## 3 Results  
### Model Validations Results  
A single-bay two-storey steel framing configuration as presented in Figure 14 was chosen to develop the model. The selected steel frame was considered appropriate for the object in the study because a simple and small structure does not require excessive computation resources. [PERSON] and [PERSON] [15] investigated the transient dynamic response of the inelastic steel frames with nonlinear connections. Geometric imperfections and residual stress with a maximum magnitude of 50% of yield stress were included in their study.  
The model of the selected steel frame was developed in ABAQUS. Before starting the simulations for the research, two different analyses namely elastic and elastic-perfectly-plastic analyses were used for validating the model by comparing the dynamic responses from numerical analyses against the dynamic responses presented by [PERSON] [19]. To differentiate the analysis, two different material properties were created representing the elastic and elastic-perfectly plastic with a yield stress of 235 MPa. The elastic and elastoplastic analyses were carried out. To verify the dynamic characteristic of the frame using theoretical calculations, elastic dynamic analysis was also carried out using CALFEM which is a MATLAB computational toolbox for teaching FEM developed at Lund University [48]. The structural lateral displacement responses are presented in Figures 15 and 16.  
Since the response based on CALFEM calculation matches the elastic response presented by [PERSON] and [PERSON] [15], their dynamic characteristics are considerably identical. This implies that the dynamic characteristic based on CALFEM calculations represents the similar dynamic characteristic of the frame presented by [PERSON] and [PERSON] [15]. According to the dynamic response in Figures 15 and 16, the maximum response from the ABAQUS analysis is 42% higher than the maximum response given by [PERSON] and [PERSON] [15]. In addition to this, the displacement response wave period of the ABAQUS results are shorter than the results from [PERSON] and [PERSON] [15].  
To investigate these discrepancies, the natural frequencies that represent the dynamic characteristic of the frames were calculated using ABAQUS and CALFEM. As shown in Figure 17, the structure natural frequency of 1.4978 Hz extracted from ABAQUS is 5.4% higher than the CALFEM result (1.4214 Hz). [PERSON] et al. [18] showed that the effect of mass and load distribution on the dynamic response of a structural system in which a structural system with distributed mass is stiffer than a system where the entire mass is concentrated at midspan points. Unlike beam finite element formulation, the structural masses in the ABAQUS model is distributed throughout the structure and not concentrated at points. This implies that the ABAQUS model should be stiffer than the CALFEM calculation, hence it will have a higher natural frequency.  
The effect of the nonlinearity of the system was also investigated. As shown in Figure 18, the Von Mises stress reaches the yield stress value. This situation is considered overstress, in which  
Figure 16: Elastoplastic analysis dynamic response ABAQUS and Chan and Chui [15].  
Figure 17: Structural natural frequency from (**a**) ABAQUS and (**b**) CALFEM/MATLAB.  
the validated model undergoes yielding and buckling. In this case, analysis using ABAQUS does have capability to consider inelastic moment redistribution [49] and P-delta effects by activating the geometric non-linearity option in the dynamic analysis. These features allow the analysis using ABAQUS to capture the more realistic dynamic behaviour of the structure.  
The preceding section explained possible factors affecting the higher dynamic responses obtained from ABAQUS compared to the dynamic response presented by [PERSON] and [PERSON] [15].