# Seismic Response of Container Crane under Near-Field and Far-Field Ground Motions
## 4 Results and Discussions
### Moment at Landside and Seaside Legs  
The bending moments \(M_{y}\) about the y-axis (perpendicular to the trolley-boom direction) and \(M_{x}\) about the x-axis (along the trolley-boom direction) were determined via four strain gauges affixed on all four sides at each section by using Equation (2). Two bending moments and an axial force were determined using three out of the four strain gauge measurements by employing Equation (2). However, if none of the four strain gauges at each section got broken during the testing, four sets of internal forces were determined from the three possible strain gauge combination (that is \(\varepsilon_{1}\), \(\varepsilon_{2}\), \(\varepsilon_{3}\), \(\varepsilon_{2}\), \(\varepsilon_{3}\), \(\varepsilon_{4}\); \(\varepsilon_{1}\), \(\varepsilon_{2}\), \(\varepsilon_{4}\), and \(\varepsilon_{1}\), \(\varepsilon_{3}\), \(\varepsilon_{4}\)). The final internal forces were then determined as the average of the four. The strain gauges locations are shown in Figure 2.  
\[\left\{ \begin{array}{l}\varepsilon_{1}\cdot E=\frac{N}{A}+\frac{M_{x}}{I_{x} }\cdot y_{2}+\frac{M_{y}}{I_{y}}\cdot x_{1}\\ \varepsilon_{2}\cdot E=\frac{N}{A}+\frac{M_{x}}{I_{x}}\cdot y_{2}+\frac{M_{y} }{I_{y}}\cdot x_{2}\\ \varepsilon_{3}\cdot E=\frac{N}{A}+\frac{M_{x}}{I_{x}}\cdot y_{3}+\frac{M_{y} }{I_{y}}\cdot x_{3}\end{array} \right. \tag{2}\]  
where \(\varepsilon\) is the strain measured from strain gauge; \(E\) is the elastic modulus of steel (200,000 N/mm\({}^{2}\)); \(x\), \(y\) is the coordinate of the strain gauge (see Figure 2); \(A\), \(J_{x}\), \(J_{y}\) are the area, moment of inertia about the x- and y-axis of the cross-section, respectively; and \(N\), \(M_{x}\), \(M_{y}\) are the axial force, and the bending moment about the x- and y-axis. The maximum bending moments and axial force in the landslide leg are shown in Figure 6, while the internal forces in the seaside leg are shown in Figure 7. Overall, the analyses show that the internal force of the near-field earthquake (Gazli USSR Iran earthquake) was higher than that of the far-field earthquakes (Nahanni Canada and Mineral Virginia earthquakes) for all of the observed locations. For example, the axial forces in the landslide leg (location S2) and seaside leg (location S6) for the near-field earthquake were approximately 6 and 7 kN, respectively, higher than the axial force of the landslide and seaside legs for the far-field earthquakes. The axial forces in the landslide (location S2) for the far-field earthquakes were approximately 4 kN for the Nahanni Canada earthquake and 6 kN for the Mineral Virginia earthquake (refer to Figure 6a). The axial forces in the seaside leg (location S6) were approximately 5 kN for both the Nahanni Canada and Mineral Virginia earthquakes (refer to Figure 7a). The bending moment \(M_{x}\) about the x-axis in the landslide leg (location S2) under the near-field earthquake was 18 kN.cm. It was higher than the bending moment under the far-field earthquakes, approximately 16 kN.cm under the Nahanni Canada earthquake and 14 kN.cm under the Mineral Virginia earthquake. In the seaside leg under the near-field earthquake, the bending moment was 26 kN.cm, which was higher than the bending moment of 18 and 22 kN.cm under the Nahanni Canada and Mineral Virginia earthquakes, respectively. A similar trend was observed for the maximum bending moment about the y-axis. Specifically, the bending moment in the landslide leg (location S2) under the near-field Gazli USSR Iran earthquake (127 kN.cm) was 20% and 10% higher than that of the far-field Nahanni Canada (102 kN.cm) and Mineral Virginia (114 kN.cm) earthquakes. Similarly, the bending moment in the seaside leg (location S6) under the near-field Gazli USSR Iran earthquake (123 kN.cm) was 27% higher than that of both the Nahanni Canada (90 kN.cm) and Mineral Virginia (90 kN.cm) earthquakes.