D5.C.5.2 Members Subject to Bending Moments

The cross section capacity of a member subject to bending is checked as per Cl .6.2.5 of the code. The condition to be satisfied is:

\frac{M_{E d}}{M_{c, R d}} \leq 1.0

Where M_c,Rd is the is the design resistance given by:

$M_{c, R d} = M_{p l, R d} = \frac{W_{p l} f_{y}}{γ_{M 0}}$ for class 1 and 2 cross-sections
$M_{c, R d} = M_{e l, R d} = \frac{W_{e l, \min} f_{y}}{γ_{M 0}}$ for class 3 cross-sections
$M_{c, R d} = \frac{W_{e f f, \min} f_{y}}{γ_{M 0}}$ for class 4 cross-sections

Cross sectional bending capacity checks will be done for both major and minor axis bending moments.

Members subject to major axis bending will also be checked for Lateral Torsional Buckling resistance as per Section 6.3.2 of the code. The design buckling resistance moment M_b,Rd will be calculated as:

M_{b, R d} = χ_{L T} W_{y} \frac{f_{y}}{γ_{M 1}}

Where:

χ_LT is the reduction factor for lateral torsional buckling. This reduction factor is evaluated per Cl. 6.3.2.2 or Cl 6.3.2.3 of the EN 1993 code depending on the section type. For I sections, the program will by default use Cl. 6.3.2.3 to evalute χ_LT and for all other sections the program will resort to Cl 6.3.2.2. However, if a particular National Annex has been specified, the program will check if the National Annex expands on Cl.6.3.2.3 (Table 6.5) to include sections other than I sections. If so, the program will use Cl. 6.3.2.3 for the cross-section(s) included in Cl. 6.2.2.3 (or Table 6.5). For all other cases the program will use Cl. 6.3.2.2.

Note: You have the option to choose the clause to be used to calculate χ_LT through the MTH design parameter. Setting MTH to 0 (default value) will cause the program to choose Cl.6.3.2.3 for I Sections and Cl 6.2.3.2 for all other section types. As mentioned above, if the National Annex expands on Cl. 6.3.2.3 to include sections other than I Sections, the program will use Cl. 6.3.2.3 by default.

When using Cl. 6.3.2.3 to calculate χ_LT, the program will consider the correction factor kc (Table 6.6 of EN 1993-1-1:2006) based on the value of the KC parameter in the design input. By default the value of KC will be taken as 1.0. If you want the program to calculate kc, you must explicitly set the value of the KC parameter to zero.

Note: If the National Annex specifies a different method to calculate kc (e.g. the British, Singapore & Polish NAs), the program will use that method by default even if the KC parameter has not been explicitly set to zero. If the NA method does not deal with a specific condition while working out kc, the program will then fall back to table 6.6 of the code, thus ensuring that kc is considered for the particular NA.

The non-dimensional slenderness λ _LT (used to evaluate χ_LT) for both the above cases is evaluated as:

{\bar{λ}}_{L T} = \sqrt{\frac{W_{y} f_{y}}{M_{c r}}}

Where:

M_cr is the elastic critical moment for lateral torsional buckling. EN 1993-1-1 does not however specify a method to evaluate M_cr. Hence, the program will make use of the method specified in Annex F of DD ENV 1993-1-1 to evaluate M_cr by default.

Note: The method specified in Annex F will be used only when the raw EN 1993-1-1:2005 code is used without any National Annex. If a National Annex has been specified, the calculation of M_cr (and λ _LT) will be done based on the specific National Annex. (Refer to D5.D. European Codes - National Annexes to Eurocode 3 [EN 1993-1-1:2005] for specific details). If the National Annex does not specify a particular method or specify a reference document, the program will use the NCCI document SN-003a-EN-EU for doubly symmetric sections and SN030a-EN-EU for mono-symmetric sections that are symmetric about their weak axis. For all other sections types the program will use Annex F of DD ENV 1993-1-1 to calculate M_cr. In cases where Annex F does not provide an adequate method to evaluate Mcr, such as for Channel sections, the program will resort to the method as per Cl.4.3.6 of BS 5950-1:2000 to calculate the lateral torsional buckling resistance moment (Mb,Rd) for the member.