The finite strip method (FSM) is a very efficient numerical method employed for performing the structural analysis of slender structures, such as cable-stayed bridges; the strip discretization of the model allows for the usage of a lower number of degrees of freedom, in comparison with the finite element method (FEM), while, as it will be discussed in the current research, the results obtained from both methods are in relatively good agreement. Moreover, to address the latest developments in the area of smart construction materials used for long-span bridges, the fiber reinforced polymer (FRP) composites were implemented for the bridge deck modeling, as part of a hybrid composite FRP cable-stayed bridge, and an extend laminate integrated finite strip method (LFSM) was applied for estimating the static structural performance of the hybrid composite FRP long-span cable-stayed bridge under several concentrated and uniformly distributed loadings. The free vibrations analysis was conducted for the Kap Shui Mun Cable-stayed Bridge model, and the natural frequencies were compared with the ones obtained from an FE model of the same bridge. One of the advantages of using the integrated finite strip method is that number of vibration modes, which can be included in the dynamic analysis when the effect of a sweeping sinus and a seismic loading are investigated when a conventional FE analysis would fail to converge. The outcomes of this research will set the stage for the hybrid long-span cable-stayed bridges modeling by the laminate integrated finite strip method (LFSM) which is more efficient and straightforward than the finite element analysis, for performing the static, free vibration, time domain, and frequency domain analyses.

As the spans of cable-stayed bridges increase, the degree of nonlinearity of structural response increases markedly. For future spans greater than (say) 800 m, existing three-dimensional software then becomes very time consuming and costly, and a finite strip approach becomes more attractive and preferable. An improved finite strip method using two types of longitudinal shape functions is developed in this paper for the analysis of girders of such bridges. The nonlinearities due to sag and angle change of the cables are taken into account by means of catenary theory. The substructuring technique and the modified Newton-Raphson iteration method are used for noninear solutions. A number of numerical examples are given to show the accuracy and efficiency of this method.

The main categories of wind effects on long span bridge decks are buffeting, flutter, vortex-induced vibrations (VIV) which are often critical for the safety and serviceability of the structure. With the rapid increase of bridge spans, research on controlling wind-induced vibrations of long span bridges has been a problem of great concern.The developments of vibration control theories have led to the wide use of tuned mass dampers (TMDs) which has been proven to be effective for suppressing these vibrations both analytically and experimentally. Fire incidents are also of special interest in the stability and safety of long span bridges due to significant role of the complex phenomenon through triple interaction between the deck with the incoming wind flow and the thermal boundary of the surrounding air. This work begins with analyzing the buffeting response and flutter instability of three dimensional computational structural dynamics (CSD) models of a cable stayed bridge due to strong wind excitations using ABAQUS finite element commercial software. Optimization and global sensitivity analysis are utilized to target the vertical and torsional vibrations of the segmental deck through considering three aerodynamic parameters (wind attack angle, deck streamlined length and viscous damping of the stay cables). The numerical simulations results in conjunction with the frequency analysis results emphasized the existence of these vibrations and further theoretical studies are possible with a high level of accuracy. Model validation is performed by comparing the results of lift and moment coefficients between the created CSD models and two benchmarks from the literature (flat plate theory) and flat plate by (Xavier and co-authors) which resulted in very good agreements between them. Optimum values of the parameters have been identified. Global sensitivity analysis based on Monte Carlo sampling method was utilized to formulate the surrogate models and calculate the sensitivity indices. The rational effect and the role of each parameter on the aerodynamic stability of the structure were calculated and efficient insight has been constructed for the stability of the long span bridge. 2D computational fluid dynamics (CFD) models of the decks are created with the support of MATLAB codes to simulate and analyze the vortex shedding and VIV of the deck. Three aerodynamic parameters (wind speed, deck streamlined length and dynamic viscosity of the air) are dedicated to study their effects on the kinetic energy of the system and the vortices shapes and patterns. Two benchmarks from the literature (Von Karman) and (Dyrbye and Hansen) are used to validate the numerical simulations of the vortex shedding for the CFD models. A good consent between the results was detected. Latin hypercube experimental method is dedicated to generate the surrogate models for the kinetic energy of the system and the generated lift forces. Variance based sensitivity analysis is utilized to calculate the main sensitivity indices and the interaction orders for each parameter. The kinetic energy approach performed very well in revealing the rational effect and the role of each parameter in the generation of vortex shedding and predicting the early VIV and the critical wind speed. Both one-way fluid-structure interaction (one-way FSI) simulations and two-way fluid-structure interaction (two-way FSI) co-simulations for the 2D models of the deck are executed to calculate the shedding frequencies for the associated wind speeds in the lock-in region in addition to the lift and drag coefficients. Validation is executed with the results of (Simiu and Scanlan) and the results of flat plate theory compiled by (Munson and co-authors) respectively. High levels of agreements between all the results were detected. A decrease in the critical wind speed and the shedding frequencies considering (two-way FSI) was identified compared to those obtained in the (one-way FSI). The results from the (two-way FSI) approach predicted appreciable decrease in the lift and drag forces as well as prediction of earlier VIV for lower critical wind speeds and lock-in regions which exist at lower natural frequencies of the system. These conclusions help the designers to efficiently plan and consider for the design and safety of the long span bridge before and after construction. Multiple tuned mass dampers (MTMDs) system has been applied in the three dimensional CSD models of the cable stayed bridge to analyze their control efficiency in suppressing both wind -induced vertical and torsional vibrations of the deck by optimizing three design parameters (mass ratio, frequency ratio and damping ratio) for the (TMDs) supporting on actual field data and minimax optimization technique in addition to MATLAB codes and Fast Fourier Transform technique. The optimum values of each parameter were identified and validated with two benchmarks from the literature, first with (Wang and co-authors) and then with (Lin and co-authors). The validation procedure detected a good agreement between the results. Box-Behnken experimental method is dedicated to formulate the surrogate models to represent the control efficiency of the vertical and torsional vibrations. Sobol's sensitivity indices are calculated for the design parameters in addition to their interaction orders. The optimization results revealed better performance of the MTMDs in controlling both the vertical and the torsional vibrations for higher mode shapes. Furthermore, the calculated rational effect of each design parameter facilitates to increase the control efficiency of the MTMDs in conjunction with the support of the surrogate models which simplifies the process of analysis for vibration control to a great extent. A novel structural modification approach has been adopted to eliminate the early coupling between the bending and torsional mode shapes of the cable stayed bridge. Two lateral steel beams are added to the middle span of the structure. Frequency analysis is dedicated to obtain the natural frequencies of the first eight mode shapes of vibrations before and after the structural modification. Numerical simulations of wind excitations are conducted for the 3D model of the cable stayed bridge. Both vertical and torsional displacements are calculated at the mid span of the deck to analyze the bending and the torsional stiffness of the system before and after the structural modification. The results of the frequency analysis after applying lateral steel beams declared that the coupling between the vertical and torsional mode shapes of vibrations has been removed to larger natural frequencies magnitudes and higher rare critical wind speeds with a high factor of safety. Finally, thermal fluid-structure interaction (TFSI) and coupled thermal-stress analysis are utilized to identify the effects of transient and steady state heat-transfer on the VIV and fatigue of the deck due to fire incidents. Numerical simulations of TFSI models of the deck are dedicated to calculate the lift and drag forces in addition to determining the lock-in regions once using FSI models and another using TFSI models. Vorticity and thermal fields of three fire scenarios are simulated and analyzed. The benchmark of (Simiu and Scanlan) is used to validate the TFSI models, where a good agreement was manifested between the two results. Extended finite element method (XFEM) is adopted to create 3D models of the cable stayed bridge to simulate the fatigue of the deck considering three fire scenarios. The benchmark of (Choi and Shin) is used to validate the damaged models of the deck in which a good coincide was seen between them. The results revealed that the TFSI models and the coupled thermal-stress models are significant in detecting earlier vortex induced vibration and lock-in regions in addition to predicting damages and fatigue of the deck and identifying the role of wind-induced vibrations in speeding up the damage generation and the collapse of the structure in critical situations.

Research Paper (postgraduate) from the year 2014 in the subject Engineering - Civil Engineering, grade: unknown, University of Weimar, language: English, abstract: The vibration characteristic of a cable stayed bridges structure is the main axis of the study in this paper, many structural parameters are used to simulate and determine the effect of vibration on the structural performance by identifying the natural frequencies of the system and the mode shapes that can occur in the real structure. Modeling the stay cables with three famous styles of arrangements such as Harp, Semi Harp and Fan styles, and assigning roller, hinged and fixed boundary conditions on the deck support of the cable stayed bridge, in addition to using two design cases of the girders and pylons dimensions in the global structure for that purpose. Through the use of ABAQUS finite element analysis, the models were generated for each mentioned cases and the results of the frequency linear perturbation step of 10 mode shapes were determined through the simulation of the deformed shapes and the determined values of the natural frequencies of each mode for each case of interest. It was seen that the roller boundary condition was much prone to the early vibration and the stay cables of the direction near to the roller support were vibrated and stressed much more than the other direction compared with the hinged and fixed boundary conditions, and the mode shapes 7, 8, 9 and 10 were the most vibrated cases for all the boundary conditions without any distinction. The week design of the girders and the pylons has the great effect on the vibration of the stay cables, pylons and deck of the structure especially near the roller support direction due to the early vibration of the case of roller support, so the use of cross ties and damping between the stay cables and the girders are very important in the cases of significant vibrations which affect the performance of the cable stayed bridges.

To meet the economic, social and infrastructure needs of the community for safe and efficient transportation systems, long span bridges have been built throughout the world. Long span bridges are one of the most challenging kinds of structures in civil engineering. The cable-stayed bridges are of great interest mainly as an alternative and a more economic solution than the one of suspension bridges. In addition, the fiber reinforced polymer (FRP) composites are, nowadays, successfully used for constructing modern bridges, where the significant weight saving provides additional benefits. Because of the great flexibility, modern long-span cable-stayed bridges are usually very susceptible to dynamic loads especially to the earthquake and strong winds. Therefore, the earthquake-resistant and wind-resistant designs become one of key issues for successful construction of bridges. The objective of the present research is to develop a very efficient spline finite strip technique, for modelling and analysis of both conventional and hybrid FRP cable-stayed bridges. The study falls into the categories of bending, free vibration, seismic, and aerodynamic flutter analysis. The spline finite strip method (SFSM) is one of the most efficient numerical methods for structural analysis of bridges, reducing the time required for estimating the structural response without affecting the degree of accuracy. In the finite strip method, the degrees of freedom could be significantly reduced due to the semi-analytical nature of this method. However, the previous versions of SFSM are not able to model the entire bridge system. For that reason, the structural interactions between different structural components of the bridge could not be handled. In addition, the vibrations and displacements of the towers and cables could not be investigated. In the present formulation, all these obstacles have been eliminated. Moreover, the proposed finite strip technique is very efficient and accurate due to the drastic reduction in the formulation time, simplicity of data preparation, rapid rate convergence of the results, and the semi-analytical nature. Last but not least, and for the first time, a fully finite strip solution is extended to the area of wind engineering. Using the spline finite strip discretization, the aerodynamic stiffness and mass properties of the long-span cable-stayed bridge are derived. The aerodynamic properties along with the structural properties of long-span plates and bridges are formulated in the aerodynamic equation of motion and are used to analyze the flutter problem. The accuracy and efficiency of the proposed advanced finite strip method is verified against the finite element and field measurement results. The results demonstrate that this methodology and the associated computer code can accurately predict the dynamic and aerodynamic responses of the conventional and FRP long-span cable-stayed bridge systems. The outcome of the present research will lead to a comprehensive structural analysis of bridges in the framework of the proposed discretization which is more efficient and straightforward than the finite element analysis.