FORMULATION OF DESIGN AIDS FOR ARCH BRIDGES

Abstract

This research effort is aimed at studying arches, their analysis and design. In this study small computer programs in MATLAB are being developed to obtain numerical solutions for arches of parabolic, circular,etc., for loadings that govern their design. . The governing differential equation of a parabolic arch is derived and it is made linearized so that solutions can be obtain effortlessly. Various design parameters are formulated in non-dimensional form so that the designer can design and analyse effortlessly and give them an intuitive understanding behaviour of the structure. For buckling analysis, instead of using curved beam elements, the arch is being modelled as consisting of a large number of small straight beam segments arranged according to the shape of the arch. This model is like the finite element model that is created in modem computer analysis, which also lack provision for curved beam elements. However, instead of using nodal DDOFS as the unknowns, these programs will use maximum of TI-IREE unknown REDUNDANTS - the horizontal reaction, the bending moment at the left-end of the arch and the bending moment at the right-end of the arch. Thus, these programs will be able to cater to three-hinged, two-hinged and fixed-fixed arches of parabolic, circular, elliptical and catenary shapes In reality a structure is in static equilibrium in the unmoving state attained after all deformations have occurred. It will be assumed that the reference arch shape corresponds to its deformed state after dead loads have been applied, because all the deformations that occur due to dead loads during construction of the arch bridge can largely be compensated by the designer by estimating them beforehand and incorporating the estimates in the construction process itself. The live load will then be applied in small increments and the change in geometry of the arch will be computed after each increment and this change shall be considered for computing the values of the redundants. It is proposed to consider change in geometry due to flexural deformations only. It is proposed to neglect shear deformations and axial deformations and geometric stiffness effects of shears and bending moments, because well-designed arches should largely be funicular for dead loads and shears and bending moments due to non-funicular loads should be small. And further, live loads are typically a small fraction in comparison to dead loads, and the axial deformations due to dead load are assumed to have been compensated by the designer during the construction process. Neglecting axial and shear deformations reduces the number of design parameters, and usually the axial and shear stiffness of arches should be quite large. The analysis model, loading and results of the analysis shall be presented in the form of non-dimensional charts, which will be specially suited for preliminary design of the arch bridge. The form of these non-dimensional charts has been decided based on results reported in research literature; and our results will be compared with results reported therein.