An Australian manufacturer has recently developed an innovative group of cold-formed steel hollow flange sections, one of them is LiteSteel Beams (LSBs). The LSB sections are produced from thin and high strength steels by a patented manufacturing process involving simultaneous cold-forming and dual electric resistance welding. They have a unique geometry consisting of rectangular hollow flanges and a relatively slender web. The LSB flexural members are subjected to lateral distortional buckling effects and hence their capacities are reduced for intermediate spans. The current design rules for lateral distortional buckling were developed based on the lower bound of numerical and experimental results. The effect of LSB section geometry was not considered although it could influence the lateral distortional buckling performance. Therefore an accurate finite element model of LSB flexural members was developed and validated using experimental and finite strip analysis results. It was then used to investigate the effect of LSB geometry. The extensive moment capacity data thus developed was used to develop improved design rules for LSBs with one of them considering the LSB geometry effects through a modified slenderness parameter. The use of the new design rules gave higher lateral distortional buckling capacities for LSB sections with intermediate slenderness. The new design rule is also able to accurately predict the lateral distortional buckling moment capacities of other hollow flange beams (HFBs)

Anapayan, Tharmarajah

Mahendran, Mahen

English

Queensland University of Technology ePrints Archive

                QUT Digital Repository:  http://eprints.qut.edu.au/ Tharmarajah, Anapayan and Mahen, Mahendran (2009) Improvements to the design of Litesteel Beams undergoing lateral distortional buckling. In: 9th International Conference on Steel Concrete Composite and Hybrid Structures, 8-10 July 2009, University of Leeds, Leeds.            © Copyright 2009 [please consult the authors] 9th International Conference on Steel Concrete Composite and Hybrid Structures. Leeds, UK, 8 – 10 July 2009  IMPROVEMENTS TO THE DESIGN OF LITESTEEL BEAMS UNDERGOING LATERAL DISTORTIONAL BUCKLING Tharmarajah Anapayan; Mahen Mahendran  Faculty of Built Environment and Engineering  Queensland University of Technology, Brisbane, QLD 4000, Australia  tharmarajah.anapayan@student.qut.edu.au; m.mahendran@qut.edu.au  Abstract An Australian manufacturer has recently developed an innovative group of cold-formed steel hollow flange sections, one of them is LiteSteel Beams (LSBs). The LSB sections are produced from thin and high strength steels by a patented manufacturing process involving simultaneous cold-forming and dual electric resistance welding. They have a unique geometry consisting of rectangular hollow flanges and a relatively slender web. The LSB flexural members are subjected to lateral distortional buckling effects and hence their capacities are reduced for intermediate spans. The current design rules for lateral distortional buckling were developed based on the lower bound of numerical and experimental results. The effect of LSB section geometry was not considered although it could influence the lateral distortional buckling performance. Therefore an accurate finite element model of LSB flexural members was developed and validated using experimental and finite strip analysis results. It was then used to investigate the effect of LSB geometry. The extensive moment capacity data thus developed was used to develop improved design rules for LSBs with one of them considering the LSB geometry effects through a modified slenderness parameter. The use of the new design rules gave higher lateral distortional buckling capacities for LSB sections with intermediate slenderness. The new design rule is also able to accurately predict the lateral distortional buckling moment capacities of other hollow flange beams (HFBs).  Keywords: Lateral Distortional Buckling; LiteSteel Beams; Cold-Formed Steel; Hollow Flange Beams 1. Introduction Cold-formed steel members have been widely used in building applications for over five decades. The popularity of these products has dramatically increased in recent years due to their wide range of applications, ease of fabrication and high strength to weight ratios. Although these cold-formed steel members are considered to be more efficient than hot-rolled steel members, they suffer from many complex buckling modes and their interactions because they are usually slender sections that are either asymmetric or singly symmetric. Australian Tube Mills (ATM) formerly known as Smorgon Steel Tube Mills (SSTM) has developed a concept of hollow flange sections which includes the LiteSteel Beams (LSBs) and the Hollow Flange Beams (HFBs). However, the LSB is the only section used in Australia, and it has recently been introduced to the USA market. Unlike the conventional hot-rolled or cold-formed steel sections, the thin-walled LSBs are made of two torsionally rigid rectangular closed flanges and a relatively slender web (Fig. 1). The section depth and flange width of 13 available LSB sections vary from 125 to 300 mm (125, 150, 200, 250 and 300) and 45 to 75 mm (45, 60 and 75), respectively. Flange height is one third of flange width for all the sections with their thicknesses varying from 1.6 to 3.0 mm. Available LSB sections are identified by the section depth, flange width and thickness, for example, 300x60x2.0LSB (ATM, 2005). The high strength steel used for LSBs is DuoSteel grade with web and flange yield stresses of 380 and 450 MPa, respectively. Figure 1:   (a) LiteSteel Beam (LSB)  (b) Hollow Flange Beam (HFB) Past research has identified that the LSB section’s moment capacity for intermediate span members is limited by lateral distortional buckling, which is characterised by simultaneous lateral deflection, twist and web distortion (Fig. 2). This buckling behaviour is mainly due to the unique geometry of the LSB section. The effects of Lateral Distortional Buckling (LDB) on the strength of conventional I-section beams have been extensively investigated by Bradford (1992) and Hancock et al. (1980). However, their results are of limited use to LSB sections. Lateral distortional buckling behaviour of HFBs was investigated by many researchers (Dempsey, 1990, Pi and Trahair, 1997, Avery et al., 2000).       Figure 2: Lateral Distortional Buckling Failure of LSB Mahaarachchi and Mahendran (2005a,b) investigated the lateral distortional buckling behaviour of LSBs by both experiments and finite element analyses and developed a design rule based on a lower bound approach and ignoring the effects of varying geometry. The quality of the LSB manufacturing process in relation to cold-forming and electric resistance welding has been improved over the last three years. Currently the LSB sections are made from a single strip of G60 galvanized steel while earlier LSB sections were manufactured from a single strip of TF 380 coil. Therefore the new LSBs were expected to have higher lateral distortional buckling moment capacities. The main objective of this research was to improve the current design rules for lateral distortional buckling moment capacity of LSBs by identifying the critical geometric parameter. Both experimental and finite element analyses were undertaken to increase the available moment capacity data for 13 LSB sections. This paper presents the details of this investigation and the results. Flange Lateral Deflection Web Distortion Section Twist Tension Compression  2. Experimental Investigation In this experimental study 12 lateral buckling tests of LSBs with varying spans were undertaken to complement the available test results of Mahaarachchi and Mahendran (2005a). Tests included compact, non-compact and slender LSB sections with different spans. The test rig used was similar to that of Mahaarachchi and Mahendran (2005a). Its support system ensured that the test beam was simply supported in-plane and out-of-plane (Fig. 3a). The quarter point loading system included two hydraulic rams connected to a wheel system, load cell and other components (Fig. 3b). The use of a universal joint at the wheel system and the connecting arm and the load application at the shear centre ensured that the load acted in the vertical plane when the test beam deformed in-plane while eliminating load height and torsional loading effects. The LSB section was restrained from twisting at the supports by connecting its web element to the support using plates with suitable thickness and 4 M10 bolts, and by connecting the inner face of the flanges using a welded steel stiffener (Fig. 3a). Figure 3: Experimental Set-Up and Typical Failure Mode Table 1: Lateral Buckling Test Results * Shear buckling failure Test Slenderness LSB Sections Span (mm) Ultimate Moment Mu (kNm) 1 Non-Compact 250 x 75 x 2.5 LSB 3500 34.13 2 Slender 300 x 60 x 2.0 LSB 4000 17.17 3 Slender 200 x 45 x 1.6 LSB 4000 5.92 4 Slender 300 x 60 x 2.0 LSB 3000 18.09 5 Slender 200 x 45 x 1.6 LSB 3000 9.24 6 Non-Compact 150 x 45 x 1.6 LSB 3000 8.27 7 Compact 150 x 45 x 2.0 LSB 3000 9.87 8 Slender 200 x 45 x 1.6 LSB 2000 10.72 9 Compact 150 x 45 x 2.0 LSB 2000 10.76 10 Non-Compact 150 x 45 x 1.6 LSB 1800 9.30 11 Compact 125 x 45 x 2.0 LSB 1200 10.83 12 Non-Compact 150 x 45 x 1.6 LSB 1200 9.29* (a) Support System (b) Overall View of the Test Set-up Loading arm Stiffener to eliminate flange twist  The use of overhang method of loading creates undesirable warping effects and hence is likely to over-predict the lateral buckling capacity. Hence quarter point loading method was used in this investigation although it creates a uniform bending moment only between the loading points. However, Kurniawan and Mahendran (2008) found that the moment modification factor for the non-uniform moment distribution caused by quarter point loading is closer to 1.0. All the test beams failed by lateral distortional buckling while some slender sections exhibited inelastic local buckling of web elements soon after the maximum moment was reached. Table 1 presents the ultimate moment capacities obtained from the lateral buckling tests. 3. Finite Element Analysis The LSB flexural members were modelled and analysed using MD/PATRAN pre-processing facilities and ABAQUS (HKS, 2006). Two types of finite element model were developed, namely, the experimental and ideal models. Experimental models were used to simulate the actual tested members and quarter point loading conditions and for comparison with the corresponding lateral buckling tests whereas ideal models were used to simulate LSB members subject to a uniform moment and to generate member capacity curves suitable for design. Experimental model included the measured section dimensions, yield and ultimate stresses while the ideal model consisted of nominal section dimensions and material properties.          Figure 4: Ideal Finite Element Model and Ultimate Failure Mode In these models (Fig. 4) S4R5 elements with an optimum size of 5 mm x 10 mm were used based on a series of convergence studies. Longitudinal tension and compression forces were applied at the supports using ‘spatial function’ available in PATRAN to create a uniform major axis bending moment in the ideal model. Only half the span was modelled because of symmetric loading and support conditions. Simply supported boundary conditions were applied at the support while symmetric boundary conditions were applied at mid-span. A global geometric imperfection of L/1000 was used based on the AS 4100 fabrication tolerance for compression members (SA, 1998) and imperfection measurements of LSBs. A negative geometric imperfection was applied to the ideal models as it was found to be critical. Both flexural and membrane residual stresses were applied to both models and the nonlinear lateral buckling moment capacities were obtained. Fig. 4 shows the ultimate failure mode from the finite element analysis of ideal models.   Original LSB Deformed LSB Elastic lateral distortional buckling moment of LSBs can be calculated approximately using Pi and Trahair’s (1997) equation shown next.            where, EIy = minor axis flexural rigidity, EIw = warping rigidity, GJe= effective torsional rigidity, GJf = flange torsional rigidity, t = thickness, d1 = clear web depth. Elastic lateral distortional buckling moments from Eq. (1) and a well established finite strip analysis program (Thin-Wall) were compared with those predicted by the ideal FE model. The results agreed well as shown in Fig. 5 (within 2%). Figure 5: Comparisons of Elastic Lateral Distortional Buckling Moments Nonlinear analysis results from the experimental finite element models also agreed well with test results, thus confirming the accuracy of these FE models in predicting the nonlinear behaviour and strength of LSBs. However, these results are not presented here as this paper is mostly concerned about the design curve development based on the ideal FE model subject to a uniform moment. The ideal finite element model was used to predict the ultimate moment capacities of all the 13 LSB sections with varying spans, and the results are compared with the current design curves. 4. Design Rules  AS/NZS 4600 (SA, 2005) provides equations for the design of members subject to distortional buckling that involves transverse bending of a vertical web with lateral displacement of the compression flange.             (3)  01020304050607080901000 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000Span (mm)Elastic Lateral Distortional Buckling Moments (Mod), kNm THINWALLFEAPi & Trahair (1997)150x45x1.6 250x60x2.5 300x60x2.0 =ZMZM ceb+=1122322391.0291.02dLEtGJdLEtGJGJffepipi (2) += 2222LEIGJLEIM weyod pipi (1) For LSBs, it is appropriate to determine the effective section modulus (Ze) at a stress corresponding Mc/Z, where Mc is the critical moment as defined in Eqs. (4a-c).   For λd ≤ 0.59:  Mc = My (4a) For 0.59 < λd < 1.70: =dyc MM λ59.0 (4b) For λd ≥ 1.70: =dyc MM 21λ  (4c) The non- dimensional slenderness λd is given by ody MM / ).     Figure 6: Comparison of FEA Results with AS/NZS 4600 Predictions  Fig. 6 compares the FEA and experimental results with the predictions from Eqs. (4a-c) (AS/NZS 4600 design rule). It shows that the current design rules provide a lower bound to the experimental and FEA capacities and are conservative in the inelastic lateral buckling region. They are reasonably accurate in the other regions of yielding/local buckling and elastic lateral buckling. Therefore a new design equation was developed for the inelastic lateral buckling region as shown next.  For λd ≤ 0.54:  Mc = My (5a)  For 0.54 < λd < 1.74: Mc = My (0.28 λ2d – 1.20 λd + 1.57) (5b)  For λd ≥ 1.74: =dyc MM 21λ  (5c) The new design equation (Eq. (5b)) was developed based on the FEA results, which gave a mean FEA to predicted ratio of 1.03 and a COV of 0.066. Fig. 7 compares the experimental results of Mahaarachchi and Mahendran (2005a) for LSB sections and the FEA results for HFBs from Avery et al. (2000) with the new design equation. The new equation has a mean FEA to predicted ratio of 1.10 and a COV of 0.048 for HFBs while the mean FEA and test to predicted ratio for LSBs was 1.02 and a COV of 0.081. A capacity reduction factor of 0.9 was calculated using the AISI (2004) procedure for Eq. (5b) and both FEA and test results of LSBs. Further attempts to simplify the above design equation (Eq. (5b)) are continuing. 0.000.200.400.600.801.001.200.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40Slenderness, λd Mu/My ,    Mb/MyAS/NZS 4600 (2005)Equation 5FEA LSBEXP this paperFigure 7: Comparison of FEA Results of HFBs with Equation 5 The FEA results of LSBs plotted in Fig. 6 has a scatter due to the influence of varying LSB geometry. This scatter was significantly reduced by using a modified slenderness which includes a geometrical parameter ‘K’ as given by Eq. (6).                                                   +=WebfEIGJK85.01  (6) The ratio of the flange torsional rigidity GJf to the web flexural rigidity EIweb was found to be the critical section geometrical parameter which eliminated the scatter of the FEA results. A modified non-dimensional slenderness (Kλd) was used to plot the FEA results of LSBs in Fig. 8. New design equations were developed, which gave a mean FEA to predicted ratio of 1.00 and a COV of 0.035.    For Kλd ≤ 0.52:  Mc = My (7a) For Kλd > 0.52: Mc = My (0.199(Kλd)2 – 1.013Kλd + 1.475)  (7b) Each LSB section has a unique K factor which ranges from 0.90 to 1.07 for the available LSB sections. Eq. (7) has a capacity reduction factor of 0.9. Since the HFB data points have less scatter the use of Eq. (7) does not make significant difference.           Figure 8: Comparison of FEA Results of LSBs with Equation 7 0.000.200.400.600.801.001.200.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40Modified Slenderness, KλdMu/MyEquation 7FEA0.000.200.400.600.801.001.200.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 2.40Slenderness, λd Mu/MyAS/NZS 4600 (2005)Equation 5FEA HFBEXP MM5. Conclusions This paper has presented the important details and results of a detailed investigation into the structural behaviour of LSB flexural members. Based on advanced finite element analyses and large scale experimental studies the current design rule provided in AS/NZS 4600 (SA, 2005) for the moment capacity of flexural members subjected to lateral distortional buckling was modified in the inelastic lateral buckling region. The new design equation is also able to predict the member moment capacity of HFBs. Hence the new design rule is recommended for both LSBs and HFBs with a capacity reduction factor of 0.9. A new parameter ‘K’ has been proposed to take into account the effect of geometry on the member moment capacity of LSBs. By including this in a modified slenderness parameter a new design rule has been developed to accurately predict the member moment capacities of all the LSB flexural members. This has therefore eliminated the conservative predictions of the current design rules. However, research is continuing to develop alternative forms of design equations.  6. References [1] AISI (2004), “Specification for the Design of Cold-Formed Steel Structural Members”, American Iron and Steel Institute, Washington, D.C., USA.  [2] Avery, P., Mahendran, M. and Nasir, A. (2000), “Flexural Capacity of Hollow Flange Beams”, Journal of Constructional Steel Research, Vol. 53, pp.201-223. [3] Bradford, M.A. (1992), “Lateral Distortional Buckling of Steel I-Section Members”, Journal of Construction Steel Research, Vol. 23(1-3), pp.97-116. [4] Dempsey, R. I. (1990), “Structural Behaviour and Design of Hollow Flange Beams”, Proceedings of the 2nd National Structural Engineering Conference, Institute of Engineers, Barton, ACT, Australia, pp.325-335. [5] Hancock, G. J., Bradford, M.A. and Trahair, N.S. (1980), “Web Distortion and Flexural Torsional Buckling”, J Struct Division, Vol. 106, No.7, pp.1557-1571. [6] HKS., (2006). Abaqus/Standard User’s Manual.Hibbitt, Karlsson & Sorensen, Inc., USA. [7] Kurniawan, C.W. and Mahendran, M. (2008), “Elastic Lateral Buckling of Simply Supported LiteSteel Beams Subject to Transverse Loading”, Thin-Walled Structures, doi:10.1016/j.tws.2008.05.012. [8] Mahaarachchi, D. and Mahendran, M. (2005a), “Lateral Buckling Tests of LiteSteel Beam Sections”, Research Report No. 1, QUT, Brisbane, Australia. [9] Mahaarachchi, D. and Mahendran, M. (2005b), “Moment Capacity and Design of LiteSteel Beam Sections”, Research Report No. 4, QUT, Brisbane, Australia. [10] Pi, Y.-L. and Trahair, N.S. (1997), “Lateral Distortional Buckling of Hollow Flange Beams”, J. Struct. Eng., ASCE, Vol. 123, No.6, pp.695-702. [11] Standards Australia (SA, 2005), “Cold-formed Steel Structures”, AS/NZS 4600, Sydney, Australia. [12] Standards Australia (SA, 1998), “Steel Structures”, AS 4100, Sydney, Australia. 

Abaqus/Standard User’s Manual.Hibbitt,

Elastic Lateral Buckling of Simply Supported LiteSteel Beams Subject to Transverse Loading”, Thin-Walled Structures,

Flexural Capacity of Hollow Flange Beams”,

Lateral Distortional Buckling of Steel I-Section Members”,

Specification for the Design of Cold-Formed Steel Structural Members”, American Iron and Steel Institute,

Structural Behaviour and Design of Hollow Flange Beams”,

Web Distortion and Flexural Torsional Buckling”,

Improvements to the design of LiteSteel beams undergoing lateral distortional buckling

Improvements to the design of LiteSteel beams undergoing lateral distortional buckling

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