CHAP. XII.] METHODS COMBINED. 187 



D, prepositive. Reaction and moment at B negative reaction 

 at A positive ; as a little consideration of what the curve of the 

 deflected beam must be, will show. The shear at C is, there- 

 fore, + H a ab + bc=+Hc. The shear at B is H b or 

 + H a a by and so on. The shear being always given by the 

 segment between H and lines parallel to A b, b c i} GI d and d D. 



2d Case. PI. 22, Fig. 85. Load in B C. 



Having found the distance B % from the equation for this dis- 

 tance of the point of inflection above, we lay off ^ 0^ = ^ i l 

 and thus draw c x E at an angle of 45. Finding then the value 

 of C 4 from its equation above, we can draw E c^ and then 

 C 2 D and <? t A. The construction is then the same as before. 

 Thus H is the pole distance, H c the negative reaction at D, 

 H b the negative reaction at A, and ^ b, c E the positive re- 

 actions at B and C. The shear at B is H c 1} etc. Thus the outer 

 forces are completely known for a weight at any point. It will, 

 however, in general, in practice, be found more satisfactory to 

 use the formulae . for the reactions which we have given than to 

 find these reactions by the above construction. 



We shall now illustrate the preceding principles by an exam- 

 ple taken from actual practice. 



124. Draw pan Example. In PI. 22, Fig. 86, we have 

 given to a scale of 20 ft. to an inch the elevation of one of the 

 trusses of the pivot draw over the Quinnipiac River at Fair 

 Haven, Conn.* 



Length of span A B = 89.88 ft. B C = 21.666 ft, divided 

 into seven panels of 12.84 ft. and two of 10.833 ft. respectively. 



Height at B and C, 16 ft. ; at A and D, 12.1 ft. Diagonal 

 bracing as shown in Fig. Line load 9 tons per panel. 



01 f 

 In this case n = ' or n = 0.24106, hence the equations 



89.88 



of Art. 120 become 



1298 ^+0.1836 



= P fl-1. 

 \ 



= C = P ( 0.6836 ? 

 \ I 



6836 -0.1836 



* Designed and erected by Clemens Herschel, C.B., and probably the only 

 structure of the kind in this country for which the strains have been accu- 

 rately and thoroughly determined. For the above data I am indebted to M. 

 Merriman, assistant engineer in charge. 



