Question

Determine the tension developed in cables AB, AC, and AD

Determine the tension developed in cables AB, AC, and AD. (FAB= 138.6 lb; FAC=202.9 lb; FAD=175.7 lb)

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Answer #1

from the given diagram it is 3-D problem.
we have to resolve all the forces into co-ordinate axis

FirstFad has 3 component ,FadCOS(45)k ,FadCOS(60)(-j) ,FadCOS(120)i

Fac has two component with angle 60FacSIN(60)k ,FacCOS(60) in x-y plane

FacCOS(60) again have two component

FacCOS(60)COS(30)j,FacCOS(60)SIN(30)(-i)

ΣFz=0=> FacSIN(60)k+FadCOS(45)k=300k---(1)

ΣFx=0 => Fabi+FadCOS(120)i+FacCOS(60)SIN(30)(-i)=0

Fab+FadCOS(120)=FacCOS(60)SIN(30)-----(2)

ΣFy=0 => FadCOS(60)=FacCOS(60)COS(30)=>Fad=Fac-------(3)

substituting (3)on (1)

Fad+FadCOS(45)=300 =>Fad=175.7 lb(ANS)

from (3)Fac=202.922 (ANS)

substituting these two in (2)Fab=Fac/4 -(-1/2)Fad

Fab=138.58 lb (ANS)

answered by: Taylah
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