LATERAL-TORSIONAL BUCKLING OF STEEL BEAMS - apcmr

LATERAL-TORSIONAL BUCKLING OF STEEL BEAMSD. Mateescu 1 , V. Ungureanu 1ABSTRACTThe slender members loaded by transversal loads or ended moments acting around themajor axis of inertia, may collapse by lateral-torsional buckling before reaching the fullplastic resistant moment, M pl . The present paper presents a comparison between Mateescuproposal [1], Eurocode 3-Part 1.1 [2] and the ECBL approach [3], used to calculate theultimate lateral-torsional buckling moment. The experimental database from Eurocode 3 –Background Documentation, Chapter 5 October 1989 [4] was used to evaluate the theoreticalresults.Key Words: Lateral-torsional buckling, buckling curves, imperfections, generalizedimperfection factor, experimental results1. INTRODUCTIONIn the final version of Eurocode 3-Part 1.1 [2] there exist two different sets of LTbucklingcurves:- in paragraph 6.3.2.2: Lateral-torsional buckling curves - General case, the columnbuckling curves a, b, c, d are specified for cross-section groups h/b , 2 and h/b>2of rolled and welded sections, with a plateau of LT 0. 2 ;- in paragraphs 6.3.2.3: Lateral-torsional buckling curves for rolled sections orequivalent welded sections, specific LT-buckling curves b, c, d are given for thegroups h/b,2 and h/b>2 of rolled and welded sections, and in contrary toparagraph 6.3.2.2 with a plateau of LT 0. 4 . The LT-buckling curves given in6.3.2.3 are based on numerical simulations of single span beams under uniformmoment with idealized end-fork conditions [5,6].Mateescu has proposed a similar method with the second one of Eurocode 3-Part 1.1,more than ten years before [1]. Consequently, a comparison of Mateescu proposal with thetwo sets of LT-buckling curves from Eurocode 3-Part 1.1 is presented in this paper. Inaddition, for comparison the LT-buckling curves obtained with the Erosion of CriticalBifurcation Load (ECBL) approach, developed by Dubina is shown.1 Romanian Academy, Timisoara Branch, Laboratory of Steel Structures, M. Viteazul 24, Timisoara, Romania

2. LATERAL-TORSIONAL BUCKLING OF BEAMS IN BENDING ACCORDINGTO EUROCODE 3-PART 1.1According to EUROCODE 3-Part. 1.1 [2], a laterally unrestrained beam subject tomajor axis bending shall be verified against lateral-torsional with the formula:M Ed 1(1)M b,Rdwhere:M Ed is the design value of the moment;M b,Rd is the design buckling resistance moment.as:whereThe design buckling resistance moment of a laterally unrestrained beam should be takenMb ,Rd LTWyfy /LT== (2)LT+ [ 12LT M12LT1/ 2] 1 (3) = 0.5[1 + ( 0.2) + ](4)LTLT LT = Wyfy / Mcr(5)whereW y is the appropriate section modulus as follows:– W y = W pl,y for Class 1 or 2 cross-sections;– W y = W el,y for Class 3 cross-sections;– W y = W eff,y for Class 4 cross-sections;LTis the reduction factor for lateral-torsional buckling;M cr is the elastic critical moment for lateral-torsional buckling of the gross cross-section;LT is the imperfection factor.The imperfection factor LT corresponding to the appropriate buckling curve may beobtained from Table 1.Table 1. “ LT ” imperfection factors for lateral-torsional buckling curvesBuckling curve a b c dImperfection factor LT 0.21 0.34 0.49 0.76The recommendations for buckling curves are given in Table 2.Table 2. Lateral-torsional buckling curve for cross-sections using equation (3)Cross-section Limits Buckling curveRolled I-sectionsh/b,2ah/b>2bWelded I-sectionsh/b,2ch/b>2dOther cross-sections - dFor the reduced slenderness LT 0. 2 (the case of short beams), lateral-torsionalbuckling effects may be ignored and only cross-sectional checking apply.LT2LT

As an alternative, for rolled or equivalent welded sections in bending the values of LTfor the appropriate non-dimensional slenderness may be determined from:LT 11LT =but 1(6)2 2 1/ 2 + LTLT [ LT LT]2 LT2LT = 0.5[1 + ( ) + ](7)LTLTLTLT,0The following values are recommended for rolled sections: LT ,0 = 0. 4value) and F = 0.75 (minimum value).The recommendations for buckling curves are given in Table 3.(maximumTable 3. Lateral-torsional buckling curve for cross-sections using equation (6)Cross-section Limits Buckling curveRolled I-sectionsh/b,2bh/b>2cWelded I-sectionsh/b,2ch/b>2dOther cross-sections - d3. LATERAL-TORSIONAL BUCKLING OF BEAMS IN BENDING ACCORDINGTO MATEESCU PROPOSALIt is important to underline that the new values of LT coefficient have been evaluatedusing the ECCS experimental database [4].On the purpose of avoiding the discontinuity in the lateral-torsional buckling curve ofbeams, as it was the case of ENV version of Eurocode 3-Part 1.1, Mateescu, at that time,suggested the following formula for LT , but with the imperfection coefficient LT =0.27, forhot-rolled I beams and LT=0.60, for welded I beams:2 = 0.5[1 + ( 0.4) + ](8)LTLTLTLTBy using this formula, to calculate the LT factor, the jump for LT = 0. 4eliminated and, evidently, LT = 1 will be obtained.will be4. THE ECBL APPROACH FOR BEAMS IN BENDINGThe Erosion of Critical Bifurcation Load (ECBL) approach, developed by Dubina [3], isa method where the erosion of the critical bifurcation load of a steel member (owing to thepresence of imperfections as well as to the coupling of instability modes) is quantified bymeans of an erosion factor, LT .The non-dimensional moment MLT , given by equation (9) represents a solution of theAyrton-Perry formula, including the generalised imperfection coefficient, = ( 04 . ):LT LT LTM21+LT(LT0.4)+LT12 2LT [1 +22 LT(LT0.4)+LT]42LT2LT= (9)The formula which link LT factor with previously defined LT factor is:2LT

LT2LT= (10)0.6( 1 )Thus, by calibrating LT factor, the resulting LT values may be obtained for series ofparticular steel sections.The ECBL approach for lateral-torsional buckling of beams is similar to that ofEurocode 3-Part 1.1, but in eqn. (4) is used a different generalised imperfection coefficientinstead of the related formula given in the code. It means the LT formula becomes:2 LT = 051 . [ + LT( LT 04 . ) + LT] (11)and LT should be calculated from eqn. (10) depending on LT erosion factor which has to beevaluated by statistical processing of relevant test specimens.There are two practical ways that can be used to evaluate the LT erosion factor: (1) theexperimental procedure; (2) the numerical approach. In the present paper the experimental“mean” approach is used.Given a specimen series characterized by the same nominal properties, the design valueof the erosion factor results from: LT = m+ 1.64s(12)Mi,expin which s is the standard deviation related to = 1 Mi,exp , where M = andm=1nn(1 Mi=1i,exp)values for all n specimens.As an alternative to the “mean” approach, the Annex D of EN1990 [7] (former Annex Zof Eurocode 3 in the ENV version) can be used for the experimental calibration of LT andLT factors [8].LT,i5. EXPERIMENTAL DATA USED FOR CALIBRATIONThe experimental results supplied in the frame of Eurocode 3-BackgroundDocumentation, Chapter 5/October1989, have been used.In case of hot-rolled steel profiles a number of 144 test results, selected by Europeanexperts as representative for lateral-torsional buckling of beams, from a total of 243 tests havebeen available (see Table 4). In what concern the structural shapes used for the tests, theprofiles are representative for most of the hot-rolled sections used around the world: I or Hsections produced in Europe, North America and Japan. It must be emphasized that the depthof the tested beams never exceeded 305mm. Because several researchers in differentlaboratories all over the world carried out 144 tests, it was accepted that they are wellrepresentative of the testing conditions.In case of welded beams, a number of 71 test results, selected as representative byEuropean experts from a total of 96 tests, have been available (see Table 5).For all the tested specimens, all mechanical and geometrical properties were measured.All tested beams were submitted to moment loading.LTi,expTable 4. Tests results for hot-rolled beams (144 tests)Plastic moment with measured propertiesPos. No. Name M u (kN m)M pl,y (kN m) M u /M pl,y LT1 2 3 4 5 6 71 516 Dibley 90.40 139.90 0.711 1.242 517 Dibley 83.90 141.40 0.653 1.253 518 Dibley 103.50 140.40 0.811 1.114 519 Dibley 102.50 140.40 0.803 1.11Mi, pl

5 520 Dibley 131.10 140.40 1.027 0.906 521 Dibley 130.60 140.40 1.023 0.907 522 Dibley 153.80 157.20 1.076 0.608 523 Dibley 457.20 464.80 1.082 0.519 524 Dibley 468.30 464.80 1.108 0.5110 525 Dibley 464.70 460.20 1.111 0.3511 526 Dibley 485.90 460.20 1.161 0.3512 527 Dibley 105.90 221.40 0.526 1.5413 528 Dibley 96.80 221.40 0.481 1.5414 529 Dibley 118.50 221.40 0.589 1.3715 530 Dibley 126.30 221.40 0.628 1.3716 531 Dibley 190.00 220.30 0.949 0.9117 532 Dibley 180.80 220.30 0.903 0.9118 535 Dibley 204.60 220.30 1.022 0.6519 536 Dibley 235.60 220.30 1.176 0.6520 537 Dibley 138.30 141.40 1.076 0.5821 538 Dibley 127.30 121.00 1.157 0.5122 752 Suzuki 56.90 61.10 1.024 0.6823 753 Suzuki 56.00 61.10 1.008 0.6824 754 Suzuki 46.30 51.40 0.991 0.7925 755 Suzuki 46.20 58.50 0.869 0.8526 756 Suzuki 46.80 55.80 0.923 0.8327 758 Suzuki 43.50 51.40 0.931 0.9528 759 Suzuki 45.20 58.50 0.850 1.0129 760 Suzuki 43.90 55.80 0.865 0.9930 761 Suzuki 49.20 61.10 0.886 1.0331 762 Suzuki 43.60 54.20 0.885 1.1232 763 Suzuki 39.80 58.50 0.748 1.1633 764 Suzuki 44.40 58.50 0.835 1.1634 765 Suzuki 37.70 53.20 0.780 1.2335 766 Suzuki 37.00 58.50 0.696 1.2936 767 Suzuki 38.80 58.50 0.730 1.2937 768 Suzuki 32.10 55.20 0.640 1.3738 769 Suzuki 32.20 57.90 0.612 1.4039 770 Suzuki 32.00 58.50 0.602 1.4140 771 Suzuki 24.30 56.50 0.473 1.6041 772 Suzuki 13.60 54.20 0.276 2.0542 773 Suzuki 35.10 56.50 0.683 1.3143 774 Suzuki 50.90 60.90 0.919 1.0044 775 Suzuki 45.50 59.90 0.836 1.1545 776 Suzuki 48.20 60.90 0.871 0.9746 777 Suzuki 50.10 60.90 0.905 0.8647 778 Suzuki 43.50 60.90 0.786 1.0748 779 Suzuki 47.10 63.00 0.822 1.1549 781 Suzuki 32.10 55.00 0.642 1.2650 782 Suzuki 34.40 59.70 0.634 1.3951 783 Suzuki 50.20 60.90 0.907 1.0052 784 Suzuki 37.20 60.90 0.672 1.3453 1177 Fukumoto 39.70 63.50 0.688 1.2254 718 Wakabayashi 66.40 62.60 1.167 0.3955 719 Wakabayashi 65.20 62.60 1.146 0.5056 720 Wakabayashi 64.80 67.70 1.053 0.6457 721 Wakabayashi 55.90 60.90 1.010 0.8058 1204 Dux 134.70 140.60 1.054 0.5859 1205 Dux 134.60 141.90 1.043 0.5060 1206 Dux 125.30 141.90 0.971 0.6761 540 Trahair 87.00 175.40 0.546 1.44

62 541 Trahair 141.40 175.40 0.887 1.0163 542 Trahair 132.90 175.40 0.833 1.1264 543 Trahair 143.50 175.40 0.900 0.8765 544 Trahair 148.10 175.30 0.929 1.0166 545 Trahair 128.50 175.50 0.805 1.1267 601 Suzuki 47.50 52.80 0.990 0.7868 602 Suzuki 44.60 52.80 0.929 0.9269 603 Suzuki 44.80 55.60 0.886 1.0870 604 Suzuki 36.60 54.60 0.737 1.1871 605 Suzuki 32.90 56.60 0.639 1.3172 606 Suzuki 25.10 58.30 0.474 1.5273 607 Suzuki 13.90 55.60 0.275 1.9474 608 Suzuki 47.10 59.70 0.858 0.8375 609 Suzuki 46.10 59.70 0.849 0.9876 610 Suzuki 40.60 59.70 0.748 1.1177 611 Suzuki 37.80 59.70 0.696 1.2478 612 Suzuki 33.20 59.70 0.612 1.3579 722 Suzuki 58.00 59.50 1.072 0.3480 723 Suzuki 58.30 59.50 1.078 0.4181 724 Suzuki 57.00 60.90 1.030 0.5082 725 Suzuki 53.90 56.50 1.049 0.4083 726 Suzuki 61.60 57.80 1.172 0.2984 733 Suzuki 57.80 60.90 1.044 0.3985 734 Suzuki 54.30 56.50 1.057 0.3786 735 Suzuki 56.60 59.50 1.046 0.5387 749 Suzuki 59.00 62.10 1.045 0.5488 750 Suzuki 57.00 58.90 1.059 0.3489 751 Suzuki 57.00 57.80 1.085 0.3590 1003 Lindner 69.80 76.30 1.006 0.9091 1004 Lindner 49.00 76.30 0.706 1.1992 1005 Lindner 49.90 76.30 0.719 1.1993 1006 Lindner 63.60 76.30 0.917 0.9794 100B Lindner 43.80 64.50 0.747 1.1395 100D Lindner 57.00 66.20 0.947 0.8496 100E Lindner 43.70 66.20 0.726 1.1997 1009 Lindner 46.80 71.40 0.721 1.1998 1010 Lindner 52.60 73.20 0.790 1.1799 1011 Lindner 65.50 73.20 0.984 0.88100 1012 Lindner 59.00 73.20 0.887 0.88101 3 L-S 48.30 57.60 0.992 0.95102 4 L-S 49.50 56.70 0.960 0.94103 5 L-S 49.50 56.80 0.959 0.94104 6 L-S 50.60 57.30 0.971 0.95105 7 L-S 46.00 56.20 0.900 0.94106 9 L-S 49.60 56.20 0.971 0.85107 11 L-S 52.00 56.00 1.021 0.84108 14 L-S 50.40 56.50 0.981 0.85109 16 L-S 48.00 55.60 0.950 0.84110 17 L-S 47.20 55.90 0.929 0.84111 32 L-S 14.40 15.00 1.056 0.91112 33 L-S 12.60 15.30 0.906 0.91113 35 L-S 12.60 15.00 0.924 0.89114 37 L-S 13.20 15.50 0.937 0.91115 42 L-S 14.40 15.80 1.003 0.82116 43 L-S 14.00 15.80 0.975 0.82117 45 L-S 14.40 15.80 1.003 0.82118 56 L-S 8.97 15.70 0.628 1.25

119 57 L-S 9.09 15.70 0.637 1.26120 58 L-S 8.74 16.00 0.601 1.26121 EV1 L-S 57.50 63.20 1.001 0.84122 EV2 L-S 58.70 63.90 1.010 0.85123 EV3 L-S 10.80 12.00 0.990 0.79124 EV4 L-S 10.80 12.00 0.990 0.79125 1 L-S 58.60 56.50 1.141 0.43126 2 L-S 55.20 53.50 1.135 0.42127 18 L-S 55.20 55.40 1.096 0.31128 19 L-S 55.20 55.80 1.088 0.31129 20 L-S 56.00 55.10 1.118 0.31130 501 UN 2.90 6.30 0.506 1.58131 502 UN 2.80 6.30 0.489 1.58132 503 UN 2.70 6.30 0.471 1.58133 504 UN 2.70 6.30 0.471 1.58134 505 UN 3.60 6.30 0.629 1.30135 506 UN 3.40 6.30 0.594 1.30136 507 UN 4.40 6.30 0.768 1.15137 508 UN 4.20 6.30 0.733 1.15138 509 UN 5.20 6.30 0.908 1.00139 510 UN 5.00 6.30 0.873 1.00140 511 UN 5.20 6.30 0.908 1.00141 512 UN 5.60 6.30 0.978 0.82142 513 UN 5.60 6.30 0.978 0.82143 514 UN 6.30 6.30 1.100 0.65144 515 UN 5.90 6.30 1.030 0.65Table 5. Tests results for welded beams (71 tests)Plastic moment with measured propertiesPos. No. Name M u (kN m)M pl,y (kN m) M u /M pl,y LT1 2 3 4 5 6 71 WA5 Fukumoto 409.37 371.00 1.214 0.292 WA5 Fukumoto 383.03 359.60 1.172 0.283 WA32 Suzuki 163.46 162.20 1.109 0.504 WA32 Suzuki 162.17 162.20 1.100 0.415 WA32 Suzuki 162.17 162.20 1.100 0.366 WA32 Suzuki 194.75 197.70 1.084 0.557 WA32 Suzuki 196.72 197.70 1.095 0.468 WA32 Suzuki 195.14 197.70 1.086 0.399 WA32 Suzuki 274.30 281.10 1.073 0.6610 WA21 Suzuki 277.11 281.10 1.084 0.4911 WA21 Suzuki 274.58 281.10 1.074 0.4212 WA31 Suzuki 421.08 440.50 1.052 0.7413 WA31 Suzuki 423.29 440.50 1.057 0.6114 WA31 Suzuki 432.54 440.50 1.080 0.5215 WA31 McDermott 354.60 349.70 1.115 0.3316 WA31 McDermott 491.49 493.00 1.097 0.3517 WA31 Suzuki 304.72 330.10 1.015 0.3218 WA31 Suzuki 306.37 330.10 1.021 0.3219 WA31 Suzuki 301.75 330.10 1.006 0.3220 WA31 Suzuki 298.44 330.10 0.994 0.3221 WA31 Suzuki 305.71 330.10 1.019 0.3222 WA31 Suzuki 308.01 330.10 1.026 0.2423 WA31 Suzuki 301.75 330.10 1.006 0.2424 WA31 Suzuki 305.71 330.10 1.019 0.4025 WA31 Suzuki 220.64 218.50 1.111 0.34

26 WA31 Suzuki 218.45 218.50 1.100 0.3427 WA31 Suzuki 127.97 125.50 1.122 0.3528 WA31 Suzuki 126.34 125.50 1.107 0.3529 WA31 Suzuki 80.60 78.60 1.128 0.3830 WA30 Suzuki 127.43 139.80 1.003 0.5331 WA30 Suzuki 123.41 139.80 0.971 0.5332 WA30 Suzuki 145.38 163.00 0.981 0.5833 WA30 Suzuki 139.50 163.00 0.941 0.5834 WA30 Suzuki 151.37 186.20 0.894 0.7935 WA30 Suzuki 92.02 155.70 0.650 0.9836 WA30 Suzuki 112.93 182.20 0.682 1.0637 WA30 Suzuki 86.72 160.10 0.596 1.3138 WA30 Suzuki 80.64 143.80 0.617 1.2439 WA30 Suzuki 50.70 70.40 0.792 0.8540 WA30 Suzuki 38.27 70.40 0.598 1.1541 WA30 Suzuki 34.44 70.40 0.538 1.4042 WA69 Fukomoto 75.44 92.50 0.897 0.7543 WA69 Fukomoto 68.67 92.70 0.815 0.7544 WA69 Fukomoto 77.89 92.70 0.924 0.9745 WA69 Fukomoto 64.84 92.70 0.769 0.9746 WA69 Fukomoto 62.10 92.70 0.737 1.0747 WA69 Fukomoto 56.41 92.70 0.669 1.0748 WA69 Fukomoto 92.21 105.70 0.960 0.6249 WA69 Fukomoto 78.48 105.70 0.817 0.6250 WA69 Fukomoto 84.37 105.70 0.878 0.8151 WA69 Fukomoto 85.94 105.70 0.894 0.8152 WA69 Fukomoto 91.04 105.70 0.947 0.8953 WA69 Fukumoto 69.85 105.70 0.725 0.8954 WA69 Fukomoto 74.36 119.20 0.686 0.7855 WA69 Fukomoto 90.25 119.20 0.833 0.7856 WA69 Fukomoto 78.77 119.20 0.727 1.0257 WA69 Fukomoto 67.49 119.20 0.623 1.0258 WA69 Fukomoto 73.38 119.20 0.677 1.1359 WA69 Fukomoto 67.59 119.20 0.624 1.1360 WA69 Fukomoto 207.48 255.80 0.892 0.9361 WA69 Fukomoto 204.93 255.80 0.881 0.9362 WA69 Fukomoto 202.87 255.80 0.872 1.1063 WA69 Fukomoto 181.88 255.80 0.782 1.1064 WA69 Fukomoto 188.83 256.50 0.810 1.2565 WA69 Fukomoto 159.41 256.70 0.684 1.2566 WA69 Fukomoto 259.67 292.70 0.976 0.7767 WA69 Fukomoto 239.46 292.70 0.900 0.9168 WA69 Fukomoto 223.57 292.70 0.840 1.0569 WA69 Fukomoto 258.20 328.60 0.864 0.9770 WA69 Fukomoto 219.94 328.60 0.736 1.1571 WA69 Fukomoto 203.85 328.60 0.682 1.326. NUMERICAL AND EXPERIMENTAL RESULTSTable 6 shows the statistical results for hot-rolled and welded I beams. Figures 1 and 2show the comparison between tests and the numerical results related to Eurocode 3 formulas,Mateescu proposal and ECBL approach. For the case of ECBL approach, the interactiveslenderness range was assumed to be LT ± = LT± 0. 20 , and a scattering value of 50% isusual for the experimental values in the field of structural engineering tests.

MethodTable 6. Statistical values for hot-rolled and welded I-beamsEurocode 3 Part 1.1Method 1I Hot-rolled Beams (144 Tests)Eurocode 3 Part 1.1Method 2MateescuECBLStatisticalparameters LT=0.21 LT=0.34 LT=0.34 LT=0.49 LT=0.27 LT=0.185m 1.178 1.286 1.106 1.190 1.165 1.108s 0.100 0.132 0.077 0.110 0.116 0.096m-1.64s 1.014 1.070 0.979 1.009 0.975 0.952v 0.085 0.103 0.070 0.093 0.100 0.086 0.963 0.944 0.959 0.939 0.958 0.968I Welded Beams (71 Tests)LT=0.49 LT=0.76 LT=0.49 LT=0.76 LT=0.60 LT=0.583m 1.188 1.313 1.055 1.142 1.150 1.144s 0.200 0.279 0.125 0.182 0.201 0.197m-1.64s 0.860 0.855 0.850 0.844 0.819 0.820v 0.168 0.213 0.119 0.159 0.175 0.172 0.876 0.857 0.893 0.890 0.892 0.8931.2M ECBL ( LT =0.282, LT=0.185)1.00.80.60.40.2M b,Rd-EC3_vers2 ( LT =0.34)M Mateescu ( LT =0.27)M b,Rd-EC3_vers1 ( LT =0.21)M b,Rd-EC3_vers1 ( LT =0.34)M b,Rd-EC3_vers2 ( LT =0.49)experiments0.00.00 0.50 1.00 1.50 2.00 2.50Fig. 1. Numerical/Experimental comparison for hot-rolled I beams7. CONCLUDING REMARKSFor the case of hot-rolled I-beams, it can be seen from Table 6 that good correlationvalues were obtained for all methods. However, Georgescu & Dubina shown in [8] the studiedhot-rolled profiles frame all on the buckling curve “a” ( max LT= 0.21), which does not complywith the classification proposal for hot-rolled profiles used by second method of Eurocode 3-Part 1.1, presented in the last column of Table 3. For the case of welded I-beams, correlationvalues are still good (see Table 6).From Figures 1 and 2 it can be seen that all curves fit well the experimental values.However, it can be seen from Figure 1 that for short hot-rolled I beams the first method ofEurocode 3 cover safety the range, using a safety factor M1 =1. For the other curves, using asafety factor M1 =1.1 the range of short beams is in the safe side. In what concern the range oflong and medium length it can be seen that the first method of Eurocode 3 is too conservative,while the curves obtained with Mateescu proposal, second method of Eurocode 3 and ECBLone, cover well the whole range. Also, the curve obtained with Mateescu proposal fit very

well with the second method of Eurocode 3 (using an imperfection factor LT =0.34). Thecurve obtained with the ECBL approach covers very well the range of medium length.From Figure 2, for welded I beams the curves obtained with the first method ofEurocode 3 is too conservative. The curves obtained with Mateescu proposal, the secondmethod of Eurocode 3 (with LT =0.76) and ECBL one, fit well the experimental results. Thecurve obtained with the second method of Eurocode 3 (with LT =0.49) need to be affectedwith a safety factor M1 =1.1.1.21.0M Mateescu ( LT =0.60)M ECBL ( LT =0.442, LT=0.583)0.80.60.4M b,Rd-EC3_vers1 ( LT =0.49)M b,Rd-EC3_vers1 ( LT =0.76)M b,Rd-EC3_vers2 ( LT =0.49)experiments0.2M b,Rd-EC3_vers2 ( LT =0.76)0.0REFERENCES0.0 0.5 1.0 1.5 2.0 2.5Fig. 2. Numerical/Experimental comparison for welded I beams[1] Mateescu, D.: Considerations on the value of reduction factor of lateral-torsional bucklingof beams in bending. Thin-Walled Structures, Vol. 20 (No. 1-4), 1994, 265-277.[2] Eurocode 3: Design of steel structures. Part 1-1: General rules and rules for buildings(EN1993-1-1). European Committee for Standardisation. 19 May 2003.[3] Dubina, D.: The ECBL Approach for interactive buckling of thin-walled steel members.Steel and Composite Structures, Vol. 1, no.1, 2001, 76-96.[4] Eurocode 3: Background Documentation (1989)-Chapter 5, Document 5.03: Evaluation ofthe test results on beam with cross-sectional classes 1-3 in order to obtain strengthfunctions and suitable model factors. October 1989.[5] Greiner, R., Salzgeber, G., Ofner, R.: New lateral-torsional buckling curves LT –numerical simulations and design formulae, ECCS Report 30. June 2000.[6] Greiner, R., Kaim, P.: Comparison of LT-buckling curves with test-results. Supplementaryreport. ECCS TC 8, TC 8-2003, May 2003, Graz University of Technology.[7] EN 1990: Eurocode – Basis of structural design. European Committee for Standardisation.July 2001.[8] Georgescu, M., Dubina, D.: Lateral-torsional buckling of steel beams: A proposal tocalibrate the coefficients in the ECCS TC8 formula. Proceedings of the 1 st InternationalConference on STEEL & COMPOSITE STRUCTURES, 14-16 June 2001, Pusan,KOREA, Vol. 1, 623-630.