Question $1(40$ marks$)$

Figure $1($a$)$ below shows a $K$ truss supported with a pin at A and a roller at G$.$ Live loads are transmitted to the bottom chord of the truss.

i$.$ Draw the influence line diagrams for the vertical reaction at support A and the force in each of the members CD$,$ IC$,$ IN and ND$.$

ii$.$ Calculate the maximum vertical reaction at support A and the maximum tensile and compressive forces in each of the members CD and IN due to a long uniform load of $20k\frac{N}{m},$ a concentrated moving load of $85KN,$ and a truss self$-$weight of $35k\frac{N}{m}.$

iii. Calculate the maximum value of the force in members $CD,IN$ and ND due to a series of truck wheel loads shown in Figure $1($b$)$ moving from right to left.

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Figure $1($a$)$: Truss