634 PBOCEEDIXGS OF SECTIQX H. 



It is seen from the diagTani that of all the values li may havCj. 

 tliat which corresponds to the greatest bending iiioment over a post, 



AA'hen an isolated load is there, is the value — . This might b& 



infen-ed from the fact that, by sj-mmetry, the point of contrary 

 flexure, when the load is over a post, is at mid-span. Or it may l3e 

 proA^ed thus : — Putting /^ for a in the expression for Ko, we get — 



Taking moments about left hand end — 



Bending moment over post = R3/1 



Differentiating this, with respect to li, and equating to 0, we get — 



and the second differential coefficient is negative ; therefore, this 

 value of Ii corresponds to a maximum value of the Iiending moment 

 over a post when the load is over that post. 



(Jj) When the load is between an abutment and a post (see Figs. 

 14 and 15),«T>and i?'t> will have the same value as in the previous 



case. 



Equation ( a) cannot be directly made use of to find ^-.t- and 



'i^^-nr ill the case shown in Pig. 14, because x < a; but we can deal 



with the case shown in Fig. 15 directlj' by means of equation ( «, ) , 

 and then substitute (Z— a) for ff, thus obtaining values of y ^ir ^^^*^ *" ' \\r 



applicable to the ease shown in Fig. 14. 



Referring to Fig. 15, putting (l — h) for x in equation (a), we 

 obtain an expression for the deflection at C, due to W, which we may 

 call /'txt- l>ecause the deflection at C, in Fig. 15, wall cori'espond to 



the deflection at B in Fig. 14 — 



%v: 



^^'^^l^'l^-'-i'-'.y-^'h 



and, putting (I -a) for a, in order to transfer the origin to the right 

 hand end, or, what is the same thing, to deduce a formula, applicable 

 to Fig. 14 — 



W (M¥A L ^ ^ ^ 3 



G/Ei ^ ^ 



Referring again to Fig. 15, putting li for x in equation {a), we 

 obtain an expression for the deflection at B, Avhich Ave shall call f'.y- 



