Advanced Stability

Advance Design comes with a new FEM engine implemented for a 2^nd order analysis with 7 degrees of freedom (DOF). The feature enables the design of a broad variety of cross-sections shapes, even mono-symmetric or asymmetric shapes, which are widely used in building design but are not covered by code rules.

Advanced Stability functionality helps structural engineers obtain more economic structures, by using thin-walled profiles, which are required more and more often in day-to-day project-related activities.

Advanced Stability feature automatically calculates 2^nd order effects on the steel elements. The functionality is available starting with Advance Design 2019.

This enhanced solver will perform a thorough analysis of individual members during the steel design sequence, considering the following:

The element imperfections by introducing a scaled eigenmode as initial deformation;
The torsional warping effects by considering it as a 7^th degree-of-freedom;
The eccentricity of the loads by taking into account the application point on the cross-section;
The boundary conditions and lateral restrains by introducing centric or eccentric nodal and continuous spring along the member;
The effects of the deformed geometry by performing a second-order analysis.

The new solver is fully integrated into the existing workflow of EC3 Steel Design and can be activated on a selection of elements;
Each element is extracted/isolated from the 3D model and the equivalent external loads are calculated by first derivation of efforts diagrams, for each load case combination;
The same diagrams of efforts and displacements are used to model the equivalent boundary conditions, including elastic supports to simulate the rest of 3D structure;
The user can impose an initial imperfection to be taken into account for 2^nd order analysis;
The cross section of the member can be any of the Advance Design’s standard sections; the member can be with variable section (different sections at extremity, but from the same family), including haunches;

A 2^nd order analysis is then carried out to compute:
- 7 displacements and rotations (T_x, T_y, T_z, R_x, R_y, R_z, R_w) per node
  - Where:
    - T_x, T_y and T_z stand for the displacement along the local x, y and z axes respectively.
    - R_x, R_y and R_z stand for the rotation about the local x, y and z axes respectively.
    - R_w is the warping.
- and 7 forces and moments (N_x, V_y, V_z, M_x, M_y, M_z, M_w) per node
  - Where:
    - N_x is the normal force.
    - V_y and V_z stand for the shear force in the local y and z directions respectively.
    - M_x is the torsional moment. It includes the 1^st order torsional moment (M_xp) as well as the 2nd order torsional moment (M_xs).
    - M_y and M_z stand for the bending moments about the local y and z axis respectively.
    - M_w is the warping moment.

All calculated internal forces and displacements / rotations are taking into account warping deformations from 7^th degree of freedom;
Standard results from the 2^nd order calculation for bending M_y, M_z, torsion M_x and warping bimoment M_w, shear F_y, F_z, axial F_x, displacements, rotations and warping rotation q are displayed;
with these 2^nd order results, stresses are calculated and the cross section is directly checked with the code limit;
The deflection verification of EC3 is done with 2^nd order displacements.

The internal forces and moments resulted from the effects of deformed geometry of the structure can be determined using a 2^nd order theory that takes into account this influence, according to EN1993-1-1 (§5.2.1). 2^nd order effects are also known as P-Δ (non-linear) effects and occur in every structure where elements are axially loaded with compression forces. P-Δ effects are associated with the magnitude of the applied axial compression (P) and displacement (Δ).

Usually, there are no analytical solutions for flexural-torsional problems that include nonlinear deformations. Therefore, a FEM approach is used in order to determine approximate solutions for the differential equations.

The impact from 2^nd order effects on a structure must be assessed for every designed structure, since they increase the deflections, moments and forces beyond those calculated by 1^st order analysis. In many cases, by calculating the elements according to 2^nd order analysis, lighter structures can be designed by using thin-walled steel profiles.

Warping is a deformation that occurs under uniform torsion and causes the section to no longer remain plane. This phenomenon has significant effect on open cross sections such as I, H or channels. For these type of sections, warping results cannot be neglected.

In thin-walled closed cross sections (the most appropriate type of cross section to resist torsion), uniform torsion is predominant. Therefore, in the analysis of thin-walled closed cross sections subjected to torsion, the warping torsion (M_xs) is normally neglected.

Torsional moment is the internal twisting moment about the beam’s longitudinal axis and it is usually considered in two components: St. Venant torsional moment and warping torsional moment. Warping moment is the bending moment in a flange acting as a result of restraint of warping. The moments in the two flanges are equal and of opposite sign.

In members with thin-walled open cross sections (such as I or H sections), inside of which only the uniform torsion component appears, it is necessary that the supports do not prevent warping and the torsional moment is constant. Otherwise, if the torsional moment is variable or warping is restrained at some cross sections (usual situation), the member is under non-uniform torsion.