172 GRAPHIC AND ANALYTIC [CHAP. TO. 



the scale of force, multiplied by A b to the scale of distance, 

 gives the moment at A, while H G is the reaction at A (Fig. 79). 

 114. Beam fixed at both ends Example. Since when 

 the points of inflection are once determined, we may draw P b 

 or P c at any inclination (Fig. 79), provided we afterwards find 

 the corresponding pole distance HO; if A b or B c be made 

 equal to the height of the truss, H O will be the strain in the 

 upper or lower flange at the wall (the flange in question being 

 always that for which there is no diagonal at its union with the 

 wall). Thus in PL 21, Fig. 80, we lay off D E = I, draw the 



vertical I at ~ I from D, and for the given position of the load 

 > 



P find the inflection point i^ by the preceding Art. A similar 

 construction on the other side gives i. Now laying off P M 

 equal by scale to the weight P, and decomposing it along P D 

 and P C, we find O H the pole distance which to the scale of 

 force will give directly the strain in the lower flange B ra at 

 the wall, provided P D is made to pass through the intersection 

 of the upper flange with the wall. If the triangulation were 

 reversed, O H would be the strain in the upper flange at the 

 wall. In any case it is the strain in that flange at wlwse junc- 

 tion with the wall there is no diagonal. 



The reaction at D is also H M, at C it is P H. Lay off then 

 B B' in Fig. 80 (a) equal to P M, and make B A = H M and 

 A B' = P H. Now draw m B parallel to O H and in A paral- 

 lel to O M, and produce both lines to intersection at m. Then 

 in B to scale of force is evidently the strain in the lower end 

 flange at the wall. We assume the following notation.* 



Let A represent all the space above the girder, B all the space 

 below, and abed, etc., the spaces within the girder included 

 by the flanges and diagonals. Then, for instance, A b is the first 

 upper flange at the left, B a the first below ; a b the first diag- 

 onal at the left, and so on. 



Now draw in Fig. 80 (a\ m I and A I parallel to the corre- 

 sponding lines in the frame, and we have at once the strains in 

 these pieces to scale. Following round the triangle according 

 to our rule (Arts. 8-13) from m to A, A to I and I to m, we 



* See an excellent little treatise on " Economies of Construction in Relation 

 to Framed Structures," by JR. H. Bow, to whom this method of notation is 

 due. 



