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Preliminary Calculations to Ensure Validity of Computer Analysis
Published in Bungale S. Taranath, Tall Building Design, 2016
The frame analysis for horizontal loads by the so-called cantilever method is obtained by assuming that (1) inflection points, that is, hinges, form at midspan of each beam and at midheight of each column and (2) the unit direct stresses in the columns vary as the distance from the frame centrodial axis. It is forces will vary as the distance from the center of gravity of the bent. Using these assumptions, the frame is rendered statically determinate, and the direct forces, shears, and moments are determined by equilibrium considerations. The application of the method to an example frame will now be considered. To get a comparison with the results of the portal method, we shall apply the cantilever method to a three-bay portal frame.
Optimisation of suspended-deck bridge design: a case study
Published in Australian Journal of Structural Engineering, 2020
Another method known as the Zero Displacement Method was initially proposed by Wang et al. (Wang, Tseng, and Yang 1993) and recently improved by Zhang and Au (Zhang and Au 2014). They look for the zero deflection configuration along the deck using iterative methods (the Kriging surrogate method in the case of Zhang and Au) that allow to find the initial optimum configuration of the bridge and the cable pre-tensioning forces but with convergence problems in presence of long spans. Four different optimisation methods are compared by Wang et al. (Wang, Vlahinos, and Shu 1997) to select the cable pre-strain that minimises the deformations and stress on the bridge girder due to dead loads (i.e. Minimising the Summation of Squares for Vertical Displacements along the girder (MSSVD), Minimising Maximum Moment of the girder (MMM), Continuous Beam Method (CBM) and Simple Beam Method (SBM)). They concluded that the optimal way to achieve the best result with minimum effort is the application of the Simple Beam Method, which is based on the equilibrium of forces and considers the bridge girder as a continuous beam on elastic supports while neglecting nonlinearities. Another method, the Force Equilibrium Method, has been widely employed in the literature (Chen et al. 2000). The chosen objective function assumes as independent variables the unknown cable pretension forces, which are determined by an iterative approach. Due to the simplicity of the method, it is very difficult to check the bending moment at the deck-tower junctions, and moreover, the nonlinearities are neglected. More recently, the Unit Load Method has been proposed by Janjic et al. (Janjic, Pircher, and Pircher 2002), among others (Asgari, Osman, and Adnan 2015; Lee, Kim, and Kang 2008b). This approach optimises the displacement, and minimises the member stresses through a multi-constraints approach, also resulting in a more uniform moment distribution along the deck. The method has the advantage of taking into account the geometric nonlinearities as well as the time-dependent effects (such as creep and shrinkage of materials, relaxation of pre-stressing tendons, etc.) and the actual construction process. Another method that takes into account the construction process is the Cantilever Method proposed by Wang et al. (Wang, Tang, and Zheng 2003). Numerous studies suggest an optimisation procedure based on minimisation of a convex scalar function (Negrão and Simões 1997; Simões and Negrão 2000; Martins, Simões, and Negrão 2015a, 2015b) that allows taking into account construction stages, geometrical nonlinearities and time-dependent phenomena. Finally, Genetic Algorithms have been employed by a number of authors (Martins, Simões, and Negrão 2016; Lute, Upadhyay, and Singh 2009; Yazdani-Paraei et al. 2011; Hassan, Nassef, and Damatty 2012; Cao et al. 2017).