Cross-Section Coordinate System
A separate coordinate system is used for defining cross-sections. The automatic cross-section property calculation is performed about the axes of this system – after moving it without any rotation to the center of gravity of the cross-section. In cases, where the directions of the principal axes differ from the chosen cross-section coordinate axes, the second moments of inertia Iz ad Iy are, by default, also computed about the cross-section system axes. The respective off-diagonal terms of the inertia tensor are neglected.
Calculation of cross-section properties (view in negative XL direction!)
In the standard case (symmetric cross-section, no eccentricities, cross-section normal to the element axis) the cross-section coordinate system translated to the gravity center will be identical to the local coordinate system of the beam element.
With respect to the axis directions, the cross-section values describing the shear resistance are also related to the cross-section coordinate system. With respect to the origin of the calculation coordinate system, they are however related to the shear center, and not to the center of gravity. In accordance with the basic assumptions of the statics of beams, the program assumes without any further checks, that the shear center and the center of gravity coincide (one unique element axis being the reference axis for all internal force components). I.e., the off-diagonal terms of the inertia tensor arising due to any offset between gravity and shear center are neglected like those arising from deviations of the principal inertia planes.
Cross-sections can also be rotated in order to match the cross-section axes with the principal axes. The cross-section properties are re-calculated for the modified system after the rotation/translation. Depending on the actually used sub-function, the β-angles of the elements with this cross-section can be updated by the user or are automatically updated, so that the orientation of the cross-section in the global system remains the same.
