106 STATICS. [177. 



Next, beginning at the vertex A the stresses in the two members 

 intersecting at A are found by resolving the reaction A along the direc- 

 tions of these members; and this is done in the stress diagram by 

 drawing parallels to these directions through the points a and b. The 

 intersection is denoted by c. 



177. It will be noticed that the three lines meeting at A have corre- 

 sponding to them, in the stress diagram, the three sides ab, be, ca of 

 a triangle. The force A = ab is represented by ab \ the stress in the 

 member be (i.e. in the member separating the compartments b, c in 

 the frame diagram) is represented in magnitude, direction, and sense by 

 the side be in the stress diagram ; and the stress in the member ca is 

 given by the side ca of the triangle abc. To obtain the sense of each 

 stress correctly, the triangle abc in the stress diagram must be traversed 

 in the sense of the known force A = ab this shows that the member be 

 is compressed, the stress at A acting towards A, while ca is subject to 

 tension. 



It will be found in general that the lines of the stress diagram corre- 

 sponding to all the lines meeting at any one vertex of the frame diagram 

 form a closed polygon. The reason is obvious : the forces at the vertex 

 must be in equilibrium. 



178. To continue the construction of the stress diagram, we pass to 

 .another vertex of the frame diagram, selecting one at which not more 



than two stresses are unknown. Thus at the vertex acd the stress in ac 

 is known, being represented by ac in the stress diagram. Hence drawing 

 through a a parallel to da, through c a parallel to cd, we find the point d 

 of the stress diagram. 



The vertex dcbef can now be attacked ; dc, cb, be are already drawn, 

 and it only remains to draw ef parallel to <f/"and ^7" parallel to df. 



The rest explains itself. Considerations of symmetry are frequently 

 helpful in affording checks. 



179. Exercises. 



(1) Check the computed stresses of Exercises (i) and (2), Art. 172, 

 by constructing the stress diagrams. 



(2) Find the stresses in the frame (Fig. 52), if the load consists of 

 : seven equal weights, of 2 tons each, applied at the joints of the upper 



chord. Owing to the symmetry of the figure, it is sufficient to construct 



