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:
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.
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.
|
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:
When the MISES parameter is set to 2 or 4, the
torsion stresses are excluded:
|
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.