Eigenvalue solution Mcr

The single element is taken out of the structure and considered as a single beam, with:

The end conditions for warping and torsion are defined as follows:

Cw_i

Warping condition at end i (beginning of the member)

Cw_j

Warping condition at end j (end of the member)

Ct_i

Torsion condition at end i (beginning of the member)

Ct_j

Torsion condition at end j (end of the member)

To take into account loading and stiffness of linked beams, see chapter "Linked Beams"”.

For this system, the elastic critical moment Mcr for lateral torsional buckling can be analyzed as the solution of an eigenvalue problem:

with

h

Critical load factor

Ke

Elastic linear stiffness matrix

Kg

Geometrical stiffness matrix

For members with arbitrary sections, the critical moment can be obtained in each section, with: (See Ref.[3],pp.176)

with

h

Critical load factor

Myy

Bending moment around the strong axis

Myy(x)

Bending moment around the strong axis at position x

Mcr(x)

Critical moment at position x

The calculated Mcr is then used in the Lateral Torsional Buckling check of SCIA Engineer.

For more background information, reference is made to Ref[2].

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