Elsevier

Engineering Structures

Volume 172, 1 October 2018, Pages 850-868
Engineering Structures

Design rules for stainless steel welded I-columns based on experimental and numerical studies

https://doi.org/10.1016/j.engstruct.2018.06.080Get rights and content

Highlights

  • Behaviour of stainless steel welded columns was studied using tests and FE modelling.

  • Material properties, residual stresses and geometric imperfections were measured.

  • Test on welded I section stub and long columns were performed.

  • Effects of cross-section geometry and material nonlinearity were thoroughly studied.

  • Imperfection parameter of Perry curve was modified to suit welded I-sections.

Abstract

Stainless steel is characterised by its nonlinear stress-strain behaviour with significant strain hardening, although current design codes treat it as an elastic, perfectly plastic material like carbon steel. The continuous strength method (CSM) is a newly developed strain based design approach which was proposed for nonlinear metallic materials. With recent developments, CSM can be used to predict the cross-section resistance for stocky and slender sections, and CSM design rules have recently been proposed for predicting the buckling resistance of cold-formed RHS and SHS columns. Welded sections, however, could behave differently from cold-formed sections due to the presence of residual stresses. Despite offering more economic options in many design cases, research on stainless steel welded sections is very limited to date. In this study, the behaviour of stainless steel welded I-sections was investigated through a test program, and the investigation was complemented by finite element (FE) modelling. The test program covered tensile coupon tests, residual stress and initial geometric imperfection measurements, stub column tests and flexural buckling tests of pin-ended long columns. FE models were developed for both major and minor axis buckling based on test results, and the verified FE modelling technique was used to investigate the effects of cross-section slenderness λp, section height-to-width ratio H/Band the ratio of flange thickness-to-web thickness tf/tw on column curves of welded I-sections. Buckling formulas for welded I-columns were eventually proposed following the same philosophy recently adopted by the authors for cold-formed hollow section columns. The imperfection parameter was recalibrated appropriately to incorporate special features of welded I-sections. Two sets of equations were proposed to tackle the observed variation in buckling behaviour against major and minor axis buckling. Buckling resistance predictions obtained from the proposed method were deemed reliable showing good accuracy and consistency with test and FE results.

Introduction

Welded sections are often used to meet the high load bearing capacity required for buildings and bridges as this type of sections can be fabricated to meet the exact design requirements, and may yield more economic design solution for a structure. During the last decade, research on structural stainless steel was mainly focused on cold-formed sections due largely to their easy availability. Limited number of studies were conducted on welded sections, and very few design codes [1], [2] have design guidelines for welded sections. In recent years, a number of research projects were reported on stainless steel welded sections. Kuwamura [3], Saliba and Gardner [4] and Yuan et al. [5] studied the local buckling behaviour of stainless steel welded I-sections. Real et al. [6], Saliba and Gardner [7], Hassanein [8] and Fortan et al. [9] studied the shear response of stainless steel plate girders. Wang et al. [10] and Yang et al. [11] investigated the lateral torsional buckling of stainless steel welded I-section beams. Yuan et al. [12] measured the residual stresses of welded box sections and I-sections, and observed that the magnitudes and the distribution of longitudinal residual stresses of stainless steel welded sections were different from those observed in carbon steel welded sections. They also proposed a model for residual stress distribution in stainless steel welded sections. Investigation on the compression resistance of stainless steel welded sections is scarce. Recently, Yuan et al. [13] studied the local-overall interactive buckling of welded box sections by testing eight specimens. Yuan et al. [14] also tested welded I-section columns produced from austenitic and duplex grades of stainless steel to study a similar behaviour. They also performed numerical analysis, and observed that residual stresses significantly affect the buckling resistance of welded I-section columns. Yang et al. [15] tested stainless steel welded I-section columns for flexural buckling, and showed that EN 1993-1-4 [1] and AS/NZS 4673 [16] predictions were conservative for predicting the buckling resistance of stainless steel welded I-columns, and ASCE 8-02 [17] predictions were very scattered. It should, however, be noted that AS/NZS 4673 and ASCE 8-02 design rules are proposed for cold-formed stainless steel structures. Recently, Gardner et al. [18] investigated the behaviour of laser welded stainless steel columns for local buckling and flexural buckling, and observed that the carrying capacity of laser welded sections were higher than the conventionally welded sections due to lower residual stress magnitudes. It is evident that there is significant lack of test data for appropriate understanding of the behaviour of stainless steel welded sections, and current design standards produce conservative or erroneous predictions for the buckling resistance of welded sections. This paper aims to fill up the knowledge gaps through an experimental program, and proposes design formulations for stainless steel welded I-section columns based on comprehensive numerical analysis.

Current design codes [1], [16], [17] treat stainless steel like carbon steel ignoring its nonlinear behaviour and, hence, its strain hardening benefits are not fully exploited. For nonlinear metallic materials like stainless steel, a new design technique named the Continuous Strength Method (CSM) [19], [20] was proposed. CSM is a strain based design method that incorporates material nonlinearity, exploits strain hardening and incorporates element interactions in predicting resistances at the cross-section level. With the recent development of CSM [21], [22], cross-section capacity for both stocky and slender cross-sections can be predicted through simple formulas using a bilinear material model and without calculating effective cross-sectional properties. Therefore, there is a clear scope for using CSM philosophies for predicting the buckling resistance of columns.

The buckling resistance of stainless steel columns are normally calculated following two different approaches: tangential stiffness method and Perry formulas. SEI/ASCE8-02 [17] and AS/NZS 4673 [16] codes use the tangential stiffness method, which recognises material nonlinearity through an iterative process to calculate the instantaneous tangent modulus but does not consider geometric imperfections of the member. This method is not applicable for welded sections as there is no provision of considering residual stresses for welded sections. On the other hand, Eurocode [1] follows Perry curves, which is a direct method specifying separate curves for different types of cross-sections based on an imperfection parameter but the technique does not incorporate material nonlinearity. Through numerical analysis, Rasmussen and Rondal [23] showed that different column curves are necessary to predict the buckling resistance of different grades of stainless steel as their nonlinearity varies significantly between grades. Hradil et al. [24] tried to include the material nonlinearity in Perry curves by defining transformed slenderness but their suggested procedure uses tangent modulus, which is iterative. Shu et al. [25] proposed two base curves and some complicated transfer formulas for hollow sections which could be used to develop multiple curves from two base curves to cover different grades of stainless steel. All of the aforementioned methods use effective areas for slender cross-sections. Huang and Young [26] proposed a method using full cross section area with material properties taken from stub column tests to predict the column capacity. Recently Ahmed and Ashraf [27] proposed new buckling formulas for predicting the buckling capacity of cold-formed stainless steel RHS and SHS columns following CSM. This proposal successfully incorporated all the characteristics of stainless steel through simple equations. However, the behaviour of welded sections is different from cold-formed sections due to the presence of residual stresses [13], [14], [15]. Further investigations are required to investigate the suitability of the proposed CSM based technique for stainless steel welded sections.

In this study, the structural behaviour of stainless steel welded I-columns are investigated through a comprehensive test program as well as FE analysis. The test program included material test, initial geometric imperfection and residual stress measurements, stub column tests and flexural buckling tests on austenitic grade stainless steel welded I-sections. Based on the results obtained from this test program, nonlinear FE models were developed and verified, and a comprehensive parametric study was carried out to identify the influential key parameters onthe flexural buckling of welded I-columns. Design formulas were developed using test and FE results for welded I section columns, and finally, the performance of the proposed CSM flexural buckling formulas was verified and compared with other standards.

Section snippets

Test program

A test program was conducted to investigate the structural behaviour of stainless steel welded I-sections produced from 316L austenitic grade stainless steel. Flanges and webs were connected by Tungsten Inert Gas (TIG) welding. Most of the recent studies used shielded metal arc welding (SMAW) for fabricating welded sections [5], [13], [14], [15]. But compared to SMAW, TIG welding offers better quality and precision. TIG welding is aesthetically good with smaller seam size, and the thermal

Tensile coupon test

Tensile coupon tests were performed to evaluate accurate material properties for the plate materials used to fabricate the considered I-sections. Plates of five different thicknesses were used for different cross-sections, and plate thicknesses varied from 2 to 6 mm. Five coupons, each representing a specific thickness, were cut from 200 × 200 mm plates taken from the same batch as the welded I-columns. Tensile coupons were produced according to EN ISO 6892-1 [28], and all tensile coupons were

Residual stresses observed in stainless steel welded I-sections

Residual stresses are unavoidable in welded sections. In this study, residual stresses were measured by sectioning method, which has been widely used for many years and is reported to produce accurate and reliable results. In 1888, Kalakoutsky [29] first proposed this method for measuring longitudinal stresses in steel bars. He slit the bars into longitudinal strips; measured the change in length of each strip before and after slitting, and residual stresses were calculated by applying Hooke’s

Initial geometric imperfection measurements

A laser scanner (scanCONTROL 2710-100(500)) was used to measure the initial local geometric imperfections in all stainless steel columns. Column specimens were mounted on the table of a milling machine, which provided a flat reference surface for accurate measurement as shown in Fig. 5. The laser scanner was set on top of the milling machine, and 3D data were collected automatically using a built-in software. The table of the milling machine was moved at a constant rate of 5 mm/s and the

Test procedure

Three stub columns were tested in axial compression, whose lengths were taken equal to three to four times the larger nominal dimension of the cross section to ensure representative distribution of geometric imperfection and residual stress but to avoid global buckling [32]. Two 200 × 200 mm plates of 16 mm thickness were welded at the top and the bottom end of stub columns. The geometric dimensions of stub column specimens were measured and are reported in Table 2, where D is the depth of the

Test procedure

To investigate the flexural buckling behaviour of stainless steel welded I-sections, 16 long columns were tested for minor axis buckling in pin-ended support condition. Considered columns represented six different cross-sections covering a wide range of tf/tw ratio, height-to-width ratio, cross-section slenderness λp and member slenderness λ. Cross-section slenderness varied from 0.26 to 0.83, whilst geometric lengths of the columns varied from 500 mm to 1500 mm providing a wide spectrum of λ,

Summary of the testing scheme

In the conducted test program, the behaviour of stainless steel welded I-sections was studied through test of tensile coupons, measurement of residual stresses and initial geometric imperfections, and testing of stub and long columns. It was observed that the measured maximum tensile residual stresses were higher than the values recommended by Yuan et al. [12]. The amplitudes of local geometric imperfection were also higher than the code [31] recommended values; however, for most of the columns

Current design methods for buckling resistance

Tangential stiffness method and Perry-Robertson formulas are two widely used methods to determine the buckling resistance of steel columns. Like carbon steel, the Perry type equations were adopted in EN 1993-1-4 [1] for stainless steel columns. Buckling equations currently used in the European code are presented in Eqs. (3), (4), (5), (6), (7), where Ag is the gross cross-sectional area, fy is the 0.2% proof stress (σ0.2), χ is the buckling reduction factor, Aeff is the effective

The Continuous Strength Method (CSM)

The Continuous Strength Method (CSM) is a strain based design approach where a base curve relates to the deformation capacity of a given section, and a material model relates to the deformation capacity with buckling stress. Gardner and Nethercot [19] first proposed this method. Recently Afshan and Gardner [21] proposed a new base curve as shown in Eq. (10), where normalized deformation capacity εcsmy was expressed as a function of cross-section slenderness λp for stocky sections. They set

Numerical model for long columns

Commercial finite element analysis package ABAQUS was used for numerical simulation of the behaviour observed in stub column and long column testing. Initially, the developed FE models were validated against test results carried out as part of the current study, and, once verified, the developed FE models were used to perform a comprehensive parametric study to identify the influence of different parameters on the flexural buckling resistance of stainless steel welded I-section columns.

Verification of FE models for long columns

The accuracy of the FE modelling technique was verified using the test results obtained from the welded I-section columns considered in this study. The comparison of ultimate load (Nu) of FE models with those obtained from tests is shown in Table 6. FE models that included measured local and global imperfections with residual stress, and the FE models that included global imperfection of L/2000 and local imperfection of b/200 with residual stress showed good agreement with test results. In both

Parametric study for welded I columns

The verified FE modelling technique was used to identify the parameters that could significantly affect the buckling resistance of stainless steel columns through a parametric study. Ahmed and Ashraf [27] recently reported that cross section slenderness λp has a significant effect on column curves for cold-formed RHS and SHS columns. Therefore, the effect of λp on column curves of welded I-section buckling about the major and the minor axis was thoroughly investigated herein. Additionally,

Analysis of FE results

To study the effect of different parameters, column curves are carefully plotted in Fig. 30, Fig. 31, Fig. 32, Fig. 33 to observe variation in non-dimensional column strength or reduction factor χ, which was calculated as Nu,FEAgfcsm. In Fig. 30, the influence of λp on column curves is shown for major axis buckling and minor axis buckling respectively. It is clearly observed that cross-section slenderness λp has a significant effect on the column curves for welded I-section, and it is similar

Imperfection factor η for welded I-sections

Ahmed and Ashraf [27] successfully used fcsm in Perry formulas to predict the buckling resistance of stainless steel cold-formed hollow compression members. In that proposal, CSM buckling stress fcsm was used instead of the material yield stress in basic Perry curves, and the imperfection parameter η was expressed as a sigmoidal function of λm, where the coefficients of that function depend on λp. Similar approach has been adopted herein to predict the buckling resistance of stainless steel

Performance of the proposed method

The accuracy of the proposed method was verified using available test results of stainless steel welded I-columns and the FE results generated in the current parametric study. A total of 46 test results, collected from different studies in the literature [14], [15], [38], and 16 test results performed in this study were considered. Among the test results, 19 columns were tested for major axis buckling and 43 columns were tested for minor axis buckling. The performance of the proposed method was

Reliability analysis

Reliability analysis of the buckling formulas proposed for stainless steel welded I-section columns was performed following the guidelines of EN1990-Annex D [40]. Although the same material model can be adopted for both austenitic and duplex stainless steel, the magnitudes of residual stresses are different for welded sections produced from different grades of stainless steel. In FE models, the maximum tensile residual stress was taken as 0.8σ0.2 considering austenitic grades, however, the

Conclusions

Welded sections play a significant role in structural engineering when readily available sections fail to meet the required high load carrying capacities. The structural response of welded members differs from that of cold-formed members due to the presence of longitudinal residual stresses. In case of stainless steel, very limited number of test evidences are available on welded sections as most of the studies are focused on commonly used cold-formed hollow sections. In this paper, the

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