{"id":14840,"date":"2025-03-28T14:14:57","date_gmt":"2025-03-28T14:14:57","guid":{"rendered":"https:\/\/support.buildsoft.eu\/?post_type=ht_kb&p=14840"},"modified":"2026-06-01T15:22:11","modified_gmt":"2026-06-01T15:22:11","slug":"ds-ec-06-buckling-and-lateral-torsional-buckling-method-1-of-an-h-section","status":"publish","type":"ht_kb","link":"https:\/\/support.buildsoft.eu\/nl\/knowledge-base\/ds-ec-06-buckling-and-lateral-torsional-buckling-method-1-of-an-h-section\/","title":{"rendered":"DS EC 06: Buckling y’ and lateral torsional buckling (Method 1) 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. Method 1 from Eurocode (EN 1993-1-1 Annex A) is used.<\/p>\n

Independent reference results<\/h2>\n
<\/span>Open handcalculations for individual buckling and LTB<\/div>
\nTo perform the check “Uniform member in bending and axial compression” 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 factor Cmi.0<\/sub><\/h4>\n

The general formula for combined end moment and transverse loads is used to determine \"C_{my.0}\":<\/p>\n

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

The formula for linearly distributed bending moment is used to determine \"C_{mz.0}\":<\/p>\n

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

Equivalent moment factors Cmi<\/sub><\/h4>\n

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

If \"\overline{\lambda_0}\" < \"\overline{\lambda_{0.lim}}\" or if \"I_t \ge I_y\" the cross-section is “torsion rigid”. Otherwise the cross-section is “torsion weak”. Different formula apply for “torsion rigid” and “torsion weak”. Since the conditions are not met for this cross-section, it is “torsion-weak”.<\/p>\n

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

Plasticity factors Cij<\/sub><\/h4>\n

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

Interaction 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\n\n\n
Results<\/th>\nIndependent reference<\/th>\nDiamonds<\/th>\nDifference<\/th>\n<\/tr>\n
\"C_{my}\"<\/td>\n1.000<\/td>\n1.000<\/td>\n0%<\/td>\n<\/tr>\n
\"C_{mz}\"<\/td>\n0.771<\/td>\n0.771<\/td>\n0%<\/td>\n<\/tr>\n
\"C_{mLT}\"<\/td>\n1.137<\/td>\n1.137<\/td>\n0%<\/td>\n<\/tr>\n
\"C_{yy}\"<\/td>\n0.984<\/td>\n0.984<\/td>\n0%<\/td>\n<\/tr>\n
\"C_{yz}\"<\/td>\n0.852<\/td>\n0.854<\/td>\n0.24%<\/td>\n<\/tr>\n
\"k_{yy}\"<\/td>\n1.164<\/td>\n1.164<\/td>\n0%<\/td>\n<\/tr>\n
\"k_{yz}\"<\/td>\n0.739<\/td>\n0.739<\/td>\n0%<\/td>\n<\/tr>\n
Unity check<\/td>\n87.2%<\/td>\n86.9%<\/td>\n-0,35%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

References<\/h2>\n