# Effects of Boundary Condition Models on the Seismic Responses of a Container Crane
## 1 Introduction  
The impact of an earthquake on civil structures (i.e., buildings, bridges, dams, tunnels, and container cranes) is always most concerning for engineers, because it badly affects people and the economy. The container crane is a steel structure built at seaports for loading and unloading container ships. It is an important link for transporting freight between countries, so it also receives the special attention of countries having seaports. However, container cranes are one of the most vulnerableelements of the port system, and are often damaged under moderate seismic loads. [PERSON]'s research [1] into disasters of the Port of Kobe after the 1995 earthquake showed that although in terms of magnitude (M\({}_{\rm w}\) = 6.9) it was a moderate earthquake, it caused an estimated US$10 billion loss (at exchange rates at the time), because the Port was essentially shut down, and the scale of damage was so large that repairs were not completed until March 1997 (over two years after the earthquake). This means that the traffic that would have gone through Kobe was diverted to other ports. Moreover, modern container cranes are larger than ever before to satisfy the demand for bigger ships, so the cranes can easily become unstable under seismic loads. For these reasons, evaluating the dynamic response of container cranes under seismic excitation needs to be studied further, to ensure their structural stability. Investigating the response of the container crane under seismic load has often been researched by experimental and numerical methods. [PERSON] et al. [2] used a shake table experiment that was performed on a 1:20 scale model to characterize the uplift behavior, then compared that with the 2-D and 3-D finite element models. The authors showed that the simulated model is sufficient to perform dynamic time history analysis for evaluating the overall behavior, including uplift and derailment phenomena. [PERSON] et al. [3] investigated the seismic behavior of the container crane by shake table test (using a 1:20 scaled container crane) and a mathematical model, and also concluded that the dynamic behavior, including in the time and frequency domains, of the crane structure could be represented by the mathematical model. [PERSON] et al. [4] carried out studies on the dynamic response of cranes by a series of shaking table tests (using 1/25 and 1/8 scaled crane models). In their research, the recoded ground motions were applied critically in the trolley-boom direction to find components that were the most destructive. The results showed that the derailment of the wheels happens often under large seismic excitations. The shake table test is an effective method to evaluate the dynamic response of the container crane under seismic excitation. However, it is not an economical method, and sometimes it may not be necessary to conduct it in small projects. In some case, the numerical method using commercial software will produce a reliable result, and is more economical. All components of a container crane are supported and moved via its wheels. In normal conditions, the crane still remains under its gravity load, which means that the wheels are fixed to the rail or ground, so that the boundary condition in a simulated model could be a pin support that can resist both vertical and horizontal forces. On the other hand, if the seismic load is large, the wheels might be uplifted. In particular, previous research in Japan has proven that the uplift and derailment of cranes can be reached under just moderate earthquakes [4; 5; 6]. In this case, the base shear of the uplifted wheels is lost, and the uplifted wheel can move freely in the vertical and horizontal directions, so the pin support is not suitable to be applied. For dealing with this problem, [PERSON] et al. [4] proposed two models: a planar two-dimensional and a three-dimensional model for evaluating the uplift and derailment events.