An Analytical Approach for Dynamic Response of Timber Railroad Bridges

In the 1970's it was reported that there were approximately 2300 track miles of timber railroad bridges in the United States and Canada. For short spans, they offer an attractive alternative to other types of bridges as they are economical, faster to construct and easy to maintain. Current design practices do not allow an independent consideration of the effects of the dynamic loads in sizing of the bridge components because very little information is available on the subject. Dynamic tests were carried out in 1986 on timber bridge spans at two test sites using test trains consisting of a locomotive unit, two loaded hopper cars and a caboose. This paper gives a brief description of the analytical approach employed for determining the dynamic response of timber bridge spans under railway vehicles travelling at a constant speed. The model comprises a multi-degree-of-freedom system with each vehicle having bounce, pitch and roll movements. Two parallel chords, each having its distributed mass lumped at discrete points, were used to idealize the bridge spans. A computer program developed on this basis was used to predict the loads at the wheelrail interfaces and the vertical displacements at the discrete points on the spans. The predicted loads were found to be in good agreement with measured values while maximum predicted displacements were up to 20% higher than measured ones. The program was utilized to study the effect of speed and other factors on the dynamic response of open-deck and ballast deck bridges. Introduction The problem of the dynamic response of bridges has interested researchers since the middle of the nineteenth century. In 1851 Willis[1] gave an approximate solution for the case of a single constant load over a beam of a negligible mass. An exact solution of the equation he formulated was obtained by Stokes[2] in 1883. Later Timoshenko[3] in 1922 pointed out three major causes of vibrations in railroad bridges: the live load effect of a smoothly rolling load, the impact effect of the balance weights of the locomotive driving wheels, and the impact effect due to irregularities of the track and fiat spots in the wheels. He examined two possible extreme cases of the live load effect: that the mass of the moving load is either large or small in comparison to the mass of the beam, for a simply supported beam using the 1aegional Engineer Bridges and Structures CN Rail Prairie Region 460-123 Main St. Winnipeg, Manitoba R3T 2P8 2 Associate Professor Civil Engineering Dept., University of Manitoba, Wmnipeg, Manitoba, R3T 2N2