# Effects of Boundary Condition Models on the Seismic Responses of a Container Crane
## 4 Results and Discussions
### Reaction of Legs  
Consider the reaction of the landslide legs in which uplift and derailment events happened first. Figure 13 shows the result of horizontal reaction of the landslide leg (node 10) at the spectral acceleration of 0.2 and 0.6 g of the Imperial Valley-02 earthquake. When the intensity of earthquake is low (\(S_{a}=0.2\) g), there is almost no difference between the boundary condition models. The maximum difference is only about 60.54 kN at 25.06 s for FC vs. PIN, while that for GAP vs. PIN is approximately 45.85 kN at 25.07 s, and FC vs. GAP is 15.48 kN at 19.61 s. As compared to the maximum values of horizontal reaction, which are 377 and 384 kN for FC and PIN, respectively, the difference determined as percentage is 15.8% for the couple of FC vs. PIN, while that for GAP vs. PIN is 6.5%, while FC vs. GAP is 4.11%.  
Figure 12: The portal drift of the FC boundary condition.  
Figure 13: Horizontal reaction of landslide leg: (**a**) at \(S_{a}=0.2\) g; (**b**) at \(S_{a}=0.6\) g.  
With regard to Figure 13b, the intensity of spectral acceleration of 0.6 g--in which uplift and derailment events occurred--when using the different boundary condition models, there is overall a fluctuation in the horizontal reaction of the landslide legs. At the beginning time, the initial equilibrium position indicates a horizontal reaction of around 53.74 kN on the landslide leg because of the effect of gravity. When the landslide leg is derailed, its reaction profile shows different behavior, as illustrated in Figure 13b. The maximum differences are 1024.75 kN at 6.21 s, 402.75 kN at 18.37 s, and 969.90 kN at 14.6 s for FC vs. PIN, GAP vs. PIN, and FC vs. GAP, respectively. As compared to the maximum value of horizontal reaction at \(S_{a}\) = 0.6 g, the values of FC and PIN are 1252 and 1045 kN, respectively, and the difference determined as percentage is high at 81.8% for the couple of FC vs. PIN, while that of GAP vs. PIN is 38.5%, and FC vs. GAP is 77.4%. Notably, the horizontal reaction of the landslide legs in the FC boundary model is equal to zero when the uplift event occurs, while the value of landslide legs for GAP and PIN does not equal zero, as in Figure 13b, which indicates that there are two periods in which the uplift event happened, 6.05 to 6.13 s, and 14.54 to 14.65 s (as can be seen the red circles of Figure 13b).  
Figure 14 shows the average total base shear obtained from the time history analyses. In this data, there are no differences in the total base shear for the other boundary models when the spectral acceleration is less than 0.4 g, and the relationship between total base shear and spectral acceleration is linear. However, the difference begins after the spectral acceleration of 0.4 g as a result of the phenomenon of uplift and derailment of the container crane, and this relationship is no longer linear. This could be explained by the effect of the boundary condition model, as the PIN boundary does not reflect the correct working condition; it fixes the legs into the ground (rail), and then the resistance of the link makes the total base shear increase significantly. In contrast, the GAP and FC boundary allow uplift or both uplift and derailment, and the effect of the free movement of the legs results in the relationship also becoming nonlinear. In the three boundary models, when uplift and derailment happen, the PIN boundary has the largest total base shear, while the FC boundary has the lowest one. Throughout, the distinction of the dynamic response of the container crane between the bonded contact model (PIN) and unbonded contact (FC or GAP) begins during the uplift and derailment event, \(S_{a}\) = 0.4 g.