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8.24 Surfaces - Equivalent Stresses - Rankine

To control the graphical display of equivalent stresses of surfaces, select Surfaces → Stresses in the Results navigator (see Figure 8.54). Table 4.24 shows the surfaces' equivalent stresses determined according to Rankine in numerical form.

Image 8.57 Table 4.24 *Surfaces - Equivalent Stresses - Rankine*

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 Rankine is also known as the "maximum principal stress criterion". It is assumed that the maximum principal stress leads to failure.

The equivalent stresses according to Rankine are determined as follows:

Table 8.17 Equivalent stresses according to Rankine
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 $σ_{e q v, +} = \frac{1}{2} \|σ_{x, +} + σ_{y, +}\| + \frac{1}{2} \sqrt{{(σ_{x, +} - σ_{y, +})}^{2} + 4 τ_{x y, +}^{2}}$
σ_eqv,−	Maximum absolute value of the equivalent stress on the negative side of the surface $σ_{e q v, -} = \frac{1}{2} \|σ_{x, -} + σ_{y, -}\| + \frac{1}{2} \sqrt{{(σ_{x, -} - σ_{y, -})}^{2} + 4 τ_{x y, -}^{2}}$
σ_eqv,m	Maximum absolute value of the membrane equivalent stress $σ_{e q v, m} = \frac{1}{2} \|σ_{x, m} + σ_{y, m}\| + \frac{1}{2} \sqrt{{(σ_{x, m} - σ_{y, m})}^{2} + 4 τ_{x y, m}^{2}}$

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8 Results