42 MOMENT OF ROTATION PARALLEL FORCES. [CHAP. V. 



2D. rORCE PARALLEL TO AXIS. [Fig. 26, PI. 6.] 



We have an example of this case in the " bayonet slide" of 

 the locomotive engine. 



We have here two pairs of forces, the reactions V\ and Vj 

 and the forces over Bj and RJ. The points of application of 

 these last change of course periodically, but for any assumed 

 position the moments are easily found. Thus draw A B t at 

 pleasure, and C Ba parallel to it, and join Bj B 2 and A C, and 

 we have at once the equilibrium polygon. To find the corre- 

 sponding force polygon, suppose P! applied at b, and join b with 

 the other support. Make b c equal to P then c d = V 2 . Lay 

 off then A a = c d = V 2 and draw a C^ which is the pole dis- 

 tance. Draw C/! e parallel to B! 83. Then A e and e A are the 

 forces acting over Bj and B^ and A a is the reaction Vj. The 

 case is, indeed, precisely similar to that in Art. 40. 



[NoTK. The moment area should properly be turned oyer upon A C as 

 an axis, so that A a should be laid off and e fall below A. This can, how- 

 ever, cause no confusion.] 



The application of the method to car axles,* crane standards, 

 and a large number of similar practical cases in Mechanics is 

 obvious. The formulae for many of these cases are too com' 

 plex for practical use ; in some, no attempt at investigation of 

 strain is ever made, the proportions being regulated simply by 

 " Engineering precedent " or rules of thumb. Those familiar 

 with the analytical discussion of such cases will readily recog- 

 nize the great practical advantages of the Graphical Method. 



3D. BEAM OR AXT.TC ACTED UPON BY FORCES LYING IN DIFFERENT 



PLANES. 



The analytical calculation in such a case for instance is of 

 considerable intricacy, but by the graphical method, on the 

 contrary, the difficulty of investigation is scarcely greater than 

 before. 



Thus, let Fig. 27, PI. 7, represent a beam acted upon by two 

 forces P! and P 2 not in the same plane. 



First, we draw the force polygons A O t M and D O 2 2 for the 

 forces P! and P 2 , having both the same pole distance G O l 

 Oj H, the pole O 2 being so taken that the closing lines of the 



* Der Constructeur, Keuleaux, pp. 215-222. 



