Mechanical response of a partially restrained column exposed to localised fires

• This article reviews the effects of non-uniform heating on the response of a column.
• Non-uniformity of temperature in the columns section is considered.
• Non-uniformity of temperature along the columns height is considered.
• A solution of the Euler beam equation is shown which describes the columns response.
• Partial rotational restraint of the column ends is considered.

Recent trends in structural fire engineering research have focussed on the response of buildings with large open plan spaces to so-called travelling fires. These fires travel horizontally across the floor plate of a building and result in time and spatially varying thermal exposure and response of the structure to the fire. What has received little attention, however, is the effect that non-uniform thermal exposure has on columns. Recent tests conducted at SP demonstrated the effect of a small non-uniformity of thermal exposure, resulting in a thermal gradient of around 1 °C/mm, on a column exposed to a pool fire. The curvature resulting from a non-uniform thermal exposure where the column is pinned, or in cases where the column is partially restrained, will result in an eccentricity in the column’s loading and large second order effects.This paper describes the effect of thermal exposure varying in both the horizontal and vertical axes to columns by means of including this thermal boundary in a solution of classical Euler beam theory. The resulting solution allows for a variation in the stiffness of the rotational restraint at both ends of the column and a non-uniform temperature exposure through the column’s section and along its height. The resulting equations help to understand better the impact of the assumptions of ‘lumped capacitance’ on steel columns, suggesting a challenge to this assumption in some instances, as well as to enhance understanding of the impact of non-uniform fires on steel columns.