162 



STRENGTH OF MATERIALS 



FIG. 117 



a system of non-concurrent forces shall be in equilibrium, h.w- 



ever, both conditions mu 

 fulfilled. 



Problem 155. Construct the re- 

 sultant of the system of concurrent 

 forces shown in ri-. 117. 



Problem 156. Determine 

 whether or not the system of par- 

 allel forces shown in Kit;. IIS 

 fies conditions 1 ami '2 above. 



131. Equilibrium polygon. 

 The preceding construction t'<>r 



the force polygon gives a method for calculating the ma-nitud, 



direction of the result- 3 tons 



ant of any given system 



of forces, but does not 



determine the line of 



action of their resultant. 



The most convenient 3 tons 



way to determine the 



line of action of the re- 

 sultant is to introduce into the given system t\\.. equal and opposite 



rl>i- 



trary annnml 

 and direetiMii. >u--h 

 as P' and /"' in 



Since /''and /'" 

 balance one. an- 



.ihiT, they will not 

 the eqnilil>- 

 rium of the uiven 

 system. Tl 

 obvious fi-Min the 

 force poh 

 in 



. 



R denote the resultant of the given system of forces P, P<. Then, 

 if OA represents in magnitude and direction the arbitrary force P 1 , OB 



