Failure temperature of a System Comprising a Restrained Column Submitted to Fire

The problem of columns submitted to fire is discussed in the intoduction with an emphasis on the differences between the case of a column acting as a single element or being part of a frame. In the latter case, failure of the column does not necessarily lead to the failure of the structure. The basic principles of the arc-length technique are given, first for the way it is applied traditionally at room temperature, then for the way it can be applied to extend a numerical simulation beyond the moment of local failures in case of fire. The technique is then applied to the case of restrained columns and it is shown how it is possible to obtain a safe estimate of the critical temperature of the column leading to the failure of the structure, even if the degree of restraint apllied to the column is unknown.