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8.27 Surfaces - Principal Strains

To control the graphical display of strains, select Surfaces → Strains in the Results navigator (see Figure 8.59). Table 4.27 shows the principal strains of surfaces in numerical form.

Figure 8.61 Table 4.27 Surfaces - Principal Strains

The table shows the principal strains sorted by surfaces. The results are listed in reference to the grid points of each surface.

The Grid Point and Grid Point Coordinates table columns correspond to those of the previous results table 4.26 Surfaces - Basic Strains.

Principal Strains

The basic strains described in Chapter 8.26 refer to the surfaces' coordinate system xyz. The principal strains, however, represent the extreme values of the strains in a surface element. The principal axes 1 (maximum value) and 2 (minimum value) are arranged orthogonally.

It is possible to display the principal axis orientations as trajectories in the work window (see Figure 8.45 for principal internal forces).

The principal strains have the following meanings:

Table 8.20 Principle strains

ε1,+

Strain in the direction of the principal axis 1 on the positive side of the surface
(i.e. side in direction of positive surface axis z)

ε1,+=12εx,++εy,++(εx,+-εy,+)2+γxy,+2 

ε2,+

Strain in the direction of the principal axis 2 on the positive side of the surface
(i.e. side in direction of positive surface axis z)

ε2,+=12εx,++εy,+-(εx,+-εy,+)2+γxy,+2 

α+

Angle between local axis x (or y) and principal axis 1 (or 2) for the strains on the positive side of the surface

α+=12arctan(γxy,+εx,+-εy,+) 

ε1,−

Strain in the direction of the principal axis 1 on the negative side of the surface

ε1,-=12εx,-+εy,-+(εx,--εy,-)2+γxy,-2 

ε2,−

Strain in the direction of the principal axis 2 on the negative side of the surface

ε2,-=12εx,-+εy,--(εx,--εy,-)2+γxy,-2 

α

Angle between local axis x (or y) and principal axis 1 (or 2) for the stresses on the negative side of the surface

α-=12arctan(γxy,-εx,--εy,-) 

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