# D9.C.10 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 left-hand side in the equation should be less than unity. These checks are performed at locations indicated by the BEAM parameter.

Note: As with other design checks, the unity check value can be modified by use of the RATIO parameter.

The von Mises stresses are evaluated and checked per AIJ clause 5.16 as follows:

$σ x 2 + 3 τ x y 2 k × f t < 1.0$
where
 σx = Longitudinal stress in beam element. The following equation is used when the MISES parameter is set to 1 or 2. This is performed multiple times, once in each corner with the appropriate sign of the moment and value of elastic modulus. The largest stress is then used. $= F x A x + M y Z y + M z Z z$ 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. $= | F x A x | + | M y Z y | + | M z Z z |$ Fx = axial force My = bending moment about y-axis Mz = bending moment about z-axis Ax = cross-sectional area Zy = section modulus about y-axis Zz = section modulus about z-axis τxy = shear stress in the beam. When the MISES parameter is set to 1 or 3, this includes torsion stresses: $= | M x Z x | + | F y A y | 2 + | F z A z | 2$ When the MISES parameter is set to 2 or 4, the torsion stresses are excluded:$= | F y A y | 2 + | F z A z | 2$ Mx = torsional moment. Fy = shear stress in the y direction Fz = shear stress in the z direction Zx = torsional section modulus Dx = depth of the member Ix = torsional constant Ay = effective shear area in the y direction Az = effective shear area in the z direction ft = allowable tensile stress k = loading duration factor as specified by the TMP parameter: 1.0 for permanent 1.5 for temporary

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 left-hand side yields the maximum ratio value, it is printed as RATIO and "VON MISES" is printed as CRITICAL COND.