CHAP. I.] COMMON POIKT OF APPLICATION. 7 



and know it to be compressive. We have then simply to draw 

 lines from and I parallel to E arid 2, and follow round the 

 triangle, to obtain the intensity and quality of the strains in E 

 and 2. "We must remember that as 1 is in compression, and 

 we are now considering apex a, we must follow round from o 

 to b in Fig. 5 (a), and so round. We thus find 2 acting away 

 from apex a and therefore in tension, and E acting towards 

 this apex, and hence com/pressed. 



Pass now to apex e. We have the strains in A. and 2 in 

 equilibrium with B and 3. [No weights are supposed to act 

 except the one at the end.] But A and 2 we already have. 

 We draw 3 and B. Diagonal 2 has been found to be in ten- 

 sion. With reference to apex c it must therefore act away 

 fromc; i.e., from d to b in the force polygon. This is suffi- 

 cient to give us the hint how to follow round. We pass from 

 d to b for 2, from b to e for A, then from e to B and from B to 

 d for B and 3. B is therefore tension and 3 compression. 

 And so we proceed. For the next apex gr, we have E and 3 in 

 equilibrium with F and 4. We draw parallels to F and 4 so 

 as to close the polygon of which we have already .two sides, E 

 and 3, given, and remembering that as 3 is in compression, it 

 must therefore act towards g, we follow round the completed 

 polygon with this to guide us, and find 4 tension and F com- 

 pression. Thus we go through the figure, and when all is 

 ready we can scale off the strains. The strains in the lower 

 flanges it will be observed all radiate from o. The upper 

 flanges are all measured off on the horizontal e C, and the dia- 

 gonals are the traverses between. We see at once that however 

 irregular the structure, we can always easily and readily deter- 

 mine the strains at any apex, provided no more than two un- 

 known strains are to be found. If more than two pieces, the 

 strains in which are .unknown, meet at an apex, we can evi- 

 dently form an indefinite number of closed polygons. The 

 problem is indeterminate, and the structure has unnecessary 

 or superfluous pieces. 



Fig. 5 (J) gives the strains for a uniform load, taken, for con- 

 venience of size, to a scale of 20 tons to an inch. Here until 

 we arrived at apex c of the frame the strains are evidently the 

 same as before. Observe the influence of the weight at c. 

 Here we have the strains in A and 2 given in the diagram, in 

 equilibrium with B, 3 and the known weight acting at c; viz., 



