184 OEAPHIO AND ANALYTIC [CHAP. XII. 



That is, the reaction at A is due to the moving load alone, 

 as evidently should be the case, and is, moreover, just what it 

 should he for a girder with level supports / viz., | m I. (See 

 also Appendix, Art. 18, Ex. 5.) 



The raising of the centre support, then, will not affect our 

 construction for the reactions as given in Figs. 81 and 82, pro- 

 vided there are only three supports. 



We have deemed it well thus to call special attention to the 

 considerations of the last two articles, both on account of their 

 practical importance and because they are not brought out 

 clearly, nor indeed, so far as we are aware, even alluded to in 

 any treatise upon the subject.* 



122. Beam continuous over four Level Supports. We 

 thus see that a draw or pivot span is more properly considered 

 as a beam of three spans instead of two, of which the centre 

 span is very small compared to the end spans ; it may be only 

 two or three panels long. Moreover, we must often in practice 

 consider the beam as a " tipper," and therefore apply the formulae 

 for reactions of Art. 120. If, however, by reason of the method 

 of construction, as often happens, for instance, by the under 

 portion of the beam coming in contact with the frame below, 

 this tipping of D D (Fig. 83) is confined between certain limits, 

 beyond which the supports must be considered fixed, it will be 

 necessary to find the reactions as for a beam over four fixed 

 supports, and determine the corresponding strains in this case 

 also. 



Comparing, then, the strains obtained each way, we take only 

 the maximum strains from each. 



The formulae for the reactions at the fixed supports A B C D 

 are as follows (PI. 22, Fig. 84) : 



1st. Load P in left end span A B at a distance a from left 

 support A, the end spans being n I and the centre span B C=2. 



We put Jc = and H=3 + 8w + 4n 2 . Then 

 nV 



R A =gj H-(H+2 tt+2 n 2 ) &+(2 n+Zn^Z* 



* Clemens Herschel, in his treatise upon " Continuous, Revolving Draw- 

 bridges" (Little, Brown & Co., Boston, 1875), notices this fact for the first 

 time. 



