--- title: "Lateral-torsional buckling; flange curtailment" subject: "Design of Steel and Timber Structure" chapter: 7 key: "semester_6/design_of_steel_and_timber_structure:ltb-curtailment-plate-girder" source: https://www.bctengineer.com/q/semester_6/design_of_steel_and_timber_structure/ltb-curtailment-plate-girder site: BCT Engineering --- # Lateral-torsional buckling; flange curtailment Design of Steel and Timber Structure · Chapter 7: Flexure Members - Asked in: 2079 Chaitra, 2+3 marks - Video: [Design of Plate Girder - Part 2 - Lateral Torsional Buckling](https://www.youtube.com/watch?v=kqdrnEDsTmU) — Ashraf Sabbagh - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/design_of_steel_and_timber_structure/ltb-curtailment-plate-girder - Whole chapter: https://www.bctengineer.com/md/semester_6/design_of_steel_and_timber_structure/chapter-7 ## Question What do you understand by lateral-torsional buckling and curtailment of flanges in plate girder? ## Short answer Lateral-torsional buckling is combined lateral bending and twisting of a beam's compression flange, reducing bending strength. Curtailment of flanges in a plate girder is the reduction of flange size where bending moment is lower, saving steel, with plates extended beyond theoretical cut-off points. ## Answer #### Lateral-torsional buckling When a beam bends about its major axis, the compression flange behaves like a column, but it is restrained by the tension flange and the web. If the compression flange is not held laterally, at a certain load the beam suddenly deflects sideways and twists at the same time. This failure by combined lateral bending and twisting is **lateral-torsional buckling (LTB)**. It reduces the bending strength below the plastic moment of the section. - The strength is governed by the elastic critical moment $M_{cr}$, which depends on the unbraced length $L_{LT}$, $EI_y$, the torsional rigidity $GI_t$ and the warping rigidity $EI_w$ (IS 800:2007 cl. 8.2.2, Annex E). - Slenderness $\lambda_{LT} = \sqrt{\beta_bZ_pf_y/M_{cr}}$; then $f_{bd} = \chi_{LT}f_y/\gamma_{m0}$ and $M_d = \beta_bZ_pf_{bd}$. - It is avoided or reduced by closer lateral bracing, a slab connected to the compression flange, wider flanges (larger $I_y$), or closed sections (box sections, which have a high $I_t$). - Short, stocky or fully restrained beams ($\lambda_{LT} \le 0.4$) are not affected. #### Curtailment of flanges in a plate girder The bending moment in a simply supported girder is largest at mid-span and zero at the supports. A flange sized for the maximum moment is more than is needed near the ends, so the flange thickness or width is **curtailed** (reduced, or extra cover plates are stopped short) where the bending moment is smaller. This saves steel. ```text actual theoretical theoretical actual end cut-off cut-off end |<-ext.->| |<-ext.->| +================================================+ <- curtailed outer plate +--------------------------------------------------------+ <- full-length flange plate | web | ^ ^ support support ``` - The theoretical cut-off point is where the moment of resistance of the reduced section, $M_{d,red}$, equals the applied moment. For a UDL $w$ on span $L$: $w\,x(L-x)/2 = M_{d,red}$, giving $x = \dfrac{L}{2} - \sqrt{\dfrac{L^2}{4} - \dfrac{2M_{d,red}}{w}}$ from the support. - The cut plate must be **extended beyond** the theoretical point (by enough length, with enough bolts or welds, to develop the force in the plate) so that it can take its share of the force, and its end is welded all round to avoid fatigue cracks. The welds or bolts between the flange and the plate over the extension must carry the plate force. - Curtailment is done in stages to keep the changes in section small, and the web-to-flange connection is checked at each change because the shear flow changes with the section. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is lateral-torsional buckling? A. Sudden sideways deflection with twist of a beam whose compression flange is not laterally held B. Local buckling of the web under a point load C. Yielding of the tension flange D. Shear buckling of the web panel Answer: A. An unrestrained compression flange behaves like a column and moves sideways while the section twists, lowering bending strength below the plastic moment. (Key point: Meaning of LTB) 2. Which measure reduces or avoids LTB? A. Closer lateral bracing or a slab connected to the compression flange B. Using a thinner web C. Using a longer unbraced length D. Reducing the flange width Answer: A. Bracing shortens L_LT; wider flanges raise I_y and box sections have high I_t, all increasing M_cr. (Key point: Ways to prevent LTB) 3. Why are flange plates curtailed in a plate girder? A. Bending moment falls towards the supports, so less flange is needed there and steel is saved B. Shear is largest at mid-span C. To raise the moment capacity at the supports D. To reduce the web thickness Answer: A. A flange sized for the maximum mid-span moment is excessive near the ends; reducing it where moment is smaller saves steel, but the cut plate must extend beyond the theoretical cut-off. (Key point: Curtailment of flanges) ## Related in Design of Steel and Timber Structure - [Size of web and flange plate in plate girder](https://www.bctengineer.com/question.md?key=semester_6%2Fdesign_of_steel_and_timber_structure%3Aplate-girder-web-flange-size) — Design of Steel and Timber Structure, chapter 7, asked 2× - [Plate girder elements; web and flange splices](https://www.bctengineer.com/question.md?key=semester_6%2Fdesign_of_steel_and_timber_structure%3Aplate-girder-elements-splices) — Design of Steel and Timber Structure, chapter 7 - [Components of welded plate girder and selection](https://www.bctengineer.com/question.md?key=semester_6%2Fdesign_of_steel_and_timber_structure%3Aplate-girder-components-selection) — Design of Steel and Timber Structure, chapter 7 - [What is plate girder? Preliminary design](https://www.bctengineer.com/question.md?key=semester_6%2Fdesign_of_steel_and_timber_structure%3Aplate-girder-preliminary-design) — Design of Steel and Timber Structure, chapter 7 - [Stiffeners in plate girder: types and function](https://www.bctengineer.com/question.md?key=semester_6%2Fdesign_of_steel_and_timber_structure%3Aplate-girder-stiffeners) — Design of Steel and Timber Structure, chapter 7 - [Bracket plate on column flange, 5 M20 bolts](https://www.bctengineer.com/question.md?key=semester_6%2Fdesign_of_steel_and_timber_structure%3Abracket-bolted-5-m20) — Design of Steel and Timber Structure, chapter 4 ## Related in other subjects - [Round bar fixed-free: buckling load from lateral deflection](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Around-bar-fixed-free-buckling-3m) — Strength of Materials, chapter 8, asked 2× - [Curtailment of tension steel in beams](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Acurtailment-of-tension-steel-in-beams) — Design of RCC Structure, chapter 7, asked 2× - [Symmetrical I-beam: moment, flange and web share](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Asymmetrical-i-beam-max-moment-flange) — Strength of Materials, chapter 7 - [Principal stresses at web-flange junction](https://www.bctengineer.com/question.md?key=semester_4%2Fstrength_of_materials_mechanical%3Aprincipal-stresses-web-flange-junction) — Strength of Materials, chapter 9