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Columns are one of the basic types of vertical load-bearing elements. In buildings, they are used where there is a requirement to create free spaces. This results in an effort to minimize the cross-section dimensions of the column and to maximize the use of its resistance. The need of the increase in resistance is the reason for columns strengthening. The choice of a suitable strengthening method must take into account the way the column is loaded. Some methods are universal, the others are more effective in the case of predominant compressive, or predominant bending loading. In presented research, the attention is focused on strengthening slender reinforced concrete columns by progressive methods - FRP (fibre reinforced polymer) and FRC (fibre reinforced concrete) applications. For slender columns, second-order effects must be taken into account. The current Eurocode lists three methods of analysing these effects. The simplified methods proposed for the analysis of a reinforced concrete column cannot be applied directly to the calculation of the resistance of a column strengthened by any of the progressive methods. The article is devoted to the calculation of column resistance using a general method that allows the contribution to column resistance from strengthening to be considered.