CHAP. XII.] METHODS COMBINED. 193 



Now these two moments and shears being once known, we 

 can find by diagram and tabulate the respective strains in every 

 piece of the span D E. Thus dividing the moment at D for 

 either case by the height of truss, we have at once the strain in 

 either upper or lower flange at D depending upon the system 

 of triangulation as explained in Art. 125. With this strain and 

 the shear at D properly laid off to scale, we can commence the 

 strain diagram precisely as though we had traced all the loads 

 through from the extreme end A or H to D or E. 



We must next find and tabulate the strains in D E due 

 to each apex load in the span itself, and for this we must 

 know to begin with the moments and shears for each separate 

 load. 



[.Afofe. Distinguish carefully between shear and reaction at 

 a support. The shear at D, or at a point just to right of D, is 

 the algebraic sum of all the reactions and weights between that 

 point and A. See also Fig. 84: (Art. 123), where the reaction 

 at B is b a, but the sJtear atB is b a + H. q = H . 

 So also the reaction at C is + b <?, but the shear at C is 

 + be ba + Ha 'H.C, etc.] 



Conceiving now that we have found and tabulated the strains 

 due to the first and second systems of loading as shown in Fig. 

 87, and also the strains for each load P in D E, the sum of these 

 strains will give the strains due to live load o-ver the whole 

 length of girder, and taking the proper proportion of these, we 

 shall have the strains due to the dead load. Combining then 

 these strains with those first found, we can easily find the total 

 maximum strains which can ever occur in D E. 



Such is the method of procedure we advise for many spans, 

 in order to find the maximum strains in any one span. The 

 method is not, however, strictly correct, and does not give the 

 theoretical maximum strains in the span required to be solved. 

 The reason is obvious. The method gives correctly the maxi- 

 mum moment and shear at the left support of the span in 

 question, but does not give the true maximum at other points 

 of that span. 



Thus, as will be seen by reference to the table of the follow- 

 ing Art., the maximum tension in A e occurs really for all the 

 spans, except the one in question, loaded, while according to 

 the above method we should have taken only the 1st, 3d, and 

 13 



