# The Effect of Subgrade Coefficient on Static Work of a Pontoon Made as a Monolithic Closed Tank
## 3 Results  
### Static Analysis of the Pontoon  
For the purpose of this work, appropriate static calculations were made in order to verify the effect that an internal elastic substrate has on the value and distribution of bending moments in closed rectangular tanks. Calculations used the finite difference method in variational approach and were made for a closed rectangular tank with axial dimensions \(\mathrm{l_{x}}\), \(\mathrm{l_{y}}\) and \(\mathrm{l_{z}}\) being at a 4:1:0.5 ratio, respectively. The value of substrate stiffness (Styrofoam) was assumed as \(\mathrm{K_{z}}\) = 5000 \(\mathrm{kN/m^{3}}\). The tank featured an internal partition in the centre of its length. The discretization grid took into account the symmetry plane of the structure, and assuming that the mesh size was \(\mathrm{s}=\mathrm{l_{y}}/12\), the system of equations with 823 unknowns was obtained. The following loads were included: hydrostatic load acting on the tank walls, uniform load acting on the bottom (Figure 3a), uniform load acting on the upper plate of the tank (Figure 3b) and ice floe pressure acting on the circumference of the tank at half its height (Figure 3c). Figure 4 shows a schematic drawing of the pontoon with its internal partition with the numbering of points for which the article gives coefficients proportional to bending moments. Figure 3: Schematic drawing of the hydrostatic load acting on the tank walls and the bottom (**a**), uniform load acting on the upper plate (**b**) and ice floe pressure (**c**), for which static calculations were made. Figure 2: The schematic drawing of the pontoon under constant load (**a**) and the schematic drawing of the pontoon under constant and variable load (**b**), where G—gravity centre of the pontoon, B—buoyancy centre of the pontoon at rest, K—keel, \(\mathrm{h_{d}}\)—immersion due to the dead weight load, \(\mathrm{h_{g}}\)—location of the gravity centre, C—centre of the visible area of the water surface, M—metacentre, W\(\mathrm{1}\)—total weight of constant and variable loads, B’—buoyancy centre of the loaded pontoon, F—floating forces in water, \(\mathrm{h_{mc}}\)—metacentre height above the gravity centre, \(\mathrm{h_{mb}}\)—metacentre height above the buoyancy centre, and \(\mathrm{h_{1d}}\)—height of the buoyancy centre. In order to create a new structural element that can be successfully used in construction and because the idea of this article is to apply the obtained numerical calculation results to practice, the specific dimensions of the pontoon were assumed. The dimensions enable its production, transport and use as a single element or as a connected floating platform, and they were adopted as length l\({}_{x}\) = 10 m, width l\({}_{y}\) = 2.5 m, height l\({}_{x}\) = 1.25 m, thickness of all walls h = 0.08 m and substrate shear modulus (Styrofoam) K\({}_{x}\) = 5000 kN/m\({}^{3}\). The results of the calculation of coefficients proportional to the values of bending moments at select points for the pontoon with and without the cooperation with its elastic substrate are presented in Table 1. In order to analyse the effect of taking into account the substrate on the change in the values of deflections and bending moments, charts were drawn up showing the distribution of the values of bending moments in longitudinal and transverse sections (Figures 5-8). The designations of points are in line with Figure 4, and as the most important, the hydrostatic load on the walls, the uniform load on the bottom of the pontoon and the uniform load of the top plate were selected. By analysing the data obtained from the numerical calculations listed in Table 1, it can be concluded that, at each point of the partition grid as well as for each type of load, the bending moments are reduced, taking into account the elastic substrate.