# Buckling of a cantilever with midway support

I'm trying to understand the implications for buckling and column sizing in the drawings below.

A 3000mm 120x60 RHS steel column supports a 350mm horizontal steel beam. The column base and right side of the beam are both fixed but can pivot. They are joined by a continual fillet weld "T" join, so the junction can rotate but will retain its angle. The only load is a vertical static force on the left-most 100mm of the horizontal beam. The column can be placed at any position under the beam, as shown in the 3 drawings (nearer to the right would be better). The thickness of the beam is thick enough that it will not deflect noticeably or materially. The thickness of steel in the RHS column is to be based on calculations.

My question is this:

The column's required cross-section clearly depends on the axial compressive force, which varies according to the column's position. But the eccentric load is a concern and I can't be quite sure if I am right to ignore it here.

Assuming that the beam is sufficiently rigid and won't noticeably deflect, then when the column position changes to the right (as shown), does the column experience only an increased axial compressive force, or should I also consider an additional bending moment imposed on the column as well?

My reason for thinking I can ignore it and only consider the axial compressive load on the column, is that wherever the force applies on the beam, the column only experiences it as an axial load. But I'm not 100% sure since if the beam deflects even slightly (as it must), this must cause bending of the column (as they are welded) and therefore a bending moment in the column (however slight).

Is this effect significant compared to the increased axial compressive force, or is it trivial and dominated by the increase in axial compression? Do I need to allow for an additional bending moment in my buckling calculations, in this situation, to ensure the column profile is adequate?

(NOTE - I am based in Europe so any specific calculations would be Eurocode not North America code based. That said, the question isn't really about specific code calculations and it shouldn't matter)

• I'm having trouble understanding the structure. Your drawing has the base of the column and the right extremity of the beam as "fixed supports (free to rotate)", which is something of an oxymoron, since a "fixed" support is usually defined as one which impedes rotation. Is this an adequate representation of your structure? – Wasabi May 30 '16 at 18:11
• Yes. The supports at right and bottom are pinned, the junction of beam/column is a welded join. (I wasn't sure how to draw them when the column/beam weren't drawn as 1-D lines) – Stilez May 30 '16 at 18:22