Try adaptive component family as it gives you freedom of placement. I see it as three distinct types of two point adaptive components:
The vertical post
The horizontal beams
The round pins
All have fixed length unlike structural columns/beams. Also your elements are not prismatic most elements of structural framing/columns would be (those kind of elements are what it excels at).
You could conceivably use structural framing and structural columns but then you'll have to consider the levels:
Structural columns are two level based so where upon the vertical element will those levels fall i.e. at the pin position with extension beyond level? Does this mean you then have to offset the structural framing because the pin is at the centre of that.
What is happening to the ends when the structural framing interfaces with the beam, is there automatic cut back that is going to affect it? Probably with the resulting poor analytical model join up you wouldn't get that.
Basically there is a lot of automatic behaviour which will work against what you want to do. The most common beam to column connection is where the beam comes into the centroid of the column and structural framing/columns work from that starting assumption. You could say model a double beam and that solves the eccentricity of connection. Wrong tool you would be using a hammer to bang in a screw.
If you are unfamiliar with both environments i.e. structural framing/column family templates and that of the adaptive component one then you may as well choose the latter.