Previously, the authors proposed a novel Sliding Keys on Inclined Deflecting-cantilevers (SKID) device for application with the Post-Tensioned (PT) frames (the PT-SKID frame). The PT frame has a nonlinear elastic feature, providing a high initial lateral stiffness and softening at large displacement. The PT frame is self-centring; the SKID device provides additional damping as it is characterised by a triangular-shaped hysteretic curve with a zero-activation threshold. Thus, the PT-SKID frame has a full self-centring capability by featuring a dual-triangular-flag-shaped hysteretic curve. This paper proposes a novel Post-Tensioned Precast Warehouse structure with the Sliding Keys on Inclined Deflecting-cantilevers Device (the PTPW-SKID structure) following the concept of the PT-SKID frame for industrial buildings. The structural arrangement and the load path are discussed first. The structure comprises the PT outer frame and the SKID inner frame. The PT outer frame supports the roof and cladding systems and carries the loads applied to them. The SKID inner frame supports the SKID devices and carries a crane system. Differing from the PT-SKID frame, the SKID inner frame of the PTPW-SKID structure involves high support columns. The impact of their elastic deformation on the hysteretic curve of the SKID inner frame is discussed first. Then, the seismic design of the PTPW-SKID structure is presented by a case frame located in L′Aquila, Italy. The Direct Displacement-Based Design (DDBD) method is utilised for the seismic design. Finally, a 3D numerical model was built in OpenSees. Both quasi-static and seismic dynamic analyses were carried out. The hysteretic behaviour and the seismic response of the case structure were investigated and discussed.