Engineering Transactions, 6, 4, pp. 559-602, 1958

Drgania Przestrzenne Mostów Jednoprzęsłowych

E. Bielewicz

This paper presents a tentative theoretical examination of space'
vibrations of single span bridges. The following generalized forces moving with constant velocity along the bridge are assumed to constitute the load: pulsating vertical force, pulsating horizontal force, pulsating torque, vertical impulse, horizontal impulse and torque impulse. The action of a vertical and horizontal force and a torque varying in time in an arbitrary manner is also considered. In Sec. 2 the structure of the bridge is replaced, with a number of simplifying assumptions, with a thin-walled bar. For the substitute thin-walled bar differential equations of motion are established, disregarding the influence of the mass of the vehicle on vibration. Solutions are obtained by means of Fourier series. Bearing in mind that the passage of a vehicle lasts for a very short time it was necessary to consider simultaneous forced and free vibration.
In the Sec. 3 a substitute model of bridge vibration is introduced for
the purpose of establishing approximate equations of bridge vibration taking the mass of the vehicle and the variability of cross-section into consideration. Vibration of open and closed bridges are considered. In birth sections the damping is assumed according to Sorokin's hypothesis.
As an example a calculation of horizontal torsional vibration is carried out for an open bridge 36,08 m in span. This enabled the obtainment of several conclusions of qualititative character.

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