# Reaction Forces on members

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1. Oct 6, 2015

### arestes

1. The problem statement, all variables and given/known data
I am given the forces on picture and I´m asked to find the reactions on both supports. I see they are pin supports so they ask me for 4 unknowns.

2. Relevant equations
Sum of forces in both directions equal to zero
Sum of torques wrt a convenient point equal to zero
THREE equations in total, four unknowns.

3. The attempt at a solution

Sum of forces in both directions equal to zero
Cx+Dx+200=0
Cy+Dy-150=0
Sum of torques wrt "C" equal to zero
3(Dy)-1,5Dx-(3) 200+ (3)150=0

Since I have THREE equations in total, four unknowns. I assumeI need to analyse members separately. I recall that members are supposed to be treated as weightless and subjected to two forces acting on the same line of action if they are part of a truss. However, Member ABC does´nt look like a truss member.

If I analyse pin B I see it can only have horizontal forces acting on it pulling from both sides. Vertically it should have zero force. If I set Cy=0 it leads me to Dx and Dy not being zero both of them and I discovera contradictions if I analyse the member BD because it would have Dx and Dy novanishing and only a horizontal force on the x axis, which produces a pair acting on that member BD.

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2. Oct 6, 2015

### SteamKing

Staff Emeritus
You should analyze member ABC as a free body by itself, using the indicated applied forces. Because the entire mechanism is in static equilibrium, you will need some additional forces at pin B to keep ABC static. You can then analyze member BD by itself, since it must also be in static equilibrium, to find the reaction at D.