GRAPHIC STATICS 209 



First, taking the forces 1 and 2, construct a parallelogram and 

 obtain the resultant. Using this resultant as a force form a 

 parallelogram with it and force 3. The resultant thus obtained 

 will be combined as a force with force 4. The final resultant 

 obtained will be the force 04. On the figure here shown the 

 resultant of 1 and 2 will be a line 02. The resultant of 02 and 

 force 3 will be a line 03. Then the resultant of force 4 and 03 

 will be 04. 



Action and reaction are equal when equilibrium is to be pre- 

 served. The arrow points on the force lines show the direction 

 in which each force acts. The resultant measures the force neces- 

 sary to preserve equilibrium; therefore, the direction is against 

 the general direction of all the forces. The arrow point on the 

 resultant indicates this, and the result is that the closed figure 

 has the arrow points so arranged that the forces can be followed 

 consecutively. This indicates equilibrium, and if the arrow 

 points do not indicate a consecutive line of travel it is evidence 

 that equilibrium does not exist. The polygon should not be 

 closed, or there is some mistake in the construction. 



The resultant is the force required to maintain equilibrium, 

 or it may be a force which can replace all the other forces. In 

 Fig. 123 is an example of where two forces are substituted for one 

 force. The vertical and horizontal components may be assumed 

 to replace the diagonal force acting against the roof. Here there 

 is, strictly speaking, no resultant considered. A certain force has 

 been resolved into two components. 



To obtain a resultant all the forces are arranged to form a tri- 

 angle or polygon and the closing line is the resultant. To resolve 

 a force into two forces acting at any angle draw the resultant to 

 scale. From one end draw a line of indefinite length in the direc- 

 tion of one component. From the other end, on the same side, 

 draw another line of indefinite length in the direction of the 

 second component. The lines will intersect and the lengths thus 

 fixed will represent to scale the amounts of the components. The 

 student is advised to study carefully the difference between 

 resultant forces and component forces. A force may have any 

 number of components, but in a system of framing the number 

 will be fixed by the number of members meeting at a joint. 



The designer of buildings will usually deal only with parallel 

 loads. The direct loads on a roof act vertically at the joints. The 



