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Johan Rhodes
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Analysis Of Cable Stayed Bridge Using Sap 2000 Free Download Full Version ((INSTALL))



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Analysis Of Cable Stayed Bridge Using Sap 2000 Free Download Full Version



When deformed configuration is derived through input parameters (main cable sag, main cable span, deck profile, etc.), the corresponding force values may be obtained using SAP2000. Analysis may begin with coordinates which specify the final deflected shape. The cable load which corresponds to the final deformed configuration should be specified in the Cable Geometry menu. This cable load can be estimated from the weight of the structure and its distribution along the bridge.


Modal parameters are critical for wind resistant design and vibrational serviceability assessments of long-span cable-supported bridges. In contrast to the successful research efforts into natural frequencies, there are still challenges in modeling the damping ratio due to the following aspects: (1) inherent errors in damping estimates, (2) lack of insight into the damping mechanisms and (3) epistemic uncertainties on the effects of environmental and operational conditions (EOCs). This paper proposes a probabilistic regression model for damping using Deep Gaussian Processes (DGP) on damping estimates compiled from 2.5 years of structural health monitoring (SHM) data from a cable-stayed bridge. Input features representative of EOCs theorized to be related to damping ratios from past literature were used. Two data cleaning strategies based on statistics and knowledge-based criteria were used for enhancing the model performance. A comparative study with DGPs and different regression models were carried out to confirm the robustness of DGPs across different datasets. A knowledge-based feature engineering process examined the most significant predictor of the damping ratios. The proposed data-driven regression model can enable a probabilistic consideration of damping in structural design and vibrational serviceability assessments.


The recent development of automated operational modal analysis (OMA) has enabled the modal tracking of environmental and operational conditions. Variations in these conditions have prevented investigations into the long-term characteristics of the damping ratio due to its inherently high degree of scattering. In this study, the long-term damping characteristics of a twin cable-stayed bridge under environmental and operational variations were investigated. A displacement reconstruction algorithm was applied to resolve the model-order dependency in OMA-based damping estimates. In order to automatically establish groups of modal estimates, optimal parameters for a density-based unsupervised clustering algorithm were proposed on the basis of gaps between target modal frequencies. The proposed clustering parameters were first validated by comparing the clustering results with those of manually determined ground truth classes. Next, the applicability of the clustering parameters for long-term damping estimation was demonstrated by quantifying the dispersion of modal estimates in each cluster. Subsequently, the framework was applied to 2.5 years of monitoring data to evaluate the long-term damping characteristics of the twin cable-stayed bridge that is often subjected to high variations in environmental and operational conditions. The following aspects are mainly discussed: (1) seasonal fluctuation in long-term damping ratios; (2) the effect that aerodynamic interference exerts on variations in the dynamic characteristics; and (3) the amplitude dependency of the damping ratio. The probability distribution of the modal damping ratio is provided based on the statistical analysis of reliable modal damping ratios.


Dischinger F. has established the need to raise cable stress in order to minimize the sag effect. This advance gave the first spark of the beginning of a system that mainly depends on cables. It should be noted that cable-stayed bridges can now be analyzed with a high level of precision using high-speed digital computers and advanced analytical methods [21]. Cable-stayed bridges currently extend over distances from 200 to 1000 m, like the Russky Bridge of 1104 m in Russia and the Sutong Bridge of 1088 m in China [38]. Some designers took the view that a cable-stayed bridge is a linear structure with cables serving as linear tension members [18]. In fact, the cables show non-linear behavior as a result of their own weights changing the tension in the cables. If we ignore the sag effect in the static analysis, an error of up to 15% may occur [21]. Other studies consider the non-linearity of cables that results from the sagging effect of different approaches. A study by Fabrizio Greco, Paolo Lonetti, and Arturo Pascuzzo was concerned with the dynamic behavior of cable-stayed bridges subjected to moving loads and affected by an accidental failure in the cable suspension system [13]. The first order by the Taylor expansion in terms of the incremental cable stress distribution, by means of a linearized equation, is the approach that was followed in their study. These equations were based on a vector containing the displacements and subjected to the stress distribution in cable, loading parameter. P. Lonetti and A. Pascuzzo investigated damage and failure behavior on the cable system in their study, which can be used to predict the response of hybrid cable-stayed suspension bridges subjected to moving loads [24, 25]. To consider the non-linearity of cables, they adopted Multi Element Cable System (MECS) approach. This approach discretized each cable using multiple truss elements. Such modeling is appropriate in the case of small bending stiffness and small sag at equilibrium. The Green Lagrange formulation is used to reproduce large deformations, and the axial strain is computed by expressing the global strains in tangential derivatives and projecting the global strains on the cable edge. Paolo Lonetti and Arturo Pascuzzo investigated in another study the description of the formulation to predict optimum post-tensioning forces and cable dimensioning for self-anchored cable-stayed suspension bridges [24, 25]. They also adopted and explained (MECS) approach. Raid Karoumi presented in his study a method for modeling cable-stayed bridges for nonlinear finite element analysis (FEA) [19]. Catenary cable element is an approach that is adopted to consider the change of cable geometry under different tension load levels (cable sag effect) in which exact analytical expressions for the elastic catenary is used. This approach was also used in [20]. Complexity is faced as cable-stayed bridges are analyzed as three-dimensional structures [3]. However, some studies made simplified assumptions on boundaries on the bridge deck to minimize the issue to a two-dimensional study [31].


Wilson and Gravelle presented approaches for modeling cable-stayed bridges in a linear finite element model for dynamic analysis. In their study findings, a linear model can work well for modeling and analyzing [36]. Wilson and Liu said that a linear elastic finite element model is able to capture with great precision much of the complex dynamic behavior of the cable-stayed bridge, compared to low complex reactions caused by environmental wind and excitations in traffic [37].


Few studies have been conducted to investigate the effect of pylon shape variation. Almas and Rajesh [2] performed 3-D models using straight and curved bridge cable-stays with A-shape, H-shape, and inverted Y-shape pylons. Modeling was performed using ANSYS software. It was concluded that the inverted Y-shaped pylon is naturally more appropriate for both curved and straight cable-stayed bridges. Shah et al. [30] performed linear and nonlinear analyses for bridges supported by three different configurations such as H-shape, A-shape & inverted Y-shape under aerostatic loading. They concluded that the H-shape gives higher straining action than the inverted Y-shape and the A-shape. That makes the conventional H-shape to be the most demanding shape. Thakkar [33] performed dynamic and aerostatic analyses on different shapes of cables-stayed pylons. This analysis was formed for different main span lengths (200, 400, 600, 800 m). He found that the increase in span increases the axial tensile force in the cable. This is because the segment length and the depth increase, so the weight of the deck increases and thus the axial force in the cables. The delta shape of the pylon has less forces than others in both the Linear and Dynamic cases for Girder axial force, while in terms of shear and pylon torsion, both H shape and A shape shaped pylons perform better, and in terms of pylon moment, the Inverted Y shape, as well as H-shape and A-shape, perform better.


The key purpose of this study is to make proposals for the design of cable-stayed bridges due to seismic loads. 3-D finite element models were performed using numerical analysis to study the behavior of different pylon shapes under static and seismic loads. Also, this study presents a methodology to follow when designing cable-stayed bridges to estimate the deck width for a certain main span length.


This study shows most of the shapes of the pylon that are adopted in the construction and design of new cable-stayed and most of the existing cable-stayed bridges. The performance of the eight pylon shapes (A-shape, A-D shape, inverted Y-shape, inverted Y-D shape, delta shape, pyramid shape, H-shape, and inclined H-shape) will be compared. Pylons have some different dimensions since each shape has its own configuration for cable. The distance between cables in a pylon is constant, but the pylon legs will converge or diverge depending on the shape as shown in Fig. 4. The deck width is equal to 18.7 m and there is a 1 m free distance between the deck and the edge of the pylon deck. The width of the pylon leg is 4 m. The first cable is located at 4 m from the top of the pylon followed by, equally located cables. The distance between them is 2 m and the total height of the pylon is 90 m. The ratio between Hp/Lm is constant equals 0.3 and the ratio between Ls/Lm is constant equals 0.5. Where Hp refers to the height of the pylon above deck. Lm refers to main span length and Ls refers to side span length. Section 1-1 intersects the center line of the lower tie beam at a distance of 24 m from the base. Then there is 10 m variable section (2-2). For H shapes, the pylon continues with the section that ended by section (3-3). Upper strut beam is located at level 69 m from the base for H-shape. A-D shape point of intersection of converged pylons is at 69 m from the base for A. For Y, Y-D, delta, and pyramid shapes, the point of intersection is located at 61.5 m from the base. Y, Y-D, delta, and pyramid shapes also have tapered sections after intersection for 7.5 m to reach the same level as other shapes (69 m from the base). Cross-sections are shown in Table 1.


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