What is the lateral torsional buckling length?
In this article, we’ll abbreviate “Lateral Torsional Buckling” to “LTB”. LTB is an instability effect in which the compressed flange of a beam wants to “buckle” under bending moment. Depending on the sign of the bending moment (My’), it will either be the upper or lower flange. That is why, Diamonds allows you to define lateral buckling supports to both flanges: top (z’>0) and bottom (z’<0).
How much resistance a bar has against LTB, depends on the LTB length. For most standards, this is the length between two LTB supports.
Note: the Netherlands (NEN EN 1993-1-1) deviates from the definition above given for the LTB length. This deviation is implemented in Diamonds.
Lateral torsional buckling supports
Advanced LT parameters
By default, Diamonds assigns default values to certain parameters regarding the LTB verification. You can modify these default values in the tab page “Advanced LT parameters”:
You can edit the parameters to determine the elastic lateral buckling moment Mcr:
- Parameters for Mcr
Diamonds calculates the elastic critical moment Mcr using (NBN EN 1993-1-1 ANB:2010 Annex D):![\[M_{cr} =C_1 \frac{\pi^2 E I_z}{(k_z L)^2} \left[ \sqrt{\left( \frac{k_z}{k_w}\right)^2 \frac{I_w}{I_z}+\frac{(k_z L)^2 G I_t}{\pi^2 E I_z} + \left(C_2 z_g - C_3 z_j \right)^2 } + \left(C_2 z_g - C_3 z_j \right) \right] \]](https://support.buildsoft.eu/wp-content/ql-cache/quicklatex.com-369a8fd856ef8d7bc5d8227db830c836_l3.png "Rendered by QuickLaTeX.com")
Diamonds assumes that the shear center coincides with the center of gravity of the cross-section (= the profile is doubly symmetrical) and that the loads act in the shear center of the cross-section. Which will simplify the formula for Mcr to:![\[M_{cr} =C_1 \frac{\pi^2 E I_z}{(k_z L)^2} \sqrt{\left( \frac{k_z}{k_w}\right)^2 \frac{I_w}{I_z}+\frac{(k_z L)^2 G I_t}{\pi^2 E I_z}}\]](https://support.buildsoft.eu/wp-content/ql-cache/quicklatex.com-0e476baedce2127e8885d23453dcaaba_l3.png "Rendered by QuickLaTeX.com")
In which:
reflects how strongly the compression flange is prevented from moving laterally;
= 0.5 (two restraints), 0.7 (one restraint/partial) and 1.0 (no restraint – default value).
reflects how much the ends of the beam are prevented from warping when the beam is subject to bending and torsion (lateral‐torsional buckling).
= 0.5 (fully prevented warping at both ends) and 1.0 (no warping restraint – default value)- C1 takes the moment distribution into consideration
Diamonds uses the method suggested by Serna, Lopez, Puente and Young to determine C1, since the tables given in for example NBN EN 1993-1-1 ANB:2010 Annex D are only valid for “standard” moment distributions.
However, you’re free to impose a different value for C1 here. - For more complex cross-sections, you can also manually impose Mcr.
- The method for the LTB curve
According to EN 1993-1-1 you can either use the general method (§6.3.2.2) or the equivalent method (§6.3.2.3).- If you uncheck the option “Always use general …”, Diamonds will apply the equivalent method were possible, and the general method when not possible.
- For the equivalent method, it’s possible to impose λLT.0 and β.
Notes:
- If you impose values for C1, Mcr, λLT.0, β,… they will be used for all the combinations of loads (even if, in theory, they may vary).
- Since the standard NEN EN 1993-1-1 describes an other methodology for determining the elastic lateral buckling moment Mcr than the one described above, it is not possible to modify the above parameters when this standard is selected.
