CHAP. IV.] SUPPLEMENT TO CHAP. XTV. 293 



curve, and the direction segments or curves. These are all we need for our 

 method of construction as given in Chap. XIV. ; once given, we can then 

 easily construct H, V and M or M, for any position of weight. 



A. PARABOLIC ABO CONSTANT CROSS-SECTION CONCENTBATED LOAD.* 



2> 



14. Determination of II, T and M . We put y = h , 



a 



dy = 2 jdat, ds = dx, as before. Then from the values of M given in 



(32) we have, according to equation (13), Art. 1, after inserting the values 

 of y and d s above, and integrating, 



and 



r- TT X -1 



A'. 



= e, A (f> = A (ft, hence $ P (z 2 ) z + A = A', or 



A-A' = iPa 1 ....... (L) 



\ 



For x = a, A $ = 0, and f or * = a, A </>' = 0, hence 



+ A, 



A', 



and by addition and subtraction, 



-22)a .... (II.) 

 sO = . . . (HL) 

 From L and IL we have 



A = iVa-iP(a-2<z2- > ) ) 

 A' = iVa-iP(a*-2a + 2 1 ) ) 



For the horizontal and vertical displacement of any point, we have from 

 15), Art. 2, after integration, 



E I A a/ =- ^Ti Mo as 1 -^ a^-i V **+* A'sM-B'l 

 a L 15 a J 



and 



iMoZ- ^ aj-i (V-P) a^- 



E I A y'=i Mo a:'- a^-i V + A' +O'. 



The discussion applies only to flat parabolic arch of constant cross-section. 



