Technical ArticleMoment factor C1 for Lateral-Torsional Buckling Peter Van Tendeloo Abstract Within this article the determination of the moment factor C1 for lateral-torsional buckling according to EN 1993-1-1 is described using three distinct methods. For each method a brief description is given and all methods are applied to the same example in order to compare the results. Introduction The lateral-torsional buckling resistance as described in EN 1993-1-1 article 6.3.2 Ref.[1] is based on the so-called elastic critical moment for lateral-torsional buckling Mcr. The EN 1993-1-1 code however does not give any expression for calculating this variable but indicates to the user that the determination of this value should be based on the following principles: - Using gross cross-sectional properties - Taking into account the loading conditions - Taking into account the real moment distribution - Taking into account the lateral restraints Using the general buckling theory an expression for Mcr can be derived in the following format in case of a doubly-symmetric section Ref.[2,3]: Within this expression, the coefficient C1 takes into account the moment distribution while C2 takes into account the loading type and boundary conditions. Method 2: ECCS 119/Galea The second method concerns ECCS 119 Annex B Ref.[3]. In the same way as the previous method, this reference gives the values of the moment factor C1 for specific shapes of the moment diagram. However, in addition, this reference also gives extensive coefficients in case of combined loading. Based on the values of the loading and end moments the moment factor C1 can be derived from figures: Within this article, the determination of the coefficient C1 is examined using three different methods available in Scia Engineer: - ENV 1993-1-1 Annex F - ECCS 119/Galea - Lopez, Yong, Serna Each method is illustrated on the same example; a beam on two supports loaded by end moments and a point load in the middle. The moment diagram for this beam has the following shape: Method 1: ENV 1993-1-1 Annex F The first method concerns the Annex F of ENV 1993-1-1 Ref.[4] This reference gives the values of the moment factor C1 for specific shapes of the moment diagram (uniform moment, point load or line load). The main disadvantage of this method is that only limited coefficients are given in case of combined loading, like the combined point load and end moments in the above example. Within Scia Engineer, the moment factors given in Annex F have been extended according to the rules given in Ref.[5] in order to account for combined loading. For the above example, this method results in a moment factor C1 of 1,89. This is quite a significant value which indicates that the elastic critical moment is 89% higher than the Mcr for a uniform moment diagram. It is however questionable if this high value can be justified. The figures given in this reference have been determined by numerical analysis. A thorough background of these figures including tabulated values can be found in Ref.[6]. For the above example, this method results in a moment factor C1 of 1,26. In comparison with the previous method it can be seen that this value is much lower i.e. 26% compared to 89%. Since the ECCS 119 method was specifically derived for the case of combined loading it can thus be concluded that the old ENV 1993-1-1 Annex F is on the unsafe side. [6] Déversement élastique d’une poutre à section bi-symétrique soumise à des moments d’extrémité et une charge répartie ou concentrée.Fax: +1 410-290-8050 . [8] Steel Code Check – Theoretical Background. EN 1993-1-1:2005. The values of the actual moment diagram are taken on different sections of the beam and inserted in the closed form expression. Yong. A.B-3540 Herk-de-Stad (Belgium) .) . 1994. NCCI: Elastic critical moment for lateral torsional buckling. Part 1 . The final method according to Lopez.nemetschek-scia.: +1 410-290-5114 . Yong. ECCS . MD (USA) [email protected]/ A1 : General rules and rules for buildings.20.A. [7] Lateral-Torsional buckling of steel beams: A general expression for the moment gradient factor. J.: +971 4 5015744 ..7150 Riverwood Drive .com Nemetschek Scia North America .N° 119. This can be freely modified by the user for any project. M. Stability and Ductility of Steel Structures.Industrieweg 1007 . Galéa.Dubai Silicon Oasis HQ Building . 2006. The method according to ECCS 119 contains specific figures for combined loading and thus leads to a much more accurate value of the moment factor C1. this method results in a moment factor C1 of 1.[8]. n° 2-2002. In contrast to the previous methods. 2006. Within Scia Engineer by default the method according to ECCS 119 is applied.: +32 13 55 17 75 . [5] Staalconstructies TGB 1990. The older method according to ENV 1993-1-1 Annex F produces a quite high value for the moment factor C1 due to the fact that this method gives only limited information in case of combined loading. A. Design of steel structures. please visit our website www. The main advantage is thus that this method can be applied to any moment diagram without the need to identify the shape of the diagram.Fax: +32 13 55 41 75 . Construction Métallique. Y. Yong. Box 341041. [3] Rules for Member Stability in EN 1993-1-1..[7].uae@nemetschek-scia. CTICM.E. When comparing the different methods it seems the ENV 1993-1-1 Annex F method overestimates the moment factor. It is clear that this method is in close approximation to the ECCS 119 method. D.com Nemetschek Scia ME . Serna. For the above example.com . 2012. Serna The final method is described in Lopez.O.Tel.Columbia. Access Steel.Fax: +971 4 5015777 . For more information reference is made to the Steel Code Check Theoretical Background Ref. Design of steel structures.usa@nemetschek-scia. Nemetschek Scia.P.Tel. 2006.Tel. Yong.com For a complete list of all our international agencies and partners. ENV 1993-1-1:1992/A1. this reference gives a closed form expression for the moment factor C1. References 1 Eurocode 3. Each method has been applied on a beam on two supports loaded by end moments and a point load in the middle.Method 3: Lopez. Background documentation and design guidelines. [4] Eurocode 3. Conclusion Within this article the determination of the moment factor C1 for lateral-torsional buckling according to EN 1993-1-1 has been described using three distinct methods. López.1991. Stabiliteit. Serna provides a closed form expression which is independent on the type of moment diagram and gives results which are in close approximation to the ECCS 119 method. [2] SN003a-EN-EU. Serna Ref. Part 1 . NEN 6771 . Nemetschek Scia nv . Dubai (U.1 : General rules and rules for buildings.