Mateescu_Ungureanu

8/6/2019 Mateescu_Ungureanu

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LATERAL-TORSIONAL BUCKLING OF STEEL BEAMS

D. Mateescu1, V. Ungureanu1

ABSTRACT

The slender members loaded by transversal loads or ended moments acting around the

major axis of inertia, may collapse by lateral-torsional buckling before reaching the full

plastic resistant moment, Mpl. The present paper presents a comparison between Mateescu

proposal [1], Eurocode 3-Part 1.1 [2] and the ECBL approach [3], used to calculate the

ultimate lateral-torsional buckling moment. The experimental database from Eurocode 3

Background Documentation, Chapter 5 October 1989 [4] was used to evaluate the theoretical

results.

Key Words: Lateral-torsional buckling, buckling curves, imperfections, generalizedimperfection factor, experimental results

1. INTRODUCTIONIn the final version of Eurocode 3-Part 1.1 [2] there exist two different sets of LT-

buckling curves:

- in paragraph 6.3.2.2:Lateral-torsional buckling curves -General case, the column

buckling curves a, b, c, d are specified for cross-section groups h/b , 2 and h/b>2

of rolled and welded sections, with a plateau of 2.0LT ;

- 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 the

groups h/b,2 and h/b>2 of rolled and welded sections, and in contrary to

paragraph 6.3.2.2 with a plateau of 4.0LT . The LT-buckling curves given in6.3.2.3 are based on numerical simulations of single span beams under uniform

moment 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 the

two sets of LT-buckling curves from Eurocode 3-Part 1.1 is presented in this paper. In

addition, for comparison the LT-buckling curves obtained with the Erosion of Critical

Bifurcation Load (ECBL) approach, developed by Dubina is shown.

1Romanian Academy, Timisoara Branch, Laboratory of Steel Structures, M. Viteazul 24, Timisoara, Romania


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2. LATERAL-TORSIONAL BUCKLING OF BEAMS IN BENDING ACCORDINGTO EUROCODE 3-PART 1.1

According to EUROCODE 3-Part. 1.1 [2], a laterally unrestrained beam subject to

major axis bending shall be verified against lateral-torsional with the formula:

1M

M

Rd,b

Ed (1)

where:

MEd is the design value of the moment;

Mb,Rd is the design buckling resistance moment.

The design buckling resistance moment of a laterally unrestrained beam should be taken

as:

1MyyLTRd,b /fWM = (2)

where

+

=2/12

LT2LTLT

LT

][

11 (3)

])2.0(1[5.02

LTLTLTLT ++= (4)

cryyLT M/fW= (5)

where

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;

Wy = Weff,y for Class 4 cross-sections;

LT is the reduction factor for lateral-torsional buckling;Mcr 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 d

Imperfection factorLT 0.21 0.34 0.49 0.76

The 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 curve

Rolled I-sectionsh/b,2

h/b>2

a

b

Welded I-sectionsh/b,2

h/b>2

c

d

Other cross-sections - d

For the reduced slenderness 2.0LT (the case of short beams), lateral-torsionalbuckling effects may be ignored and only cross-sectional checking apply.


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As an alternative, for rolled or equivalent welded sections in bending the values of LTfor the appropriate non-dimensional slenderness may be determined from:

+=

2LT

LT

LT

2/12LT

2

LTLT

LT 1

1

but][

1(6)

])(1[5.02LT0,LTLTLTLT ++= (7)

The following values are recommended for rolled sections: 4.00,LT = (maximumvalue) and F = 0.75 (minimum value).

The recommendations for buckling curves are given in Table 3.

Table 3. Lateral-torsional buckling curve for cross-sections using equation (6)

Cross-section Limits Buckling curve

Rolled I-sections h/b,2h/b>2

bc

Welded I-sectionsh/b,2

h/b>2

c

d

Other cross-sections - d

3. LATERAL-TORSIONAL BUCKLING OF BEAMS IN BENDING ACCORDINGTO MATEESCU PROPOSAL

It 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 of

beams, as it was the case of ENV version of Eurocode 3-Part 1.1, Mateescu, at that time,

suggested the following formula forLT, but with the imperfection coefficient LT=0.27, forhot-rolled I beams and LT=0.60, for welded I beams:

])4.0(1[5.02LTLTLTLT ++= (8)

By using this formula, to calculate the LT factor, the jump for 4.0LT = will beeliminated and, evidently, 1LT = will be obtained.

4.

THE ECBL APPROACH FOR BEAMS IN BENDING

The Erosion of Critical Bifurcation Load (ECBL) approach, developed by Dubina [3], is

a method where the erosion of the critical bifurcation load of a steel member (owing to the

presence of imperfections as well as to the coupling of instability modes) is quantified by

means of an erosion factor, LT.The non-dimensional moment MLT , given by equation (9) represents a solution of the

Ayrton-Perry formula, including the generalised imperfection coefficient,

LT LT LT= ( . )0 4 :

2

LT

22

LTLTLT2LT

2LT

2LTLTLT

LT 4])4.0(1[2

1

2

)4.0(1M ++

++= (9)

The formula which linkLT factor with previously defined LT factor is:


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( )LT

2LT

LT16.0

= (10)

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 coefficient

instead of the related formula given in the code. It means the LT formula becomes:

LT LT LT LT= + +0 5 1 0 42

. [ ( . ) ] (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 value

of the erosion factor results from:s64.1mLT += (12)

in which s is the standard deviation related to exp,ii,LT M1= , wherepl,i

exp,iexp,i

M

MM = and

)M1(n

1exp,i

n

1im =

=

values for all n specimens.

As an alternative to the mean approach, the Annex D of EN1990 [7] (former Annex Z

of Eurocode 3 in the ENV version) can be used for the experimental calibration ofLT andLT factors [8].

5. EXPERIMENTAL DATA USED FOR CALIBRATIONThe experimental results supplied in the frame of Eurocode 3-Background

Documentation, Chapter 5/October1989, have been used.

In case of hot-rolled steel profiles a number of 144 test results, selected by European

experts as representative for lateral-torsional buckling of beams, from a total of 243 tests have

been available (see Table 4). In what concern the structural shapes used for the tests, the

profiles are representative for most of the hot-rolled sections used around the world: I or H

sections produced in Europe, North America and Japan. It must be emphasized that the depth

of the tested beams never exceeded 305mm. Because several researchers in different

laboratories all over the world carried out 144 tests, it was accepted that they are well

representative of the testing conditions.

In case of welded beams, a number of 71 test results, selected as representative by

European 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.

Table 4. Tests results for hot-rolled beams (144 tests)Plastic moment with measured properties

Pos. No. Name Mu (kN m)Mpl,y (kN m) Mu/Mpl,y LT

1 2 3 4 5 6 7

1 516 Dibley 90.40 139.90 0.711 1.242 517 Dibley 83.90 141.40 0.653 1.25

3 518 Dibley 103.50 140.40 0.811 1.11

4 519 Dibley 102.50 140.40 0.803 1.11


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5 520 Dibley 131.10 140.40 1.027 0.90

6 521 Dibley 130.60 140.40 1.023 0.90

7 522 Dibley 153.80 157.20 1.076 0.60

8 523 Dibley 457.20 464.80 1.082 0.51

9 524 Dibley 468.30 464.80 1.108 0.51

10 525 Dibley 464.70 460.20 1.111 0.35

11 526 Dibley 485.90 460.20 1.161 0.35

12 527 Dibley 105.90 221.40 0.526 1.54

13 528 Dibley 96.80 221.40 0.481 1.54

14 529 Dibley 118.50 221.40 0.589 1.37

15 530 Dibley 126.30 221.40 0.628 1.37

16 531 Dibley 190.00 220.30 0.949 0.91

17 532 Dibley 180.80 220.30 0.903 0.91

18 535 Dibley 204.60 220.30 1.022 0.65

19 536 Dibley 235.60 220.30 1.176 0.65

20 537 Dibley 138.30 141.40 1.076 0.58

21 538 Dibley 127.30 121.00 1.157 0.51

22 752 Suzuki 56.90 61.10 1.024 0.68

23 753 Suzuki 56.00 61.10 1.008 0.68

24 754 Suzuki 46.30 51.40 0.991 0.79

25 755 Suzuki 46.20 58.50 0.869 0.85

26 756 Suzuki 46.80 55.80 0.923 0.83

27 758 Suzuki 43.50 51.40 0.931 0.95

28 759 Suzuki 45.20 58.50 0.850 1.01

29 760 Suzuki 43.90 55.80 0.865 0.99

30 761 Suzuki 49.20 61.10 0.886 1.03

31 762 Suzuki 43.60 54.20 0.885 1.12

32 763 Suzuki 39.80 58.50 0.748 1.16

33 764 Suzuki 44.40 58.50 0.835 1.16

34 765 Suzuki 37.70 53.20 0.780 1.23

35 766 Suzuki 37.00 58.50 0.696 1.29

36 767 Suzuki 38.80 58.50 0.730 1.29

37 768 Suzuki 32.10 55.20 0.640 1.37

38 769 Suzuki 32.20 57.90 0.612 1.40

39 770 Suzuki 32.00 58.50 0.602 1.41

40 771 Suzuki 24.30 56.50 0.473 1.60

41 772 Suzuki 13.60 54.20 0.276 2.05

42 773 Suzuki 35.10 56.50 0.683 1.31

43 774 Suzuki 50.90 60.90 0.919 1.00

44 775 Suzuki 45.50 59.90 0.836 1.15

45 776 Suzuki 48.20 60.90 0.871 0.97

46 777 Suzuki 50.10 60.90 0.905 0.8647 778 Suzuki 43.50 60.90 0.786 1.07

48 779 Suzuki 47.10 63.00 0.822 1.15

49 781 Suzuki 32.10 55.00 0.642 1.26

50 782 Suzuki 34.40 59.70 0.634 1.39

51 783 Suzuki 50.20 60.90 0.907 1.00

52 784 Suzuki 37.20 60.90 0.672 1.34

53 1177 Fukumoto 39.70 63.50 0.688 1.22

54 718 Wakabayashi 66.40 62.60 1.167 0.39

55 719 Wakabayashi 65.20 62.60 1.146 0.50

56 720 Wakabayashi 64.80 67.70 1.053 0.64

57 721 Wakabayashi 55.90 60.90 1.010 0.80

58 1204 Dux 134.70 140.60 1.054 0.5859 1205 Dux 134.60 141.90 1.043 0.50

60 1206 Dux 125.30 141.90 0.971 0.67

61 540 Trahair 87.00 175.40 0.546 1.44


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62 541 Trahair 141.40 175.40 0.887 1.01

63 542 Trahair 132.90 175.40 0.833 1.12

64 543 Trahair 143.50 175.40 0.900 0.87

65 544 Trahair 148.10 175.30 0.929 1.01

66 545 Trahair 128.50 175.50 0.805 1.12

67 601 Suzuki 47.50 52.80 0.990 0.78

68 602 Suzuki 44.60 52.80 0.929 0.92

69 603 Suzuki 44.80 55.60 0.886 1.08

70 604 Suzuki 36.60 54.60 0.737 1.18

71 605 Suzuki 32.90 56.60 0.639 1.31

72 606 Suzuki 25.10 58.30 0.474 1.52

73 607 Suzuki 13.90 55.60 0.275 1.94

74 608 Suzuki 47.10 59.70 0.858 0.83

75 609 Suzuki 46.10 59.70 0.849 0.98

76 610 Suzuki 40.60 59.70 0.748 1.11

77 611 Suzuki 37.80 59.70 0.696 1.24

78 612 Suzuki 33.20 59.70 0.612 1.35

79 722 Suzuki 58.00 59.50 1.072 0.34

80 723 Suzuki 58.30 59.50 1.078 0.41

81 724 Suzuki 57.00 60.90 1.030 0.50

82 725 Suzuki 53.90 56.50 1.049 0.40

83 726 Suzuki 61.60 57.80 1.172 0.29

84 733 Suzuki 57.80 60.90 1.044 0.39

85 734 Suzuki 54.30 56.50 1.057 0.37

86 735 Suzuki 56.60 59.50 1.046 0.53

87 749 Suzuki 59.00 62.10 1.045 0.54

88 750 Suzuki 57.00 58.90 1.059 0.34

89 751 Suzuki 57.00 57.80 1.085 0.35

90 1003 Lindner 69.80 76.30 1.006 0.90

91 1004 Lindner 49.00 76.30 0.706 1.19

92 1005 Lindner 49.90 76.30 0.719 1.19

93 1006 Lindner 63.60 76.30 0.917 0.97

94 100B Lindner 43.80 64.50 0.747 1.13

95 100D Lindner 57.00 66.20 0.947 0.84

96 100E Lindner 43.70 66.20 0.726 1.19

97 1009 Lindner 46.80 71.40 0.721 1.19

98 1010 Lindner 52.60 73.20 0.790 1.17

99 1011 Lindner 65.50 73.20 0.984 0.88

100 1012 Lindner 59.00 73.20 0.887 0.88

101 3 L-S 48.30 57.60 0.992 0.95

102 4 L-S 49.50 56.70 0.960 0.94

103 5 L-S 49.50 56.80 0.959 0.94104 6 L-S 50.60 57.30 0.971 0.95

105 7 L-S 46.00 56.20 0.900 0.94

106 9 L-S 49.60 56.20 0.971 0.85

107 11 L-S 52.00 56.00 1.021 0.84

108 14 L-S 50.40 56.50 0.981 0.85

109 16 L-S 48.00 55.60 0.950 0.84

110 17 L-S 47.20 55.90 0.929 0.84

111 32 L-S 14.40 15.00 1.056 0.91

112 33 L-S 12.60 15.30 0.906 0.91

113 35 L-S 12.60 15.00 0.924 0.89

114 37 L-S 13.20 15.50 0.937 0.91

115 42 L-S 14.40 15.80 1.003 0.82116 43 L-S 14.00 15.80 0.975 0.82

117 45 L-S 14.40 15.80 1.003 0.82

118 56 L-S 8.97 15.70 0.628 1.25


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119 57 L-S 9.09 15.70 0.637 1.26

120 58 L-S 8.74 16.00 0.601 1.26

121 EV1 L-S 57.50 63.20 1.001 0.84

122 EV2 L-S 58.70 63.90 1.010 0.85

123 EV3 L-S 10.80 12.00 0.990 0.79

124 EV4 L-S 10.80 12.00 0.990 0.79

125 1 L-S 58.60 56.50 1.141 0.43

126 2 L-S 55.20 53.50 1.135 0.42

127 18 L-S 55.20 55.40 1.096 0.31

128 19 L-S 55.20 55.80 1.088 0.31

129 20 L-S 56.00 55.10 1.118 0.31

130 501 UN 2.90 6.30 0.506 1.58

131 502 UN 2.80 6.30 0.489 1.58

132 503 UN 2.70 6.30 0.471 1.58

133 504 UN 2.70 6.30 0.471 1.58

134 505 UN 3.60 6.30 0.629 1.30

135 506 UN 3.40 6.30 0.594 1.30

136 507 UN 4.40 6.30 0.768 1.15

137 508 UN 4.20 6.30 0.733 1.15

138 509 UN 5.20 6.30 0.908 1.00

139 510 UN 5.00 6.30 0.873 1.00

140 511 UN 5.20 6.30 0.908 1.00

141 512 UN 5.60 6.30 0.978 0.82

142 513 UN 5.60 6.30 0.978 0.82

143 514 UN 6.30 6.30 1.100 0.65

144 515 UN 5.90 6.30 1.030 0.65

Table 5. Tests results for welded beams (71 tests)Plastic moment with measured properties

Pos. No. Name Mu (kN m)Mpl,y (kN m) Mu/Mpl,y

LT1 2 3 4 5 6 71 WA5 Fukumoto 409.37 371.00 1.214 0.29

2 WA5 Fukumoto 383.03 359.60 1.172 0.28

3 WA32 Suzuki 163.46 162.20 1.109 0.50

4 WA32 Suzuki 162.17 162.20 1.100 0.41

5 WA32 Suzuki 162.17 162.20 1.100 0.36

6 WA32 Suzuki 194.75 197.70 1.084 0.55

7 WA32 Suzuki 196.72 197.70 1.095 0.46

8 WA32 Suzuki 195.14 197.70 1.086 0.39

9 WA32 Suzuki 274.30 281.10 1.073 0.66

10 WA21 Suzuki 277.11 281.10 1.084 0.49

11 WA21 Suzuki 274.58 281.10 1.074 0.4212 WA31 Suzuki 421.08 440.50 1.052 0.74

13 WA31 Suzuki 423.29 440.50 1.057 0.61

14 WA31 Suzuki 432.54 440.50 1.080 0.52

15 WA31 McDermott 354.60 349.70 1.115 0.33

16 WA31 McDermott 491.49 493.00 1.097 0.35

17 WA31 Suzuki 304.72 330.10 1.015 0.32

18 WA31 Suzuki 306.37 330.10 1.021 0.32

19 WA31 Suzuki 301.75 330.10 1.006 0.32

20 WA31 Suzuki 298.44 330.10 0.994 0.32

21 WA31 Suzuki 305.71 330.10 1.019 0.32

22 WA31 Suzuki 308.01 330.10 1.026 0.24

23 WA31 Suzuki 301.75 330.10 1.006 0.2424 WA31 Suzuki 305.71 330.10 1.019 0.40

25 WA31 Suzuki 220.64 218.50 1.111 0.34


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26 WA31 Suzuki 218.45 218.50 1.100 0.34

27 WA31 Suzuki 127.97 125.50 1.122 0.35

28 WA31 Suzuki 126.34 125.50 1.107 0.35

29 WA31 Suzuki 80.60 78.60 1.128 0.38

30 WA30 Suzuki 127.43 139.80 1.003 0.53

31 WA30 Suzuki 123.41 139.80 0.971 0.53

32 WA30 Suzuki 145.38 163.00 0.981 0.58

33 WA30 Suzuki 139.50 163.00 0.941 0.58

34 WA30 Suzuki 151.37 186.20 0.894 0.79

35 WA30 Suzuki 92.02 155.70 0.650 0.98

36 WA30 Suzuki 112.93 182.20 0.682 1.06

37 WA30 Suzuki 86.72 160.10 0.596 1.31

38 WA30 Suzuki 80.64 143.80 0.617 1.24

39 WA30 Suzuki 50.70 70.40 0.792 0.85

40 WA30 Suzuki 38.27 70.40 0.598 1.15

41 WA30 Suzuki 34.44 70.40 0.538 1.40

42 WA69 Fukomoto 75.44 92.50 0.897 0.75

43 WA69 Fukomoto 68.67 92.70 0.815 0.75

44 WA69 Fukomoto 77.89 92.70 0.924 0.97

45 WA69 Fukomoto 64.84 92.70 0.769 0.97

46 WA69 Fukomoto 62.10 92.70 0.737 1.07

47 WA69 Fukomoto 56.41 92.70 0.669 1.07

48 WA69 Fukomoto 92.21 105.70 0.960 0.62

49 WA69 Fukomoto 78.48 105.70 0.817 0.62

50 WA69 Fukomoto 84.37 105.70 0.878 0.81

51 WA69 Fukomoto 85.94 105.70 0.894 0.81

52 WA69 Fukomoto 91.04 105.70 0.947 0.89

53 WA69 Fukumoto 69.85 105.70 0.725 0.89

54 WA69 Fukomoto 74.36 119.20 0.686 0.78

55 WA69 Fukomoto 90.25 119.20 0.833 0.78

56 WA69 Fukomoto 78.77 119.20 0.727 1.02

57 WA69 Fukomoto 67.49 119.20 0.623 1.02

58 WA69 Fukomoto 73.38 119.20 0.677 1.13

59 WA69 Fukomoto 67.59 119.20 0.624 1.13

60 WA69 Fukomoto 207.48 255.80 0.892 0.93

61 WA69 Fukomoto 204.93 255.80 0.881 0.93

62 WA69 Fukomoto 202.87 255.80 0.872 1.10

63 WA69 Fukomoto 181.88 255.80 0.782 1.10

64 WA69 Fukomoto 188.83 256.50 0.810 1.25

65 WA69 Fukomoto 159.41 256.70 0.684 1.25

66 WA69 Fukomoto 259.67 292.70 0.976 0.77

67 WA69 Fukomoto 239.46 292.70 0.900 0.91

68 WA69 Fukomoto 223.57 292.70 0.840 1.05

69 WA69 Fukomoto 258.20 328.60 0.864 0.97

70 WA69 Fukomoto 219.94 328.60 0.736 1.15

71 WA69 Fukomoto 203.85 328.60 0.682 1.32

6. NUMERICAL AND EXPERIMENTAL RESULTSTable 6 shows the statistical results for hot-rolled and welded I beams. Figures 1 and 2

show 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 interactive

slenderness range was assumed to be 20.0LTLT = , and a scattering value of 50% isusual for the experimental values in the field of structural engineering tests.


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Table 6. Statistical values for hot-rolled and welded I-beamsI Hot-rolled Beams (144 Tests)

Eurocode 3 Part 1.1

Method 1

Eurocode 3 Part 1.1

Method 2Mateescu ECBL

Method

Statistical

parametersLT=0.21 LT=0.34 LT=0.34 LT=0.49 LT=0.27 LT=0.185

m 1.178 1.286 1.106 1.190 1.165 1.108s 0.100 0.132 0.077 0.110 0.116 0.096

m-1.64s 1.014 1.070 0.979 1.009 0.975 0.952

v 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 1.144

s 0.200 0.279 0.125 0.182 0.201 0.197

m-1.64s 0.860 0.855 0.850 0.844 0.819 0.820

v 0.168 0.213 0.119 0.159 0.175 0.172

0.876 0.857 0.893 0.890 0.892 0.893

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.00 0.50 1.00 1.50 2.00 2.50

experiments

Mb,Rd-EC3_vers1 (LT=0.21)

MMateescu (LT=0.27)

MECBL (LT=0.282, LT=0.185)




Fig. 1. Numerical/Experimental comparison for hot-rolled I beams

7. CONCLUDING REMARKSFor the case of hot-rolled I-beams, it can be seen from Table 6 that good correlation

values were obtained for all methods. However, Georgescu & Dubina shown in [8] the studied

hot-rolled profiles frame all on the buckling curve a ( )21.0max =LT , 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, correlation

values 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 of

Eurocode 3 cover safety the range, using a safety factorM1=1. For the other curves, using asafety factorM1=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 ECBL

one, cover well the whole range. Also, the curve obtained with Mateescu proposal fit very


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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 of

Eurocode 3 is too conservative. The curves obtained with Mateescu proposal, the second

method 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 factorM1=1.1.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0 0.5 1.0 1.5 2.0 2.5

experiments


MMateescu (LT=0.60)

MECBL ( LT=0.442, LT=0.583)




Fig. 2. Numerical/Experimental comparison for welded I beams

REFERENCES

[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 1st International

Conference on STEEL & COMPOSITE STRUCTURES, 14-16 June 2001, Pusan,KOREA, Vol. 1, 623-630.

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