8.25 Surfaces - Equivalent Stresses - Bach

To control the graphical display of equivalent stresses of surfaces, select Surfaces → Stresses in the Results navigator (see Figure 8.54). Table 4.25 shows the surfaces' equivalent stresses according to Bach in numerical form.

Image 8.58 Table 4.25 *Surfaces - Equivalent Stresses - Bach*

The Grid Point and Grid Point Coordinates table columns correspond to those of result table 4.22 Surfaces - Equivalent Stresses - von Mises.

The equivalent stress hypothesis by Bach is also called "principal strain criterion". It is assumed that the failure occurs in the direction of the greatest strain. The approach is similar to the stress determination according to Rankine described in Chapter 8.24. Here, the principal strain is used instead of the principal stress.

The equivalent stresses according to Bach are determined as follows:

Table 8.18 Equivalent stresses according to Bach
σ_eqv,max	Maximum equivalent stress on the positive or negative side of the surface
σ_eqv,+	Maximum absolute value of the equivalent stress on the positive side of the surface $σ_{e q v, +} = \max [\frac{1 - ν}{2} \|σ_{x, +} + σ_{y, +}\| + \frac{1 + ν}{2} \sqrt{{(σ_{x, +} - σ_{y, +})}^{2} + 4 τ_{x y, +}^{2}}]; ν \|σ_{x, +} + σ_{y, +}\|$ where ν: Poisson's ratio (see Chapter 4.3)
σ_eqv,−	Maximum absolute value of the equivalent stress on the negative side of the surface $σ_{e q v, -} = \max [\frac{1 - ν}{2} \|σ_{x, -} + σ_{y, -}\| + \frac{1 + ν}{2} \sqrt{{(σ_{x, -} - σ_{y, -})}^{2} + 4 τ_{x y, -}^{2}}]; ν \|σ_{x, -} + σ_{y, -}\|$
σ_eqv,m	Maximum absolute value of the membrane equivalent stress $σ_{e q v, m} = \max [\frac{1 - ν}{2} \|σ_{x, m} + σ_{y, m}\| + \frac{1 + ν}{2} \sqrt{{(σ_{x, m} - σ_{y, m})}^{2} + 4 τ_{x y, m}^{2}}]; ν \|σ_{x, m} + σ_{y, m}\|$

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8 Results