The increase of the load carrying capacity of columns being reinforced with Textile Reinforced Concrete (TRC) is partly achieved by the additional concrete cover. But then it is also decisively caused by the confinement effect of the textile reinforcement, which is particularly in the support region of great importance. The confinement is thereby producing a three axial state of stress within the concrete core of the column. The effectiveness of such a confinement is especially dependent on the geometry of the concrete column to be strengthened. With the help of experiments on column heads with all possible cross sections from square to circle with different transition radiuses the influence of the transition radius onto the local bearing capacity of the reinforcing textile was recorded. Furthermore the impact of different fibre materials and reinforcement degrees of the TRC strengthening layer have been examined and compared with usual CFK-Sheet strengthenings. A computation model for the load increase by the TRC strengthening is introduced.