BY LITE LOAD ON GIEDEE. 5 



The beudiug moment ilf. at the same poiut P with the second distributiou is given 

 by the equation, 



M, = B,{l—z)—Wj,+i(aj,+)i-x — z)— . . . — !i),(a,+a: — s) — !«^+i ((/,+! +J.'—^)— • • • 

 — !«,.+, (o.,.+, + X — -) 



= 11,(1 — z)—B,. — E,. + H,) i — (.r - 2) ( IF, — W,.+ T) 

 Hence, 



according as 



R^(l — z) — E,. I + .-. W, ><E,(l — z) — (B, — B,, + R,).l — (x — z) ( TF, — W„+ T) 



or {B,— B.;)l ><(B^,~B^.l — x.W,— (z — x)iW> — T) 



X z — x 



or {l-z){B, — B, • W„- W,;)><1\ B,-B,- - TF, (TF„- T) [ 



I I t I ) 



Corollary. — If no weights advance upon or leave the girder, R„ R^„ and TF,, become 

 severally nil, and the last relation reduces to 



— {l — z).-. W„><l(—B,— . TF,+ ' .T) 



I I I 



Let the r"' weight be at the point P in the first distribution, and let the distance of 

 transfer be equal to that between the r"' and (r+1)"' weights. 



.■.z = a„ a; = fl, — a,+i, T^w,-+\, and B^.lw,.+i.n,.+i. 



Hence Mi will be >< Mi according as 



X a,.+i X a,.+ i 



or — (I —a,). -.W„><1( . Wr+i TF,.+ . w,.+i ) 



I ^ I 11^ 



W, TF„ 

 > < — . 



I — a, I 



B. — Tn words, the bending moment with the fii'st distribution will be greater or less 

 than that with the second distribution, according as the sum of the first r weights, 

 divided by the corresponding segment, is greater or less than the total weight divided by 

 the span. 



Note. — Results A and B will be found very useful in determining the maximum 

 shears and bending moments at the panel points of a truss with horizontal chords, 

 subjected to an arbitrarily distributed live load, e.g., a passing train. In such a case, 



