D.5.B.14.5 Lateral-Torsional Buckling Curves

In case of Cl: 6.3.2.2 of EC3, the Dutch National Annex tells to refer to appendix NB.NB to determine the critical elastic buckling moment M_cr.

The general formula for the critical elastic moment is

M_{cr} = k_{red} \times \frac{C}{L_{g}} \sqrt{E \times I_{z} \times G \times I_{t}}

For the special case of a beam supported at either end subject to constant bending moment is, the critical elastic moment can be calculated as:

M_{cr} = k_{red} \times \frac{π}{L_{g}} \sqrt{E \times I_{z} \times G \times I_{t} (1 + \frac{π^{2} E \times I_{w}}{{L_{g}}^{2} \times G \times I_{t}})}

where

k_{red}

1 when h / t_w ≤ 75

if h / t_w > 75 and ɑ ≤ 5,000:

= {}_{min}{| \begin{array}{l} -5.4 \times 10^{-5} α + 1.03 \\ 1 \end{array}}

α

\frac{h \times t_{f} \times 10^{12}}{{t_{w}}^{3} \times b \times {L_{g}}^{2}} > 575

C

coefficient that depends on the nature of the load, application location of the load, and the cross-section dimensions of the beam:

\frac{π C_{1} L_{g}}{L_{kip}} {\sqrt{1 + [\frac{π^{2} S^{2}}{{L_{kip}}^{2}} ({C_{2}}^{2} + 1)]} + \frac{π C_{2} S}{L_{kip}}}

(NB.NB.11)

L_{kip}

the unsupported tipping length between to clevises, between on clevis and one clevis support, or between two tipping supports. This value can be directly entered using the LKP parameter. Otherwise, the member length is used. Refer to NB.NB.4.3 for details on the evaluation of

L_{kip}

S

\sqrt{\frac{E I_{w}}{G I_{t}}}

For an I-section, this may be taken as:

\frac{h}{2} \sqrt{\frac{E I_{z}}{G I_{t}}}

For the Dutch NA 2016, you must specify values for C₁ and C₂ using the C1 and C2 parameters in the design input mode. Otherwise, the default loading condition of a simply supported beam with uniform load is assumed (i.e., C1 = 1.13 and C2 = 0.45). Refer to D5.A.6 Design Parameters