Compressive resistance of hot-rolled elliptical hollow sections

Transcription

1 Chan, T. M. and Gardner, L. (28). Compressive resistance of hot-rolled elliptical hollow sections. Engineering Structures. 3(2), Compressive resistance of hot-rolled elliptical hollow sections T. M. Chan 1 and L. Gardner 2 1 Research student, Corresponding author, Department of Civil and Environmental Engineering, South Kensington Campus, Imperial College London, SW7 2AZ, UK. Ken.chan@imperial.ac.uk 2 Lecturer in Structural Engineering, Department of Civil and Environmental Engineering, South Kensington Campus, Imperial College London, SW7 2AZ, UK. Leroy.gardner@imperial.ac.uk Abstract In recent years, hot-rolled elliptical hollow sections have attracted significant attention from engineers and architects owing to their complementary qualities of aesthetic appearance and structural efficiency. However, there is currently a lack of design guidance for elliptical hollow sections inhibiting more widespread use in construction. The present paper addresses this shortcoming for the fundamental loading condition of axial compression. Laboratory testing, numerical modelling and the development of design rules are described herein. The experimental programme comprised 25 tensile coupon tests and 25 stub column tests. All tested elliptical hollow sections had an aspect ratio of two and section sizes ranged from up to 5 25 mm. Results, including geometric imperfection measurements and full load-end shortening curves have been presented. Non-linear finite element models were developed and validated against the generated test data. The validated numerical models were employed to perform parametric studies in order to investigate elliptical hollow sections of varying slenderness and varying aspect ratios. The resulting structural performance data have been used to establish a relationship between crosssection slenderness and cross-section compressive resistance, which demonstrates that the Class 3 slenderness limit of 9 from Eurocode 3 for circular hollow sections can be safely adopted for elliptical hollow sections based upon the proposed cross-section slenderness parameter. The equivalent semi-compact slenderness limit given in BS 595-1, non-compact limiting slenderness in AISC 36-5 and yield slenderness limit given in AS 41 are also valid. A modified effective area formula from BS can also be safely adopted. Further investigation into effective area formulations for slender (Class 4) elliptical hollow sections is currently underway. 1

2 Key words: Compression, cross-section classification, elliptical hollow sections, laboratory testing, numerical modelling, oval hollow sections, slenderness limits, steel structures. 1. Introduction The introduction of hot-rolled structural steel elliptical hollow sections has drawn considerable attention from engineers and architects in the construction industry. Their aesthetic appearance and structural efficiency have already resulted in a number of applications ranging from sculpture (Honda Central Sculpture) to main structural components (Jarrold Department Store in Norwich) [1]. However, to facilitate their wider application, comprehensive and validated structural design guidance is required. This paper focuses on the compressive resistance of elliptical hollow sections, and provides the results of 25 stub column tests and extensive numerical results, complementing the previous findings of the authors [2, 3, 4]. The experimental study included material tensile coupon tests for each of the tested cross-sections together with geometric imperfection measurements. All tested elliptical hollow sections had an aspect ratio of two and section sizes ranged from up to 5 25 mm. The generated structural performance data have been used to establish a relationship between cross-section slenderness and cross-section compressive resistance and to develop cross-section classification limits. The distinct feature of an elliptical hollow section (EHS) from other tubular sections is its varying radius of curvature around the circumference. This varies from a minimum rmin=b 2 /a at the end of the cross-section minor (z-z) axis to a maximum rmax=a 2 /b at the end of cross-section major (y-y) axis as shown in Fig. 1. The associated stiffness of each constituent segment depends upon its corresponding radius of curvature. The sum of these segments characterises the overall compressive response of the cross-section, as given by Eq. (1). P N t dp (1) c where N is the axial load, σc is the axial compressive stress, and t and P are the thickness and mean perimeter of the cross-section, respectively. Eq. (1) allows for variation of axial compressive stress around the cross-section with the stiffer parts attracting more load. As described in Section 4, the test and numerical results indicate that stocky elliptical hollow sections offer greater load carrying capacity in comparison to their circular counterparts, due to the achievement of strain hardening in 2

3 the stiffer regions of the section of low radii of curvature. 2. Experimental study A series of precise full-scale laboratory tests on EHS (grade S355), manufactured by Corus Tubes [5], was performed at Imperial College London. The test programme comprised a total of 25 material tensile coupon tests and 25 cross-section capacity stub column tests. 2.1 Tensile coupon tests The primary objective of the tensile coupon tests was to determine the basic engineering stressstrain behaviour of the material for each of the tested section sizes. Results were used to facilitate the numerical study described in Section 3 and the development of cross-section classification limits in Section 4. Tests were carried out in accordance with EN 12-1 [6]. Parallel coupons, each with the nominal dimensions of 36 3 mm or 32 2 mm, depending on section size, were machined longitudinally along the centreline of the flattest portions of each of the tested elliptical hollow sections. All tensile tests were performed using an Amsler 35 kn hydraulic testing machine. To ensure no slippage of the coupons in the jaws of the testing machine, pins were inserted into reamed holes located 2 mm from each end of the coupons. Linear electrical strain gauges were affixed at the midpoint of each side of the tensile coupons and a series of overlapping proportional gauge lengths was marked onto the surface of the coupons to determine the elongation parameters. Load, strain, displacement and input voltage were all recorded using the data acquisition equipment DATASCAN and logged using the DALITE and DSLOG computer packages. Mean measured dimensions and the key results from the 25 tensile coupon tests are reported in Table Stub column tests Stub column tests were conducted to develop a relationship between cross-section slenderness, deformation capacity and load-carrying capacity for elliptical hollow sections under uniform axial compression. A total of 25 stub column tests were performed. Full load-end shortening histories were recorded, including into the post-ultimate range. The nominal length of the stub columns was two times the larger outer diameter (2 2a = 4a) of the cross-section. This was deemed sufficiently long to ensure that the stub columns contained a representative distribution of geometric 3

4 imperfections and residual stresses and to minimise the influence of the end conditions, but suitably short to avoid overall column buckling. The ends of the tubes were milled flat and square. Four LVDTs were located between the parallel end-platens of the testing machine to determine the average end shortening of the stub columns. Four linear electrical resistance strain gauges were affixed to each specimen at mid-height, and at a distance of five times the material thickness from the ends of cross-section minor axis. The strain gauges were initially used for alignment purposes. The testing arrangement is shown in Fig. 2. Load, strain, displacement, and input voltage were all recorded using the data acquisition equipment DATASCAN and logged using the DALITE and DSLOG computer packages. The mean measured dimensions of the stub columns are summarised in Table 2. The cross-sectional area A was calculated from Eq. (2), A P t (2) m where Pm is the mean perimeter and t is the thickness of the elliptical hollow section. The exact mean perimeter Pm can be obtained by integrating around the circumference of the ellipse to give Eq. (3). 2 2 b m 2 P 4a sin cos d m m (3) 2 a m 2 in which am = (2a - t)/2, bm = (2b - t)/2 and is the angle for each element measured from the z-axis, as shown in Fig. 1. Ramanujan [7] proposed the approximate formula of Eq. (4), 3h m P (a b ) 1 (4) m m m 1 4 3h m where am and bm are defined as above and hm = (am - bm) 2 / (am + bm) 2. The maximum deviation of the approximate formula of Eq. (4) for determining the perimeter of an ellipse compared to the exact solution of Eq. (3) is only -.4%. A simpler approximate formula (Eq. (5)) is also provided in EN [8] for the determining the mean perimeter of an ellipse. P m (a b )(1.25h ) (5) m m m 4

5 For an aspect ratio a/b of 2, the deviation of Eq. (5) from the exact solution of Eq. (3) is -.2%. However, as the aspect ratio increases, the maximum deviation increases up to -1.8%. It should also be noted that EN [8] recommends that the cross-sectional area of an elliptical hollow section be evaluated through Eq. (6). π A (2a 2b) (2a 2t) (2b 2t) (6) 4 However, Eq. (6) consistently underestimates the cross-sectional area of an EHS with constant thickness. For example, for a typical EHS of dimensions 2a = 4 mm, 2b = 2 mm and t = 1 mm, Eq. (2) yields A = 9384 mm 2 whereas Eq. (6) gives A = 9111 mm 2 ; an underestimation of 2.9%. For accuracy, it is therefore recommended that Eqs. (2) and (4) be adopted for the determination of the cross-sectional area of an EHS, and this approach has been used throughout this paper. Initial geometric imperfections measurements were taken along the centrelines of the faces of the stub column specimens with the datum being a straight line connecting the ends of each stub column face. The primary aim of this exercise was to record the maximum amplitudes of imperfections inherent in hot-rolled elliptical tubes; information on the form of the imperfections was also traced. The maximum amplitude of imperfection for each tested specimen is reported in Table 2. The full load-end shortening histories from the stub column tests were recorded and are depicted in Figs. 3 to 14. The key results from the stub column tests have been summarised in Table 3 where the ultimate test load Fu has been normalised by the yield load Fy = Aσy. Values for the ratio Fu/Fy of greater than unity indicate that the cross-sections are capable of reaching the yield load. For slender sections, however, this ratio may be less than unity due to local buckling in the elastic material range. Figs. 9 and 14 show the load-end shortening histories for this type of failure. For sections where Fu/Fy is greater than unity, two patterns of load-end shortening histories were observed. Moderately stocky sections reach and maintain the yield load (along the plastic yield plateau) before failing by inelastic local buckling, examples of which are shown in Figs. 3, 4, 1 and 11. For very stocky sections, as shown in Figs. 5, 6, 7, 12 and 13, the load-end shortening behaviour enters the material strain-hardening regime before local buckling occurs, resulting in ultimate loads greater than the yield load. The full load-end shortening response of the stockiest 5

6 elliptical hollow sections may be best explained with reference to Fig. 7, which shows the results for the stub columns. The load-end shortening curves may be considered as four regions (labelled 1 to 4 in Fig. 7). The first region is the elastic loading path which is controlled by the Young s modulus of the material. The second region is the plastic yield plateau which is related to the yield plateau of the material, with the intersection between regions 1 and 2 corresponding to the yield load Fy. The third region reflects the strain-hardening of the material and extends up to the ultimate load Fu, whereupon inelastic local buckling prevents any further increase in load carrying capacity. Region 4 represents the unloading path of the stub columns where growth of local buckles and spreading of plasticity occur. 3. Numerical simulations A numerical modelling study, using the finite element (FE) package ABAQUS [9], was carried out in parallel with the experimental programme. The primary aims of the programme were to replicate the experimental compression tests and, having validated the models, to perform parametric studies. The elements chosen for the FE models were 4-noded, reduced integration shell elements with six degrees of freedom per node, designated as S4R in the ABAQUS element library, and suitable for thin or thick shell applications [9]. These elements have been shown to perform well in similar applications [1, 11, 12]. A uniform mesh density was carefully chosen by carrying out a mesh convergence study based on elastic eigenvalue predictions with the aim of achieving accurate results whilst minimising computational effort. A suitable mesh size was found to be 2a/1(a/b) 2a/1(a/b) mm with the upper bound of 2 2 mm. The stub column tests were modelled using the measured dimensions of the test specimens and measured material stress-strain data. The form of geometric imperfections was taken to be the lowest elastic eigenmode pattern, typically symmetrical in shape, an example of which is shown in Fig. 15. The imperfection amplitude w was considered as three fixed fractions of the material thickness t (t/1, t/1 and t/5) in addition to the measured imperfection values. No residual stress data were measured, but the negligible deformation observed when the material tensile coupons were machined from the elliptical specimens indicated that the residual stresses were low. Therefore, residual stresses were not incorporated into the numerical models in this study. The true stress-strain relations were generated from the engineering stress-strain curves obtained from the tensile coupon tests and material non-linearity was incorporated into the numerical models by means of a piecewise linear stress-strain model to mimic, in particular, the strain-hardening region. 6

7 Boundary conditions were applied to model fixed ends and this was achieved by restraining all displacements and rotations at the base of the stub columns, and all degrees of freedom except vertical displacement at the loaded end of the stub columns; this vertical displacement was monitored throughout the analysis. The modified Riks method [9] was employed to solve the geometrically and materially non-linear stub column models, which enabled the unloading behaviour to be traced. The numerical failure mode of EHS SC2 is illustrated in Fig. 16 and compared with the corresponding deformed test specimen. Results of the numerical simulations are tabulated in Table 4, in which, the ratio between the FE ultimate load and the experimental ultimate load are shown and compared for different imperfection levels. Replication of test results has been found to be satisfactory with the numerical models able to successfully capture the observed stiffness, ultimate load, general load-end shortening response and failure patterns. Comparison between test and FE results are shown for EHS SC2 and EHS SC1 in Figs. 17 and 18, respectively. The ultimate loads of the three stub columns of section size are consistently under-predicted by the numerical models, regardless of the imperfection amplitude. Possible explanations for this under-prediction include variation of the material thickness around the cross-section and along the length of the stub columns and variation in material yield strength (either around the cross-section or between tensile and compressive properties). Sensitivity to imperfections is generally relatively low, with the stockier sections showing the greatest variation in response. For example, in the case of the EHS models, the ultimate load reduces by 2% with an increase of imperfection amplitude from t/1 to t/1. This sensitivity is due to the level of strain-hardening achieved by the constituent elements before local buckling occurs. The less stocky sections lie on or marginally below the yield plateau and are therefore less sensitive (in terms of ultimate load) to variation in the point of local buckling. Increased sensitivity would be anticipated for slender elliptical hollow sections where the yield load and elastic buckling load were of similar value. Having verified the general ability of the FE models to replicate test behaviour for EHS with aspect ratio of 2, a series of parametric studies were conducted. The primary aim of the parametric studies was to investigate the influence of cross-section slenderness and aspect ratio on the ultimate load carrying capacity. A piecewise linear material stress-strain model was developed from the tensile coupon tests conducted on the sections, and is shown in Fig. 19. Initial geometric imperfections in the non-linear parametric analyses adopted the form of the lowest elastic 7

8 eigenmode with an amplitude w of t/1, which has demonstrated the best agreement with the test results (Table 4). The section sizes considered in the parametric studies were 15 15, 15 1, and 15 5 with varying thickness to cover a spectrum of cross-section slenderness. The results have been utilized for the validation of proposed slenderness parameters and cross-section classification limits for elliptical hollow sections and are discussed in detail in the following section. 4. Cross-section classification Axial compression represents one of the fundamental loading arrangements for structural members. For cross-section classification under pure compression, of primary concern is the occurrence of local buckling in the elastic material range. Cross-sections that reach the yield load are considered Class 1-3, whilst those where local buckling of the slender constituent elements prevents attainment of the yield load are Class 4. For uniform compression, the cross-section slenderness parameter given by Eq. (7) has been proposed by Gardner and Chan [13]: D t e 2 2 (a / b) 2 2 t (7) where De is the equivalent diameter and ε 2 = 235/ y to allow for a range of yield strengths. It has been proposed that the equivalent diameter De be based upon the point along the circumference of an ellipse at which local buckling initiates this point corresponds to the maximum radius of curvature (rmax = a 2 /b) which occurs at the end of the major axis of the cross-section. The relationship between test Fu/Fy and the resulting cross-section slenderness parameter 2(a 2 /b)/tε 2 is plotted in Fig. 2. A value of Fu/Fy greater than unity represents meeting of Class 1-3 requirements, whilst a value less than unity indicates a Class 4 section where local buckling prevents the yield load from being reached. Fig. 2 demonstrates the anticipated trend of reducing values of Fu/Fy with increasing slenderness. For comparison, existing compressive test data from circular hollow sections (CHS) have also been added to Fig. 2. Both hot-rolled [1, 14] and cold-formed [11, 15] CHS data have been included, since these are both treated similarly in structural design (because for cold formed structural hollow sections, Eurocode 3 Part 1-3 [16] simply refers designers to Eurocode 3 Part 1-1 [17] for hot-rolled sections). It is worth noting that the material yield stress for the presented hot-rolled CHS data ranges from 334 N/mm 2 to 365 N/mm 2 whereas the.2% proof stress of the presented cold-formed CHS data ranges between 283 N/mm 2 and 835 N/mm 2. Comparing the performance of the tested elliptical hollow sections with their circular counterparts 8

9 (Fig. 2) shows, particularly in the stocky range, that the EHS generally exhibit superior loadcarrying capacity; this is more clearly evident from the FE results shown in Fig. 21. The greater load-carrying capacity of the stocky EHS is believed to result from the higher level of strainhardening achieved by stiffer regions of the section that have low radii of curvature. For more slender sections, local buckling occurs before the strain hardening regime is reached. A lower bound to the experimental results suggests that the Class 3 slenderness limit of 9 from Eurocode 3 Part 1-1 [17] for circular hollow sections (CHS) can be safely adopted for EHS based upon the proposed cross-section slenderness parameter (Eq. 7). The equivalent semi-compact slenderness limit given in BS [18] and the non-compact limiting value in AISC 36-5 [19], both of which have a value of 94 (having converted to the Eurocode base material strength of 235 N/mm 2 ) and the corresponding yield slenderness limit given in AS 41 [2], which has a converted value of 87 are also valid. In addition to experimental results, results from the described parametric studies on elliptical hollow sections with aspect ratios a/b of 1., 1.5, 2. and 3. have also been plotted in Fig. 21. As noted above, for stocky sections, increasing aspect ratio leads to increased load carrying capacity for a given cross-section slenderness, a feature believed to be related to the achievement of strain hardening in the stiffer parts of the section. For the highest aspect ratio considered (a/b = 3), the FE ultimate loads converge to the yield load at slenderness of about 15. For the lower aspect ratios (a/b = 1, 1.5 and 2) the FE Fu/Fy converges to unity by a slenderness of about 9. Overall, the FE results echo the experimental findings on the appropriateness of adopting the Class 3 CHS slenderness limit of 9 from Eurocode 3 Part 1-1 [17] for EHS. The equivalent CHS slenderness limits from BS [18], AISC 36-5 [19] and AS 41 [2] may also be adopted in conjunction with the proposed measure of slenderness for EHS. Having identified a suitable slenderness limit above which the yield load of the cross-section may be obtained, it is instructive to consider the treatment of more slender sections. The elastic buckling stress σcr of an elliptical hollow section in compression may be approximated through Eq. (8), as discussed in [2]. σ cr E (8) 2 3(1 )(D / 2t) e where De is the equivalent diameter (2a 2 /b), E is Young s modulus and is Poisson s ratio. Plotting the normalised ultimate loads Fu/Fy (= σu/σy) from the test specimens (which represent the current 9

10 range of commercially available elliptical hollow sections) against the measure of slenderness σy/σcr yields Fig. 22. The relationship between this measure of slenderness (σy/σcr) and the proposed cross-section slenderness parameter (De/tε 2 ) is given by Eq. (9). σ σ y cr (1 ν e 2 2E ) D tε (9) The non-dimensionalised material yield stress σy and the elastic buckling stress σcr have been added to Fig. 22. These two bounds indicate that the cross-section compression resistance of the practical range of available elliptical hollow sections would be expected to be dominated by material yielding, which has indeed been shown to be the case from the tests and finite element results. Fig. 22 also illustrates why the test and FE results for the slender sections of Fig. 21 appear to converge to the yield load Fy; clearly, although local buckling features in the examined slenderness range, far higher cross-section slenderness is necessary before elastic buckling becomes dominant. Failure to reach the yield load in compression due to the occurrence of local buckling is generally treated in design using either an effective stress or an effective area approach, with recent trends favouring the latter. A preliminary effective area formula (Aeff) for slender (Class 4) elliptical hollow sections has been developed with reference to the formulation for circular hollow sections in BS [18]. This preliminary formula is given by Eq. (1). A eff A (1) D t e y For the current practical range of elliptical hollow sections, based upon the experimental and numerical results, Eq. (1) has been found to be conservative and can be safely adopted for slender (Class 4) elliptical hollow sections. Further investigation into effective area formulations is currently underway. 5. Conclusions In view of the current lack of available design guidance for structural elliptical hollow sections, a series of laboratory tests and numerical investigations have been performed. The experimental 1

11 programme comprised a total of 25 tensile coupon tests and 25 stub column tests in pure axial compression. Results, including geometric imperfection measurements and full load-end shortening curves have been presented. Numerical models, created using the non-linear FE package ABAQUS, were verified against the test results. Following satisfactory agreement between tests and numerical results, parametric studies were performed to investigate the compressive response of elliptical hollow sections with different aspect ratios and of varying slenderness. The resulting structural performance data have been used to establish a relationship between cross-section slenderness and cross-section compressive resistance, which demonstrates that the Class 3 slenderness limit of 9 from Eurocode 3 for circular hollow sections can be safely adopted for elliptical hollow sections based upon the proposed cross-section slenderness parameter. The equivalent semi-compact slenderness limit given in BS 595-1, non-compact limiting slenderness in AISC 36-5 and yield slenderness limit given in AS 41 are also valid. A preliminary effective area formulation for slender elliptical hollow sections has been proposed. 6. Acknowledgements The authors are grateful to the Dorothy Hodgkin Postgraduate Award Scheme for the project funding, and would like to thank Corus for the supply of test specimens and for funding contributions, Eddie Hole and Andrew Orton (Corus Tubes) for their technical input and Ron Millward, Alan Roberts, Trevor Stickland and Gemma Aubeeluck (Imperial College London) for their assistance in the laboratory works. 7. References [1] Corus (26). Celsius 355 Ovals, Corus Tubes Structural & Conveyance Business. [2] Gardner, L. (25). Structural behaviour of oval hollow sections. International Journal of Advanced Steel Construction. 1(2), [3] Gardner, L. and Ministro, A. (25). Structural steel oval hollow sections. The Structural Engineer. 83(21),

12 [4] Chan, T. M. and Gardner, L. (26). Experimental and numerical studies of elliptical hollow sections under axial compression and bending. Proceedings of the 11 th International Symposium on Tubular Structures. 31st August to 2nd September 26, Québec City, Canada, [5] Corus (26). Celsius 355 Ovals Sizes and Resistances Eurocode Version, Corus Tubes Structural & Conveyance Business. [6] EN 12-1 (21). Metallic materials Tensile testing Part 1: Method of test at ambient temperature, CEN. [7] Almkvist, G. and Berndt, B. (1988). Gauss, Landen, Ramanujan, the Arithmetic-Geometric Mean, Ellipses, π, and the Ladies Diary. The American Mathematical Monthly. 95(7), [8] EN (26). Hot finished structural hollow sections of non-alloy and fine grain steels Part 2: Tolerances, dimensions and sectional properties, CEN. [9] ABAQUS (24). ABAQUS/Standard User s Manual Volumes I-III and ABAQUS CAE Manual. Version 6.4. Hibbitt, Karlsson & Sorensen, Inc. Pawtucket, USA. [1] Teng, J. G. and Hu, Y. M. (27). Behaviour of FRP-jacketed circular steel tubes and cylindrical shells under axial compression. Construction and Building Materials. 21(4), [11] Tutuncu, I. and O Rourke, T. D. (26). Compression behavior of nonslender cylindrical steel members with small and large-scale geometric imperfections. Journal of Structural Engineering, ASCE. 132(8), [12] Ellobody, E. and Young, B. (25). Structural performance of cold-formed high strength stainless steel columns. Journal of Constructional Steel Research. 61(12), [13] Gardner, L. and Chan, T. M. (26). Cross-section classification of elliptical hollow sections. Proceedings of the 11 th International Symposium on Tubular Structures. 31st August to 2nd September 26, Québec City, Canada, [14] Giakoumelis, G. and Lam, D. (24). Axial capacity of circular concrete-filled tube columns. Journal of Constructional Steel Research. 6(7),

13 [15] Sakino, K, Nakahara, H, Morina, S and Nishiyama, I (24). Journal of Structural Engineering, ASCE. 13(2), [16] EN (26). Eurocode 3: Design of steel structures Part 1-3: General rules- Supplementary rules for cold formed thin gauge members and sheeting, CEN. [17] EN (25). Eurocode 3: Design of steel structures Part 1-1: General rules and rules for buildings, CEN. [18] BS (2). Structural use of steelwork in building Part 1: Code of practice for design Rolled and welded sections, BSI. [19] AISC 36-5 (25). Specification for structural steel buildings, AISC. [2] AS 41 (1998). Steel structures, Australian Standard. 13

14 y t b b θ z a a Figure 1. Geometry of an elliptical hollow section Concentric loading Stub column L LVDT Strain gauge C L (a) Schematic arrangement (b) Test arrangement Figure 2. Testing arrangements for stub column 1

15 SC SC1 Load F (kn) End shortening δ (mm) Figure stub column load-end shortening curves SC2 Load F (kn) SC End shortening δ (mm) Figure stub column load-end shortening curves 2

16 SC SC1 Load F (kn) End shortening δ (mm) Figure stub column load-end shortening curves SC SC4 Load F (kn) End shortening δ (mm) Figure stub column load-end shortening curves 3

17 SC SC1 Load F (kn) End shortening δ (mm) Figure stub column load-end shortening curves SC1 Load F (kn) SC End shortening δ (mm) Figure stub column load-end shortening curves 4

18 SC2 Load F (kn) SC End shortening δ (mm) Figure stub column load-end shortening curves SC2 Load F (kn) SC End shortening δ (mm) Figure stub column load-end shortening curves 5

19 SC SC1 Load F (kn) End shortening δ (mm) Figure stub column load-end shortening curves SC SC2 Load F (kn) End shortening δ (mm) Figure stub column load-end shortening curves 6

20 SC SC1 Load F (kn) End shortening δ (mm) Figure stub column load-end shortening curves SC SC1 Load F (kn) End shortening δ (mm) Figure stub column load-end shortening curves 7

21 Figure 15. Typical symmetrical eigenmode shape ( SC2) (a) Numerical simulation (b) Laboratory test Figure 16. Typical failure mode ( SC2) 8

22 7 Load F (kn) Test FE End shortening δ (mm) Figure SC2 stub column load-end shortening curves (FE Imperfection = t/1) 9 75 Test Load F (kn) FE End shortening δ (mm) Figure SC1 stub column load-end shortening curves (FE Imperfection = t/1) 9

23 6 5 4 Stress (N/mm 2 ) Strain Figure 19. Piecewise linear stress-strain model 1

24 EC3 Hot-rolled EHS Hot-rolled CHS Cold formed CHS Fu/Fy Class 1-3 Class D e /tε 2 Figure 2. Normalised compressive resistance versus cross-section slenderness 11

25 a/b = 3 EC3 Hot-rolled EHS (Tests) FE results Fu/Fy a/b = 2 a/b = 1.5 a/b = Class 1-3 Class D e /tε 2 Figure 21. Comparative studies between experimental and parametric results 12

26 2. Hot-rolled EHS 1.5 Elastic buckling σu/σy 1. Material yielding σ y /σ cr Figure 22. Ultimate strength of hot-rolled EHS under uniform axial compression 13

27 Table 1. Mean measured dimensions and key results of tensile coupons tests Specimen Width b (mm) Thickness t (mm) Young s Modulus E (N/mm 2 ) Yield stress y (N/mm 2 ) Ultimate tensile stress u (N/mm 2 ) TC TC TC TC TC TC TC TC TC TC TC TC TC TC TC TC TC TC TC2 29, TC TC TC TC TC TC

28 Table 2. Mean measured dimensions of stub column specimens Specimen Larger outer diameter 2a (mm) Smaller outer diameter 2b (mm) Thickness t (mm) Area A (mm 2 ) Length L (mm) Measured maximum imperfection w (mm) SC SC SC SC SC SC SC SC SC SC SC SC SC SC SC SC SC SC SC SC SC SC SC SC SC

29 Table 3. Summary of results from stub column tests Specimen Ultimate load F u (kn) End shortening at F u, δ u (mm) F u /F y SC SC SC SC SC SC SC SC SC SC SC SC SC SC SC SC SC SC SC SC SC SC SC SC SC

30 Table 4. Comparison of stub column test results with FE results for varying imperfection amplitude w Specimen FE F u /Test F u w =t/1 w =t/1 w =t/5 Measured w SC SC SC SC SC SC SC SC SC SC SC SC SC SC SC SC SC SC SC SC SC SC SC SC SC MEAN COV