{"id":13859,"date":"2024-11-18T11:14:18","date_gmt":"2024-11-18T11:14:18","guid":{"rendered":"https:\/\/support.buildsoft.eu\/?post_type=ht_kb&p=13859"},"modified":"2025-03-21T14:51:39","modified_gmt":"2025-03-21T14:51:39","slug":"ds-ec-05-lateral-torsional-buckling-of-an-h-section","status":"publish","type":"ht_kb","link":"https:\/\/support.buildsoft.eu\/fr\/knowledge-base\/ds-ec-05-lateral-torsional-buckling-of-an-h-section\/","title":{"rendered":"DS EC 05: Lateral torsional buckling of an H-section"},"content":{"rendered":"

Description<\/h2>\n

\"\"<\/p>\n

\n\n\n\n\n\n\n\n
Geometry<\/th>\nCross-section:<\/td>\nHEA 280<\/td>\n<\/tr>\n
Material:<\/td>\nS355<\/td>\n<\/tr>\n
Load<\/th>\nULS FC:<\/td>\n300kNm<\/td>\n<\/tr>\n
Standard<\/th>\n<\/td>\nEN 1993-1-1 [- -]<\/td>\n<\/tr>\n
Design parameters<\/th>\n<\/td>\nSection class 3
\nLLT<\/sub>=4m<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

Independent reference results<\/h2>\n
<\/span>Open handcalculations<\/div>
\n

Moment factor C1<\/sub><\/h4>\n

Values for the moment factor C1<\/sub> is given in for example the Belgian annex NBN EN 1993-1-1 ANB:2010 Annex D. These are tables, valid for certain \u00ab\u00a0standard\u00a0\u00bb moment distributions. But the loads on a 3D building aren’t always \u00ab\u00a0standard\u00a0\u00bb. Nor will be the moment distribution calculated by Diamonds. Which makes it difficult to unambiguously find a value for C1<\/sub> based on those tables.
\nTherefor the method suggested by Serna, Lopez, Puente and Young<\/em><\/a> is implemented in Diamonds.
\nFor deviating projects, the user can impose C1<\/sub> via \"\".<\/p>\n

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

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

The formula for the elastic critical moment Mcr<\/sub> is for example given in the Belgian annex NBN EN 1993-1-1 ANB:2010 Annex D.<\/p>\n

  <\/span>   <\/span>\"\[M_{cr} =C_1 \frac{\pi^2 E I_z}{(k_z L)^2} \left[ \sqrt{\left( \frac{k_z}{k_w}\right)^2 \frac{I_w}{I_z}+\frac{(k_z L)^2 G I_t}{\pi^2 E I_z} + \left(C_2 z_g - C_3 z_j \right)^2 } + \left(C_2 z_g - C_3 z_j \right) \right] \]\"<\/p>\n

Diamonds assumes that the shear center coincides with the center of gravity of the cross-section (= the profile is doubly symmetrical) and that the loads act in the shear center of the cross-section. Which will simplify the formula for Mcr<\/sub> to:<\/p>\n

  <\/span>   <\/span>\"\[M_{cr} =C_1 \frac{\pi^2 E I_z}{(k_z L)^2} \sqrt{\left( \frac{k_z}{k_w}\right)^2 \frac{I_w}{I_z}+\frac{(k_z L)^2 G I_t}{\pi^2 E I_z}}\]\"<\/p>\n

For deviating projects, the user can impose Mcr<\/sub> via \"\".<\/p>\n

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

Resistance against lateral torsional buckling Mb.Rd<\/sub><\/h4>\n

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

Unity check UC<\/h4>\n

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

Diamonds results and comparison<\/h2>\n

\"\"<\/p>\n

Stability verification of the beam according to EN 1993-1-1<\/strong><\/p>\n

\"\"<\/p>\n

Intermediate results in Diamonds for lateral torsional buckling<\/strong><\/p>\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_1\"<\/td>\n1.136<\/td>\n1.136<\/td>\n0,00%<\/td>\n<\/tr>\n
\"M_{cr}\"<\/td>\n1099.6kNm<\/td>\n1099.6kNm<\/td>\n0,00%<\/td>\n<\/tr>\n
\"\bar{\lambda_{LT}}\"<\/td>\n0.572<\/td>\n0.572<\/td>\n0,00%<\/td>\n<\/tr>\n
\"\varPhi_{LT}\"<\/td>\n0.702<\/td>\n0.702<\/td>\n0,00%<\/td>\n<\/tr>\n
\"\chi_{LT}\"<\/td>\n0.900<\/td>\n0.900<\/td>\n0,00%<\/td>\n<\/tr>\n
\"M_{b.Rd}\"<\/td>\n323.7kNm<\/td>\n323.8kNm<\/td>\n0,00%<\/td>\n<\/tr>\n
Unity check \"\frac{M_y}{M_{b.Rd}}\"<\/td>\n92.7%<\/td>\n92.7%<\/td>\n0,00%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

References<\/h2>\n