspension bridges and the cable stayed bridges maintained by cables present the dangerous possibility of a ship running through the bottom of the bridge. Due to hangers and main cables in the upper structural system, the bridge is also susceptible to disasters. However, these cable bridges are usually used for long span bridges over the sea. This structure is relatively more exposed to disasters, such as wind, hail, and earthquake, than other structures. This structure also has the potential to cause car accidents on account of the poor visibility due to foggy conditions. If a fire breaks out because of a car accident due to wind, a car explosion will likely occur.

• Structural Engineering and Mechanics
• /
• v.87 no.3
• /
• pp.255-272
• /
• 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
• /
• v.31 no.1
• /
• pp.57-68
• /
• 2023

Bridge hangers, such as those in suspension and cable-stayed bridges, suffer from cumulative fatigue damage caused by dynamic loads (e.g., cyclic traffic and wind loads) in their service condition. Thus, the identification of damage to hangers is important in preserving the service life of the bridge structure. This study develops a new method for condition assessment of bridge hangers. The tension force of the bridge and the damages in the element level can be identified using the Bayesian optimization method. To improve the number of observed data, the additional mass method is combined the Bayesian optimization method. Numerical studies are presented to verify the accuracy and efficiency of the proposed method. The influence of different acquisition functions, which include expected improvement (EI), probability-of-improvement (PI), lower confidence bound (LCB), and expected improvement per second (EIPC), on the identification of damage to the bridge hanger is studied. Results show that the errors identified by the EI acquisition function are smaller than those identified by the other acquisition functions. The identification of the damage to the bridge hanger with various types of boundary conditions and different levels of measurement noise are also studied. Results show that both the severity of the damage and the tension force can be identified via the proposed method, thereby verifying the robustness of the proposed method. Compared to the genetic algorithm (GA), particle swarm optimization (PSO), and nonlinear least-square method (NLS), the Bayesian optimization (BO) performs best in identifying the structural damage and tension force.

• Steel and Composite Structures
• /
• v.22 no.5
• /
• pp.1001-1018
• /
• 2016

The purpose of this paper is to compare the structural responses obtained from the stochastic analysis of a suspension bridge subjected to uniform and partially correlated seismic ground motions, using different spatial correlation functions commonly used in the earthquake engineering. The spatial correlation function employed in this study consists of a term that characterizes the loss of coherency. To account for the spatial variability of ground motions, the widely used four loss of coherency models in the literature has been taken into account in this study. Because each of these models has its own characteristics, it is intended to determine the sensitivity of a suspension bridge due to these losses of coherency models which represent the spatial variability of ground motions. Bosporus Suspension Bridge connects Europe to Asia in Istanbul is selected as a numerical example. The bridge has steel towers that are flexible, inclined hangers and a steel box-deck of 1074 m main span, with side spans of 231 and 255 m on the European and Asian sides, respectively. For the ground motion the filtered white noise model is considered and applied in the vertical direction, the intensity parameter of this model is obtained by using the S16E component of Pacoima Dam record of 1971 San Fernando earthquake. An analytically simple model called as filtered white noise ground motion model is chosen to represent the earthquake ground motion. When compared with the uniform ground motion case, the results obtained from the spatial variability models with partial correlation outline the necessity to include the spatial variability of ground motions in the stochastic dynamic analysis of suspension bridges. It is observed that while the largest response values are obtained for the model proposed by Harichandran and Vanmarcke, the model proposed by Uscinski produces the smallest responses among the considered partially correlated ground motion models. The response values obtained from the uniform ground motion case are usually smaller than those of the responses obtained from the partially correlated ground motion cases. While the response values at the flexible parts of the bridge are totally dominated by the dynamic component, the pseudo-static component also has significant contributions for the response values at the rigid parts of the bridge. The results also show the consistency of the spatial variability models, which have different characteristics, considered in this study.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.28 no.2A
• /
• pp.215-222
• /
• 2008

This paper introduces an experimental verification of a tension estimation method based on system identification approach for a double hanger system on a suspension bridge. A laboratory model of such double hanger system has been made for this study. Total nine cases of the vibration tests have been conducted with respect to three levels of applied tension and three cases of the location of clamp. For a set of the collected acceleration response data, modal analysis has been followed in order to extract the natural frequencies and mode shapes of the selected cable systems. For the extracted modal parameters, the existing tension estimation methods based on the string theory and axially loaded beam theory have been firstly applied to estimate the tensile force on the double hanger cable system. Next, the tensile force on cables has been estimated by the system identification approach. It is seen that the errors in the tension estimation using the frequency-based system identification technique are about 3% for all cases while the estimation error using the existing method is up to 53.1%.

• Structural Engineering and Mechanics
• /
• v.75 no.4
• /
• pp.487-496
• /
• 2020

Most of the previous works on numerical analysis of galloping of transmission lines are generally based on the quasisteady theory. However, some wind tunnel tests of the rectangular section or hangers of suspension bridges have shown that the galloping phenomenon has a strong unsteady characteristic and the test results are quite different from the quasi-steady calculation results. Therefore, it is necessary to check the applicability of the quasi-static theory in galloping analysis of the ice-covered transmission line. Although some limited unsteady simulation researches have been conducted on the variation of parameters such as aerodynamic damping, aerodynamic coefficients with wind speed or wind attack angle, there is a need to investigate the numerical simulation of unsteady galloping of two-dimensional iced transmission line with comparison to wind tunnel test results. In this paper, it is proposed to conduct a two dimensional (2-D) unsteady numerical analysis of ice-covered transmission line galloping. First, wind tunnel tests of a typical crescent-shapes iced conductor are conducted firstly to check the subsequent quasisteady and unsteady numerical analysis results. Then, a numerical simulation model consistent with the aeroelastic model in the wind tunnel test is established. The weak coupling methodology is used to consider the fluid-structure interaction in investigating a two-dimension numerical simulation of unsteady galloping of the iced conductor. First, the flow field is simulated to obtain the pressure and velocity distribution of the flow field. The fluid action on the iced conduct at the coupling interface is treated as an external load to the conductor. Then, the movement of the conduct is analyzed separately. The software ANSYS FLUENT is employed and redeveloped to numerically analyze the model responses based on fluid-structure interaction theory. The numerical simulation results of unsteady galloping of the iced conduct are compared with the measured responses of wind tunnel tests and the numerical results by the conventional quasi-steady theory, respectively.

• Journal of Korean Society of Steel Construction
• /
• v.10 no.4 s.37
• /
• pp.589-600
• /
• 1998

This study was planned to verify the usefulness of Latin square design method in fatigue tests of cables and to see the axial fatigue behavior of wire ropes being used as hangers in suspension bridges. Three parameters : mean stress, stress range. and specimen length, were adopted for verification. The effects of these parameters are in argument except for stress range. Three classes in each parameter were used. Triple replication was performed in each cell to increase the number of replication (or degree of freedoms). The major cause of fatigue failure was fretting fatigue at trellis contact point. Three chosen parameters were proved to be significant. It was verified that the effect of stress range was in agreement with expectation, but the effect of specimen length was contrary to the expectation. It was also observed that the effect of mean stress depended upon the chosen level. Therefore Latin square design method is effective for verifying the parameters that affect fatigue behaviour under orthogonality conditions.