1.1 



where *i, :*, are the* influence ordinaten beluw tiir 



corresponding load*. 1 1 \\ til lie convenient to *peak of urh 

 a quantity as UK as an ordinalr-luad product. 

 Formula 1 therefore may be expreiwed thus: 

 Z Sum of urdinatc-ltMtl products. 

 The area between the influence line and the bate line 

 is calli-'l th< influence area. It may be ahown that tin- 

 value of Z caused by a uniform load on the bridge t pro- 

 tonal to the area A, of the influence line between th- 

 onlinates at the extn-mitii^ i.f th<- uniform load. If the 



mi l.ia.l in Fig. la ha* an intensity of g per ui 

 length, the load in tin- length dx equal* qdx, and the influ- 

 hi- rlniM-htary load on the value of Z i* tq dj. 

 " : i- thr intluriirr ..nlinatc below q dr. Summing up 

 the Irn^th >f the uniform load, 



z- 



If a MTU-* of equal load* w i* on the span, the value of 

 Z - Ztftf - w 



If a S4ri<*s of unequal load*, IT,, tr lf etc., i* multiplied !> 

 tin- r..rn's|H!iilins nrdinutes of an influrnrr line or a por- 

 tion of an inllurnrr lino which has a constant ordin.. 

 a* in IMR. lr. the vahu- of / 



Z . *(ir, + ir, + ...)- xSir - iff 



where H" wjuaU thr MINI f these loads. 



a series of unequal load* i* multiplier! by the 



i'mates of an influence line or a portion of an 

 influence line coiiM-ting of two diverging lines, as shown 

 In N alue of Z, or the sum of the ordinate load 

 products and thr uhirh / varies as the loading 



advances, arc nix-en by thr t\\<. theorems that follow. 

 ,l,.tin.-.l at thr Inclining f A- 



