Lateral Torsional Buckling (2nd order) analysis - LTB-II (esasd.14)



The esasd.14 module establishes a bidirectional link with the Frilo BTII solver. In this solver, FEM calculations are performed using elements with 7 degrees of freedom per node. This type of element formulation captures warping in the member and any lateral-torsional buckling (LTB) that may occur.

The member of interest is exported and analysed in the Frilo BTII solver, taking into account the defined boundary conditions and applied loads. Various three-dimensional loading scenarios can be simulated and results may be used for verifications in the ultimate and serviceability limit states, including fire resistance.

Accurate determination of the critical buckling moment Mcr via an eigen buckling analysis.
2nd order analysis aimed at establishing lateral and torsional instabilities.
Circumvention of any additional LTB checks (normally prescribed in design codes).


Hot-rolled or cold-formed elements may be analysed, with both open (e.g., an I- or U-section) or closed (e.g., a RHS) cross-sections.

A single beam element is taken out of the structure and is considered as an isolated beam, with:

  • appropriate boundary conditions (including the ones related to torsion and warping);
  • forces at the beam ends (calculated during the preceding calculation in SCIA Engineer);
  • all applied loads on the beam;
  • intermediate restraints (diaphragms, LTB restraints, linked beams);
  • initial imperfections (used only in the case of 2nd order analysis).

In both types of module application (i.e. in the determination of the critical buckling moment as well as in the 2nd order analysis), results are sent from the Frilo BTII solver to SCIA Engineer, where they can be displayed and added to the project documentation (Engineering Report).


The software distinguishes between loads applied in the centroid of a section and loads applied in the shear centre. Loads not applied in the shear centre of a section are supplemented by additional torsional moments (automatically determined by the software).

The following load types may be used on the analysed member:

  • point force in node (if the node is part of the analysed beam); point force on beam;
  • line force on beam;
  • moment in node (if the node is part of the analysed beam); moment on beam;
  • line moment on beam along the beam axis (torsional);

The loads defined using a standard procedure in SCIA Engineer and their eccentricities are transformed into the local coordinate system of the beam member. The self-weight is converted to an equivalent line load on the beam. Moving loads may also be defined to design e.g. crane runways.

Intermediate supports

The module analyses 3-dimensionally-loaded beams with any boundary conditions. The following intermediate restraints are supported:

  • Discrete intermediate supports may be defined along the analysed beam. These supports may be situated and oriented freely in the 3D environment, are characterised by a user-defined distance from the shear centre of the section, and may be rigid or flexible (spring stiffness is defined by the user).
  • Continuous supports may be defined as an elastic foundation. They can be freely oriented and the user may specify their stiffness and distance to the shear centre.
  • The basic steel check in SCIA Engineer does not take into account the LTB (or other) restraints when these are located on the tension side of a member. The esasd.14 module does take such restraints into account during the design verifications. Although the effect of constraints on the tension side is limited and more modest in comparison to restraints on the compression side, taking it into account leads to a more economical design.

Intermediate lateral restraints are defined via the SCIA Engineer entities: LTB restraints, diaphragms and linked beams.

  • LTB restraints are transformed to elastic springs in Frilo BTII.
  • Diaphragms are transformed into elastic foundations (linear springs and rotations springs).
  • Linked beams are transformed to supports with elastic restraint.


Initial imperfections are taken into account during the 2nd order analysis of beam stability.

  • Bow imperfections along the strong bending axis (in the shape of weak-axis bending) are always taken into account, as recommended in EN 1993-1-1, Article 5.3.4 (3). The standard indicates that, during a 2nd order calculation which takes into account LTB, only these imperfections need to be considered.
  • Eccentricity along the weak bending axis may also be taken into account, if desired.
  • For verifications according to the DIN, ONORM, EC-EN, and EAE standards, the size of initial imperfections may be calculated according to the design code.

Mcr eigen values calculation

  • This application of the module calculates the bifurcation load corresponding to the LTB eigen mode.
  • Subsequently, the critical moment value is sent back to SCIA Engineer, where reduction factors for stability are determined using the equivalent bar method.
  • The calculated buckling length may be overwritten during the subsequent checks performed in SCIA Engineer; a warning is issued in such a case.
Supported national codes
  • EC3, EN 1993-1
  • EC3, ENV 1993-1
  • SIA 263
  • DIN18800
  • ÖNORM B 4300
  • NEN 6770/6771
  • IS 800
  • EAE 2004
  • 2nd order calculation of torsion and warping

    The module allows you to perform 2nd order analysis in the ultimate and serviceability limit states for beam members with any type of supports and loading.

    • Internal forces, elastic deformation, normal and shear stresses are calculated with consideration of warping deformations. An additional 7th degree of freedom represents the value of warping in the cross-section.
    • Boundary conditions are defined separately for torsion and warping; in this way, a member may be fixed at either end against torsion, while warping remains unrestrained.
    • Using results from 2nd order calculation that captures LTB, many code-prescribed checks may be skipped. This means that only the stress levels in the cross-section need to be checked (i.e. see general method described in EN 1993-1-1).
    • The calculated torsional and warping moments (St. Venant torque, warping torque, and bimoment) are used subsequently in a stress check which is performed in SCIA Engineer.
    • The stress check takes into account the normal force in the beam member (calculated in SCIA Engineer) and the maximum values of shear forces and bending moments (obtained either from the calculation in SCIA Engineer or from the Frilo BTII solver).
    • When torsion is present in the beam member, it is strongly recommended to perform the 2nd order analysis instead of the eigenvalue calculation.
    Supported national codes
  • EC3, EN 1993-1
  • EC3, ENV 1993-1
  • SIA 263
  • DIN18800
  • ÖNORM B 4300
  • NEN 6770/6771
  • EAE 2004
  • Limitations

    • Only linearly elastic material response in supported;
    • The modulus of elasticity and the shear modulus should be constant over the entire beam member.
    • The analysed beam members should be straight.
    • Normal forces acting along the beam axis are ignored during the numerical analysis in the BTII solver.

    Export to Frilo BTII

    If the standalone Frilo BTII application has been installed, it is possible to directly export a beam member from SCIA Engineer to it via the 'Export to BTII' action button. All relevant properties and additional data are exported as well.

    There are a few additional features and tweaks that are available in the standalone BTII, e.g.:

    • In the case of open sections, additional considerations are taken into account for secondary flange bending due to eccentric loading on the lower flange. The additional stress generated by secondary flange bending is considered during the final stress verification.
    • Various moving loads can be defined via the GUI of the standalone application. These can be used in the verification of different types of crane beams.