ADVANCES in NATURAL and APPLIED SCIENCES

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1 ADVANCES in NATURAL and APPLIED SCIENCES ISSN: Published BYAENSI Publication EISSN: June 11(8): pages Open Access Journal Structural performance of cold-formed lean duplex stainless steel flat oval hollow columns M. Anbarasu Assistant Professor, Department of Civil Engineering, Government College of Engineering, Salem , Tamilnadu, India. Received 28 February 2017; Accepted 22 May 2017; Available online 6 June 2017 Address For Correspondence: M. Anbarasu, Assistant Professor, Department of Civil Engineering, Government College of Engineering, Salem , Tamilnadu, India. gceanbu@gmail. com Copyright 2017 by authors and American-Eurasian Network for ScientificInformation (AENSI Publication). This work is licensed under the Creative Commons Attribution International License (CC BY). ABSTRACT This paper deals with the numerical study on structural performance of the cold-formed lean duplex stainless steel (LDSS) flat oval hollow columns under axial compression. The flat oval hollow section consists of two flats and two semi-circular curved faces. Finite element (FE) models were developed up using the ABAQUS software and validated against the experimental results reported in the literature. Developed FE models included material, geometric nonlinearities as well as initial geometric imperfections. A comprehensive parametric study has been carried out by covering a wide range of slenderness with different cross section geometries for the considered flat oval hollow columns. Column resistances obtained from the numerical parametric study were compared with the current American specifications, AS/NZS standard, EC 3 code and Direct Strength Method (DSM) guidelines when applied for cold-formed lean duplex stainless steel columns. Reliability analysis was carried out to assess the reliability of the existing and proposed design rules for the lean duplex stainless steel flat oval hollow columns. KEYWORDS: Direct Strength Method; Flat oval hollow columns, Lean duplex stainless steel; Local-flexural buckling; Numerical modelling; INTRODUCTION The familiar range of tubular members currently comprises square, rectangular, and circular hollow sections. The recently introduced structurally efficient section is flat oval hollow section. The low nickel stainless steel alloy such as Lean Duplex Stainless Steel (LDSS) such as grade EN in particular, is popular in recent years and it has increased strength compared to conventional austenitic and ferritic stainless steels. Gardner et. al [1-2] studied the structural performance of hot-rolled structural steel elliptical hollow sections. Ashraf et al. [3] reported the finite element modelling of different types of cross sections made up of stainless steel. Gardner and Ashraf [4] developed two stage material model for stainless steel. Gardner and Chan [5] developed cross section limits for the elliptical hollow sections. Silvestre [6] developed Generalised Beam Theory (GBT) formulations for elastic buckling behaviour of elliptical cylindrical shells and tubes under compression and validated the results by shell finite element analyses. Becque et al. [7] proposed modifications to the direct strength method for stainless steel compression members. Based on the numerical and experimental study, Theofanous and Gardner [8] proposed new design method for LDSS hollow section columns. Theofanous et al. [9] performed experimental and numerical study on cold-formed stainless steel oval hollow sections (OHS), and proposed a class 3 limit for stainless steel OHS in compression and a suitable buckling curve for OHS columns. Chan and Gardner [10] conducted tests on hot-finished steel elliptical hollow sections, followed ToCite ThisArticle: M. Anbarasu., Structural performance of cold-formed lean duplex stainless steel flat oval hollow columns. Advances in Natural and Applied Sciences. 11(8); Pages:

2 203 M. Anbarasu., 2017/Advances in Natural and Applied Sciences. 11(8) June 2017, Pages: by numerical parametric study, finally proposed design rules for the member buckling resistance of elliptical hollow section columns. Huang and Young [11-13] performed experiments on LDSS hollow stub columns, followed by wide range of numerical parametric study to propose design modifications to AS/NZ , EC3 and Direct Strength Method for LDSS hollow columns. Zhu and Young [14-15] conducted tests on coldformed steel oval hollow section columns, then the experimental and numerical parametric column strengths are compared with the design strengths calculated using the current North American, Australian/New Zealand, European specifications and DSM for cold-formed steel structures, also evaluated the design rules by reliability analysis. Patton and Singh [16] numerically examined the effect of different cross sections (Square, L-, T-,and +-shaped cross sections) effect on ultimate strength of LDSS compression members. Sachidananda and Singh [17] numerically investigates the effect of cross-section thickness, flat length and curvature of end parts, on the compression resistance of the fixed ended LDSS (Lean Duplex Stainless Steel) flat oval stub columns also compared the results with current design specifications. Anbarasu and Ashraf [18] developed DSM formulation for cold-formed lean duplex stainless steel lipped channel columns, especially failed in local and global buckling. Anbarasu and Ashraf [19] proposed modifications to AS/NZ specifications, European Specifications and DSM specifications for cold-formed lean duplex stainless steel hollow columns subjected to local-flexural buckling interaction. This paper presents investigation on the behaviour and strength of flat oval hollow section columns based on analytical and numerical studies. A finite element model is established with geometric and material nonlinearities and verified against the test results carried out by Zhu and Young [14]. Parametric study was performed to investigate the effect of cross section geometries and member slenderness on the behavior flat oval hollow columns. The results obtained from the finite element analysis were compared with design strengths calculated using the American specifications (ASCE 8-02)[20], Australian/ New Zealand Standard (AS/NZS 4673)[21], European Specifications (EN [22]) and North American Specification direct strength method (AISI S )[23] for cold-formed steel structures. The main focus of the work is to assess the suitability of current codal provisions for the compression resistance of LDSS flat oval hollow columns. 1. Finite Element Modelling: Numerical modelling was performed using the non-linear finite element (FE) analysis program, ABAQUS version 6.10 [24] to predict the ultimate compression resistance and failure modes to simulate the behaviour of cold-formed flat oval hollow columns test results published in [14]. The elements chosen for the FE models were four-noded, reduced integration shell elements with six degrees of freedom per node in the ABAQUS element library. This element has performed well in similar applications involving the modelling of LDSS members [8]&[19]). Convergence studies were conducted to decide the appropriate mesh size of 5mm x 5mm with the aim of minimum computational effort by performing elastic eigen value buckling analysis. The Gardner-Ashraf material model [4] as shown in Eqn. 1 was used in the current study to investigate the behaviour of LDSS flat oval hollow columns. ε = σ ( σ n ) σ σ E 0 σ ε = σ σ 0.2 E (ε t1.0 ε t0.2 σ 1.0 σ 0.2 E 0.2 ) ( σ σ 0.2 σ 1.0 σ 0.2 ) n 0.2,1.0 + εt0.2 σ 0.2 σ σ u (1) Where, σ and ε are engineering stress and strain, respectively. E0 is the initial tangent modulus, σ0.2 and σ1.0 are the 0.2% and 1.0% proof stress respectively, σ1.0 is the ultimate tensile strength, n and n 0.2,1.0 are strain hardening exponents for the compound Ramberg-Osgood model, εt1.0 and εt0.2 are the total strain corresponding to σ1.0 and σ0.2 respectively. Reference points (RP1 and RP2) were created at the geometric centroid of the section at both the ends of the column. The column ends were constrained through multi point constraint (MPC) available in ABAQUS [24]. The fixed-ended boundary condition was simulated by arresting all degrees of freedom at unloaded end. At the loaded end, Except for the vertical translation, all degrees of freedom were restrained. This MPC acted as a rigid surface that was rigidly connected to the upper and lower ends of the column (Fig. 1). The displacement control loading method was used in FE models, which is identical to that used in the column tests. Fig.1 illustrates the application of load and boundary condition in the columns.

3 204 M. Anbarasu., 2017/Advances in Natural and Applied Sciences. 11(8) June 2017, Pages: Fig. 1: Loading and Boundary condition The local geometric imperfection of magnitude of 10% of plate thickness was used in the FE analysis as proposed by Chan and Gardner [10]. The overall geometric imperfections value of L/1500 was also used in the model where L is the specimen length, as suggested in [8]. Both local and global initial geometric imperfections in the form of the lowest elastic and local and global buckling modes were incorporated into the models to initiate the nonlinear analysis. Two types of analysis were performed for each model; linear elastic eigen buckling analysis were initially carried out to determine buckling mode shapes, which were subsequently incorporated in model to incorporate the geometric imperfections. The modified Riks method was employed for the non-linear analyses, which enabled the post ultimate behaviour to be traced. Validation: A result of the experimental investigation by Zhu and Young [14] on cold-formed steel oval hollow section A-series has been used to verify the developed FE modelling approach in this study. The tested specimen dimensions of the oval hollow section models are shown in Table 1. Fig. 2: Typical flat oval hollow column Table 1: Tested column dimensions (Zhu and Young [14]) SPECIMEN Length (L) (mm) Depth (D) (mm) Width (W) (mm) Thickness (t) (mm) A A360# A A A1200# A A A B

4 Axis Load (kn) 205 M. Anbarasu., 2017/Advances in Natural and Applied Sciences. 11(8) June 2017, Pages: Table 2: Material Properties (Zhu and Young [14]) Coupon E (Gpa) σ 0.2 (MPa) σ u (MPa) A (flat) A(curved) B (flat) B(curved) Table 2 shows the material properties of the sections considered for the validation. The comparison of FE results with the test results for the oval hollow columns are shown and compared in Table 3. The mean ratio of the ultimate resistance from the finite element model and experiment was with a standard deviation of Table 3: Comparison of Experimental and FEA Ultimate Load Specimen ID P EXP (kn) P FEA (kn) P EXP/ P FEA A A360# A A A1200# A A A B Mean Std. Dev Fig. 3 shows the comparison of the load vs end shortening curve for the test and FE analysis for the specimen A360. Based on the comparison of results, a reasonable agreement has been achieved End Shortening (mm) Fig. 3: Comparison of Test and FE Load vs end shortening curve for the specimen A360 Comparison of failure mode predicted by FE modelling with the experimental one for the specimen B1200 is shown in Fig. 4. TEST FEA

5 206 M. Anbarasu., 2017/Advances in Natural and Applied Sciences. 11(8) June 2017, Pages: Fig. 4: Comparison of failure modes from the Test with FE modelling for B1200 From the comparison of test results, it was found to be satisfactory with the numerical models able to successfully predict the ultimate resistance, load-end shortening response, and failure modes observed in the tests. 4. Parametric Study: The parametric study included 120 specimens that consisted of 24 series, as shown in Table 4. The specimens were labeled such that the specimen dimensions could be easily identified, as shown in Table 3 & 4. For example, the label 150X75X1.5 defines the OHS with cross-section dimension of 150mm as overall depth (D), 75mm as overall width (W) and 1.5mm as thickness (t) of the section, respectively. The column lengths varying from m, which provided a range of cross-sectional slenderness values (λs ~ from 0.64 to 3.54), five overall slenderness values (λ0 = 0.25, 0.75, 1.25, 1.75 and 2.25) for thicknesses of 1.5 mm, 2.5mm and 4.0 mm, were analysed in the FE parametric studies of flat oval hollow columns. In order to reduce the computational time, half of the section was modelled for longer specimens and suitable symmetry boundary conditions were applied at the centre. Table 3: Section dimensions and critical buckling stress Section Dimensions (mm) Critical Buckling Sl.No. Specimen ID λ s Depth Width Thickness Area (mm 2 Stress ) (D) (w) (t) (N/mm 2 ) σ cr X75X X75X X75X X50X X50X X50X X37.5X X37.5X X37.5X X30X X30X X30X

6 207 M. Anbarasu., 2017/Advances in Natural and Applied Sciences. 11(8) June 2017, Pages: x125x x125x x125x x83.33x x83.33x x83.33x x62.5x x62.5x x62.5x x50x x50x x50x The overall slenderness λ 0 of a stainless steel column is commonly defined as: 0 = σ 0.2% /σ E = ( Le ) σ r 0.2%/π 2 E 0 (2) Where, σ 0.2% = 0.2% proof stress, L e = Effective length of the column, r = radius of gyration, E 0 = initial modulus. The cross-sectional slenderness λs is defined as: s = σ 0.2% /σ cr (3) In the parametric study, theoretical and numerical analysis was carried out for the selected cross-sections for the 0.2% proof stress value of the flat and curved portion, shown in Table 5 [8] is used in deriving stress strain of LDSS material. Table 5: Material properties for parametric study (Theofanous and Gardner [8]) Specimen ID 100x100x4 E (N/mm 2 ) σ 0.2 (N/mm 2 ) σ 1.0 (N/mm 2 ) σ u (N/mm 2 ) Compound R-O Coefficients n n' Flat Corner The unfactored design strengths (nominal strengths) were calculated using the ASCE 8-02 [20], Australian/New Zealand Standard (AS/NZS) [21] for cold-formed stainless steel structures, European Code (EC3) [22]: Design of steel structures Part 1.4: General rules Supplementary rules for stainless steels and Direct Strength Method (AISI-S100:2007) [23] for cold-formed steel structures. Table 6 compares the FE analysis results with the results obtained from current ASCE 8-02, AS/NZS, EC3 and DSM codal provisions, for LDSS flat oval hollow columns. Table 6: Comparison of Results Specimen ID λ 0 P FEA P FEA / P FEA / (kn) P ASCE P AS/NZ P FEA/ P EN P FEA / P DSM X75X x75x x75x x50x x50x x50x

7 208 M. Anbarasu., 2017/Advances in Natural and Applied Sciences. 11(8) June 2017, Pages: x37.5x x37.5x x37.5x4 150x30x x30x x30x4 250x125x x125x x125x4 250x83.33x x83.33x x83.33x4 250x62.5x x62.5x

8 209 M. Anbarasu., 2017/Advances in Natural and Applied Sciences. 11(8) June 2017, Pages: x62.5x4 250x50x x50x x50x Mean Std. Dev Capacity reduction factor (φ) Reliability index ( 0) The specimens of short in length mainly failed in local buckling. The long column specimens are failed in minor axis flexural buckling and the intermediate length specimens failed in combined local and flexurl buckling as expected and the deformed shape from finite element analysis for the 150x75x1.5 and 150x75x2.5 series are shown in Fig. 5. The reliability of the current design rules for cold-formed-steel columns was evaluated by using reliability analysis. Reliability analysis is detailed in the commentary on the North American specification [23] for the design of cold-formed-steel structural members and described in [15]. The load combinations with resistance factors (ϕ) of for concentrically loaded compression members were used in calculating the reliability index β0 for ASCE, AS/NZS, EC3 and DSM are as described by authors in [27-28]. (a) For 150x75x1.5 (b)for 150x75x2.5 Fig. 5: Deformation shapes

9 210 M. Anbarasu., 2017/Advances in Natural and Applied Sciences. 11(8) June 2017, Pages: Fig. 6 shows the load vs axial shortening curves for 150x75x1.5 series. Fig. 6: Load Vs Axial shortening response of 150x75x1.5 series The design strengths predicted by ASCE 8-02 is unconservative and unsafe, with the load ratios P FEA/P ASCE, and the corresponding standard deviation of The AS/NZS, EC3 Code and DSM specifications are generally conservative and safe, with the load ratios P FEA/P AS/NZ, P FEA/P EN and P FEA/P DSM of 1.074, and and the corresponding standard deviation of 0.167, and respectively. The ASCE 8-02, AS/NZS and EC3 Code provides unreliable predictions. But the DSM provides reliable predictions. Conclusion: The paper studied the structural response of fixed ended cold-formed lean duplex stainless steel flat oval hollow columns. Finite element models were developed and compared well with experimental results available in the literature. Parametric studies were sub sequentially performed to assess the structural response of flat oval hollow columns over a wide range of geometries and member slenderness. A total of 120 results were generated numerically. With the aid of the numerically derived results, the column buckling curves used in the specifications ASCE 8-02 [19], AS/NZ-4673 [20], Euro code -3 [21] and Direct Strength Method [22] were examined. The design strengths predicted by the ASCE 8-02 Specification were unconservative. The design strength predicted by the Australian/New Zealand specification, European Specification and current North American specification (DSM) is conservative and safer side. The current DSM design rules are shown to provide reliable predictions for cold-formed lean duplex stainless steel oval hollow section columns. Considering the accuracy and reliability, it is recommended that the column design rules in the current North American specifications (DSM) for cold-formed steel structures can be used for flat oval hollow sections. There is no acknowledgment. ACKNOWLEDGMENTS REFERENCES 1. Gardner, L., Structural behaviour of oval hollow sections. International Journal of Advanced Steel Construction., 1(2): Gardner, L and A. Ministro, Structural steel oval hollow sections. Structural Engineer, 83(21): Ashraf, M., L. Gardner and D.A. Nethercot, 2006 Finite element modelling of structural stainless steel cross-sections. Thin-Walled Structures, 44(10): Gardner, L. and M. Ashraf, Structural design for non-linear metallic materials, Engineering Structures, 28: Gardner, L. and T.M. Chan, Cross-section classification of elliptical hollow sections. Steel Composite Structures, 7(3): Silvestre, N., Buckling behaviour of elliptical cylindrical shells and tubes under compression, International Journal of Solids and Structures, 45: Becque, J., M. Lecce and K.J.R. Rasmussen, The direct strength method for stainless steel compression members, Journal of Constructional Steel Research, 64: Theofanous, M. and L. Gardner, Testing and numerical modelling of lean duplex stainless steel hollow section columns, Engineering Structures, 31(12): Theofanous, M., T.M. Chan and L. Gardner, Structural response of stainless steel oval hollow section compression members. Engineering Structures, 31(4):

10 211 M. Anbarasu., 2017/Advances in Natural and Applied Sciences. 11(8) June 2017, Pages: Chan, T.M. and L. Gardner, Flexural buckling of elliptical hollow section columns. Journal of Structural Engineering, 135(5): Huang, Y., and B. Young, Material properties of cold-formed lean duplex stainless steel sections, Thin-Walled Structures, 54: Huang, Y., B. Young, Structural performance of cold-formed lean duplex stainless steel columns, Thin-Walled Structures, 83: Huang, Y., and B. Young, Tests of pin-ended cold-formed lean duplex stainless steel columns, Journal of constructional steel research, 83: Zhu, J.H., B. Young, Cold-formed-steel oval hollow sections under axial compression. Journal of Structural Engineering ASCE 137(7): Zhu, J.H., B. Young, Design of cold-formed steel oval hollow section columns. Journal of constructional steel research, 71: Patton, M.L., and K.D. Singh, Numerical modelling of lean duplex stainless steel hollow columns of square, L-,T-,and +-shaped cross sections under pure axial compression, Thin-Walled Structures, 53: Sachidananda, K., K.D. Singh, Numerical study of fixed ended lean duplex stainless steel (LDSS) flat oval hollow stub column under pure axial compression, Thin-Walled Structures, 96: Anbarasu, M., and M. Ashraf, Behaviour and design of cold-formed lean duplex stainless steel lipped channel columns, Thin-Walled Structures, 104: Anbarasu, M., and M. Ashraf, Interaction of local-flexural buckling for cold-formed lean duplex stainless steel hollow columns, Thin-Walled Structures, 112: ASCE Specification for the design of cold-formed stainless steel structural members. SEI/ASCE8-02; Reston, VA: American Society of Civil Engineers. 21. AS/NZS Cold-formed stainless steel structures. Australian/New Zealand Standard, AS/NZS 4673:2001. Sydney, Australia: Standards Australia. 22. EC Design of steel structures Part 1.4: General rules Supplementary rules for stainless steels. European Committee for Standardization, EN , Brussels. 23. American Iron and Steel Institute (AISI), North American Specification (NAS) for the Design of Cold-Formed Steel Structural Members, Washington DC. 24. ABAQUS, Standard User's Manual. Dassault Systemes Simulia Corporation, Version 6.11, USA. 25. Schafer, B.W., CUFSM3.12, elastic buckling analysis of thin-walled members by finite strip analysis EN Stainless steels part 4: Technical delivery conditions for sheet/ plate and strip of corrosion resisting steels for general purposes. CEN. 27. Anbarasu, M. and G. Murugapandian, Experimental study on distortional-global buckling mode interaction on thin-walled lipped channel. Materials and Structures, 49(4): Anbarasu, M., Local-distortional buckling interaction on cold-formed steel lipped channel beams, Thin-Walled Structures, 98: