In today's society it becomes more and more necessary to build high houses. Floors are added on existing buildings, which mean that the supporting structure must be reinforced to handle the extra load. In this thesis a pillar structure of steel is studied were the cross-section is reinforced by plates on each flange. When design of reinforced steel columns, according to Eurocode 3, the reinforced cross-section is designed as a new cross-section and all loads imposed in one step. In the real case, when the higher load is applied it gives a deflection, which in turn gives an additional deflection of the existing load. In addition, yielding can occur in parts of the cross-section that reduces bending stiffness and provides a lower failure load. The aim of this thesis is to give an indication of the degree to which reinforcement plates need to be increased when the residual stress and partial yielding is considered. The work was done with an analytical solution based on Eurocode 3. The thesis consisted largely of finding effective methods of calculation which made it possible to conduct a parametric study. The study has been carried out both analytically and with FE-analysis. The results have a high level of agreement and the numerical calculation is therefore verified. The results of the study show that at high slenderness where utilization of the existing pillar is high, design according to Eurocode 3 is not on the safe side. When residual stress and partial yielding is counted for, the reinforcement plates at slenderness 100 needs to be increased by approximately 55 % - 100 % to cope with a design load of 1.5 of the existing load in comparison with design with Eurocode 3. The study results are clearly interesting in the design of slender columns at high utilization rates. For the reinforcement of a building where the utilization rate of existing steel columns is under 60 %, the design according to standards can be used.