FEA simulation of double joints in shear loading

Hi all,

I have a question about an FEA simulation. Particularly, about the boumndary conditions that need to be applied to run this simulation. 

attempt1:

I fixed the right end of the plates and applied loading to the left end. This resulted in stresses go through only the top joint region (W1 in figure attached). 

From our understanding, the deformation is got to be symmetric on both the plates. But, when we applied these BCs, it is not smmetric. 

attempt-2:

I applied forces on both the ends as shown on top of the attached image. I contrained 2 nodes on exact middle portions of the plates in X direction. Constrained right most and left most edges where force is applied in Y direction. 

The deformation looks pratical, but this is not the best case as we are not letting the plate portion that is constrained in Y direction to deform as result of poisson's ratio.

Any thoughts on this simulation will be beneficial. 

Also, 

are there any symmetry anti-symmetry conditions that I haven't looked into? Please let me know.

Yuan Krishna