Columns in sway frames may be divided into laterally ``supporting (bracing) sway columns'', which can resist applied lateral shears, and ``supported (braced) sway columns'', which must have negative shears from the rest of the frame to support them. The supported sway column acts like a braced column with an initial displacement of one end relative to the other. The maximum moment will occur at the end of a supporting sway column, but may occur between the ends of a supported sway column. Mechanics of such columns, single or part of panels, are studied using elastic second-order theory. The main objective is to establish simple, explicit expressions for characteristic points in the moment versus axial load space. Such results may be useful in teaching, in design practice to assist in the assessment of the often complicated column response, and also useful as a supplement to full, second-order structural analyses.