# Virtual Scene Construction for Seismic Damage of Building Ceilings and Furniture
## 3 Technical Method
### Simulation of the Movement of Damaged Nonstructural Components
#### 3.3.2 Movable furniture  
Movable furniture will move or overturn during an earthquake. To simulate such movements, three steps need to be performed: (a) create a physical model of the movable furniture; (b) implement the simulation in PhysX; and (c) validate the simulation results. 1. Physical model  
The physical model of the movable furniture is shown in Figure 5. A furniture object on the floor will be subjected to an inertial force (denoted as \(F\)) caused by the floor acceleration (denoted as \(a_{floor}\)) of the structural seismic response. In addition, the object will also be subjected to gravity (i.e., \(G\)), a friction force (i.e., \(F_{f}\)), and a normal force (denoted as \(N\)). In the \(y\)-direction, gravity is equal to the normal force to maintain balance, i.e., \(G=N\), while in the \(x\)-direction, the inertial force, \(F\), and friction force, \(F_{f}\), will cause the object to move. The moment caused by the inertial force, \(F\), and gravity, \(G\), determines whether the object will overturn. Therefore, these forces will fully determine the movement status of the object, which can be calculated using the equations  
\[F_{f}=N\mu=G\mu=mg\mu \tag{9}\]  
\[F=ma_{floor} \tag{10}\]  
where \(m\) and \(\mu\) are the mass of the object and the friction coefficient between the object and the floor, respectively. 2. Simulation implementation  
The Equation (9) has been embedded in PhysX, which is similar with the aforementioned simulation implementation of ceiling tiles, therefore the same implementation steps are performed for movable furniture, as follows:  
(1) Create rigid-body models  
In this study, all of the movable furniture is modeled as rigid bodies. (2) Determine key coefficients  
The masses and friction coefficients of movable furniture are key coefficients of the physical models. The masses can be calculated by using the component data in BIM, while friction coefficients can be determined according to the empirical values for common materials [38]. (3) Define initial physical status  
With regard to movable furniture, the initial physical status is static, thus no additional work is needed. (4) Add the forces  
Using the function \"AddForce()\" in PhysX, an inertial force can be applied at the centroid of a rigid body. The inertial force can be calculated with Equation (10) using the floor accelerations obtained from the results of the seismic THA. By activating the gravity, the friction force and normal force will  
Figure 5: Physical model of movable furniture. be calculated automatically by PhysX according to Equation (9). Based on these forces, the movements of these objects will be also automatically simulated by PhysX. 3. Validation with a shaking table test  
To validate the proposed physical model for movable furniture, an existing shaking table test is employed for comparing with the simulation result. Specifically, this is a full-scale shaking table test of a five-story steel frame structure (see Figure 6a), which was performed by the National Research Institute for Earth Science and Disaster Resilience (NIED) of Japan using the E-Defense shaking table [39]. Some movable furniture (e.g., a wardrobe and lamp) are placed in the third story of the structure, and the entire shaking process of the indoor furniture was recorded, as shown in Figure 6b. For comparison, the above experimental scene was first replicated with the proposed BIM-based modeling framework and imported to Unity. Subsequently, the physical models of the indoor furniture were created in PhysX. The masses and friction coefficients of the indoor furniture in Figure 6b are listed in Table 2. The masses of the pieces of furniture are calculated based on their densities and volumes, which can be obtained from the component attributes in the BIM, while the friction coefficients are empirical values for common materials [38]. In addition, the recorded time-history data [39] is used directly for the floor acceleration, as shown in Figure 7.