# Dynamic Analysis of an Offshore Knuckle-Boom Crane Under Different Load Applications Laws
## 2 Materials and Methods  
### Description of the Analyzed Crane  
The offshore knuckle-boom crane studied consists mainly of three main areas that compose the entire structure:  
* loading section, composed of the movable parts that allow the uplift;
* translation and rotation module, which are the moving parts that allow relative movement between the loading and handling module;
* movement module, composed of the moving parts that allow relative motion between the ground and the structure.  
Figure 1 shows the 3D model of the analyzed crane.  
Specifically, the loading section is composed of different elements: the stick, which is the beam where the load is applied; the boom, the beam that links the stick to the main frame of the loading section; the counterweight arm; the tie rods, connecting pins, the main frame, and the control cabin. The moving parts facilitate the relative motion between the ground and the structure. To understand the dimensions, the length of the stick is 14 m,  
Figure 1: 3D model of the offshore knuckle-boom crane studied.  
and the length of the boom is 17.5 m. The following components define the translation and rotation module:  
* the translation cart (needed for the translation movement);
* the cylinder;
* the fifth wheel (needed for the rotation movement, an example [34]);
* the anti-tilting system.  
The movement module basically consists of a portal structure that can be moved by four handling carts. To comprehend the size, this structure is 10 m tall and 30 m long. The following are the project specifications:  
* liftable load with the boom in horizontal position: 300,000 N;
* spreader weight: 100,000 N;
* maximum outreach: 30 m;
* maximum height to take the container: 20 m;
* maximum depth reached below the ground level: 20 m.  
Structural steel S355 JR (EN 10025-2 [35]) (steel alloy with \(\sigma_{y}\) = 355 MPa for thickness \(t\)\(\leq\) 16 mm; \(\sigma_{y}\) = 345 MPa for thickness 16 mm \(\leq t\)\(\leq\) 40 mm; \(\sigma_{r}\) = 510 MPa and elastic modulus \(E\) = 206,000 MPa) was adopted for the construction of the crane, being a common material for big structures such as earth-moving machinery [36; 37] and even for marine applications [38]. The main parameters implemented for the crane design are defined according to the series of standards EN 13001 [7]; in Figure 2a, it is possible to see the operating range of the crane. Analytical evaluation identified two configurations as critical for the crane, which were named C1 and C2 in this research study. The main criteria for the two configurations of the crane stands in the highest stress for its components, as already shown in a previous research work [39]. The first position is critical mainly for the boom: with this component horizontal and the stick perpendicular to the ground, as can be observed in Figure 2b, the bending moment for the boom here is higher than every other configuration, considering also that the liftable load here can reach 300,000 N. The second position, where the position of the boom and stick is shown in Figure 2c, is perilous for the component called stick, with an upper value of the liftable load equal to 100,000 N. Here, it is also possible to notice where the displacement is analyzed in Section 3: a probe at the end of the stick is placed to extrapolate the displacement along the Y-axis.