APPENDIX.] PIVOT SPAN. 371 



them we can easily find the reactions for the apex loads of 10 

 tons each. 



Thus, for P t make a = 1, and we have 



R A = 7.415, R B = RC = 1-58, R D = - 0.585. 



For P 2 make a = 2, and 



R A = 4.964, R B = R c = 3.035, R D = - 1.035. 



For P 3 make a = 3, and 



R A = 2.78, R B = R = 4.22, R D = - 1.22. 



For P 4 make a = 4, and 



RA = I? RB RO ^5 RD = ! 



Loads upon the centre of the span B C acting, that is, at 

 apex 10, give no reactions, but are supported directly by the 

 turn-table. Hence, for P 5 ; R A , R B , R c and R D are zero. For 

 the first load, P 7 to the right of C, the reactions at A and B are 

 the same as for P 3 at D and C, already found. For the next 

 load, P 8 , the reactions at A and B are the same as for P 2 at D 

 and C, already found. For P 9 , the same as for P t . For P 6 , as 

 for P 4 , etc. 



We thus have the reactions at A and B due to every indi- 

 vidual apex load, and can now proceed to find the strains. 



Our formulae, it will be observed, thus become very simple 

 and easy of application for any particular case. 



2^. FLANGES BRIDGE SHUT. 



Let us first find the strains in the flanges. We have only to 

 apply the method of moments, and tire work is so simple that 

 an example or two will suffice. 



We repeat again the rule. Conceive a section cutting only 

 three strained pieces. Take the intersection of two of these as 

 the centre of moments for finding the strain in the third. The 

 moment of the strain in this last about this point must be equal 

 to the algebraic sum of the moments of all the forces acting 

 between the section and one end. Take P x for example. Its 

 upward reaction at A is 7.415. [A negative reaction acts 

 dcwn. Thus, for P 7 above, the reaction at A is, from our for- 

 mulae, 1.22. The minus sign indicates that the reaction is 

 down, and that, neglecting the dead load, the girder must be 

 held down to the support A. If the reader will draw roughly 

 the curve of deflection, he will see that this is so.] 



