CFDST sections with square stainless steel outer tubes under axial compression: Experimental investigation, numerical modelling and design — Source link

concrete-filled double skin CHS with austenitic Experimental Study of Square and Rectangular CFDST Sections with Stainless Steel Outer Tubes under Axial Compression concrete-filled steel tubular (CFST) structures: Members Finite element modelling of concrete-filled steel stub columns under axial compression Numerical modeling of rectangular concrete-filled double-skin steel tubular columns with outer stainless-steel skin Abstract 16 The use of concrete-filled double skin tubular (CFDST) cross-sections for compression 17 members has become increasingly popular in construction. A recently proposed innovative 18 form of CFDST cross-section, ultilising stainless steel for the outer tube, offers the combined 19 advantages of the composite action seen in CFDST member alongside the durability and 20 ductility associated with stainless steel. CFDST sections with stainless steel outer tubes, for 21 which there are currently little experimental data, are the focus of the present study. A 22 comprehensive experimental and numerical investigation into the compressive behaviour of 23 CFDST sections with square stainless steel outer tubes is presented in this paper. A total of 19 24 specimens was tested under uniform axial compression, and the test observations are fully 25 reported. The ultimate loads, load-displacement curves and failure modes from the tests were 26 used for the validation of finite element (FE) models. Parametric finite element analyses were 27 then performed. The combined set of experimentally and numerically derived data was 28 employed to assess the applicability of the existing European, Australian and American design 29 provisions for composite carbon steel members to the design of the studied CFDST cross- 30 sections. Overall, the existing design rules are shown to provide generally safe-sided (less so 31 for the higher concrete grades) but rather scattered capacity predictions. Modifications to the 32 current design codes are also considered — a higher buckling coefficient k of 10.67 to consider 33 the beneficial restraining effect of the concrete on the local buckling of the stainless steel outer 34 tubes, as well as a reduction factor η to reflect the reduced relative effectiveness of higher 35 concrete grades. Overall, the comparisons demonstrated that improved accuracy and 36 consistency were achieved when the modified design rules were applied.

found to be rather scattered. With the aim of exploiting the most favourable properties of the 77 constituent materials in CFDST columns to the greatest possible extent, a novel type of CFDST 78 section is proposed in this study, employing a high strength steel circular hollow section (CHS) 79 for the inner tube and a stainless steel square hollow section (SHS) for the outer tube. The  given in the European Code EN 1994-1-1 (EC4) [21], Australian Standard AS5100 [22] and 93 American Specifications AISC 360 [23] and ACI 318 [24] to the design of the studied CFDST   99

100
A typical CFDST section with a high strength steel CHS as the inner tube and a stainless steel 101 SHS as the outer tube is presented in Fig. 1. The stainless steel grade employed in the present 102 study was austenitic grade EN 1.4062 [25]. Two cross-sections, SHS 120×120×6 mm (depth × D and t are the diameter and thickness for the CHS. The subscripts o and i are used to 118 differentiate between the outer and inner tubes; rint and rext denote the internal and external 119 corner radii of the outer tubes and Ai, Ao and Ac correspond to the calculated cross-sectional 120 areas of the inner tube, outer tube and sandwiched concrete. A labelling system for the studied CFDST specimens was designed so as to identify the CFDST 122 cross-section constituents directly. For example, AS120×6-HC22×4-C120 defines a CFDST 123 specimen with an AS120×6 (Do×to) outer tube, with the letter "A" standing for austenitic 124 stainless steel and "S" representing an SHS, and an HC22×4 (Di×ti) inner tube, with "H" 125 standing for high strength steel and "C" representing a CHS. The letter "C" after the second 126 hyphen denotes concrete infill, followed by the nominal concrete grade of C120. A label with 127 a suffix "R" represents a repeat specimen. 128 129 Longitudinal tensile coupon tests were carried out to obtain the material stress-strain properties 130 of the metal tubes. Since cold-formed metal tubes undergo strength enhancement due to cold-131 working during production, which is particularly pronounced in the corner areas of sections, 132 coupons were extracted from both the corner and flat regions of the SHS outer tubes, as 133 illustrated in Fig. 3(a). For the cold-formed CHS inner tubes, a curved coupon was extracted 134 from the quarter position around the cross-section relative to the weld, whereas for the seamless 135 hot-rolled inner tube, a coupon was extracted from a random location within the cross-section, 136 as shown in Fig. 3(b). Each tensile coupon extracted from the CHS inner tubes was labelled by 137 its cross-section identifier, while the flat (F) and corner (C) coupons extracted from the SHS 138 outer tubes were differentiated by their cross-section identifier and a suffix (either F or C)  flat coupons were gripped using a set of end-clamps, while a pair of steel rods was inserted into the drilled holes of the corner coupons, through which the tensile force was applied, as shown 145 in Fig. 4. A contact extensometer was attached to the coupons and a strain gauge was affixed 146 to each side of the coupons at mid-length. All the longitudinal tensile coupon tests were 147 displacement controlled and conducted in an MTS 50 kN testing machine. A constant 148 displacement rate of 0.05 mm/min was used in the elastic range of the stress-strain curves, 149 whereas a higher rate of 0.4 mm/min was used in the inelastic range; in the post-ultimate range, 150 a rate of 0.8 mm/min was adopted, as recommended in Huang and Young [28].

154
The process of cold-forming was shown to result in a moderate enhancement in both σ0.2 and 155 σu in the corner regions, though this is accompanied by a reduction in ductility. Comparisons 156 of the full stress-strain curves in Fig. 5 reveal that the high strength steel inner tubes possess 157 higher 0.2% proof stresses and ultimate strengths, but less pronounced strain hardening and 158 much lower ductility than the stainless steel outer tubes.

159
Concrete cylinder tests were performed to obtain the material properties of the concrete. Three 160 concrete grades-C40, C80, and C120 MPa-were produced in the laboratory using 161 commercially available materials. Their mix proportions are presented in Table 3. For each 162 batch of concrete, cylinders were cast and air-cured together with the CFDST test specimens.

163
Two concrete cylinders were utilised to obtain the average 28-day concrete strengths and the 164 remainder were tested on the days of the respective CFDST specimen tests. Table 4 summarises 165 the mean measured strengths and the test number for each concrete grade.

Axial compressive testing
A total of 19 CFDST specimens, including four repeated to assess the variability of the results, 168 was tested under uniform axial compression in an INSTRON 5000 kN capacity servo-169 controlled hydraulic machine. A typical CFDST stub column test setup is illustrated in Fig.   170 6(a). The ends of each specimen were clamped using a steel reinforcing frame with a 25 mm 171 height to avoid premature end failure, as shown in Fig. 6(b). A thin layer (< 1 mm) of plaster 172 was applied to the top surface of the cast CFDST specimens to eliminate any gaps arising due   [33,34]. The load-true average axial strain curves were derived by assuming 184 that the end platen deformation was proportional to the applied load and shifting the load-axial 185 strain curve derived from the LVDTs such that its initial slope matched that obtained from the

Test results
The load (P) versus average axial strain (ε) curves for all the stub column specimens are plotted  Table 1. The ultimate strength of test specimen  HC89×4-C80 appeared to be slightly lower than expected. This may have stemmed from the 197 presence of excess air voids in the concrete, that were not eliminated during the specimen 198 preparation. The P-ε curves for two stocky specimens did not reach a peak value despite large 199 plastic deformations; these specimens are marked with an asterisk in Table 1. For these 200 specimens, the ultimate load was defined as the load at which the tangential stiffness of the 201 load-average axial strain curve reached 1% of its initial stiffness, taken as the average slope in 202 the initial linear portion of the curve. This approach was proposed by dos Santos et al. [35] and 203 has been employed for the definition of the ultimate loads of CFDST stub columns in [8]. From 204 the load-deformation curves, it was observed that CFDST columns using stainless steel for the 205 outer tubes generally exhibited a rather more rounded and ductile response than that seen from 206 existing tests on carbon steel CFDST stub columns [9,10]; this mirrors the findings for 207 concrete-filled stainless steel tubular members in [13]. This behaviour is directly linked to the 208 rounded stress-strain response and substantial strain hardening that characterises stainless steel 209 alloys.

210
The ductility of the CFDST stub columns was assessed through the ductility index (DI) 211 [8,18,20], which is defined as the ratio of the axial displacement when the load dropped to 85%  deformation. Overall, it is evident that all the tested stub columns generally possessed high 217 ductility, and that higher concrete strengths resulted in increased compressive resistance but 218 lower ductility. It can also be seen that the DI values for the specimens with the highest strength 219 inner tubes (HC89×4) were generally lower than their counterparts with lower strength inner 220 tubes (HC22×4 and HC32×6).   An FE model of each test specimen presented in Section 2 was established based on the 236 measured geometries using S4R shell elements [36] for the metal tubes and C3D8R solid elements for the sandwiched concrete, in line with previous FE modelling of concrete-filled 238 tubular members [8,[37][38][39][40]. In the tests, the geometry, loading and failure modes were doubly 239 symmetric. Hence, to enhance computational efficiency, only one-quarter of the cross-sections 240 and half of the member lengths were modelled, with suitable boundary conditions assigned to 241 the planes of symmetry, as depicted in Fig. 9. Following a prior mesh sensitivity study, uniform 242 mesh seed sizes of min(Do/30, πDi/60) were chosen for the CFDST cross-sections, while 30 243 seeds were applied in the longitudinal direction; these mesh settings were found to produce 244 accurate yet computationally efficient results.

245
The measured material properties were incorporated into the respective FE simulations for 246 validation purposes. For the metal tubes, the measured engineering stress-strain curves, 247 characterised by at least 100 points from the tensile coupon test curves, were converted into 248 true stress-true plastic strain curves, and input into ABAQUS. For the austenitic stainless steel 249 SHS, the coupon tests revealed that the yield strength of the corner material was about 20% 250 higher, on average, than that of the flat material. Allowance for this was therefore made in the 251 developed FE models by assigning the corner material properties to the curved corner regions 252 of the SHS plus an extended region equal to two times the section thickness into the adjacent 253 flat region, following the recommendations of [41]. For the sandwiched concrete, the Abaqus 254 concrete damage plasticity (CDP) model [36] was adopted, with the confined concrete stress-255 strain response, based on that proposed by Tao et al. [37] for CFST stub columns, as modified 256 by Wang et al. [8] for application to CFDST stub columns with CHS outer tubes. The 257 modifications were concerned primarily with the confinement factor (ξc), defined in Eq. (1), where Ace is an equivalent cross-sectional area of concrete, defined as the full area enclosed by 260 the outer tube, as given by Eq. (2).
The Poisson's ratio of the concrete and modulus of elasticity Ec were taken respectively as 0.2 263 and 4733 c f , according to the recommendations of ACI 318 [24]. For the tensile stress-strain 264 properties of the concrete, a linear response was assumed before reaching the tensile strength 265 (taken as 0.1 fc) ; the subsequent post-peak behaviour was characterised through fracture energy 266 (GF) [36,37].

267
The interaction between the outer and inner tubes and the concrete was simulated by surface- parameter sensitivity study had indicated that the behaviour of the studied CFDST stub 272 columns was relatively insensitive to the value of this parameter [42]. This is principally 273 because the slip at the interfaces was negligible since the concrete and the metal tubes deformed 274 simultaneously during the tests.

275
Initial local geometric imperfections and residual stresses are known to influence the 276 compressive performance of bare steel members [43][44][45][46], but have been shown [37]  compared; a typical series of specimens with three concrete grades are displayed in Fig. 10; for 293 the FE models, the true average axial strain was determined as the average axial shortening 294 divided by the original length of the modelled specimen. The comparisons showed that the FE 295 models could reproduce accurately the full loading histories of the respective stub column tests.

296
Good agreement was also obtained for the exhibited failure modes, as shown in Fig. 8 200. Table 5 summarises the range of the aforementioned parameters investigated in this study.

310
All the modelled specimen lengths were set equal to 2.5Do, mirroring the test specimens.

311
Overall, a total of 290 CFDST specimens was modelled in the parametric study.    (4) and (5), is used for calculating the effective area of the outer tube:  The Australian Standard AS 5100 [22] adopts the same approach to obtain the axial 349 compressive design strengths as EC4 [21], with the only difference being the slenderness limit.  where  is a local slenderness, Fn is the overall buckling stress of the column and requires the 362 calculation of the tangent modulus (Et) using an iterative design procedure, and the other 363 symbols are as previously defined in Eq. (4). In this study, Fn is essentially equal to σ0.2,o due to the short length of the stub columns and k is again taken as 4 referring to AS/NZS 4673 [49]. 365 Hence, the slenderness  defined by Eq. (8) simplifies to that employed in EN 1993-1-4 [47], where Pp and Py are determined from Eq. (10) and (11) respectively, =do/to is the local 376 slenderness of the outer tube, p and r correspond to the limits between compact/noncompact 377 and noncompact/slender sections, and fcr is the elastic critical local buckling stress of the outer It should be noted that the contribution from the inner tube is treated as an independent term, 383 rather than a concrete dependent term as for the reinforcing bars, in the resistance function; 384 further explanation has been provided in previous work by the authors [8,20].

385
The American Concrete Institute design provisions for CFST sections, as set out in ACI 318 386 [24] are also assessed herein. The confinement afforded to the concrete from the steel tube is

391
The gross area of the outer tube may be used in Eq. (13) provided that the tube thickness 392 satisfies to ≥ Do(σ0.2,o/3Eo) 0.5 [24]. No guidance is given in ACI 318 for sections outside this where p  is the local slenderness, termed  in SEI/ASCE-8-02 [50], Fn is the column buckling 400 stress, calculated using an iterative tangent modulus approach, and the other symbols are as 401 previously defined. Taking k equal to 4 according to SEI/ASCE-8-02 [50], Fn equal to σ0. 2

Modification for high strength concrete
The accuracy in predicting the cross-section strengths for all the studied codes can be seen in 425 The experimental and numerical results are compared with the modified capacity predictions 437 in Table 8  infill alters the failure mode of the outer steel tube by restricting it from buckling inwards. It has been shown that the elastic buckling coefficient k increases from 4 for conventional (two-447 way) local buckling of simply-supported plates to 10.67 for outward only local buckling [53].

448
A modified local buckling coefficient k of 10.67, rather than 4, has therefore been employed 449 previously by the authors [20] to reflect the restraining effect of the concrete on the local 450 buckling of the stainless steel outer tubes. This approach is also assessed herein in the 451 implementation of the design rules in EC4 [21], AS 5100 [22] and ACI 318 [24], taking the  [54,55], a slenderness limit of 2.26(E/Fy) 0.5 is adopted for concrete-filled 460 tubes in AISC 360 [23].

461
The modified axial capacity predictions from EC4 [21], AS 5100 [22] and ACI 318 [24] 462 incorporating the higher buckling coefficient k of 10.67, and the unmodified design predictions, 463 with k=4, are compared with the test and FE ultimate strengths in Table 9   test and FE data were then employed to assess the applicability of the rules given in EC4 [21], 488 AS 5100 [22], AISC 360 [23] and ACI 318 [24] for composite carbon steel members to the 489 design of the studied CFDST cross-sections. Overall, the current design rules in EC4 [21] and 490 AS 5100 [22] provide good average axial capacity predictions but result in a high number of 491 strength predictions on the unsafe side, while AISC 360 [23] and ACI 318 [24] provide