186 GRAPHIC AND ANALYTIC [CHAP. XIL 



123. Construction. We may, if desired, apply our method 

 of construction to the determination of the reactions. Thua 

 from the above reactions we may easily determine general ex- 

 pressions for the inflection points. For the case of a load in 

 C D = n I (PI. 22, Fig. 85), we have, when i is the distance of 

 the inflection point from C, 



- Bp x (n J - 1) + P (o - *) = ; 



P a R D n I 

 whence ^ = = . 



XT J\jj 



For the inflection point distant i from B in the unloaded 

 span, 



R.(nl + i) R B *= 0; 



R.nl 

 hence ^ = = =-. 



*** K A 



For the second case of load in B C = I, we have for the in- 

 flection point between B and P 



R A (n l+i) + R n i = 0, or 



IR.nl 



4. ., . A 



RB-R; 



For the point between P and C 



R D (n l + i) + R * = 0, or 



._ R D nl 



RC~KT> 



The insertion of the proper values of the reactions for each 

 case, as given above, will easily give general expressions for the 

 inflection points, which the reader may, if desired, deduce for 

 himself. 



Our construction is, then, as follows [PI. 22, Fig. 84] : 



\8t Case. Load in C D. 



Having found i^ draw a line at any inclination, as ^ d through 

 1} intersecting P at d, and the vertical through C at c^ Then 

 lay off B i and draw d D, ^ b and b A. 



Make d c = P by scale, and c D drawn parallel to GI d then 

 gives the pole distance H. The ordinates, then, to the broken 

 line A J ^ d "D taken to scale of distance, multiplied by H to 

 scale of force, give the moments at every point. Moreover, H d 

 is the reaction at D. Draw D b parallel to c t J, then c b is the 

 reaction at C. In like manner a b is the reaction at B, and H a 

 the reaction at A. The moment at C, and reactions at C and 



