Drgania i Stateczność Masztów oraz Iglic - Naleszkiewicz, J.; Szaniawski, A. (Engineering Transactions, 1953)
The paper is composed of two parts: the first containing the derivation of the general integral equation of oscillation and stability of a mast, and the second containing an example of computation of the period of oscilation and of the critical force of the obelisk erected in Wrocław in 1947. Taking an elastically fixed cantilever whose flexural rigidity varies incontinuously, the influence function is calculated for a transverse load and its partial derivatives. The load at a certain height is assumed to be composed of (1) a vertical load Q, (2) a horizontal load by the force of inertia P, and (3) a concentrated moment of inertia N. These assumptions permit to find the partial deflection yq (xc, s). For the real load, composed of the concentrated loads Qi, the radii of Inertia being equal to O1, and the weight of the cantilever, q (s) and o (s) denoting the weight of unit length and the radius respectively, we up all the partial deflections. sum After some transformations we obtain the desired integral equation of the resulting deflection. In the second part the influence of shearing forces and moments of inertia is approximately estimated, the values of rigidity, the radii of inertia and the weights being calculated from the drawing of the obelisk. In the case considered and in many other practical applications a simplified integral equation can be used, neglecting the influence of shearing forces and that of rotation of cross section. The process of integration is replaced here by approximate numerical formulae, approximate equations being established for the period of oscillations and for the critical load. Hence the required quantities are found by the method of successive approximations.