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UBC Theses and Dissertations

Magnification factors for hingeless arches. Pelton, Thomas Edward

Abstract

This thesis presents a simple method for the determination of bending moments in flexible symmetrical hingeless arches. The deflection theory bending moments are obtained by multiplying elastic theory bending moments by predetermined magnification factors. The problem was to provide magnification factors for all cases of loading on a wide range of flexible symmetrical hingeless arches. By studying the differential equation a modified method of superposition was developed. Therefore, it was only necessary to determine magnification factors for a concentrated load at a number of positions along the arch axis. A convenient set of coordinates for the magnification factor was determined by dimensional analysis. Finally, an electronic computer was used to calculate the required magnification factors by a numerical method. Tables of magnification factors are presented for symmetrical parabolic hingeless arches. Magnification factors are given for rise to span ratios of 1/8, 1/6, 1/4, and 1/3 ; for constant and variable moment of inertia; and for values of [formula omitted]from 0 to 7, where H = the total horizontal thrust, L = the span, EIa = the average flexural rigidity.

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