The Continuous Strength Method for Structural Stainless Steel Design. S. Afshan and L. Gardner

Transcription

1 The Continos Strength Method for Strctral Stainless Steel Design S. Afshan and L. Gardner Department of Civil and Environmental Engineering, Imperial College London, UK Abstract Crrent stainless steel design standards are based on elastic, perfectl plastic material behavior providing consistenc with carbon steel design expressions, bt often leading to overl conservative reslts, particlarl in the case of stock elements. More economic design rles in accordance with the actal material response of stainless steel, which shows a ronded stress-strain crve with significant strain hardening, are reqired. Hence, the continos strength method (CSM) was developed. The CSM replaces the concept of cross-section classification with a cross-section deformation capacit and replaces the assmed elastic, perfectl plastic material model with one that allows for strain hardening. This paper smmarises the evoltion of the method and describes its recent simplified form, which is now sitable for code inclsion. Comparison of the predicted capacities with over 140 collected test reslts shows that the CSM offers improved accrac and redced scatter relative to the crrent design methods. The reliabilit of the approach has been demonstrated b statistical analses and the CSM is crrentl nder consideration for inclsion in Eropean and North American design standards for stainless steel strctres. 1 Introdction Stainless steel is being increasingl sed as a constrction material in varios strctral applications, taking advantage of its well known corrosion resistance, fire resistance and material properties. Given the high initial material costs of stainless steel, associated primaril with its alloing elements, it is essential that its distinctive properties are recognised in the development of strctral design rles. This paper focses on ke characteristics of stainless steels material stress-strain behavior, in particlar strain hardening, and its implications on strctral design. Unlike carbon steel which has an elastic response, with a clearl defined ield point, followed b a ield platea and a moderate degree of strain hardening, stainless steel has predominantl non-linear stress-strain behavior with significant strain hardening. The crrent generation of international stainless steel design standards [1, 2] have been developed largel in line with carbon steel design gidelines, which are based on the idealised elastic, perfectl plastic material behavior, hence neglecting the beneficial strain hardening effects. The continos strength method (CSM) is a newl developed design approach, providing consistenc with the observed stainless steel stress-strain response and allowing for strain hardening. The CSM replaces the concept of cross-section classification, which is the basis for the treatment of local bckling in the crrent design standards for metallic materials sch as carbon steel, stainless steel and alminim allos, with a non-dimensional measre of cross-section deformation capacit. Backgrond to the method and detailed descriptions of its development over the past decade are pblished in [3-5]. More recent advancements and simplifications of the CSM, inclding its extension to carbon steel design ma also be fond in [6, 7]. The application of the CSM to stainless steel strctres, incorporating its recent modifications, is described in this paper. Test data on stainless steel stb colmns and beams have been sed to generate a simple and continos relationship between cross-section slenderness and cross-section deformation capacit, referred to as the design base crve. An elastic, linear hardening material model, enabling exploitation of strain hardening, is also described. Althogh the scope of the CSM is not limited to specific strctral loading cases, cross-section capacities in compression and bending are the primar focs of this paper. 2 Crrent Codified Treatment of Local Bckling The concept of cross-section classification is the crrent codified approach for the treatment of local bckling in metallic sections and is sed to determine the appropriate strctral design resistance. The method is most sitable for materials with a stress-strain response resembling the idealised elastic-perfectl plastic material model, where the presence of a clearl defined ield point allows cross-sections to be set into discrete behavioral classes. EN [1] adopts the carbon steel cross-section classification approach set ot in EN [8], with the ield stress f taken as the 0.2% proof stress σ0.2. A series of limits for the width-to-thickness ratios (b/t), in terms of the material properties = [(235/f)(E/210000)] 0.5, edge spport conditions (i.e. internal or otstand) and the form of the applied stress field, are provided. The overall cross-section classification is assmed to relate to that of its most slender constitent element, ths neglecting the benefits of element interaction. Slenderness limits are generall derived on the basis of experimental reslts at the cross-section level. Owing to the relativel recent emergence of stainless steel as a strctral material, the crrent cross-section classification limits in Paper Presented b Dr. Lero Gardner - lero.gardner@imperial.ac.k S. Afshan & L. Gardner, Imperial College London 1

2 EN [1] were derived on the basis of a limited nmber of test data. Analsis of reslts b Gardner and Theofanos [5], based on a more comprehensive experimental database, has shown that the crrent classification limits are ndl conservative and ma in man cases, be relaxed; where possible it was proposed [5] that the stainless steel slenderness limits be harmonised with those for carbon steel. Analses of experimental reslts from stb colmn and in-plane bending tests have shown a significant conservatism in EN [1] rles which limit the cross-section compression resistance to the ield load and the cross-section bending resistance to the plastic moment capacit. Figre 1 shows the reslts of stb colmn tests on stainless steel SHS, RHS, angle sections, lipped channel sections and I-sections [9-22]. The test ltimate load N has been normalised b the cross-section ield load determined as the prodct of the gross cross-sectional area A and the material 0.2% proof stress σ 0.2 and plotted against the cross-section slenderness λ cs. Figre 2 shows the reslts of bending tests on stainless steel SHS, RHS and I-sections [10, 12, 13, 15, 20, 23-28] where the test ltimate moment M has been normalised b the plastic moment capacit M pl determined as the prodct of the section plastic modls W pl and the material 0.2% proof stress σ 0.2 and plotted against the cross-section slenderness λ cs. The slenderness λcs has been taken as the cross-section slenderness making de allowance for element interaction in sections comprised of plate assemblies, as explained in Section The occrrence of strength enhancements indced dring manfactring of cold-formed sections is well-known and predictive models [29-31] have been developed to determine these strength increases. Hence, for the comparisons shown in Figres 1 and 2, in order to demonstrate the increases in cross-section resistances in compression and bending de to strain hardening effects nder load onl, and not dring section forming, the cross-section weighted average 0.2% proof stress, allowing for the strength enhancements in the corner regions and flat faces of cold-formed sections as recommended in [30] has been emploed Test data EN N,test /Aσ Cross-section fll effective Cross-section not fll effective Cross-section slenderness Fig. 1 Comparison of 81 stb colmn test reslts with EN provisions The collected reslts shown in Figres 1 and 2 clearl reveal significant nder-prediction of the capacit of stock cross-sections de to the lack of allowance for strain hardening. The continos strength method, described in the following sections, is proposed to address this shortcoming. Paper Presented b Dr. Lero Gardner - lero.gardner@imperial.ac.k S. Afshan & L. Gardner, Imperial College London 2

3 Test data EN M,test /W pl σ W pl σ 0.2 Class 1 & 2 W el σ 0.2 Class 3 W effσ 0.2 Class Cross-section slenderness Fig. 2 Comparison of 65 beam test reslts with EN provisions. 3 Development of the Continos Strength Method The continos strength method (CSM) is a strain based design approach featring two ke components (1) a base crve that defines the level of strain that a cross-section can carr in a normalised form and (2) a material model, which allows for strain hardening and, in conjnction with the strain measre, can be sed to determine the cross-section resistance. 3.1 Design base crve A fndamental featre of the CSM is relating the cross-section resistance to the cross-section deformation capacit, which is controlled b the cross-section slenderness and its ssceptibilit to local bckling effects. The cross-section deformation capacit determines the abilit of the section to advance into the strain hardening region and hence sstain increased loading. A design base crve, providing a continos relationship between the normalised cross-section deformation capacit and the cross-section slenderness, has been established on the basis of both stb colmn test data and beam test data Cross-section slenderness definition Within the CSM, the cross-section slenderness is defined in non-dimensional form as the sqare root of the ratio of the ield stress f to the elastic bckling stress of the section. For strctral sections consisting of a series of interconnected plates, the elastic bckling stress of the fll cross-section σ cr,cs, allowing for element interaction, ma be determined b means of existing nmerical [32] or approximate analtical methods [33]. This approach is sed in the Direct Strength Method (DSM) [34] and also adopted in the analsis performed herein. This cross-section slenderness definition is given b Eq. (1) and will initiall relate to the centreline dimensions. To maintain consistenc with the codified slenderness definitions in [1, 35], which is based on the flat element widths, the reslting slenderness vales can be mltiplied b the maximm flat to centreline width ratio (c flat /c cl ) max of the section as given b Eq. (2) Alternativel, as recommended in EN [1] and EN [35], the section elastic bckling stress ma be taken as the lowest of those of its individal plate elements σ cr,p,min, reslting in the section slenderness definition given in Eq. (3). In Eq. (3), b is element width, t is the thickness, is the material factor and k σ is the appropriate bckling coefficient, taking de accont of the plate spport conditions and the applied stress distribtion, as otlined in EN [35], of the plate element with the lowest elastic bckling stress. λ cs = based on centreline dimensions σ f cr,cs (1) Paper Presented b Dr. Lero Gardner - lero.gardner@imperial.ac.k S. Afshan & L. Gardner, Imperial College London 3

4 f c c flat λ cs = based on flat widths σ cr,cs cl max (2) λ cs = = σ f cr,p,min b/t 28.4 k σ (3) Cross-section deformation capacit definition Cross-section deformation capacit is defined in a normalised format and is taken for stock sections as the strain at the ltimate load divided b the ield strain. This normalised deformation capacit, referred to as the strain ratio /, can be determined from both stb colmn and beam test reslts. First, the limiting slenderness defining the transition between slender cross-sections (i.e. those that fail de to local bckling below the ield load) and non-slender cross-section (i.e. those that benefit from strain hardening and fail b inelastic local bckling above the ield load) shold be defined. This limit ma be determined with reference to stainless steel test data shown in Figre 1, eqivalent test data for other metallic materials inclding carbon steel [7] and alminim allos [36] and existing Class 3-4 slenderness limits [1, 5, 8]. A linear regression fit to the test data of Figre 1 indicates that, the point on the line where N,test /Aσ 0.2 eqals nit occrs at λ cs = 0.68 ; a similar vale is obtained from eqivalent carbon steel and alminim allo test data. A range of slenderness limits appear in different design standards and research papers. The existing slenderness limits corresponding to the Class 3-4 width-to-thickness ratio (shown in brackets) are: for internal compression elements, (42) [8] for carbon steel, (30.7) [1] and (37) [5] for stainless steel; for otstand elements, (14) [8] for carbon steel, (11.9) and (11) for cold-formed and welded stainless steel respectivel [1] and (14) [5] for stainless steel. Based on the complete carbon steel cross-sections, a limit of [34] is given b the DSM, bt, in conjnction with a higher partial safet factor than recommended in Eropean standards. Considering the available information, to make the transition between slender and non-slender sections a common limit for stainless steel, carbon steel and alminim allos, λ cs = 0.68 is adopted. This slenderness vale also marks the limit of applicabilit of the CSM (i.e. λp 0.68 ), since beond this limit there is no significant benefit to be derived from strain hardening, and slender sections ma be adeqatel treated b means of the existing effective width method [1, 35] or the DSM [34]. For stb colmns where the ltimate test load N exceeds the section ield load N, the end shortening at the ltimate load δ divided b the stb colmn length L is sed to define the failre strain of the cross-section lb de to inelastic local bckling as shown in Figre 3. For compatibilit with the adopted simplified material model (see Section 3.2), the deformation capacit is obtained b sbtracting the plastic strain at the 0.2% proof stress (i.e ) from the actal local bckling strain lb, as given in Eq. (4). Expressing the cross-section deformation capacit in a normalised format, b dividing b the defined ield strain (=f /E) enables materials of different strength and stiffness to be considered together and be compared. For sections that fail before reaching their ield load, the deformation response is inflenced b elastic bckling and post-bckling behavior, and the former definition of the local bckling strain is inappropriate and wold lead to over predictions of capacit [4]. Hence the ratio of the ltimate load attained to the ield load is sed to provide a sitable alternative measre of the strain ratio as given in Eq. (5) δ L lb = = for N N and λp 0.68 N (4) = for N < N (5) N Paper Presented b Dr. Lero Gardner - lero.gardner@imperial.ac.k S. Afshan & L. Gardner, Imperial College London 4

5 Fig 3 Stb colmn load end shortening response (N > N ) In bending, assming plane sections remain plane and normal to the netral axis, there is a linear relationship between strain and crvatre κ as given b Eq. (6), where is the distance from the netral axis. Hence, analogos to the se of stb colmn tests data, similar definitions of normalised cross-section deformation capacit ma be established based on beam test reslts. The reslts of 4 point bending tests, which have a region of niform crvatre between the loading points, have been considered herein. For beams where the ltimate moment resistance M exceeds the section elastic moment capacit M el, the total crvatre at the ltimate moment κ mltiplied b the distance from the neral axis to the extreme compressive fibre in the cross-section max is sed to define the strain at failre de to inelastic local bckling lb see Figre 4. The corresponding strain ratio is obtained following a similar approach to the stb colmn test reslts and is given b Eq. (7). For sections which fail before reaching their elastic moment capacit, the ratio of the ltimate moment resistance to the section elastic moment capacit is sed to define the strain ratio, as given in Eq. (8). The assmed compressive and bending strain distribtions across the cross-section are illstrated for an I-section in Figre 5. = κ κ lb max = = for M M el and λp 0.68 κelmax M = for M < Mel Mel (6) (7) (8) Fig. 4 Beam moment-crvatre response (M > M Paper Presented b Dr. Lero Gardner - lero.gardner@imperial.ac.k S. Afshan & L. Gardner, Imperial College London 5

6 Fig. 5 (a). I-section geometr (b). Compressive strain distribtion (c). Bending strain distribtion Experimental database and proposed base crve Test data on stainless steel stb colmns and 4 point bending tests from a broad spectrm of existing testing programs [9-15, 19-22, 25, 26] were gathered and combined with eqivalent carbon steel data [7] for the development of the design base crve. Using the criteria described above, the test data were plotted on a graph of normalised deformation capacit / verss cross-section slenderness λ cs, as shown in Figre 6. A continos fnction of the general form given b Eq. (9) was then fitted to the test data; this fnction is similar in form to the established relationship between normalised critical elastic bckling strain cr / and plate slenderness for flat plate elements given b Eq. (10), bt will differ de to the effects of inelastic bckling, imperfections, residal stresses and post-bckling response. The vales of A and B were determined following a regression fit of Eq. (9) to the test data, ensring that the reslting crve passes throgh the identified limit between slender and non-slender sections, i.e. (0.68, 1) point, reslting in Eq. (11). Two pper bonds have been placed on the predicted cross-section deformation capacit; the first limit of 15 corresponds to the material dctilit reqirement expressed in EN [8] and the second limit of 0.1 /, where is the strain corresponding to the ltimate tensile stress, is related to the adopted stress-strain material model, and ensres no significant over-predictions of the cross-section resistance can occr. = A B λ cs (9) 1 = cr 2 λ cs = bt min , λ cs (10) (11) Paper Presented b Dr. Lero Gardner - lero.gardner@imperial.ac.k S. Afshan & L. Gardner, Imperial College London 6

7 25 20 CSM Effective width method Stainless steel - stb colmn data Stainless steel - beam data Carbon steel - stb colmn data Strain ratio / Fig Cross-section slenderness Base crve relationship between strain ratio and slenderness 3.2 Material model Earlier versions of the CSM tilised the Ramberg-Osgood material model [3-5], which reslted in relativel complex resistance expressions. It was fond that similar accrac cold in fact be achieved with simpler material models, and the design expressions become more sitable for strctral designers and inclsion in design codes. The CSM emplos an elastic, linear hardening material model. The origin of the adopted material model starts at 0.2% off-set plastic strain, which combined with the strain ratio definitions, provided in Section 3.1.2, predicts the correct corresponding stress. The ield stress point is defined as (f, ), where f is taken as the material 0.2% proof stress and is the corresponding elastic strain = f /E, where E is the slope of the elastic region and is taken as the material s Yong s modls. The strain hardening slope is determined as the slope of the line passing throgh the 0.2% proof stress point (f, ) and a specified maximm point ( max,f max ) with max taken as 0.16, where is the ltimate tensile strain, and f max is taken as the ltimate tensile stress f, as given b Eq. (12). The strain at the material ltimate tensile stress is determined from Annex C of EN [1] and is given b Eq. (13). A schematic diagram of the material model emploed is shown in Figre 7. f -f E sh = ( ) (12) f =1- f (13) Paper Presented b Dr. Lero Gardner - lero.gardner@imperial.ac.k S. Afshan & L. Gardner, Imperial College London 7

8 Stress Ramberg-Osgood model CSM model f f Strain Fig 7 CSM elastic, linear hardening material model 3.3 Cross-section compression and bending resistance Having established the normalised deformation capacit of the cross-section / from the design base crve (Eq. (11)), the limiting strain ma now be sed in conjnction with the proposed elastic, linear hardening material model to determine the cross-section resistances in compression and bending. For sections with λcs 0.68, the cross-section compression resistance N c,rd is given b Eq. (14), where A is the gross cross-sectional area, f is the limiting stress determined from the strain hardening material model, reslting in Eq. (15) and γ is the material partial safet factor as recommended in EN [1]. M0 Af N c,rd =N,Rd = γ M0 f =f +Esh ( -1) Assming that plane sections remain plane and normal to the netral axis in bending, the corresponding linearl-varing strain distribtion ma be sed in conjnction with the material model to determine the cross-section in-plane bending resistance M throgh Eq. (16), where f is the limiting stress, is the distance from the netral axis and da is the incremental cross-sectional area. A (16) M = f da For sections with λcs 0.68, the cross-section bending resistance M c,rd is given b Eq. (17) and (18) for major axis and minor axis bending, respectivel, where W pl is the plastic section modls, W el is the elastic section modls and α is 2.0 for SHS/RHS and 1.2 for I-sections. A detailed description of the derivation of the CSM bending resistance eqations is given in [7]. 2 Wpl,f E W sh el, W el, M,c,Rd = M,,Rd = γm0 E W pl, W pl, (17) (14) (15) Paper Presented b Dr. Lero Gardner - lero.gardner@imperial.ac.k S. Afshan & L. Gardner, Imperial College London 8

9 α W f E W W (18) pl,z sh el,z el,z M z,c,rd = M z,,rd = γ M0 E W pl,z W pl,z 4 Comparison with Test Data and Design Models The predictions from the method have been compared with experimental reslts on 81 stainless steel stb colmns [9-14, 16-22] and 65 beams [10, 12, 13, 20, 23-28]. It has been shown that the method offers improved mean resistance and redced scatter compared to the EN [1] design rles which are known to be conservative for stock crosssections as illstrated in Figres 8 and 9. Ke nmerical comparisons, inclding the mean and the coefficient of variation (COV), of the CSM and the EN [1] predictions with the test data are presented in Tables 1 and 2 for the stb colmns and the beams, respectivel CSM EN N,test /N,pred Cross-section slenderness Fig. 8 Comparison of the stb colmn tests with the CSM and EN predictions CSM EN M,test /M,pred Cross-section slenderness Fig. 9 Table 1 Comparison of the beam tests with the CSM and EN predictions. Comparison of the CSM and EN predictions with the stb colmn test reslts Paper Presented b Dr. Lero Gardner - lero.gardner@imperial.ac.k S. Afshan & L. Gardner, Imperial College London 9

10 No. of tests: 81 N test /N EC3 N test /N N /N EC3 Mean COV Table 2 Comparison of the CSM and EN predictions with the beam test reslts No. of tests: 65 M test /M EC3 M test /M M /M EC3 Mean COV Reliabilit Analsis In order to verif the CSM design eqations, a standard reliabilit analsis in accordance with EN 1990 Annex D [37] was performed and a smmar of the ke statistical parameters are presented in Tables 3. The following smbols are sed: k d,n = design (ltimate limit state) fractile factor for n tests, where n is the poplation of test data nder consideration; b = average ratio of experimental to model resistance based on a least sqares fit to the test data; V δ = coefficient of variation of the tests relative to the resistance model; and V r = combined coefficient of variation incorporating both model and basic variable ncertainties. The analses indicate that CSM provides reliable reslts, with improved mean resistance and considerabl lower scatter than the EN [1], as also illstrated in Figs. 10 and 11. EN (2006) emplos a partial safet factor γ M0 of 1.1. The reslts of the reliabilit analsis show that this vale is safe for CSM, and is the recommended vale. Table 3 Smmar of the CSM reliabilit analsis reslts Test data n k d,n b V δ V r γ M0 Stb colmns Beams N,test (kn) N,pred (kn) CSM EN Fig. 10 Experimental and predicted compression resistance. Paper Presented b Dr. Lero Gardner - lero.gardner@imperial.ac.k S. Afshan & L. Gardner, Imperial College London 10

11 M,test (knm) M,pred (knm) CSM EN Fig. 11 Experimental and predicted bending resistance. 6 Worked Examples Two examples are provided in this section to demonstrate the workings of the CSM for the design of stainless steel cross-sections in compression and bending. The design calclations for an I-section in compression and a RHS in bending are presented in Examples I and II, respectivel. The geometric and material properties of the tested specimens have been sed and all factors of safet have been set to nit, to allow direct comparison with the test reslts. Example I: Compression resistance The CSM predicted compression resistance of stb colmn, tested in [20], was determined as follows: Cross-section geometric and material properties: h = mm t w = 6.00 mm E = N/mm 2 = 299/198000= b = mm Weld size = 4.24 mm f =299 N/mm 2 = 1-299/610=0.51 t f = 9.86 mm A = mm 2 f =610 N/mm 2 Determine cross-section slenderness f 299 σ λ cs = = = 0.40 cr,cs Mltipling b (c flat /c cl ) max, where c flat is the flat element width and c cl is the centreline element width = 0.35 (< 0.68 CSM applies) Determine cross-section deformation capacit: = = < min 15, Determine the strain-hardening slope: Paper Presented b Dr. Lero Gardner - lero.gardner@imperial.ac.k S. Afshan & L. Gardner, Imperial College London 11

12 f -f E sh = = = 3984 N / mm ( ) Determine the cross-section compression resistance: ( ) 2 f =f +Esh ( -1) = ( ) = N / mm N c,rd = N,Rd = = kn 1.0 [Test ltimate load = kn; EN predicted compression resistance = kn] Example II: In-plane bending resistance The CSM predicted in-plane bending resistance of RHS abot its major axis, tested in [12], was determined as follows: Cross-section geometric and material properties: h = mm r i = 4.50 mm W el = mm 3 f =654 N/mm 2 b = mm A = mm 2 E = N/mm 2 =367/193000= t = 5.85 mm W pl = mm 3 f =367 (1) N/mm 2 =1-367/654=0.44 (1) This is the cross-section weighted average ield strength, allowing for corner strength enhancement b means of recommendations in [30]. Determine the cross-section slenderness f 367 σ 3533 λ cs = = = 0.32 cr,cs Mltipling b (c flat /c cl ) max, where c flat is the flat element width and c cl is the centreline element width = (< 0.68 CSM applies) Determine the cross-section deformation capacit: = = > min , = Determine the strain-hardening slope: f -f E sh = = = 4328 N / mm ( ) Determine the cross-section in-plane bending resistance: ( ) 2 W f E W W pl, sh el, el, M,c,Rd = M,,Rd = = γm0 E W pl, W pl, ( 15-1) - 1- ( 15 ) = knm [Test ltimate moment = knm; EN predicted bending resistance = knm] 7 Conclsions The importance of strain hardening in the design of stainless steel strctres was highlighted. A newl developed design method called the continos strength method, providing a rational exploitation of strain hardening was presented. The evoltion of the method for stainless steel strctres, covering its recent simplifications and refinements, was described Paper Presented b Dr. Lero Gardner - lero.gardner@imperial.ac.k S. Afshan & L. Gardner, Imperial College London 12

13 in detail. Test data on stainless steel stb colmns and in-plane bending tests were sed to make comparisons with the predicted reslts from the proposed method and EN gidelines. Reliabilit analses were also performed to statisticall validate the method for compression and in-plane bending resistance of stainless steel strctral sections. It was shown that the method offers improved mean resistance and lower scatter compared to the EN provisions, leading to more economical design. 8 References [1] EN Erocode 3: Design of steel strctres - Part 1-4: General rles - Spplementar rles for stainless steels. Brssels: Eropean Committee for Standardisation (CEN); [2] AISC Design Gide 30: Strctral Stainless Steel. American Institte of Steel Constrction; [3] Gardner L. A new approach to strctral stainless steel design. PhD Thesis. UK: Imperial College London; [4] Ashraf M, Gardner L, Nethercot D. Strctral stainless steel design: resistance based on deformation capacit. Jornal of Strctral Engineering, 2008;134(3): [5] Gardner L, Theofanos M. Discrete and continos treatment of local bckling in stainless steel elements. Jornal of Constrctional Steel Research, 2008;64(11): [6] Gardner L. The continos strength method. Proceedings of the ICE - Strctres and Bildings, 2008;161(3): [7] Gardner L, Wang F, Liew A. Inflence of strain hardening on the behavior and design of steel strctres. International Jornal of Strctral Stabilit and Dnamics, 2011;11(5): [8] EN Erocode 3: Design of steel strctres - Part 1-1: General rles and rles for bildings. Brssels: Eropean Committee for standardisation (CEN); [9] Kwamra H. Local bckling of thin-walled stainless steel members. Steel Strctres, 2003;3: [10] Saliba N, Gardner L. Cross-section stabilit of lean dplex stainless steel welded I-sections. Jornal of Constrctional Steel Research, 2013;80:1-14. [11] Gardner L, Nethercot D. Experiments on stainless steel hollow sections Part 1: Material and cross-sectional behavior. Jornal of Constrctional Steel Research, 2004;60(9): [12] Talja A, Salmi P. Design of stainless steel RHS beams, colmns and beam-colmns. Research note Finland. VTT bilding technolog,1995. [13] Gardner L, Talja A, Baddoo N. Strctral design of high-strength astenitic stainless steel. Thin-Walled strctres, 2006;44(5): [14] Theofanos M, Gardner L. Testing and nmerical modelling of lean dplex stainless steel hollow section colmns. Engineering Strctres, 2009;31(12): [15] Afshan S, Gardner L. Experimental std of cold-formed ferritic stainless steel hollow sections. Jornal of Strctral Engineering (ASCE), In press. [16] Yong B, Li WM. Behavior of cold-formed high strength stainless steel sections. Jornal of Strctral Engineering, 2005;131(11): [17] Yong B, Li Y. Experimental investigation of cold-formed stainless steel colmns. Jornal of Strctral Engineering, 2003;129(2): [18] Li Y, Yong B. Bckling of stainless steel sqare hollow section compression members. Jornal of Constrctional Steel Research, 2003;59(2): [19] ECSC. Work Package 6 WP6. ECSC project development of the se of stainless steel in constrction. Docment RT810, Contract No SA/ 842. UK: The Steel Constrction Institte; [20] ECSC. Work Package 2 WP2. ECSC project development of the se of stainless steel in constrction. Docment RT810, Contract No SA/ 842. UK: The Steel Constrction Institte; [21] Rasmssen K, Hancock G. Design of cold-formed stainless steel tblar members. I: Colmns. Jornal of Strctral Engineering (ASCE), 1993;119(8): [22] Yan HX, Wang YQ, Shi YJ, Gardner L. Stb colmn tests on stainless steel bilt-p sections. Thin-Walled strctres, Special Isse for Experts Seminar, Sbmitted. [23] Real E, Mirambell E. Flexral behavior of stainless steel beams. Engineering Strctres, 2005;27(10): Paper Presented b Dr. Lero Gardner - lero.gardner@imperial.ac.k S. Afshan & L. Gardner, Imperial College London 13

14 [24] Gardner L, Nethercot D. Experiments on stainless steel hollow sections Part 2: Member behavior of colmns and beams. Jornal of Constrctional Steel Research, 2004;60(9): [25] Zho F, Yong B. Tests of cold-formed stainless steel tblar flexral members. Thin-Walled strctres, 2005;43(9): [26] Rasmssen K, Hancock G. Design of cold-formed stainless steel tblar members. II: Beams. Jornal of Strctral Engineering (ASCE), 1993;119(8): [27] Theofanos M, Gardner L. Experimental and nmerical stdies of lean dplex stainless steel beams. Jornal of Constrctional Steel Research, 2010;66(6): [28] Theofanos M, Gardner L. Plastic design of stainless steel strctres. International colloqim on stabilit and dctilit of steel strctres (SDSS Rio 2010). Rio de Janeiro, Brazil; p [29] Ashraf M, Gardner L, Nethercot D. Strength enhancement of the corner regions of stainless steel cross-sections. Jornal of Constrctional Steel Research, 2005;61(1): [30] Crise RB, Gardner L. Strength enhancements indced dring cold forming of stainless steel sections. Jornal of Constrctional Steel Research, 2008;64(11): [31] Rossi B, Afshan S, Gardner L. Strength enhancements in cold-formed strctral sections Part II: Predictive models. Jornal of Constrctional Steel Research, Sbmitted. [32] Schafer B, Ádán S. Bckling analsis of cold-formed steel members sing CUFSM: conventional and constrained finite strip methods. Eighteenth international specialt conference on cold-formed steel strctres; p [33] Seif M, Schafer BW. Local bckling of strctral steel shapes. Jornal of Constrctional Steel Research, 2010;66(10): [34] Schafer BW. Review: the direct strength method of cold-formed steel member design. Jornal of Constrctional Steel Research, 2008;64(7): [35] EN Erocode 3: Design of steel strctres - Part 1-5: Plated strctral elements. Brssels: Eropean Committee for standardisation (CEN); [36] S MN, Yong B, Gardner L. Compression tests of allminim allo cross-sections. Forteenth international smposim on tblar strctres (ISTS 14). London, UK; p [37] EN Erocode - Basis of strctral design. Brssels: Eropean Committee for Standardisation (CEN); Paper Presented b Dr. Lero Gardner - lero.gardner@imperial.ac.k S. Afshan & L. Gardner, Imperial College London 14