Engineering Transactions, 10, 1, pp. 97-113, 1962

Przybliżone Obliczanie Dużych Ugięć Sprężystych Belki na Podporach Nieprzesuwnych

Z. Waszczyszyn
Politechnika Krakowska

This is an approximate solution of the problem treated in a rigorous manner in Ref. [5]. The equations obtained in that reference require, however, previous solution of a set of transcendental equations in order to obtain the deflection angles in function of the load. The solution of these equations by iteration, for instance, is very toilsome and complicates considerably the analysis. In the present paper, the application of power series to the solution of transcendental equations has led to approximate equations expressing in a closed form the deflection angle 8, the horizontal reaction force X and the deflection angle f. This enables us to plot diagrams of ô, x and fin function of the external load e, for beams of various slenderness r. From the graphs it follows that the rejection of the influence of the horizontal reaction with small deflections is justified for beams of small slenderness. For slender ones, even with relatively small deflections, great horizontal reactions appear and the deflection itself undergoes considerable reduction.
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[in Russian]

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