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UBC Theses and Dissertations

Analysis of flexible hingeless arch by an influence line method. Lee, Richard Way Mah

Abstract

An influence line method for the analysis of flexible hingeless arch by the deflection theory is presented in this thesis. To facilitate the work, tables of dimensionless magni fication factors are provided. Prom these tables, influence lines taking into account the flexibility of the arch may be readily drawn and used very much in the ordinary way. The flexibility of the arch was conveniently measured by a dimensionless ratio, [ equation omitted ], and called the stiffness factor of the arch. The tables are for parabolic hingeless arches having rise ratios of 1/8,1/6,1/4,1/3, with constant EI or a prescribed variable EI. Values are given for β = 3 and 5 with some for β = 7. Also the tables contain magnification factors for maximum moments at eleven points in the arch, when the arch is loaded with a uniform load. Although the given tables are good only for parabolic hingeless arches with constant EI or a prescribed variation in EI, the tables may be reasonably extended to other hingeless arches whose shapes are not too different from a parabola and to a wide variety of variation in moment of inertia, provided these variations are not unrealistic. The possibility of using superposition in the deflection theory is based on the fact that calculations showed the horizontal thrust acting on the arch was approximately the same either by the deflection theory or the elastic theory. Because of this, the horizontal thrust becomes independent of deflection and the differential equation for bending of an arch is linear. Thus superposition may be used. The differential equation was hot convenient for calculation. Instead, the solutions in the tables were calculated by a numerical procedure of successive approximations, using the conjugate beam concept. This procedure was conveniently programmed for an electronic computer, the ALWAC III E, at the University of British Columbia. In the first cycle of approximation, the programme assumed the horizontal and vertical deflections were zero. This represented the elastic theory analysis. In subsequent cycles, the deflected shape of the arch from previous analysis was assumed. Successive approximation as such led to a solution based on the deflection theory. Three numerical examples shown in this thesis indicated that the error introduced by the linearized deflection theory was small, and the influence line method may be used for analysis of flexible arches.

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