For the truss shown below determine the member forces in BC, CH, and HI in pound

Question

For the truss shown below determine the member forces in BC, CH, and HI in pounds. (Assume that there is a hinge at S and a roller at T. Due to the nature of this problem, do not use rounded intermediate values in your calculations-including answers submitted in WebAssign.) 5@5ft-25 ft 291 lb A 582 lb 1,164 lb 1,164 lb 5@5ft 25ft 582 lb 582 lb 291 lb BC magnitude sense lb FCH magnitude Ib sense HI magnitude sense Ib Also identify any zero force members in the truss. (Enter your answers as a comma-separated list.)

Explanation / Answer

The problem can be solved using method of sections. if we consider a vertical section between B and C and considering the free body diagram of the part of truss to the right of the section cut

Angle member CH makes with horizontal = tan-1(5/5)=45o

From vertical equilibrium of forces,we get

FCHsin45 = 1164+1164

FCH = 3292.29 lb(tension)

Considering moment equilibrium about H,we get

(1164*15)+(1164*20) - 5FBC=0

FBC = 8148 lb(tension)

from equilibrium of section in horizontal direction,we get

FHI = -8184+3292.29cos45 = -5856 lb = 5856 lb(compression)

There are 2 zero force members in the truss : ST and LK

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