Real-time monitoring on various structural behaviors, particularly displacement and acceleration, serves important and valuable information for people; for example, they can be used for active control or damage warning. With recent advancement of Internet of Things (IoT) and client-side web technologies, wireless integrated sensor devices nowadays can process real-time raw sensor signal data into target measurements, such as displacement, and then send the results through a standard protocol to the servers on the Internet (i.e., the cloud). The monitoring results are further processed for visualization purpose in the servers and the computed results are pushed to connected clients like browsers or mobile applications in real-time. We build a real-time cloud-based system that can receive heterogeneous IoT data, allow users to create a three dimensional (3D) model online according to the real world structure, and the monitoring results can be visualized in that model. In this paper, we illustrate the software architecture of the proposed system and focus on the technologies that are used, like client-side scripting, NoSql database, and socket communication. We also present the challenges of displaying the overall movement and shape transformation of the 3D structural model. Thus, each internal connected element's rotations and translations are obtained by converting the monitoring results of each sensor device measured in global coordinate system. To overcome this, we create the inverted movement calculation method. A simple 3D two-level structural model and simulated sensor displacements are use to demonstrate system function and validate the inverted movement calculation method.