A Review on Various Methods used in the Analysis of Bridge Decks

Abstract

There are various methods which are used by the researchers for the analyzing of bridge decks. These individual methods have their own advantages and limitations. The methods which have been discussed are Plate Theory, Grillage Method and Finite Element Method. However Nowadays the FE Method is being used commonly due to various reasons, but this paper presents the various work done by the few researches using the mentioned methods and their findings. Literature Review Harrop J. (1970) had supplied the strip method of design of skew slabs. The Practical necessities often dictate that during skew slabs the reinforcement be placed parallel to the Sides of the slab in place of in an orthogonal layout, and it's far therefore higher to recall Equilibrium moment fields where the moments are oriented in the reinforcement instructions. The vital equilibrium conditions have been derived and an affinity relationship between skew and square slabs was established. In this situation use become made of the equilibrium equation inside the square coordinate system, because if the slab is to be strengthened with metal parallel to the edges of the slab then it is high quality to apply equilibrium second fields with the moment directions being similar to the reinforcement guidelines. The strip approach offers a relatively simple way of designing strengthened concrete slabs for closing load carrying capacity. The fall apart load of a slab designed by means of this approach will be equal to or more than the design closing load relying on whether or not or no longer the reinforcement is curtailed to give precise correspondence among the equilibrium moment field and the last resistance second area. The design moments for the radial and angular directions are distributed to the corresponding strips. The cost of material in the curved slab is treated as the objective function that is to be minimized. This will be a function of the design variables that are usually the effective depth and the transformed percentage of steel ratios. The objective function is then minimized subject to the behavior constraints, which are the various limit states, and side constraints. Thus the limit states will define the feasible region in the design variable space within which an acceptable design solution can be found. The search for the optimum is carried out in stages. Initially, the feasible region defined by the critical limit states, namely, the intersection point of the ultimate limit state and one of the serviceability limit states, is considered. The optimum solution for the section at which the maximum moment occurs is obtained in this feasible region. This solution is then checked to see whether it lies in the feasible region defined by the other limit states. In order to determine the optimum solutions in this region, the successive linear programming is introduced as an analytical method of nonlinear optimization. The convergence of the solution is extremely fast; Four to six iterations were sufficient. The optimization procedure developed in this study can be extended to other curved structural elements. And they also suggested that other design codes may be incorporated by appropriate changes in the program. Issam E. Harik and Bassam F. Haddad (1986) extended the application of the Analytical Strip Method (ASM) of solution to stiffened sector plates. The plate was idealized as a system of horizontally curved plate strips and beam or rib segments rigidly connected to each other. The behavior of the system was derived by imposing the edge and continuity conditions on the closed form solutions of the individual plate strips and beam elements. The method is applicable to plate-stiffener systems subjected to various loading conditions and with different boundary conditions along the straight and circular edges. The advantage of the ASM solution over the "equivalent" orthotropic plate substitute is that unequally spaced stiffeners and stiffeners of different cross-sectional properties can be introduced in the solution. Results are presented for stiffened sectors with different edge and loading conditions. The ASM can deal with mixed boundary conditions, uniform loads, line and point loads, Similar to the finite strip and spline finite strip methods, the ASM is limited to clamped and or simple supports along the straight edges. Issam E. Harik and Joseph M. Abou-Khali (1986) studied horizontally curved plates on elastic foundations. Horizontally curved concrete (or rigid) pavements of highways are problems of considerable practical importance, which were related to the solution of sector