MOMENTS IN GIRDERS. 77 



Solving the two equations y and z. 





= — J )«,.-i-««-2-W'i+«»-i-a»-2-a„-i-0,-3-l-!<'2— «"-i-a»-3-«„-i-«„-i-3.!i'3+ .. 



and, 



+»n„-i-«-i-l) 



± — "^ • j— «n-2-M'i+«»-i+«„-:j— a„-2-M',— 3.a„.i+a„.4-a„.3.2<)3 



TOn-i-<»„-3-«,.-i-'^«-4-3.M'„-2±fl„_i.a„.2— «„-i-a„-3— l-îf„-i±a„-i-a„-2 î^'n^ 



Hence, since w^, iv., w„ are positive integers, the value of m„ yviWh^ greatest when 



Wi, '"2, w^, u\, iVg are greatest 



^ii<i w^, w^, M', , are least. 



and the value of ?h„_i will be greatest when 



^n< w'n-i, ?<'„-3, M'„-4, are greatest 



and • w„_2, î/'„_4, ?<j„.o , are least. 



In other words, the bending-moments at the 1-st and «—1-th intermediate supports have 

 their maximum values when the two spans adjacent to the support iu question, and then 

 every alternate span are loaded, and the remaining spans unloaded, 

 wio, W3 7ra„_2 may now be easily determined. 



Thus, by Eq. 1 :— 



^' — T— . ^' \ 4 o 



~~Ma^ — ^^ |4-i-l-4.a„.i.a„.2.Wi-f a^i— l-4.a„.i.a„.2 4- 4.a„_i.a„_3+ 4.î<),+ | 



But, «„_, = 4 . a„_2 — a„_3 



r^ ( ) 



.-. m,= --— — ZUl" «»-i-'^«-3+ l-M'i + 3.a„..i-««-3+3.M', + , 



and is greatest when 



M'2, w^, W5, w,, are greatest 



and Wj, w,, ?f)„, ?o^ are least. 



