I73-] 



JOINTED FRAMES. 



103 



through the successive panels, it will in the more simple cases 

 be possible to draw the line /3 so as to intersect not more than 

 three members whose stresses are unknown. Thus the stresses 

 in all the members can be determined. 



172. Exercises. 



(i) Find the stresses in the braced beam A (Fig. 49), carrying 

 a weight of 5 tons at each joint of the upper chord. The horizontal 

 width of the panels is 10 ft., the middle vertical is 8 ft. 



Fig. 49. 



(2) In Fig. 50, the dimensions are in feet, the loads in tons. After 

 the first panel the sections cannot be so taken as to intersect not more 

 than three unknown stresses. But the girder can be regarded as 

 obtained by the superposition of two girders (each carrying half the 

 load) , in one of which the diagonals CF, EH are wanting, while in the 

 other DE, FG are wanting. Each of these can readily be computed. 



Fig. 50. 



4. GRAPHICAL METHODS. 



173. The graphical method explained in Art. 108 for deter- 

 mining the resultant of a system of parallel forces can be 

 extended without difficulty to the general case of a plane sys- 

 tem of forces. The only difference will appear in the form of 

 the force polygon, which for parallel forces collapses into 

 a straight line, while in the general case it is an ordinary 

 (unclosed) polygon whose closing line represents the resultant 



