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UBC Theses and Dissertations

Analysis of continuous arches on elastic piers. Wong, Dick Chao

Abstract

This thesis presents the investigation of the behaviour of continuous arches on elastic piers about which little is currently known. A series of studies were made to indicate the effects of pier dimensions on extreme fiber stresses at a number of critical sections of arches. Such results are of particular interest to the bridge designer. Six numerical examples of symmetrical arch systems have been solved, using an interesting variation of the force distribution method of the late Prof. Hardy Cross. The relative proportions of the system were based primarily upon aesthetic considerations. In the six structures which were investigated two systems of arches and piers, called I and II, were considered. Each system has five spans. The variable span lengths are the same in each system. The arches in each were selected from Whitney's paper and are linear arches for dead load only. In System I the arch ribs are lighter and flatter than in System II, and the piers are more flexible. In each system the variation of span lengths and arch rises are such so that there is no unbalanced dead load horizontal thrust on the piers. In both systems all piers are of single equal batter. Three different heights of pier 40', 60', and 80' were investigated in each system. Figs. 1, 2 and 3 clarify the foregoing while Tables 1 and 2 give the properties of the elements making up each system. In System I twenty influence lines for upper, lower, right, and left kern moments at springings, crowns, and pier tops were constructed. In System II "portions" of sixteen influence lines for upper and lower kern moment at springings and crowns sufficient to establish the trend of alteration of proportions were constructed. The large number of variables involved in the design of such indeterminate structures as continuous arch systems makes it inadvisable to draw too definite conclusions, but some results of studies obviously indicate that : (1) All controlling L.L. fiber stresses are greater than those in fixed ended arches and increase as the height of piers increases, but the maximum D.L. + L.L. fiber stresses do not exhibit this characteristic as might be expected but depend, of course, upon the ratio of dead load to live load as well as upon the proportions of the structure. (2) It would appear that the analysis may be confined to three spans for arches and two spans for piers, save in the case of a long centre span combined with very flexible piers. In such a case the complete structure must be involved in the analysis. (3) The effect of rotation of the pier tops on L.L. stresses at crowns is small and almost independent of pier height, whereas the effect on L.L. stresses at springings is somewhat greater and increases slowly as the height of piers increases. The effect of translation of the pier tops on L.L. stresses at springings and crowns is usually the greatest and increases rapidly as the height of piers increases. The results presented herein are, of course, true only for this particular type of system, but the author feels that the system chosen is more representative of a structure which might be constructed than are the typical three or four equal span systems of the text book variety with which some writers, more concerned with simplicity than reality, have dealt.

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