62 Mr. J. M. Heppel on the Theory of Continuous Beams. 



and let the part of this bending moment, which results alone from the 

 load on the beam between 1 and x> be called 



between 1 and a f"(x\ 



between a and b f^{x\ 



between b and 2 f 3 "( x ) 5 

 and let the first and second integrals of these functions, as of 

 be denoted by F/(^), //(#), and F 1 (a?), f x {x), and the value of any one, as 

 F^-r), for a particular value of x, as a by F 1 (a) ; 



then £"(*>*fty (1) 



/ 2 "(*)= ft «(*'-0+ft ( ^^) (2) 



f^)=^- a ^ + ^b-a)^- b ^Y^^. . (3) 



Also, from equality of moments about the point (a? . y), 



K(^-**+fi'W, ......... (4) 



F a "( a? )=0 1 -P a? +/ a "W > (5) 



W=^-^+/3"W; ...... (6) 



and, from equality of moments about the point 2, 



F-i^-fc+Za"®) (7) 



Substituting for P in (4), (5) and (6), 



W-(i-j)fi+|#.-f/;'(o+X''H (8) 



F 3 »=(l-f)0 1 +ff -|/ 3 "©+/ a ». • • •• • • • O) 



F 3 »=(l-|^ 1 +^ 2 -|/ 3 "(0+/ 3 'W, • (10) 



equations from which for a given value of oo s Y"{pB) t F 2 "(^) 5 F 3 "(#) may 

 be determined if fa and 2 are known. 

 From the nature of the deflection curve, 



from 1 to a, 



s 



from « to 5, 



