42 STRESSES IN FRAMED STRUCTURES 



Applying equations (a) and (b) to the cut section 



3-y + 2-3 cos oc 2-x sin 9 =0 (13) 



2-3 sin a 2-3? cos 6 + ^ P l = (14) 



Now, if all but two of the external forces are known, the un- 

 knowns may be found by solving equations (13) and (14). If more 



(a) 



(b) 



FIG. 26. 



than two external forces are unknown the problem is indeterminate as 

 far as equations (13) and (14) are concerned. 



Graphic Resolution. In Fig. 27 the reactions R and R 2 are 

 found by means of the force and equilibrium polygons as shown in (b) 

 and (a). The principle of the force polygon is then applied to each 

 joint of the structure in turn. Beginning at the joint L the forces 

 are shown in (c), and the force triangle in (d). The reaction R 1 is 

 known and acts up, the upper chord stress \-x acts downward to 

 the left, and the lower chord stress i-y acts to the right closing the 

 polygon. Stress i-x is compression and stress i-y is tension, 

 as can be seen by applying the arrows to the members in (c). The 

 force polygon at joint U 1 is then constructed as in (f). Stress i-x 

 acting toward joint U 1 and load P 1 acting downward are known, and 

 stresses 1-2 and 2-x are found by completing the polygon. Stresses 

 2-x and 1-2 are compression. The force polygons at joints L 

 and C7 2 are constructed, in the order given, in the same manner. The 

 known forces at any joint are indicated in direction in the force poly- 



