Wire arc additive manufacturing (WAAM) is an additive manufacturing process based on gas metal arc welding. It allows the fabrication of large-volume metal components by the controlled deposition and stacking of weld beads. Next to the near-net-shape manufacturing of metal components, WAAM is also applied in the local reinforcement of structural parts, such as shell geometries. However, this procedure can lead to undesired thermally induced distortions. In this work, the distortion caused by the WAAM reinforcement of half-cylinder shell geometries was investigated through experiments and transient thermo-mechanical finite element simulations. In the experiments, the weld beads were applied to the specimen, while its thermal history was measured using thermocouples. The developing distortions were registered using displacement transducers. The experimental data were used to calibrate and validate the simulation. Using the validated model, the temperature field and the distortions of the specimens could be predicted. Subsequently, the simulation was used to assess different deposition patterns and shell thicknesses with regard to the resulting part distortions. The investigations revealed a non-linear relation between shell thickness and distortion. Moreover, the orientation and the sequence of the weld beads had a significant impact on the formation of distortion. However, those effects diminished with an increasing shell thickness.