AXIAL BEHAVIOR OF STAINLESS STEEL SQUARE THIN-WALLED TUBES STIFFENED INTERNALLY

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1 International Journal of Civil Engineering and Technology (IJCIET) Volume 6, Issue 11, Nov 2015, pp , Article ID: IJCIET_06_11_006 Available online at ISSN Print: and ISSN Online: IAEME Publication AXIAL BEHAVIOR OF STAINLESS STEEL SQUARE THIN-WALLED TUBES STIFFENED INTERNALLY Mona M. Fawzy Assistant Professor, Department of Civil Engineering Higher Institute of Engineering, Shorouk City, Cairo, Egypt ABSTRACT Two different schemes called ties and longitudinal stiffeners were proposed for improving the performance of stainless steel square thin walled tubes. An analytical study using finite element models loaded axially has been conducted. Both geometric and material nonlinearities were considered. Those models were verified against the results obtained from previous researches. The analytical study compared between unstiffened, ties stiffened and longitudinally stiffened stainless steel square thin walled tubes. The studied parameters were square thin walled tube width-to-thickness ratio (W/t) and the axial spacing of stiffening along the length. It was observed that the axial load strength can be enhanced by proposed ties stiffening schemes. Key words: Stainless Steel, Square Thin Walled Tubes, Ultimate Strength, Finite Element Analysis, Ties, Longitudinal Stiffeners Cite this Article: Mona M. Fawzy. Axial Behavior of Stainless Steel Square Thin-Walled Tubes Stiffened Internally. International Journal of Civil Engineering and Technology, 6(11), 2015, pp INTRODUCTION The excellent properties of the tubular shapes have been recognized for a long time which led to wide use of concrete filled hollow tubes. Many researches showed that filling hollow tubes with concrete decreased the local buckling and increased ultimate strength. Another scheme that decreased the local buckling of tubular shapes is stiffening the tubes internally. This procedure is preferred especially for square hollow tube because many studies have shown that the performance of square hollow tube is not as good as its circular counterpart regarding the local buckling of the tube. This fact has now been widely reflected in modern design codes in which the allowable width-to-thickness ratio (W/t) for the tubes with square cross-section is more restricted than that for circular one. Such stiffening modifications will consequently encourage the use of square hollow tubes in construction. Two 45 editor@iaeme.com

2 Mona M. Fawzy stiffening measures have been suggested for enhancing the behaviors of those tubes. One is to weld longitudinal stainless steel ties on the internal surface of a tube, while the other one is to use internal longitudinal stiffeners as shown in Figs. (1) and (2) respectively. The author did not find any researches on stiffened stainless steel square hollow tubes (SSSHTs), meanwhile plenty of researches were conducted on unstiffened stainless steel hollow cross-sections or stiffened concrete filled steel hollow tubes. Gee-Yu Liu et al. [1] experimentally studied the effectiveness of using ties internally on the behavior of square concrete filled steel hollow columns under both axial load and bending. It was found that the axial load strength increased because the ties contribute in the strength. Also, the spacing instead of dimensions of the ties is the dominant factor to the behavior. Zhong Tao et al. [2] proposed another alternative for improving the performance of square concrete filled steel hollow columns with thinwalled tubes. In his research, longitudinal stiffeners for the steel tubes were used. The limit of W/t for the sub-panels and dimensions requirement for the stiffeners was discussed experimentally. The results showed that AISC [3] and EN [4] gave a member capacity about 40% and 36% lower than the results obtained in the tests. Compression strength of unstiffened stainless steel hollow cross-sections was discussed by M. Ashraf et al. [5]. Sophisticated numerical models have been developed in order to use the material stress strain behavior to obtain the local buckling stress for the open section stub columns. Several relevant researches were conducted discussing the behavior of composite concrete filled hollow sections without internal stiffeners [6-7]. That led to a new design method for stainless steel structures which uses a common technique to determine the compressive strength for all types of cross-sections without the need for traditional section classification. This paper discusses stiffening measures for the SSSHTs that are manufactured of duplex stainless steel material. Duplex stainless steel combines well the advantages of both austenitic and carbon steel materials. The duplex grades have higher strength than austenitic in addition to superior corrosion resistance. High nickel prices led to a demand for lean duplexes with low nickel content, such as grade EN [8]. Therefore a parametric study is conducted considering W/t and the axial spacing of stiffening either by ties or by longitudinal stiffeners. Figure 1 Square hollow tube stiffened with ties Figure 2 Square hollow tube stiffened with longitudinal stiffeners 2. FINITE ELEMENT MODEL AND VERIFICATION 2.1. General To conduct a parametric study, the full three dimensional (3D) simulation using ANSYS [9] software was performed. The SSSHTs, end plates and stiffeners were simulated by using four-node quadrilateral shell element SHELL181. Membrane and bending capabilities along with six degrees of freedom at each node: three translations 46 editor@iaeme.com

3 Axial Behavior of Stainless Steel Square Thin-Walled Tubes Stiffened Internally and three rotations were observed in this shell element. The model was divided into elements with aspect ratio one as shown in Fig. (3). Non-linear static analysis was carried out considering both geometric i.e. an initial geometrical imperfection of (L/1000) and material nonlinearities. The results were accurately estimated by incremental steps until failure occurs. Solution technique was the arc length method. Figure 3 Finite element mesh of SSSHTs 2.2. Boundary conditions and load application Axially concentric load was applied at the surface of the upper end plate. The end plates of the SSSHTs were restrained. One end was modelled with all three translation degrees of freedom restrained as well as the rotational degree of freedom. The other end was modelled with two translation degrees of freedom restrained except for the longitudinal direction of steel beam, and also restraining the rotational degree of freedom Stainless steel modelling A minimum % proof stresses (σ) of 530 MPa and an ultimate tensile strength (σu) ranging from MPa were the strengths of cold-formed lean duplex stainless steel Grade EN [8] that was used. Von Mises material with isotropic hardening was modeled. Stress and strain nonlinearity for stainless steel was generally represented by the Ramberg Osgood [10] equation as given below ɛ = σ ( E ο σ ) n σ ο In Eq. (1), the nonlinearity index (n) indicated of the nonlinearity of the stress strain behavior, with lower n values indicated a greater degree of nonlinearity. Different grades of stainless steel had different degrees of nonlinearity. Increasing n converged the material behavior to the elasto-plastic behavior of carbon steel (elasticperfectly plastic behavior for n = ), meanwhile decreasing n values caused higher hardening behavior. Eq. (1) gave good agreement with experimental stress strain data up to the σ only. For this purpose, Rasmussen [10] proposed the use of an expression for the complete stress strain curve for stainless steel alloys. Eq. (2) involved the conventional Ramberg Osgood parameters (n, E0, σ) as well as the σu and strain (ɛu). Good agreement between stress strain curves with tests over the full range of strains up to the ultimate tensile strain was observed. Consequently, Eq. (2) was used in the current investigation to generate the stress strain curve of the lean duplex stainless steel material Grade EN , as presented in Fig. (4). (1) 47 editor@iaeme.com

4 Mona M. Fawzy ɛ = σ σ 0.002( ) n E0 σ σ - σ - u ( E σu - ) m for σ σ for σ σ (2) In the equations, E0 was the initial modulus of elasticity (e.g. 200 GPa), E represented the tangent modulus of the stress strain curve at the % proof stress and given as E 0 E = (3) n/e Where, e was the non-dimensional proof stress given as e = σ/e0. Multilinear stress strain curve was used in ANSYS. Elastic behavior represented in the first part of the multilinear curve up to the proportional limit stress with measured Young s modulus E0 = 200 GPa, and Poisson s ratio was taken as 0.3. The proportional limit was found to be σ0.01= 300 MPa. Figure 4 Lean duplex stainless steel stress strain curve [8] 2.4. Finite element model verification The main aim of this section is to check the accuracy of the results obtained using the proposed finite element model. Gardner et. al., [11] prepared several experimental tests on square, rectangular and circular hollow tubes that were made of stainless steel material Grade EN The tests showed the relationship between cross section slenderness and cross section deformation capacity. Rectangular hollow tubes axially loaded were tested experimentally and their ultimate loads were compared with the ANSYS models as shown in table (1). The table showed tube cross section dimensions, the corresponding wall thickness and tube lengths all in millimeters In addition to that E 0 and σ were included in the table. The end conditions of the tubes were pinned. The verified results demonstrate that the used finite element model is proper to the nonlinear analysis which gives an opportunity to use it in a wide parametric study editor@iaeme.com

5 Axial Behavior of Stainless Steel Square Thin-Walled Tubes Stiffened Internally Specimen (mm) Thickness (mm) Table 1 Test versus ANSYS Length (mm) E 0 (GPa) σ Test (kn) ANSYS (kn) (MPa) 60X X X X X X X Mean 1.01 Standard deviation 0.07 Test/ANSYS 3. PARAMETRIC STUDY A parametric study is conducted using the proposed finite element model, where the first parameter is the presence of a SSSHT stiffener either ties or longitudinal internal stiffeners. Second parameter is W/t of SSSHT and finally, the third parameter is the axial spacing of stiffening along the length. The dimensions of stiffeners are not included in the parameters because according to previous researches the spacing instead of dimensions of the stiffeners is the dominant factor to the behavior. To highlight the effect of stiffener on the behavior of the SSSHTs, each case involving presence of stiffener is compared with another without a stiffener (unstiffened). The width of the SSSHT is constant and equals to 400 mm, while the thickness changes and ranges from 4 mm to 20 mm. Therefore the studied W/t ranges from 20 to 100. All sections can be classified as class 4 according to EN The height of the SSSHTs (L) is constant and equals to 1500 mm. Three different axial spacing of stiffening are studied. They are expressed as factor of L i.e. L/2, L/4 and L/8. Stiffeners dimensions are shown in Figs. (1) and (2). The thickness of the stiffeners tst is taken a minimum value of 4 mm, while the width bst is 50 mm. The lengths of both ties and longitudinal stiffeners Lst are 140 mm. The results of the parametric study obtained using the proposed finite element model are represented in the form of tables and curves. The axial loads achieved using the finite element model PFEM are normalized against the ultimate loads Pu which are obtained when ultimate stress σu is multiplied by corresponding gross unstiffened cross section area. 4. RESULTS AND DISCUSSIONS The results of the parametric study are shown in this section. Table (2) contains the results of the parametric study where the effect of using either ties or longitudinal stiffeners is demonstrated. The table demonstrates different values of W/t and their corresponding PFEM/PU values discussing three different cases: unstiffened SSSHT columns stiffened using ties and finally, stiffened using longitudinal stiffeners Deformed shape The deformed shape of unstiffened SSSHT columns is shown in Fig. (5) where failure occurs in the column wall. When the SSSHTs are stiffened using the different stiffening schemes, failure occurs in column wall. The deformed shape of SSSHTs 400x20 using ties every L/4 is shown in Fig. (6), where there is increase in the 49 editor@iaeme.com

6 Mona M. Fawzy movement of the column wall. The deformed shape of SSSHTs 400x20 using longitudinal stiffeners at L/4 is shown in Fig. (7), the outward movement of the column wall is decreased by up to 3 times. Table 2 Parametric study results SSSHT (mm) 400 x 400 Thickn ess (mm) W/t Unstiffen ed P FEM /P U Ties every L/2 Ties every L/4 Ties every L/8 Long. stiffeners every L/2 Long. stiffene rs every L/4 Long. stiffene rs every L/ Figure 5 Deformed shape of unstiffened SSSHTS 400x20 Figure 6 Deformed shape of 400x20 SSSHTS stiffened using ties every L/ editor@iaeme.com

7 Axial Behavior of Stainless Steel Square Thin-Walled Tubes Stiffened Internally Figure 7 Deformed shape of 400x20 SSSHTS stiffened using longitudinal stiffeners at L/ Effect of using ties as internal stiffeners A comparison is conducted between P FEM /P U of SSSHT columns that are unstiffened and SSSHT columns that are stiffened with ties. It is clear that ties enhance the behavior of SSSHTs especially for higher W/t. Fig. (8) shows different SSSHTs with W/t from 20 to 100 when they are either unstiffened or stiffened with ties every L/2, L/4 and L/8 and their corresponding P FEM /P U. For W/t equals to 20, stiffening SSSHTs with ties every L/8 increases P FEM /P U more than the unstiffened case by up to 7% as shown in Fig. (8). Meanwhile, stiffening SSSHTs every L/8 where W/t equals to 100, improves P FEM /P U more than the unstiffened case by up to 34%. Accordingly, using ties has better effect when W/t increases. Higher W/t means smaller SSSHT wall thickness and when ties are used, redistribution of stresses between the ties and the column walls occurs Effect of using longitudinal stiffeners as internal stiffeners Stiffening SSSHTs with longitudinal stiffeners has no effect on the ultimate load of SSSHTs with W/t equals to 20, 22 and 25 when they are compared with the corresponding unstiffened cases. Unfortunately, longitudinal stiffeners decrease ultimate load of SSSHTs with W/t that ranges 29 to 100 when compared with unstiffened case by up to 7%. The worst case is SSSHTs with W/t equals to 100 because the longitudinal stiffeners buckled when P FEM /P U reaches 6 despite the stiffening position as shown in Fig. (9). It can be concluded that the orientation of these longitudinal stiffeners did not allow redistribution of stresses between them and the column wall especially in SSSHTs with W/ t equals to Effect of the axial spacing of ties along the length When the number of ties increases, P FEM /P U increases as well for all SSSHTs as shown in Fig. (8). For SSSHTs with W/t equals to 20, the presence of ties every L/2, L/4 and L/8 improves P FEM /P U more than unstiffened SSSHTs by 1%, 6% and 7% respectively as shown in Fig. (10). This Fig. shows the different values of P FEM /P U for SSSHT that corresponds to W/t equals to 20. It displays P FEM /P U for all six cases studied in this research versus W/t. The first three cases show P FEM /P U due to stiffening the SSSHT with ties while the other three cases show P FEM /P U due to stiffening the SSSHT with longitudinal stiffeners. The maximum increase in P FEM /P U more than 51 editor@iaeme.com

8 Mona M. Fawzy unstiffened SSSHTs is by 15%, 32% and 34% for W/t equal to 100 when placing ties every L/2, L/4 and L/8 respectively as shown in Fig. (11) Effect of the axial spacing of longitudinal stiffeners along the length When the number of longitudinal stiffeners increases, P FEM /P U is slightly increased for all SSSHTs as shown in Fig. (9). For SSSHTs with W/t from 20 to 67, the presence of longitudinal stiffeners every L/2, L/4 and L/8, improves P FEM /P U more than unstiffened SSSHTs up to 2%. Fig. (11) shows the same values of P FEM /P U for SSSHT with W/t equals to 100 when the SSSHT is either unstiffened or stiffened with longitudinal stiffeners every L/2, L/4 and L/8. This shows that the orientation of these longitudinal stiffeners did not allow redistribution of stresses between them and the column wall so increasing their number is not effective P FEM /P U Unstiffened L/2 L/4 L/ W/t Figure 8 P FEM /P U of SSSHTs with different W/t from 20 to 100 due to stiffening using ties at L/2, L/4 and L/ P FEM /P U W/t Unstiffened Longitudinal stiffeners every L/2 Longitudinal stiffeners every L/4 Longitudinal stiffeners every L/8 Figure 9 P FEM /P U of SSSHTs with different W/t from 20 to 100 due to stiffening using longitudinal stiffeners at L/2, L/4 and L/ editor@iaeme.com

9 Axial Behavior of Stainless Steel Square Thin-Walled Tubes Stiffened Internally P FEM /P U W/t Ties every L/2 Ties every L/4 Ties every L/8 Unstiffened every L/2 every L/4 every L/8 Figure 10 P FEM /P U of SSSHT with W/t equals to 20 due to stiffening using either ties or longitudinal stiffeners at L/2, L/4 and L/8 P FEM /P U W/t Ties every L/2 Ties every L/4 Ties every L/8 Unstiffened every L/2 every L/4 every L/8 Figure 11 P FEM /P U of SSSHT with W/t equals to 100 due to stiffening using either ties or longitudinal stiffeners at L/2, L/4 and L/8 5. CONCLUSIONS This paper discusses axial behavior of thin walled stainless steel square hollow tubes (SSSHTs) when using two stiffening schemes i.e. ties and longitudinal stiffeners. This paper aims to expand the application of lean duplex stainless steel because of the relatively low prices, higher strength than austenitic and superior corrosion resistance. According to the results of the parametric study the following observations are obtained: (1) The axial load strength of SSSHT columns can be enhanced by only one of the proposed stiffening schemes, which are ties by up to 34%. (2) The ratio between column widths to thickness (W/t) is an effective parameter as the role of internal stiffeners increases when W/t increases. (3) The orientation of the longitudinal stiffeners did not allow redistribution of stresses between them and the column wall which decreases the axial strength of SSSHTs especially with W/ t equals to 100. (4) The stiffening spacing is a dominant factor to the tie s effectiveness. (5) For SSSHTs with W/t equals to 20, the presence of ties every L/2, L/4 and L/8 improves the axial strength more than unstiffened SSSHTs by 1%, 6% and 7% respectively. Finally, the author recommends discussing stiffening scheme by using Tee sections and internal ring stiffeners editor@iaeme.com

10 Mona M. Fawzy REFERENCES [1] Gee-Yu Liu, Yeoug-Kae Yeh and Keh-Chyuan Tsai, The axial and flexural load behavior of concrete-filled steel thin walled tubes with stiffened square sections, research in support of the eurocde at JRC-ELSA. [2] Zhong Tao, Brian Uy, Zhi-Bin Wang, Analysis and design of stiffened concretefilled thin walled steel tubular columns, Thin Walled Structures, 47(12), 2009, [3] AISC, Design Guide 30: Structural stainless steel. American Institute of Steel Construction, [4] EN Eurocode 3: Design of Steel Structures, Part 1-4: General rules, Supplementary rules for stainless steel. CEN, British Standards Institute (BSI) (1994), Design of Composite Steel and Concrete Structures, Eurocode 4, ENV , London. [5] M. Ashraf, L. Gardner, D. A. Nethercot, Compression strength of stainless steel cross sections, Journal of Constructional Steel Research, 62, 2006, [6] Vipulkumar Ishvarbhai Patel, ME, Nonlinear inelastic analysis of concrete-filled steel tubular slender beam-columns, PHD, College of Engineering and Science, Victoria University, Australia, [7] Athar Nihal, N.S Kumar, Experimental investigation on monotonic behavior of circular steel stiffened composite column under compression, International Journal of Research in Engineering and Technology, 4 (04), May [8] M.F. Hassanein, Finite element investigation of shear failure of lean duplex stainless steel plate girders, Thin-Walled Structures 49, 2011, [9] ANSYS, Finite element program, Swanson Analysis System, Inc., Release. 12: 1. [10] Rasmussen KJR. Full range stress strain curves for stainless steel alloys. Journal of Constructional Steel Research, 59, 2003, [11] L. Gardner, D. A. Nethercot, Experiments on stainless steel hollow sections-part 1: Material and cross sectional behavior, Journal of Constructional Steel Research, 60, 2003, [12] S. Lincy Rubina, S. Vishnuvardhan, G. Raghava and A. Sivakumar. Fatigue Life Estimation of Type 304ln Stainless Steel under Strain-Controlled Cyclic Loading. International Journal of Civil Engineering and Technology, 5(3), 2014, pp [13] Karim M Pathan. Finite Element Analysis of M High Roller Compacted Concrete (RCC) Gravity Dam - Special Emphasis on Dynamic Analysis. International Journal of Civil Engineering and Technology, 3(2), 2012, pp editor@iaeme.com