APPENDIX.] PIVOT SPAN. 369 



NOTE TO CHAPTER XII, ART. 124. 



16. In Arts. 120 and 121 we have given the formulae and 

 principles necessary for the complete solution of the pivot span. 

 We propose here to illustrate more fully their application by a 

 simple example. 



Fig. IX. represents such a structure. The two outer spans 

 A B C D = 40 f t. The central or turn-table span, B C = 

 20 ft. Centre height at B and C = 10 ft. End height = 6 ft. 

 Panel length, 10 ft. ; each apex live load, 10 tons, or 1 ton per 

 foot. Dead load, half as much. Two systems of triangulation, 

 as shown in the Fig. 



Our proportions are taken for the sake of illustration merely, 

 and not as an example of actual practice. All the points to be 

 observed are, however, illustrated as well as by a much longer 

 span, and more usual proportions. 



It is to be observed that the end verticals are compression 

 members only, and cannot take tension. This is necessary to 

 prevent ambiguity as to the way in which the strains go. A 

 negative reaction might otherwise cause tension in 1 2, and 

 compression in F, or tension in 1 5, compression in 5 6, and 

 tension in A. If 1 5 cannot take tension, we have but one 

 course for the strains, and the problem is determinate. 



We also, for similar reasons, construct the centre span so 

 that the diagonals take tension only, $ftd the verticals compres- 

 sion only. These points as to construction being settled, let us 

 proceed, first, to determine the reactions. 



1st. REACTIONS. 



We shall consider the case of the " Tipper" or secondary 

 central span only [Art. 120], as this case most nearly ap- 

 proaches the true state of things. The method of procedure 

 for four fixed supports is precisely similar, only taking the for- 

 mulae for that case from Art. 122. 



The less the span B C, the nearer the case approaches to three 

 fixed supports ; and when the distance B C is zero, n is zero, and 

 our formulae are the same as for beam over three supports. 



For a load in the left span distant a from A, these formulae 

 are as follows [Art. 120] : 

 S4 



