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:
ψ | C_{1} |
---|---|
+1,00 | 1,00 |
+0,75 | 1,14 |
+0,50 | 1,31 |
+0,25 | 1,52 |
0,00 | 1,77 |
-0,25 | 2,05 |
-0,50 | 2,33 |
-0,75 | 2,57 |
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 = k_{w} = 1.0). STAAD.Pro takes into account of the end conditions using the CMN parameter for EC3. A value of K = k_{w} =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). For members with partial or end fixities (i.e., CMN = 0.5 or CMN = 0.7), this implementation will fall back on to the method and coefficients in DD ENV 1993-1-1:1992 – Annex F.
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.
For the term z_{j}, please refer to Annex E of NBN NA 2018.
The term z_{g} in the equation to calculate M_{cr} 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 z_{g} 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 z_{g} in the equation will have a value of zero.