Su Luo & Yun 2010  'Literature Review' chapter

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This therefore renders the bifurcation point instability null and void for the cable strayed as well as suspension bridges (Ren,1999). Cheng, Jiang, Xiao and Xiang (2001) pointed out that in theory, the analysis of the aerostatic stability of such kinds of bridges should be regarded as a limit point instability challenge. In their paper, which is based on the limit point instability concept; Cheng, Jiang, Xiao and Xiang (2001) presented a nonlinear finite element method (NFEM) in order to evaluate in a more direct manner, the critical velocity of the wind for all cases of suspension bridges suffering from aerostatic instability. In these bridges, the three main components of the wind loads together with the geometric nonlinearity are taken into consideration. This required the employment of a specialized computer program called NASAB which had its basis on the nonlinear technique was tested for numerical examples. Jiang Yin suspension bridge's aerostatic stability was investigated via the NFEM. The outcome was found to give information on the critical wind velocity of the NFEM which was noted to be greater that the magnitude obtained via the linear technique. The cause of the difference was explained. In their study, they also explored certain other aerostatic stability parameters necessary for various bridges.

Mikkelsen & Jakobsen (2010) performed a flutter analysis on the Hardanger bridge. In their analysis, they investigated the aeroelastic stability of the bridge which is a suspension bridge having a main span of about 1310 meters and was being constructed in Norway. The wind and structure system was described via a state-space format in a multimodal flutter analysis format. The outcome of the multimodal flutter analysis on the basis of the ambient vibration data had earlier in been reported by Jakobsen and Hjorth-Hansen (2007). Their work on the otherhand had its basis on the motion-dependent loads that were obtained from the forced vibration wind-tunnel tests using a 3 DOF-section model. The resulting aeroelastic loads were then approximated using the rational function approach that is closely associated with the frequency independent system matrix. This eliminated the need for iterating the eigen-values.

Xin-jun (2005) on the other hand performed an advanced aerostatic analysis for suspension bridges that are lengthy. He employed an advanced method aerostatic analysis that relies on the consideration of the geometric nonlinearity, spatial non-uniformity of the wind speed as well as the nonlinear wind-structures. The example of suspension bridge that was considered for this work was Runyang Bridge that runs over the Yangtze River. The parameter that were investigated included the effects of the nonlinear interaction of wind, the spatial uniformity of the wind speed as well as the wind load of the cable on the overall behavior of the suspension bridge.

Quite a number of studies regarding nonlinear aerostatics stability analysis of suspension bridges have been conducted. For instance, Liu et al. (2004, p.56) conducted an analysis on aerostatic responses of the cable-stayed bridges that are having long life spans. He took into consideration the geometric parameter's uncertainties and again, he took into consideration the aerostatic coefficients of the major girder. On the other hand, nonlinear impacts because of the interactions from wind-structures and geometric nonlinearity were not taken into consideration since the cost of computation was so high because the technique needs a fresh round of the analysis of FE for every sampling check. Cheng et al., (2004, p.780) also carried out a stochastic study of aerostatic stability for suspension bridges through the use of MCM that had its basis on cycle solutions. This needs very minimal work of computation. On the contrary, the cycle solutions are majorly appropriate for the study of torsional divergence, and therefore it is hard to widen the technique to analyze other kinds of bridges.

Similarly, the aerostatic behaviors of suspension bridges having long-span was expansively studied by Boonyapinyo et al. (1994, p.500), Xiao and Cheng et al. (2002, p.45).

The aerodynamic stability and static stability of bridges that are cable-stayed have been researched by numerous authors. Aerostatic instability may be grouped into two kinds depending on static instability modes: lateral-torsional buckling and torsional divergence. The two aerostatic instability phenomena were studied by Boonyapinyo (1994, p.504).

Simiu and Scanlan (1978) developed a linear technique to critically analyze the long span bridge's torsional divergence. Similarly, Xiang et al. (1996, p.) wrote the method that was used by them. These two techniques had their basis on the suppositions of linear structural inflexibility matrix and also of linearized pitch moment. Hence, critical velocity of wind that causes aerostatic instability can't be calculated accurately, the instability mode and also the coupling impacts can't be taken into consideration. The quick development of computers and also the finite-element methods that are nonlinear has resulted into the consideration of the nonlinear impacts that arises from the structures of the bridge and also the three wind load elements, and to assess the aerostatic reaction by NFEM. Boonyapinyo et al. (1994, p.501) also used a nonlinear technique that merges eigenvalue scrutiny and also bound algorithms so as to examine the wind-induced non- linear lateral-torsional buckling of cable-stayed bridges. On the other hand, it is having three disadvantages. First, the notion of divergence point instability with its basis on eigenvalue study may not be valid for the bridges that are cable-stayed. This is due to the fact that: its components like the towers and girder are subject to bending moments and also axial forces; before the application of wind loads, the bridges may have sustained very heavy built-in loads of construction in order that the first stresses and deformations are present in all the members.

Probabilistic analysis is providing a device for including the uncertainties of structural modeling so as to estimate the factor of cable safety by stating that the uncertainties are random variables. Matteo et al. (1994, p.3200) came up with a methodology to approximate the present safety feature for the major suspension cables. This methodology is estimating the factor of cable safety through the use of elastic frail wire models and ductile wire. Cremona (2003, p.379) came up with a probabilistic method for the assessment of the residual strength of the cables. The usage of probabilistic method in the cable safety has resulted into a number of applicable representations of actual consistency of the major cables. The present standards of the designs of bridges have been come up with so as to ensure that there is structural safety through the definition of target dependability index . Li and Foschi (1998, p.260) came up with an contrary reliability technique for determining parameters of design, and used it to provide solutions to the perils of offshore engineering and earthquakes. Fitzwater et al. (2003, p.250) also used inverse reliability techniques for stall-regulated wind turbines and great loads on pitch.

Hirai et al. (1967, p.90) established that lateral-torsional buckling of the suspension bridge may take place through the action of static wind loads. A number of researchers have conducted studies regarding nonlinear buckling bridges that are having long-span. This is because of stationary wind loads from the hypothetical viewpoint.

A computer program (BSNAA) was come up with for aerostatic study regarding bridge structures (Zhang et al., 2002, p.1065). In the year 1967, Hirai et al.1 illustrated that lateral -- torsional collapsing of suspension bridges may take place below stationary wind loads. For quite sometimes, researches on performance of the longspan bridges below wind loads have gained lot of momentum. A number of studies have also been conducted regarding the growth of arithmetical techniques for aerostatic scrutiny of the bridge structures having long-span bridge structures. Boonyapinyo et al.2 provided a presentation of a finite-component method to direct the purpose of wind speed for lateral -- torsional buckling instability that is non-linear. They established that the combination of the three elements of displacement-dependent loads of wind and also geometric non-linearity was capable of giving more dependable outcomes for critical wind speed. Researchers like Cheng et al.,(2002, p.44), Xie et al., (1997, p.770) and Fang et al.(2000) have also conducted investigations regarding similar problem.

With the fast growth of transportation, the span length of bridges is always growing. Besides, bridges are getting lighter, more susceptible and more flexible to problems that are induced by wind. Current outcomes of wind tunnel checks and studies are indicating that aerostatic unsteadiness of supported bridges may take place (Boonyapinyo, et al., 1994, p.490; Cheng, et al., 2002, p.42; Fang, et al., 2000,). Under a given wind speed, torsional deformation and bending of the deck of bridge takes place. Again, the deformation alters the inflexibility (Xiang, et al., 2005). The incremental iteration technique (Cheng, et al., 2002, p.40) is efficient and effective in the calculation of aerostatic firmness of bridges. It is widely used. 'incremental' implies that wind speed is increasing with a given proportion. Internal iteration can be applied in the calculation of structural nonlinearity. Similarly, outer iteration may…

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