Design methods for torsional buckling of steel structures
- 1. DESIGN METHODS FOR TORSIONAL BUCKLING OF STEEL STRUCTURES COMPARISON BETWEEN: PRESENTED BY- BEGUM EMTE AJOM
- 2. What is lateral torsional buckling? When a slender beam- column is subjected to axial load and bending about the major axis z-z and not restrained out of plane bending, the beam- column fails due to combination of column buckling about the y-y axis and lateral torsional buckling as shown in the figure. video Fig. – (a) Buckling (b) Torsional buckling of a beam column (Rf. DSS by Subramanium)
- 3. • Clause 8.2.2 Laterally Unsupported Beams Resistance to lateral torsional buckling need not be checked separately (member may be treated as laterally supported) in the following cases: a) Bending is about the minor axis of the section, b) Section is hollow (rectangular/ tubular) or solid bars, and c) λLT is less than 0.4. • Clause 6.3.2.1 (1) Buckling resistance A laterally unrestrained member subjected to major axis bending should be verified against lateral torsional buckling as follows: (MEd/Mb,Rd ) ≤ 1 where MEd is the design value of moment Mb,Rd is the design buckling resistance moment
- 4. • Clause 8.2.2 Laterally Unsupported Beams The design bending strength of laterally unsupported beam as governed by lateral torsional buckling is given by: Md = βbZpfbd where, o fbd= design bending compressive stress fbd = χLT fy/ ϒm0 • Clause 6.3.2.1 (3) Buckling resistance The design buckling resistance moment of a laterally unrestrained beam should be taken as: Mb,Rd = χLT Wy fy/ ϒM1 where,
- 5. o Zp, Ze = plastic section modulus and elastic section modulus with respect to extreme compression fibre o βb = 1.0 for plastic and compact sections = Ze/Zp for semi-compact sections o ϒm0 = Partial safety factor against yield stress and buckling (Table 5) where, o Wy is the appropriate section modulus as follows: - Wy = Wpl,y for Class 1 or 2 cross-sections - Wy = Wel,y for Class 3 cross-sections o YM1 particular partial safety factor (NA.2.15)
- 6. o χLT = bending stress reduction factor to account for lateral torisonal buckling , given by: o χLT is the reduction factor for lateral-torsional buckling • Clause 6.3.2.2 Lateral torsional buckling curves -General case (1) Unless otherwise specified, given in 6.3.2.3, for bending members of constant cross- section, the value of χLT for the appropriate non-dimensional slenderness should be determined from:
- 7. where o αLT ,the imperfection parameter is given by: αLT = 0.21 for rolled steel section αLT = 0.49 for welded Steel section where o αLT ,the imperfection factor for lateral torsional buckling curves (Table 6.3) The recommendations for buckling curves are given in Table 6.4 of the code.
- 8. o The non-dimensional slenderness ratio, λLT , is given by: where Mcr = elastic critical moment fcr,b = extreme fibre bending compressive stress o The non-dimensional slenderness, ,is given by: where Mcr = elastic critical moment for lateral-torsional buckling
- 9. • Clause 8.2.2.1 Elastic lateral torsional buckling moment In case of simply supported, prismatic members with symmetric cross-section, the elastic lateral buckling moment, Mcr , can be determined from: Commentary on Mcr , Determination of the non- dimensional lateral torsional buckling slenderness, first requires calculation of the elastic critical moment for lateral torsional buckling, Mcr . EN 3 offers no formulations and gives no guidance on how Mcr should be calculated, except to say that Mcr should be based on gross cross- sectional properties and should take into account the loading conditions, the real moment distribution and the lateral restraints (clause 6.3.2.2(2)) Guidance for calculating Mcr is given, however, in NCCI SN003 (SCI, 2005b)
- 10. • fcr of non-slender rolled steel sections in the above equation may be approximately calculated from the values given in Table 14, which has been prepared using the following equation: o Values of the reduction factor χLT for the appropriate non- dimensional slenderness may be obtained from Figure 6.4 (clause 6.3.2.2(3)).
- 11. • The following simplified equation may be used in the case of prismatic members made of standard rolled I- sections and welded doubly symmetric I-sections, for calculating the elastic lateral buckling moment, Mcr • Clause 6.3.2.3 Lateral torsional buckling curves for rolled sections or equivalent welded sections (1) For rolled or equivalent welded sections in bending the values of χLT for the appropriate non-dimensional slenderness may be determined from: NOTE: The parameters and β and any limitation of validity concerning the beam depth or hlb ratio may be given in the National Annex. The recommendations for buckling curves are given in Table 6.5
- 12. where, o Iw = warping constant o Iy, ry = moment of inertia and radius of gyration, respectively about the weaker axis o LLt = effective length for lateral torsional buckling (table 15) o hf = centre-to-centre distance between flanges; and o tf = thickness of the flange. o Mcr , for different beam sections, considering loading, support condition, and non-symmetric section, shall be more accurately calculated using the method given in Annex E of the code. NCCI: Elastic critical moment for lateral torsional buckling. • The method given hereafter only applies to uniform straight members for which the cross- section is symmetric about the bending plane. Where, o E is the Young modulus o G is the shear modulus o Iz is the second moment of area about the weak axis
- 13. • The elastic critical moment corresponding to Iateral torsional buckling of a doubly symmetric prismatic beam subjected to uniform moment in the unsupported length and torsionally restraining lateral supports is given by: This equation in simplified form for I-section has been presented in 8.2.2.1 o It is the torsion constant o Iw is the warping constant o L is the beam length between points which have lateral restraint o k and kw are effective length factors o zg is the distance between the point of load application and the shear centre. o C1 and C2 are coefficients depending on the loading and end restraint conditions (Table 3.2, NCCI)
- 14. • In case of a beam which is symmetrical only about the minor axis, and bending about major axis, the elastic critical moment for lateral torsional buckling is given by the general equation:
- 15. where, o G = modulus of rigidity o It = tortional constant = ∑ biti 3/3 o c1,c2,c3 = factors depending upon the loading and end restraint conditions (Table 42). o K = effective length factors of the unsupported length o Kw = warping restraint factor o yg = y distance between the point of application of the load and the shear centre of the cross-section o o ys = co-ordinate of the shear centre with respect to centroid o y, z = co-ordinates of the elemental area with respect to centroid of the section
- 16. References - IS 800 : 2007 EN 1993-1-1 : 2005 DESIGNERS’ GUIDE TO EUROCODE 3 UK NATIONAL ANNEX TO EURO CODE 3 NON- CONTRADICTORY COMPLEMENTARY INFORMATION (NCCI) SN003 (SCI, 2005b) DESIGN OF STEEL STRUCTURES BY N. SUBRAMANIUM