## 3 Results
### Lateral Displacement Response and Ductility Ratio  
Structural ductility was calculated using Equation 8 and the value of structural displacement at first yield was determined using initial yield or the tangent method [41]. A new model was developed by modifying the analysis model. The static pushover analysis was performed with only lateral loading applied at the top corner of the frame considered. The force-displacement resulting from the analysis is presented in Figure 20. By using the curve, the structural displacement at first yield was determined by estimating the yield point location which is defined as the intersection between the tangential lines of elastic and plastic behaviour, where the displacement at first yield is 71 mm. Subsequently, the structural ductility ratio was calculated as the ratio of peak displacement under blast load to the displacement at first yield. Figure 21 describes the general displacement direction of the frame swaying horizontally in the same direction as the blast excitation load. Two different points depicted in the figure that represents structural height and beam elevations were selected as the node locations to extract the global lateral displacement responses. The lateral displacement at the top right corner (Point A) was considered as a good measurement point for the frame system deformation, whereby the maximum lateral displacements at Point B were used in structural ductility ratio calculation. Figure 19: Structural eigen modes and eigen periods. (**a**) Mode shape 1; (**b**) Mode shape 2; (**c**) Mode shape 3; and (**d**) Mode shape 4. Figure 20: Structural displacement at first yield approximation. The sway histories for these two observation points are presented in Figure 22a,b for all frame analysis with different beam-column connection. The maximum sway responses at lower and upper beam elevations, points A and B, were observed during the blast duration. The maximum responses of the frame without reinforcement are higher than the frames that are reinforced with haunches. To measure the frames dynamic performance based on the sway responses, the extracted maximum sway displacements at the top elevation for each frame during blast and post blast are presented in Table 1 and Figure 23. Subsequently these maximum sway responses were used to calculate the ductility ratios as tabulated in Table 1. The maximum lateral displacement of 94.6 mm occurred in the frame without haunch reinforcement. Since the ductility ratio is proportional with the maximum displacement, the maximum ductility ratio of 1.33 also occurred in the same frame without haunch. The calculated results as presented in Table 1 show that all maximum sway responses and maximum ductility ratios are less than the maximum criteria recommended [40; 46]. The allowable deflection and ductility ratio of frame structures are 1.5 and 240 mm (Height/25), respectively [40; 46]. Figure 21: Selected points for structural displacement location. Figure 22: (**a**) Lateral displacement response history at top right corner of the frame; (**b**) Lateral displacement response history at right end of the lower beam. To evaluate the relative differences between frames performance using ductility criteria, the ductility ratios are presented in Figure 24. The trends show that the frames with haunches performed better compared to the frame without haunches. Qualitatively, the Haunch_03 impact on the frame sway response is the highest among all the haunch types. The Haunch_03 connection reinforcement reduced the ductility ratio by 12% against the frame without haunches, while in the case of the Haunch_02 the reduction is 5% and for the Haunch_01 is 4%. The results demonstrated that the Haunch_03 provides a enhanced dynamic performance. It was also observed that the plate stiffeners on beam-column joints (Haunch_02) provided slightly better ductility ratio than the case of the haunch without the plate stiffeners (Haunch_01). In general, the biggest haunch configuration provided the best frame dynamic performance.