34 



GRAPHIC STATICS 



\ 



(b) 



FIG. 20. 



left of b, acting through points b and a. Through o draw c" and 

 o b" parallel to closing lines a c' and a b', respectively. Point c" de- 

 termines the reactions R^ and R 2 , and point ?" determines the reac- 

 tions acting through a and b of the forces to the left of point b. 



Points c" and b" are common to all force polygons, and lines 

 c" o' and b" o' drawn parallel to the closing lines of the required equi- 

 librium polygon, a c and a b will meet in the new pole o'. With pole o' 

 the required equilibrium polygon a b c can now be drawn. 



Center of Gravity. To find the center of gravity of the figure 

 shown in (a) Fig. 21, proceed as follows: Divide the figure into 

 elementary figures whose centers of gravity and areas are known. 

 Assume that the areas act as the forces P lt P 2 , P 3 through the centers 

 of gravity of the respective figures. Bring the line of action of these 

 forces into the plane of the paper by turning them downward as in 

 (b) and to the right as in (c). Find the resultant of the forces for 

 case (b) and for case (c) by means of force and equilibrium polygons. 

 The intersection of the resultants R will be the center of gravity of the 

 figure. The two sets of forces may be assumed to act at any angle, 

 however, maximum accuracy is given when the forces are assumed to 

 act at right angles. If the figure has an axis of symmetry but one 

 force and equilibrium polygon is required. 



