The behavior of steel and composite steel and concrete columns with restrained thermal elongation in case of fire has been studied for several years. The influence of the restraining to thermal elongation may, in some cases, have a pernicious effect leading to the sudden collapse of the column but in other cases, for higher values of rotational stiffness, the collapse of the column is slow and gradual. In this paper are presented the results of numerical simulations performed on some of the columns of the BRE's Cardington Steel Framed Building calibrated with results from experimental tests carried out on this building structure by the third author of the paper. They were compared gas and steel temperatures, strains, displacements and rotations of the columns ends. The results of the experimental tests were used to calibrate a numerical model of the entire building structure. In these numerical simulations, performed with the finite element program Abaqus, was considered the fire at different locations in the building. They were calculated strains and displacements at critical points of the structure. This work allowed to study the influence of the thermal restraining on the behavior of the columns when subjected to a localized fire. It could be observed a redistribution of forces along the structure in such a way that the collapse of a column did not affect the stability of the whole building. However the collapse of more than one important column could lead to the collapse of the entire structure.