# D5.D.8.3 Clause 6.3.2.2 –Elastic critical moment and imperfection factors for LTB checks

The Polish NA recommends the use of Table 6.3 and 6.4 of PN EN 1993-1-1:2005 to calculate the imperfection factors for Lateral Torsional Buckling (LTB) checks.

The calculation of the LTB reduction factor χ_{LT},
requires the calculation of the
"Elastic Critical Buckling Moment", M_{cr}. The
Polish National Annex does not specify a particular method to calculate
M_{cr}. Hence the calculation of M_{cr} has been based on the
following NCCI documents:

## SN003a-EN-EU – Elastic critical moment for Lateral torsional Buckling

This document provides a method to calculate
M_{cr} specifically for doubly symmetric sections only. Hence only
doubly symmetric sections will be considered for this method. The equation to
evaluate M_{cr} is given in the NCCI as:

C_{1} and C_{2} are factors that depend
on the end conditions and the loading conditions of the member. The NCCI
provides values for C_{1} and C_{2} for the different cases as
given in the tables below:

This NCCI considers three separate loading conditions:

- Members with end moments
- Members with transverse loading
- Members with end moments and transverse loading.

STAAD.Pro accounts for the
loading condition and the bending moment diagram through the
`CMM` parameter.

## SN030a-EN-EU – Mono-symmetrical uniform members under bending and axial compression

This document provides a method to evaluate the elastic
critical moment (M_{cr}) for uniform mono symmetric sections that are
symmetric about the weak axis. Hence, the elastic critical moment for
"Tee-Sections" will be worked out using the method in
this NCCI.

The equation to evaluate M_{cr} for mono
symmetric sections is given as :

The factors C_{1}, C_{2}, and
C_{3} are dependent on the end conditions and loading criteria. This
implementation will consider C_{1}, C_{2}, and C_{3} as
given in the tables below:

The
`CMM` parameter specified during design input will
determine the values of C_{1}, C_{2}, and C_{3}. The
default value of
`CMM` is 0, which considers the member as a pin ended
member with UDL along its span. This NCCI does not however consider the end
moments and transverse loading condition. You can use the
`C1`,
`C2`, and
`C3` parameters to input the required values for
C_{1}, C_{2}, and C_{3} to be used in calculating
M_{cr}.

Both the NCCI documents mentioned above assume that the member under consideration
is free to rotate on plan and that there are no warping restraints for the member (
k = kw = 1.0). STAAD.Pro takes into account of the end
conditions using the `CMN` parameter for EC3. A value of K = kw =1 is
indicated by a value of `CMN` = 1.0 in the design input. Hence the
above methods will be used only for members which are free to rotate on plan and
which have no warping restraints (i.e., `CMN` = 1.0). Other values of
CMN (i.e., `CMN` = 0.5 or `CMN` = 0.7) are
*not* applicable to the Polish NA.

For all cases that are not dealt with by the National Annex (or the NCCI documents) this implementation will use the method as per the DD ENV 1993-1-1:1992 code.

The term
"zg" in the equation to calculate Mcr refers to the
distance between the point of application of load on the cross section in
relation to the shear center of the cross section. The value of ‘zg’ is
considered positive, if the load acts towards the shear center and is negative
if it acts away from the shear center. By default, the program will assume that
the load acts towards the shear center at a distance equal to (Depth of
section/2) from the shear center. The use will be allowed to modify this value
by using the
`ZG` parameter. Specifying a value of ZG = 0 in the
design input would indicate that the load acts exactly at the shear center of
the section so that the term
"zg" in the equation will have a value of zero.