The buckling problem is the same whether you push in the X or the Y direction. The arc will buckle out of plane at a very low force.  I created a linear material to run two Eigenvalue Buckling analyses to find out the Load multiplier for X or Y direction loads when the upstream Static Structural model has a 0.0001 N unit load.  The load multiplier is 0.997 for a load in the Y direction and 0.852 or a load in the X direction.