## Conventions

There are four parameters that define a load column in Flex2D. These parameters can be entered in the table of the "Loads" view (Figure 1):

Figure 1. Entering loads in Flex2D

For each load column, it is necessary to enter:

1. xmin = The x coordinate at the left side of the column in kilometers.

2. xmax = The x coordinate at the right side of the column in kilometers

3. h = The column height in meters

4. ρ = The column density in kg/m3.

The x coordinate at the right side of the column should be higher than the x coordinate at the left side of the column, otherwise the load is not plotted and not included in the computation. Please notice that when the semi-infinite beam solution is selected, loads with x coordinates lower than zero are not considered in the computation. The load height can be positive or negative. The load density should be positive. The meaning of each column in the "loads" table can be observed by placing the mouse over the column labels (each label has a "help tip" associated to it, Figure 2):

Figure 2. The meaning of the columns in the table of the "Loads" view. In this case for the h column.

Notice that x coordinates (distance) are given in kilometers and y coordinates (height) are given in meters.

There are five parameters that define the "flexural" model:

1. E = The Young Modulus (E) of the elastic lithosphere in GPa (1e9 Pa).

2. ν = The Poisson ratio of the elastic lithosphere. This parameter is dimensionless and it should be between 0.0 and 0.5.

3. T = The elastic thickness in kilometers. This is the thickness of the outmost layer of the earth that behaves elastically (i.e. the elastic lithosphere). This thickness can be constant or variable along the profile (see the Interface section).

4. ρf = Density of foundation in kg/m3. This is the difference between the density of the mantle and the density of the material filling the basin.

5. Xint = The x interval of computation in kilometers. In Flex2D the profile is divided in intervals of length Xint. The deflection is computed at these intervals.

These parameters can be set through the "Inspector" panel (see the Interface section).

In the table of the "Flexure" view, the resultant topography (t) is reported in meters above sea level, and the displacement (u) as "downward" displacement in meters. Positive and negative values indicate downward and upward displacement, respectively. The meaning of each column in the table of the "Flexure" view can be observed by moving the mouse over the column labels (each label has a "help tip" associated to it, Figure 3):

Figure 3. The meaning of the columns in the table of the "Flexure" view. In this case for the t column.

### Density of the foundation

- If the resultant depression is not filled with any material, ρf should be equal to the density of the mantle.
- If the resultant depression is filled with water, ρf should be equal to: (density of mantle - density of water).
- If the resultant depression is filled with sediment of average density ρs, ρf should be equal to: (density of mantle - ρs)

  ### Infinite or broken beam

  There are two types of solutions in Flex2D: Infinite beam solution, and semi-infinite beam solution (broken beam). In the infinite beam solution the elastic beam extends infinitely along the x axis (positive and negative x values). In the semi-infinite beam solution, the beam is broken (has a free end) at x = 0, and extends infinitely in the positive x direction. Since the free end of the semi-infinite beam is at x = 0, loads wih x coordinates lower than zero are not considered in this case.

  The type of beam, infinite or semi-infinite, can be set through the "Inspector" panel (see the Interface section). By default, Flex2D uses the infinite beam solution.

  The elastic thickness can be set constant or variable and its value(s) can be edited in the "Inspector" panel (see the Interface section). By default, Flex2D uses a constant elastic thickness.

  The equations for the deflection of elastic, infinite and semi-infinite beams of constant thickness are from Hetenyi (1946). The equations for the deflection of elastic, infinite and semi-infinite beams of variable thickness are from Bodine (1981). A short description of the equations is given in the formulas section.