When defining your 2D cross section for a thermal analysis, you can chose the position of the origin of your system of co-ordinates in a way that is most convenient for you. For example, a good solution is at the bottom left corner of the section, so that all co-ordinates are positive, see Figure 1.
Figure 1 : position of the "node line"
When this section is used later on in a mechanical analysis, you may not necessarily want to have the nodes of the beam finite element located at the same position (this position is called "the node line" in the beam finite element, because this is the longitudinal line that joints the 2 end nodes of the element). For example, a commonly used position is at the geometrical centre of the section. (Yo;Zo) is the position of the nodes of the beam finite element in the system of co-ordinates that you used to define the section.
Note that, in a simple column for example, changing the position of the node line changes the position of the supports and of the applied node forces. A node line located at the centre of the section will produce no bowing of the column, whereas a node line given with an eccentricity will produce bowing in the column even if only a vertical load is applied.
Note also that all printed bending moments are evaluated with respect to the node line. In the later case of a node line with an eccentricity, the software would give no first order bending moment, and the column would nevertheless bow.
N1,N2 axial forces and M1, M2 bending moments in the beam element
The axial forces and the bending moments given in the output files result from integration of the internal stresses in the cross-section. These integrations are made at the longitudinal points of integration in the beam element. If 2 points of Gauss are used, the 2 axial forces and bending moments are thus calculated at (0.211 * L) and (0.789 * L) if L is the length of the element. This is the reason why, for example, the bending moment M1 in the first element near a simple support is not equal to 0.
The plot made by DIAMOND assumes a linear distribution on the length of the element based on the values given at the 2 integration points. With this "extrapolation" from the integration points to the end of the element, the bending moment is "nearly" exactly equal to 0 at simple supports.
EI as well as ES are calculated with respect to the node line, because “y” is measured from the position of the nodeline.
The center of gravity is not known by SAFIR. It fact, this is not needed provided that the term ES is included in the model.
Note also that the position of the centre of gravity changes during the fire. Imagine that SAFIR recalculates the position of the centre of gravity at every minute, the user would then be confused to have a result linked to point the position of which would change constantly.
The node line is located by the user at any place in the section or, even, outside the section. You can, for example, represent a concrete slab by shell elements and represent the steel beam under the slab by its section and giving the nodeline above the section, for example at mid level in the slab.
The stiffness matrix (in 2D) is based on 3 DoF at each end node + the non linear part of the axial displacement at a (more or less fictitious) central node. It has thus 7 DoF. The integration along the length is by points of Gauss (we normally use 2) and the integration on the section is based on a fibre model. It is formulated in large displacements. In 3D, we have non linear torsion, which makes 7 DoF at each end node, plus the central DoF = 15 DoF per element.
To be sure to have the good solution (no problem with GJ but for EIw), you have to block (fix) one of the node that is located on one of the symetrical axes. If the whole section is modelled (no symmetry is used), IT IS ABSOLUTELY REQUIRED to fix the value of the solution to 0 in at least one node of the axis of symmetry. If not, the torsional stiffness will be correctly evaluated, but the warping function at all nodes will be offset by an arbitrary value and this will create amazing results in torsion during the mechanical analysis.