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5 Load Cases and Combinations

8.15 Surfaces - Basic Internal Forces

To control the graphical display of the basic internal forces, select Surfaces → Basic Internal Forces in the Results navigator. Table 4.15 shows the basic internal forces of surfaces in numerical form.

Image 8.39 *Results* navigator: Surfaces → Basic Internal Forces

Image 8.40 Table 4.15 *Surfaces - Basic Internal Forces*

The table shows the basic internal forces sorted by surfaces. The results are listed in reference to the grid points of each surface.

Grid Point

The numbers of the grid points are listed by surface. For more information about grid points, see Chapter 8.13.

Grid Point Coordinates

Table columns B to D show the coordinates of grid points in the global coordinate system XYZ. When you click into a table row, the corresponding grid point is indicated by an arrow in the work window.

Moments / Shear Forces / Axial Forces

In contrast to member internal forces, internal forces in surfaces are symbolized by small letters. The integral definition of the bending moments m_x and m_y shows that moments are related to the directions of the surface axes where the corresponding normal stresses are created. To display the surface axes, use the surface shortcut menu (see Figure 4.122).

When curved surfaces are analyzed, internal forces refer to the local axes of the individual finite elements. The axes can be displayed by selecting the corresponding check box in the Display navigator:

Image 8.41 *Display* navigator: FE Axis Systems x,y,z

Note

There is a fundamental difference between understanding surface internal forces and member internal forces: A member moment M_y "rotates" about the local member axis y, whereas a surface moment m_y acts in the direction of the local surface axis y, i.e. about the x-axis of this surface.

The following figure illustrates the definition of basic internal forces in surfaces:

Image 8.42 Surface internal forces and surface stresses

Moments and shear stresses perpendicular to the surface run parabolically across the surface thickness.

The algebraic signs help you to see on which side of the surface the internal force is available. However, the signs also depend on the orientation of the global axis Z: If the global Z-axis is directed downwards (standard), positive internal forces generate tension stresses on the positive side of the surface (i.e. in direction of the positive surface axis z). They are visualized by blue bars in the table. Negative internal forces result in compression stresses on the positive side of the surface. They are represented by red bars in the table.

If the global Z-axis is directed upwards, the algebraic signs of the bending moments and shear forces are inverted.

When the Z-axis is directed downwards, basic internal forces are determined as follows:

Table 8.8 Basic internal forces
m_x	Bending moment that creates stresses in direction of the local axis x $m_{x} = \int_{- d / 2}^{d / 2} σ_{x} z d z$
m_y	Bending moment that creates stresses in direction of the local axis y $m_{y} = \int_{- d / 2}^{d / 2} σ_{y} z d z$
m_xy	Torsional moment $m_{x y} = m_{y x} = \int_{- d / 2}^{d / 2} τ_{x y} z d z$
v_x	Shear force v_x $v_{x} = \int_{- d / 2}^{d / 2} τ_{x z} d z$
v_y	Shear force v_y $v_{y} = \int_{- d / 2}^{d / 2} τ_{y z} d z$
n_x	Axial force in direction of the local axis x $n_{x} = \int_{- d / 2}^{d / 2} σ_{x} d z$
n_y	Axial force in direction of the local axis y $n_{y} = \int_{- d / 2}^{d / 2} σ_{y} d z$
n_xy	Shear flow $n_{x y} = \int_{- d / 2}^{d / 2} τ_{x y} d z$

Parent section

8 Results