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Straight and curved rectangular plate and box-girder bridge 

Straight and curved rectangular plate and box-girder bridge 

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The plated structures are one of the most frequently used engineering structures. The object of this research work is the optimal design of curved folded plates. This work is an ongoing investigation. There are various solution methods to analyze this type of structures. Here the finite strip method is used. At first single load condition is consid...

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... expression (55) K g means ∂ t g t g . As usual, the box constraints are treated separately from the compliance inequality constraint, as they are not involved in the formulation of the La- grangian function, but examined at every iteration cycle. Therefore, if a thickness happens to fall outside of the feasible set, in the next cycle it is forced to start with the boundary value ( t max or t ) of the box. In the following, sample problems are introduced to illustrate the above explained methods. As already mentioned, the Finite Strip Method is used for the evaluation of the state variables, which excels in the calculation of structures with constant cross section. These include the following examples: At each run, quadratic base functions were used in the cross section. The boundary conditions are also the same, according to the rules of the classical finite strip method (CFSM). This means that hinged supports were prescribed by choosing the proper trigonometric functions, while no additional boundary conditions were imposed. Here we note, that in all cases, the cross sections should be understood in the x-z plane, therefore in Fig. 5 size ‘a’ means the width of the plate and size ‘b’ means it’s width and accordingly the thickness is the size in the ‘z’ direction. The introduced plate was subjected to various loads, which positions are given with coordinates relative to the upper left corner, as seen in Fig. 7. The first load case is a single concentrated force F 100 kN pointing downwards, acting in the geometric middle of the structure, so according to the notation of Fig. 7, ξ = 3 m and η = 4 m in this case. The obtained thickness distribution can be seen on the left of Fig. 8. The result for the same setup, but with a hor- izontal load is presented on the right of the same picture. With two concentrated forces of both 100 kN placed at ξ = 2 m and 4 m , η = 4 m : The setup of these examples is the same as at the straight plate, with the di ff erence, that the loads positions should be understood with the same value, but in a cylindrical relative coordinate system, illustrated on the next figure. The geometry of this example is presented on Fig. 12. On the next figure (Fig. 13), the loads are always placed at the mid-span on the top flange at the position of the webs, so according to the notation of Fig. 11: ξ = 2 m and / or 4 m , η = 5 m . The geometry of this example shows no di erence to the pre- vious one, except that the bridge has a curved geometry around the vertical axis. Only one load case was investigated, which can be put into comparison with the upper left picture of Fig. 13. The position of the concentrated forces should be understood as before. A numerical procedure and computer program were elaborated for optimization of folded plates subjected to multiple loadings. The computational method is based on the finite strip method. The elaborated procedure with a slight modification can be suitable for the case of stochastic loading and / or multiple loading cases, as well. The surrogate loading system is problem dependent. To make more appropriate models it is needed to make some additional investigations on the topic. The present study was supported by the Hungarian National Scientific and Research Foundation (OTKA) (grant K ...

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