Calculation of elastic critical moment for lateral-torsional buckling

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:

SN003a-EN-EU - "NCCI: Elastic critical moment for lateral torsional buckling", January 23, 2008

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

Hint: Select custom profile in order to manually specify the cross-section dimensions

Cross-section

Select custom profile in order to manually specify the cross-section dimensions

Total height of cross-section

Flange width

Flange thickness

t_f

Thickness of web

t_w

Root radius

Lateral torsional buckling (consider the shape of M_y bending moment diagram inside effective length between points braced along the lateral y-y direction)

Buckling length between lateral supports for lateral torsional buckling

L_LT/L

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.

Shape of M_y bending moment inside the length L_LT

When in doubt the uniform bending moment diagram may be specified to produce conservative results

Ratio of end moment with smallest absolute value to end moment with largest absolute value, taking into account signs, inside the length L_LT

ψ_LT

Support conditions corresponding to bending moment diagram My at the ends of length L_LT

Point of load application

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

Effective length factor referring to end rotation on plan

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

Effective length factor referring to end warping

k_w

Unless special provision for warping fixity is made, k_w should be taken as 1.0