LIVE-LOAD STRESSES 



\ini< 1 1; i. 



LOOKS. DEf 



INFLUENCE lines are uaeful in 

 <>f live load on a bridge to produce 

 offer also a convenient method of deriving 

 braic formulas for stresses and rules for 



general relations between influence lines and algebrmir 



formula.- aiv oiu-r unlrrMM,.l. and in ?1,.- BJM sj ''' ' R 



complex problems of skew bridges, arches, cantilever brijsjss, 

 th<> influence lines themselves serve as a most dirm 

 UK -t hod for the determination of the maximum live-load 

 fames. 



An influence line may be defined as a line showing the 

 variation in any function caused by a single unit load a* 

 it moves across tin bridge. Vertical loads only will br 

 1. Tin- function may be a reaction, ^^^f 

 moment, shear, stress, deflection, or any quantity what- 

 soever :it ;. -;. ii part of a bridge, provided that it* value 

 is a function of tli" position of the unit load on the bridge. 



i; la. Consider the span AB, and 1* 



any function at the fixed position C on the span /. 1: 

 the load unity moves across the span AB and the value* 

 .>f / be calculated for each position of the unit load and 

 its value : plotted below the eoi responding position of thi 

 load as an or. i inatr from a horiiontal baae line, the lon 

 of the plotted |H)ints will IK* the influence line for Z. For 

 example, if / U- the bending moment at the fixed 

 c in a beam of span L, the influence line will be as 

 Ig, II) In plotting influence 



i 



