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Eurocode 3 Calculation of elastic critical moment for lateral-torsional buckling of doubly-symmetric flanged cross-section (IPE, HEA HEB, HEM or custom)

Description:
Calculation of elastic critical moment Mcr for lateral-torsional buckling of a uniform steel member with I-section or H-section (IPE, HEA HEB, HEM or custom) according to elastic buckling theory
According to:
SN003b-EN-EU - "NCCI: Elastic critical moment for lateral torsional buckling", October 12, 2010
Applicable for:
Steel members (beams/columns) with uniform cross-section, doubly symmetric rolled I or H sections or equivalent welded sections
Supported National Annexes:
No Nationally Defined Parameters (NDPs) in the calculation
All Calculations
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Lateral torsional buckling (consider the shape of My bending moment diagram inside effective length between points braced along the lateral y-y direction)

m
For standard fork supports it is the distance between points braced along y-y direction for bending about y-y axis as a portion of the system length. It is recommended to use the distance between lateral supports also for the cases where additional restraints exist as a conservative approximation.
When in doubt the uniform bending moment diagram may be specified to produce conservative results
It is assumed that loads act in the same direction as gravity, otherwise the flange designation top/bottom must be reversed
Considered shapes of bending moment My diagram for lateral-torsional buckling
Considered shapes of bending moment My diagram for lateral-torsional buckling
In general the value of k should be taken as not less than 1.0 unless the value less than 1.0 can be justified
Unless special provision for warping fixity is made, kw should be taken as 1.0