# Coplanar Equilibrium Analysis

1. Mar 14, 2014

### MrMechanic

1. The problem statement, all variables and given/known data
The two couples act at the midpoints of bars AB and BD. Determine the magnitudes of the pin reactions at A and D. Neglect the Weights of the members. [See Attachments for Figure]

2. Relevant equations
Sum Moment Along A & D = 0
Sum of Forces along X-axis
Sum forces along y-axis

3. The attempt at a solution
so i tried getting the answer at the back which is A = D = 4.22kN.
i tried moment at A
20 -20 + Rd = 0
Rd = 0?
After that i can't find a way to answer the question. Can someone guide me through it.

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2. Mar 15, 2014

### paisiello2

I would break the components of the reactions down so you have the following number of unknowns:

Rd_x and Rd_y
Ra_x and Ra_y

I would then take a free body diagram of member AB or BD to get another equation for the reactions. Then take if from there with the other equations you already listed.

3. Mar 15, 2014

### MrMechanic

Do you mean that I should separate each members and draw a Free-body diagram of each and do the equilibrium equations?

So i tried getting Bx and By.. by summing moments along member AB and member BD. I got Bx = 0 and By = 20/3. Can't seem to proceed from here.

4. Mar 15, 2014

### paisiello2

Yes, that's what I meant.

You must have done something wrong since you should have gotten Bx = Dx and By=Dy. Summing moments for member BD then would give you one relationship between Dx and Dy.

5. Mar 15, 2014

### MrMechanic

I tried this one
At member AB
Sum Moment along Pin A [Clockwise Positive] = 20 - 4Bx - 3By = 0
and should i moment at Member BD?
Also, what's next at my solution. Is it correct?

6. Mar 15, 2014

### MrMechanic

hey Thanks i got it now. heres my solution

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7. Mar 15, 2014

### paisiello2

A couple of suggestions so that other people can understand better what you are trying to communicate:

- put a ∑ sign in front of Ma and Mb so that it is clear that you are summing up the moments about point A and B respectively; otherwise someone may be thinking you are stating the moment reactions at A and B.

- make a statement that you are explicitly looking at member BD by itself e.g. "For member BD:" or better still draw a free body diagram right at this point.

- I think your sign convention might have been mixed up but you were consistent (or just lucky) so that it still gave the right answer at the end. I would state explicitly what sign convention you are using somewhere
e.g. "$\rightarrow$ -ve $\uparrow$ +ve"
which is what I think you used in your solution.