{"id":15371,"date":"2025-07-04T07:48:44","date_gmt":"2025-07-04T07:48:44","guid":{"rendered":"https:\/\/support.buildsoft.eu\/?post_type=ht_kb&p=15371"},"modified":"2025-07-04T12:12:01","modified_gmt":"2025-07-04T12:12:01","slug":"ds-ec-07-buckling-y-and-lateral-torsional-buckling-method-2-of-an-i-section","status":"publish","type":"ht_kb","link":"https:\/\/support.buildsoft.eu\/fr\/knowledge-base\/ds-ec-07-buckling-y-and-lateral-torsional-buckling-method-2-of-an-i-section\/","title":{"rendered":"DS EC 07: Buckling y’ and lateral torsional buckling (Method 2) of an I-section"},"content":{"rendered":"

Description<\/h2>\n

\"\"<\/p>\n

\n\n\n\n\n\n\n\n
Geometry<\/th>\nCross-section:<\/td>\nIPE 500<\/td>\n<\/tr>\n
Material:<\/td>\nS235<\/td>\n<\/tr>\n
Load<\/th>\nULS FC:<\/td>\n\"M_y=200 \text{kNm}\"
\n\"M_z=12.5 \text{kNm}\"
\n\"N=500 \text{kN}\"<\/td>\n<\/tr>\n
Standard<\/th>\n<\/td>\nEN 1993-1-1 [- -]<\/td>\n<\/tr>\n
Design parameters<\/th>\n<\/td>\nSection class 1 for pure bending
\nLy<\/sub>=Lz<\/sub>=3.75m
\nLLT<\/sub>=3.75m<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

This article verifies the interaction of buckling and lateral torsional buckling due to axial force and bending around the strong axis. Methode 2 in Eurocode (EN 1993-1-1 Annex B) is used.<\/p>\n

Independent reference results<\/h2>\n
<\/span>Open handcalculations for individual buckling and LTB<\/div>
\nTo perform the check \u00ab\u00a0Uniform member in bending and axial compression\u00a0\u00bb according to EN 1993-1-1 \u00a76.3.3, we need a few factors related to buckling resistance. We’ll determine those here without much context. The context is already can be found here.<\/p>\n

Buckling around the strong axis y’<\/h4>\n

(6.50) <\/span>   <\/span>\"\begin{align*}<\/p>\n

Because the relative slenderness \"\overline{\lambda_y}\" is smaller than 0.2, \"\chi_{y}\" equals 1.<\/p>\n

Buckling around the weak axis z’<\/h4>\n

(6.50) <\/span>   <\/span>\"\begin{align*}<\/p>\n

Torsional buckling (buckling around the x’ axis)<\/h4>\n

  <\/span>   <\/span>\"\begin{align*}<\/p>\n

Lateral torsional buckling<\/h4>\n

We only included the intermediar results. If you want to learn more about the resistance again laterial torsional buckling, follow this example.<\/p>\n

  <\/span>   <\/span>\"\begin{align*}<\/p>\n<\/div><\/div><\/div>\n

<\/span>Open handcalculations for interaction<\/div>
\n

Moment factors Cmi<\/sub><\/h4>\n

For the bending moment \"M_{y'}\" (EN 1993-1-1 Table B.3):<\/p>\n

  <\/span>   <\/span>\"\begin{align*}<\/p>\n

For the bending moment \"M_{z'}\" (EN 1993-1-1 Table B.3):<\/p>\n

  <\/span>   <\/span>\"\begin{align*}<\/p>\n

Elastic critical moment Mcr.0<\/sub><\/h4>\n

  <\/span>   <\/span>\"\begin{align*}<\/p>\n

If \"\overline{\lambda_0}\" < \"\overline{\lambda_{0.lim}}\" the cross-section is \u00ab\u00a0torsion rigid\u00a0\u00bb. Otherwise the cross-section is \u00ab\u00a0torsion weak\u00a0\u00bb. Different formula apply for \u00ab\u00a0torsion rigid\u00a0\u00bb and \u00ab\u00a0torsion weak\u00a0\u00bb. Since the conditions are not met for this cross-section, it is \u00ab\u00a0torsion-weak\u00a0\u00bb.<\/p>\n

Interation factors kij<\/sub><\/h4>\n

  <\/span>   <\/span>\"\begin{align*}<\/p>\n

Unity check<\/h4>\n

  <\/span>   <\/span>\"\begin{align*}<\/p>\n

<\/div><\/div><\/div><\/h4>\n

Diamonds results and comparison<\/h2>\n

\"\"<\/p>\n

Intermediate results for lateral torsional buckling calculated by Diamonds (EN 1993-1-1 Method 1)<\/strong><\/p>\n

\n\n\n\n\n\n\n\n\n
Results<\/th>\nIndependent reference<\/th>\nDiamonds<\/th>\nDifference<\/th>\n<\/tr>\n
\"C_{my}\"<\/td>\n0.925<\/td>\n0.925<\/td>\n0%<\/td>\n<\/tr>\n
\"C_{mz}\"<\/td>\n0.6<\/td>\n0.6<\/td>\n0%<\/td>\n<\/tr>\n
\"k_{yy}\"<\/td>\n0.924<\/td>\n0.924<\/td>\n0%<\/td>\n<\/tr>\n
\"k_{yz}\"<\/td>\n0.489<\/td>\n0.489<\/td>\n0%<\/td>\n<\/tr>\n
Unity check<\/td>\n71.5%<\/td>\n71.3%<\/td>\n-0.28%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

References<\/h2>\n