Numerical Methods for the Multi Physical Analysis of Long Span Cable Stayed Bridges 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. Sobols 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.