SECTION XIV 



SIMPLE STRUCTURES 



107. Composition and resolution of forces. It will now be neces- 

 sary to recall some of the results previously obtained concerning 

 the composition and resolution of forces. 



It was shown in article 11 that any number of concurrent forces 

 may be combined by means of a vector triangle or vector polygon 

 into a single resultant. Also that, conversely, any force may be 

 resolved into components forming with the given force a closed 



triangle or polygon. 



In finding the resultant 

 of several forces it is usually 

 more convenient to resolve 

 each of the given forces into 

 components parallel to a set 

 of rectangular axes, then 

 take the algebraic sum of the 

 components along each axis, 

 and, finally, recombine these 

 into the required resultant. 



Thus, in Fig. 115, if F^ F^ denote two forces and R their result- 

 ant, resolve F l into rectangular components x^ y^ and F 2 into com- 

 ponents x^ y z . Then, if re, y, denote the components of the resultant 



R, we have 



x = x l + x 1f y = 



and, consequently, 



a?, 



FIG. 115 



In article 10 the moment of a force with respect to any point 

 was defined as the product of the force by its perpendicular distance 

 from the point in question ; that is, 



Moment = force X lever arm. 



176 



