What are the pin reactions at A and D?

[MrMechanic]

Homework Statement

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]

Homework Equations

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

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.

 

[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.

 

[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.

 

[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.

 

[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?

 

[MrMechanic]

hey Thanks i got it now. here's my solution

 

[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.