ALGEBRAIC RESOLUTION 41 



It will be seen from the foregoing that the method of algebraic 

 resolution consists in applying the principle of the force polygon to the 

 external forces and internal stresses at each joint. 



Since we have only two fundamental equations for translation 

 (resolution) we can not solve a joint if there are more than two forces 

 or stresses unknown. 



Where the lower chord of the truss is horizontal as in Fig. 25, we 



R 



FIG. 25. 



have by applying fundamental equations (a) and (b) to the joint at 

 the left reaction 



!-.*= + #! sec 8 (11) 



l-y = RI tan (12) 



the plus sign indicating compression and the minus sign tension. Equa- 

 tions (n) and (12) may be obtained directly from force triangle (c). 

 Equations (n) and (12) are used in calculating the stresses in trusses 

 with parallel chords and lead to the method of coefficients (Chapter X). 



(b) Forces on One Side of a Section. The principle of resolu- 

 tion of forces may be applied to the structure as a whole or to a por- 

 tion of the structure. 



If the truss shown in Fig. 26 is cut by the plane A A, the internal 

 stresses and external forces acting on either segment, as in (b) will be 

 in equilibrium. The external forces acting on the cut members as 

 shown in (b) are equal to the internal stresses in the cut members and 

 are opposite in direction. 



