Art. 142. 



EQUIVALENT LOADINGS. 



287 



bridge. Thus, a uniform load is used which will give the same 

 maximum moment in the stringer as the specified wheel loads; 

 another which will give the same maximum shear in the stringer, 

 another that will give the same maximum floor beam concentra- 

 tration (and stress in the hip vertical) ; and another that will give 

 the same maximum moment or end shear in the truss. A 

 through plate girder is treated like a truss and a deck plate 

 girder like a stringer. This method of equivalent uniform loads 

 gives exact results then, so far as the maximum moments and 

 shears in stringers, girders, and floor beams are concerned. In 

 trusses, it gives results which are approximate except for the 

 maximum moment or maximum end shear. This method ne- 

 cessitates the determination of equivalent uniform loads for 

 different spans, for shears and moments, for each typical loading 

 (only one set is needed for all Cooper Loadings). Having de- 

 termined them for any particular loading for spans varying by 

 suitable intervals, a table may be made or a diagram plotted 

 for use in determining the equivalent uniform loads for any span 

 lengths. This reduces the calculations to that for uniform load 

 entirely and with results which, for ordinary bridges, may be 

 accepted with full confidence. 1 



Some engineers calculate stresses from wheel loads and 

 some use equivalent loads. One who is in the habit of calculating 

 stresses from wheel loads can do so with facility, but never with 

 the certainty and never in so short a time as from the simpler 

 load. In most cases the uniform load should be used as a check 

 if the stresses are calculated from wheel loads. 



In order to be able to calculate equivalent uniform loads, we 

 shall consider briefly methods of finding maximum moments and 

 shears from a series of concentrated loads. From the moments 

 we obtain the chord stresses and from the shears the web stresses. 



143. Preliminary Considerations in the Calculation of 

 Stresses from Wheel Loads. The problem is to find the position 

 of the loads that will give the greatest possible moment or shear 

 at any point of a bridge. Having the proper position of the loads, 

 it is a simple matter to calculate the moment or shear. (Chapters 

 Illto VI). 



The maximum stress in any member may be found by trial 



1 For comparison of results by different methods, with those by wheel 

 loads, see Trans. Am. Soc. C. E., Vol. 42, pp. 206 and 215. Also Eng. News, 

 Also Johnson's " Modern Framed Structures," Part I, p. 246 (9th Edition). 

 Also Du Bois's " Stresses in Framed .Structures." 



