D9.B.4 Von Mises Stresses Check
The von Mises stress equation shown below, which is modified for beam elements based on the corresponding equation in AIJ steel design code (both 2002 and 2005 editions of AIJ), indicates that the lefthand side in the equation should be less than unity. These checks are performed at locations indicated by the BEAM parameter.
The von Mises stresses are evaluated and checked per AIJ clause 5.16 as follows:
=  $=\frac{{F}_{x}}{{A}_{x}}+\frac{{M}_{y}}{{Z}_{y}}+\frac{{M}_{z}}{{Z}_{z}}$
When the MISES parameter is set to 3 or 4, then the longitudinal stress is calculated once using the smalles elastic modulus for each axis as follows. $=\left\frac{{F}_{x}}{{A}_{x}}\right+\left\frac{{M}_{y}}{{Z}_{y}}\right+\left\frac{{M}_{z}}{{Z}_{z}}\right$
 
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=  $=\left\frac{{M}_{x}}{{Z}_{x}}\right+\sqrt{{\left\frac{{F}_{y}}{{A}_{y}}\right}^{2}+{\left\frac{{F}_{z}}{{A}_{z}}\right}^{2}}$
When the MISES parameter is set to 2 or 4, the torsion stresses are excluded: $=\sqrt{{\left\frac{{F}_{y}}{{A}_{y}}\right}^{2}+{\left\frac{{F}_{z}}{{A}_{z}}\right}^{2}}$
 
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In the STRESSES output category, stress value of (numerator of the von Mises stress equation) is output as the value of fm. Along with slenderness ratios, stresses, and deflections, von Mises stress equation is checked. When its lefthand side yields the maximum ratio value, it is printed as RATIO and "VON MISES" is printed as CRITICAL COND.