4 



STRESSES IN FRAMED STRUCTURES 



Algebraic Resolution. In calculating the stresses in a truss by 

 algebraic resolution, the fundamental equations for equilibrium for 

 translation 



S horizontal components of forces = (a) 



S vertical components of forces = (b) 



are applied (a) to each joint, or (b) to the members and forces on one 

 side of a section cut through the truss. 



(a) Forces at a Joint. The reactions having been found, the 

 stresses in the members of the truss shown in Fig. 24 are calculated as 



FIG. 24. 



follows : Beginning at the left reaction, R lt we have by applying equa- 

 tions (a) and (b) 



\-x sin 6 \-y sin Oc = (9) 



\-x cos 9 l-y cos a ^! = (10) 



The stresses in members \-x and i-y may be obtained by solving 

 equations (9) and (10). The direction of the forces which rep- 

 resent the stresses in amount will be determined by the signs of the 

 results, plus signs indicating compression and minus signs indicating 

 tension. Arrows pointing toward the joint indicate that the member 

 is in compression; arrows pointing away from the joint indicate that 

 the member is in tension. The stresses in the members of the truss at 

 the remaining joints in the truss are calculated in the same way. 



The direction of the forces and the kind of stress can always be 

 determined by sketching in the force polygon for the forces meeting 

 at the joint as in (c) Fig. 24. 



