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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 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
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 |

axial force
bending moment about y-axis
bending moment about z-axis
cross-sectional area
section modulus about y-axis
section modulus about z-axis
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

torsional moment.
shear stress in the y direction
shear stress in the z direction
torsional section modulus
depth of the member
torsional constant
effective shear area in the y direction
effective shear area in the z direction
allowable tensile stress
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.