A geometric digital twin (gDT) model capable of leveraging acquired 3D geometric data plays a vital role in digitizing the process of structural health monitoring. This study presents a framework for generating and updating digital twins of existing buildings by inferring semantic information from as-is point clouds (gDT’s data) acquired regularly from laser scanners (gDT’s connection). The information is stored in updatable Building Information Models (BIMs) as gDT’s virtual model, and dimensional outputs are extracted for structural health monitoring (gDT’s service) of different structural members and shapes (gDT’s physical part). First, geometric information, including position and section shape, is obtained from the acquired point cloud using domain-specific contextual knowledge and supervised classification. Then, structural members’ function and section family type is inferred from geometric information. Finally, a BIM is automatically generated or updated as the virtual model of an existing facility and incorporated within the gDT for structural health monitoring. Experiments on real-world construction data are performed to illustrate the efficiency and precision of the proposed model for creating as-is gDT of building structural members.