A composite textile reinforced concrete (TRC) material is developed to overcome the difficulties of constructing double-curved freeform structures. This is possible by shear-deformation of the woven reinforcement. It affects the direction of reinforcement and thickness, resulting in variable orthotropic properties over the surface. The research translated the properties of aerospace materials to the scale and limitations of building construction materials. To accomplish this, knowledge about TRC is combined with strength and geometric knowledge about the design of shear-deformation. This resulted in a new type of material and design method that links material properties, digital formfinding, and construction documents/process. This new material should primarily be used as formwork for concrete, a very laborious part of double-curved construction. To conclude the research, a case-study building was created to confirm the complete process from digital formfinding, though structural analysis, to construction documentation. The case-study building, a landmark double-curved concert hall, is used as a narrative to connect the various research realms.