Engineering Transactions, 14, 1, pp. 49–68, 1966

Pewien przypadek kształtowania belek pod obciążeniem ruchomym

Wojciech MARKS
Instytut Podstawowych Problemów Techniki PAN

A certain case of determination of the optimum form of prestressed beams under moving load

The object of the present paper is to propose a method for determining the form of a prestressed beam under moving load. The criterion chosen for the determination of the shape is that of equal extreme unit potentials of elasticity Ψ produced by the moving load, at possibly many points. This is equivalent to the criterion of maximum rigidity under the same load and does not concern any strength theory.

The configurations of the moving load that produce in an isostatic beam of a given cross-section the maximum unit potential are analysed. The author obtains a function g(u, y) expressing the thickness of the beam, which is variable in the longitudinal and vertical directions. The relations obtained are made use of in a numerical example illustrating, the determination of the form of a beam for a prestressed railway bridge.

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Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).


Z. Wasiutyński, A. BRANDT, The present state of knowledge in the field of optimum design of structures, Appl. Mech. Rev., 5, 16 (1963).

Z. Wasiutyński, O ksztaltowaniu wytrzymaloiciowym, Akad. Nauk Techn., Warszawa 1939.

O. Gross, W. Prager, Minimum weight design for moving loads, Proceedings of the Fourth U.S. National Congress Applied Mechanics, Vol. 2, 1962.

M. Save, W. Prager, Minimum weight design of beam subjected to fixed and moving loads, J. Mech. Phys. of Solids, 4, 11 (1963).

Ю. А. Радо, Статически неопределимые фермы найменыиего объема, Труды Казанского Авиациовного Инстиl.ута, в. 51, Казань 1960.

А. И. Виноградов, Некоторые вопросы расчета стержневых систем з заданными напряжениями, Исследования по теории сооружений, т. 6, 1954.

A. Brandt, Ksztaltowanie belek sprężonych przez wyrównywanie skrajnych naprężeń, Rozpr. Inżyn., 2, 8 (1960).