Statyka Mostu o Przekroju Otwartym w Łuku

The subject of this paper is the derivation of accurate and approximate equations of structural analysis for an open cross-section bridge (Fig. 1). It is assumed that the total torque is equilibrated by a pair of shearing forces in principal girders. The theory of double-tee beams, curved in the plane of the flanges, in conditions for which it can be assumed that the torque of pure torsion is equal to zero, has been treated in detail by Umanskij, [4]. The present author applies this theory to a double tee-beam curved in the plane of the web. In order to preserve the simplifications introduced by Umanskij, the author defines the bimoment as an integral of the torque (2.10). The bimoment thus defined will not be a pair of moments. Starting from the equations of equilibrium of an element (Fig. 11), formulae for such a bimoment are derived, (2.14). For the purpose of determining the reaction due to a concentrated force points are first determined for which the corresponding bimoment of only one reaction is different from zero. Next to be determined, setting equal to zero the sum of bimoments of all forces (including the reactions) in relation to these points, is the influence lines for the reactions (2.21) and (2.22). After determining the influence lines for the reactions, next come the influence lines for shear forces in the outer girder (2.25) and the inner girder (2.25.2), and the lines for bending moments (2.26.1) and (2.26.2). The approximate solution is the first iteration for the solution of the corresponding system of differential equations.
The computation of approximate formulae for the influence lines is very simple, since the approximate differential equation of the bimoment is identical with that of beam deflection. The approximate statical quantities the approximate equations (3.11) - (3.14) are determined by means of polynomials. The numerical example discussed shows a high degree of accuracy in the approximate equations.