Axial slenderness limits for austenitic stainless steel-concrete composite columns

Journal of Constructional Steel Research xxx (xxxx) xxx

Contents lists available at ScienceDirect

Journal of Constructional Steel Research journal homepage: www.elsevier.com/locate/ijcard

Axial slenderness limits for austenitic stainless steel-concrete composite columns Sina Kazemzadeh Azad*, Dongxu Li, Brian Uy School of Civil Engineering, The University of Sydney, Sydney, NSW, 2006, Australia

a r t i c l e i n f o

a b s t r a c t

Article history: Received 20 March 2019 Received in revised form 22 October 2019 Accepted 2 November 2019 Available online xxx

The use of stainless steel in steel-concrete composite construction is an emerging topic considering the higher durability, corrosion resistance, and fire resistance as well as aesthetic benefits and ease of maintenance of stainless steel compared to carbon steel. In line with this, the present paper reports the results of a series of experimental and numerical investigations on the local and post-local buckling of austenitic stainless steel-concrete composite columns with an aim to propose axial slenderness limits as well as effective width/diameter formulae for these members. Such limits have not yet been established for stainless steel-concrete composite members in international design standards. Three section types, namely, concrete-filled box, concrete-filled circular, and partially-encased I-sections are thoroughly studied. The investigated columns include some of the largest and most slender stainless steel-concrete composite sections studied to date. The obtained results are compared with theory as well as approaches currently in use by international design standards. It is demonstrated that the codified slenderness limits developed for carbon steel-concrete composite columns cannot be directly used for the stainless steel counterparts and modifications are required. The modifications are recommended in light of the findings of the present study. In addition to axial slenderness limits, effective width/diameter formulae are also recommended for the studied section types. © 2019 Elsevier Ltd. All rights reserved.

Keywords: Stainless steel Austenitic Concrete-filled Partially-encased Slenderness limit Fabricated

1. Introduction Steel-concrete composite columns are used extensively as economic load-carrying members in buildings and bridges. In these columns, steel and concrete are used efficiently by combining the advantages of each material type. Composite columns can be broadly categorised into encased, partially-encased, and concretefilled. Encased composite columns (Fig. 1a) were initially introduced in the 1890s to enhance the fire and corrosion resistance of steel columns while their structural advantages were revealed later [1e3]. Partially-encased composite columns (Fig. 1b), which became popular in the 1980s in Europe, can reduce the required amount of formwork while enhancing the fire resistance as well as the load-bearing capacity of the steel section through preventing the web buckling and inward flange buckling [4]. The steel tube in concrete-filled steel tubular (CFST) columns (Fig. 1ced) acts as a permanent formwork as well as a confinement mechanism for the concrete. In return, the concrete prevents the inward buckling of the steel tube [5e7]. An enormous amount of research has been

* Corresponding author. E-mail address: [email protected] (S. Kazemzadeh Azad).

conducted on the behaviour and design of composite columns during the last decades covering a wide range of topics. Comprehensive reviews of these studies have been presented by Shanmugam and Lakshmi [8] and more recently by Han et al. [9]. The use of stainless steel in structural applications, first studied in the 1950s in North America [10e12], has gained notable popularity in recent years considering its benefits such as improved durability, corrosion resistance, and fire resistance as well as its aesthetic benefits, sustainability and recyclability, and ease of maintenance compared to carbon steel [13e16]. Austenitic and duplex are the most commonly used stainless steel groups in structural applications considering issues such as the required corrosion resistance, weldability, formability, toughness, and ductility. A new family of cost-effective duplex stainless steels, namely lean duplex, has also been recently developed with lower nickel and molybdenum content [17e19]. A recent development in the field of composite construction is the use of stainless steel instead of carbon steel. Roufegarinejad et al. [20] proposed the concept of concrete-filled stainless steel tubular (CFSST) columns in 2004. This was followed by the numerical and experimental studies of other researchers such as Young and Ellobody [21,22], Dabaon et al. [23], and Lam and

https://doi.org/10.1016/j.jcsr.2019.105856 0143-974X/© 2019 Elsevier Ltd. All rights reserved.

Please cite this article as: S. Kazemzadeh Azad et al., Axial slenderness limits for austenitic stainless steel-concrete composite columns, Journal of Constructional Steel Research, https://doi.org/10.1016/j.jcsr.2019.105856

2

S. Kazemzadeh Azad et al. / Journal of Constructional Steel Research xxx (xxxx) xxx

Fig. 1. Examples of composite columns.

Gardner [24] on short square, rectangular, circular, and stiffened CFSST columns. Comprehensive experimental results were reported by Uy et al. [25] in 2011 where over 110 short and long, hollow and filled stainless steel columns were experimented under concentric and eccentric axial forces. The study was followed by a comprehensive numerical study by Tao et al. [26] where a simplified design formula was also developed. Lately, the behaviour of CFSST columns with other types of outer tubes such as elliptical [27] or spiral-welded tubes [28] have also been investigated. Notably more tests have been carried out to date on austenitic CFSSTs with fewer experiments on duplex [21] and lean duplex specimens [29,30]. A comprehensive review of studies on CFSST columns has recently been conducted by Han et al. [31]. The common consensus in the above studies is that CFSST is an attractive alternative to CFST particularly in corrosive environments and regions where the maintenance cost is high. A careful examination of the literature revealed that the experiments conducted on CFSSTs have mostly focused on sections with low width-to-thickness ratios. Furthermore, there are no studies specifically on determining the slenderness limits for CFSST or partially-encased stainless steel columns. In other words, the first step in the design of a stainless steel-concrete composite column, which is the classification of its section type (compact, slender, etc.), has not yet been properly explored. Consequently, the main aim of the present study is to determine the axial slenderness limits for these columns by studying their local and post-local buckling behaviour through experimental and numerical investigations. The experimental programme is discussed in the next section followed by the presentation of the test results in Section 3. Details of the numerical investigation including the verification of the finite element (FE) modelling approach and a parametric study are given in Section 4. Both the experimental and numerical results are thoroughly discussed in Section 5 and synthesised to propose new slenderness limits and effective width/diameter formulae. Conclusions of the study are presented in the last section. 2. Experimental programme 2.1. Details of specimens A total of 16 stainless steel-concrete composite columns with a wide range of section slenderness values were tested at the J. W. Roderick Laboratory of the Centre for Advanced Structural Engineering (CASE) of the University of Sydney. As shown in Fig. 2, concrete-filled box and circular sections as well as partiallyencased I-sections were tested as part of the study. The box and I-sections (Fig. 2a,c) were fabricated from austenitic stainless steel plates of 5 mm thickness which were laser cut and fillet welded together. Each circular section (Fig. 2b), on the other hand, was fabricated by first rolling a 3 mm thick austenitic stainless steel plate to the required diameter and then longitudinally welding it with a single-V groove weld. The only exception was the largest circular specimen, with a diameter of 540 mm, which was

fabricated as two longitudinally welded cans connected together with a girth weld. This was necessary due to the dimensional limitations associated with the supplied stainless steel plates. Specimen welding and inspection were carried out in accordance with the requirements of AS/NZS 1554.6 [32]. A gas metal arc welding (GMAW) procedure, more specifically metal inert gas (MIG) welding, was used during the fabrication of specimens utilising dual-certified ER308/308L consumables. Geometric details of the specimens are summarised in Table 1. Nominal as well as measured sectional dimensions are presented. The measured width of the box and I-section specimens was calculated as the average of the widths measured at three sections along the member length using a digital calliper. For circular specimens, a circumference measuring tape was used at three sections along the specimen to calculate an average circumference which was then used to back-calculate the measured outer dimeter of the specimen. In order to measure the thickness of the utilised plates, the thickness of the coupons extracted from the plates for material testing (Section 2.2) was measured using a digital calliper with 0.1 mm accuracy. As reported in Table 1, the measured thicknesses were found to be identical to the nominal values considering the accuracy of the measurement device. The specimens are designated with an “A”, for austenitic, followed by their sections type (“B” for box, “C” for circular, and “I” for I-section) and nominal width/diameter in millimetres. For instance, A-C480 is an austenitic circular section with a diameter of 480 mm. Based on initial analyses, the nominal slenderness values (b/t or d/t) for the specimens were selected with the aim of covering a reasonable range of compact and slender sections as well as adhering to the limitations of the testing facility. It is worth noting that the investigated columns include some of the largest and most slender stainless steel-concrete composite sections studied to date. For instance, specimen A-B500, the largest box section tested herein, weighed over 1500 kg after concrete pouring and connection of its end-plates. The length (L) of each column was selected as three times the total width (or diameter) of the section under consideration in order to avoid any global buckling modes while ensuring that the results are representative of the sectional behaviour [5,24,25,33,34]. As schematically shown in Fig. 2, a recess of 40 mm at each end was considered in the concrete infill of all specimens. The idea was to ensure that the axial loading was applied only to the stainless steel section (and not the concrete infill) in order to have an isolated and focused investigation on the local stability of the stainless steel sections in the studied composite columns. This approach has been successfully used in previous studies [5,7,33,35] and is further elaborated later. The recess at the bottom was created by inserting, sealing, and fixing special waterjet cut extruded polystyrene foam inside the section prior to concrete pouring whereas the top recess was created by filling the concrete shorter than the stainless steel section. In addition to the parameters depicted in Fig. 2, Ns in Table 1 represents the number of evenly-distributed stiffeners at each end of a specimen. For instance, Fig. 2a shows a box section

Please cite this article as: S. Kazemzadeh Azad et al., Axial slenderness limits for austenitic stainless steel-concrete composite columns, Journal of Constructional Steel Research, https://doi.org/10.1016/j.jcsr.2019.105856

S. Kazemzadeh Azad et al. / Journal of Constructional Steel Research xxx (xxxx) xxx

3

Fig. 2. Details of tested specimens: (a) box; (b) circular; and (c) I-section (all dimensions in mm).

Table 1 Details of tested specimens. Type Box

Circular

I-Section

a b

Specimen A-B200 A-B250 A-B300 A-B350 A-B400 A-B450 A-B500 A-C300 A-C360 A-C420 A-C480 A-C540 A-I50 A-I100 A-I150 A-I200

b or d (mm) 200 [199.1] 250 [249.1] 300 [298.6] 350 [348.3] 400 [399.1] 450 [449.0] 500 [498.8] 300 [300.3] 360 [360.0] 420 [420.3] 480 [479.8] 540 [540.3] 50 [49.8] 100 [99.7] 150 [149.9] 200 [199.8]

a

t (mm) 5 5 5 5 5 5 5 3 3 3 3 3 5 5 5 5

b

L (mm)

s (mm)

Ns

b/t or d/t

L/b or L/d

600 750 900 1050 1200 1350 1500 900 1080 1260 1440 1620 300 600 900 1200

25 25 45 45 45 45 45 25 25 45 45 45 25 25 45 45

8 12 12 12 12 12 16 8 8 8 10 10 4 4 4 4

40 50 60 70 80 90 100 100 120 140 160 180 10 20 30 40

3 3 3 3 3 3 3 3 3 3 3 3 6 6 6 6

The dimensions outside the bracket are nominal whereas those inside the bracket are measured. The thickness of the extracted coupons was measured as 5.0 mm and 3.0 mm using a 0.1 mm-accuracy calliper.

with Ns ¼ 12 as a representative case. These stiffeners were included to prevent the occurrence of premature local buckling near the recesses, where the stainless steel section did not have an internal restraint. After initial preparations, the concrete was directly poured into the box and circular sections. For I-sections, plywood with moisture resistant film was connected to the sides of the column as formwork and stiffened with timber battens, and then, concrete was poured inside the formwork. Concrete pouring, compacting, curing, and removal of formwork were conducted in accordance with AS/ NZS 2327 [36] and AS 3600 [37].

2.2. Material properties All specimens were fabricated from grade 304/304L (EN 1.4301/ 1.4307) austenitic plates. Both 304 and 304L grades are among the most commonly used stainless steel grades in structural applications. While the mechanical characteristics of the two grades are quite similar, the “L” in grade 304L indicates a low-carbon version with reduced corrosion risk in the vicinity of welds. Similar to the plates utilised herein, stainless steel manufacturers have often been producing dual-certified austenitic grades (304/304L) in recent years [19].

Please cite this article as: S. Kazemzadeh Azad et al., Axial slenderness limits for austenitic stainless steel-concrete composite columns, Journal of Constructional Steel Research, https://doi.org/10.1016/j.jcsr.2019.105856

4

S. Kazemzadeh Azad et al. / Journal of Constructional Steel Research xxx (xxxx) xxx

A total of eight standard coupons were extracted from the original plates used in the fabrication of the specimens; four along the rolling direction of the plates (longitudinal) and four in the perpendicular direction (transverse). The coupons were tested in accordance with AS 1391 [38] using an MTS Sintech 65/G testing machine. A procedure with two stress relaxation periods, described in detail by Huang and Young [39], was followed in order to obtain static material properties from the coupon tests. The obtained material properties, including the modulus of elasticity (E), 0.01% and 0.2% proof stresses (s0.01 and s0.2 respectively), ultimate stress (fu), strain at fracture (εf), and RambergOsgood parameter (n) are summarised in Table 2 for the utilised 3 mm- and 5 mm-thick austenitic plates. Each coupon is designated with an “A” for austenitic followed by its thickness and direction (“L” for longitudinal and “T” for transverse). The results compared well with the nominal properties of the studied austenitic grade [40] as well as the material certificates provided by the plate manufacturer. The recorded stress-strain curves are also depicted in Fig. 3 along with the photos of the failed coupons. Due to the roundness of material response and lack of yield plateau, s0.2 is typically used as the yield stress (fy) for stainless steels; a similar approach was used herein. As expected for austenitic materials, very high levels of ductility (in excess of 60%) and strain hardening were recorded. By comparing the results for the longitudinal and transverse coupons, it can be observed that the level of anisotropy was reasonably low in the plates. As noted earlier, only the stainless steel sections were loaded in the studied columns. The concrete infill therefore acted only as a means of preventing the inward buckling of the stainless steel section. Consequently, the material properties of the concrete infill did not have a crucial role in the behaviour of the specimens. Nevertheless, a series of concrete cylinder samples with a diameter of 150 mm and height of 300 mm were cast during the pouring, cured, capped, and tested as per AS 1012 [41]. The mean compressive strength of the concrete (fc) was found to be 42 MPa at 28 days, which was the start of the column tests as well.

2.3. Measurement of imperfections The geometrical imperfections of the columns were measured prior to their testing. Compared to cold-formed sections, such measurements are infrequent in the literature for fabricated stainless steel sections, such as those studied in the present paper [42,43]. Considering the length of the specimens, only local imperfections were measured. Compared to a carbon steel fabrication, more attention was given by the fabricator to avoid extensive welding distortions in the fabricated stainless steel sections due to the lower thermal conductivity and higher coefficient of thermal expansion of the latter material. Post-fabrication straightening was however not performed on the columns.

2.3.1. Box and I-Sections The imperfections for the box and I-section columns were measured using an AR200-25 laser-based distance measurement sensor with an accuracy of 0.0508 mm and a resolution of 0.0076 mm. As shown in Fig. 4a, the laser was mounted on a special trolley which was smoothly guided along two straight bars at a constant speed with the help of a stepper motor. Imperfections were measured for all four sides of the box and for both flanges and the web of the I-section specimens, at five equally-spaced sections along the length (S1 to S5). Based on the classic categorisation of steel imperfections [44], the local imperfections for the box and Isection specimens were defined as the deviation from the reference sectional geometries as shown in Fig. 5. Imperfections were measured for half of the specimens, namely A-B200, A-B350, A-B500, A-I100, and A-I200, as representative cases. A MATLAB code was developed which analysed the laser measurements, compares them with the reference geometry, calculated the imperfections accordingly, and summarised the results in a scaled plot as shown in Fig. 6 for some of the specimens. In this figure, S1 to S5 indicate the measurements at the five equallyspaced sections. The numerical values for all the measurements are given in Table 3. In this table, d for box sections indicates the maximum of d1 to d4 in Fig. 5a, dfl for I-sections indicates the maximum of d1 to d4 in Fig. 5b, and dw is equal to d5 in Fig. 5b. Based on Table 3, an average value of b/450 for box sections and bf/120 for flanges of I-sections (bf is the flange width) can be considered as the maximum amplitude of local imperfections for the studied fabricated sections. The corresponding fabrication tolerances are b/125 and bf/150 to bf/100, respectively, as per AS/NZS 5131 [45] and EN 1090-2 [46]. 2.3.2. Circular sections Measurement of local imperfections is much more complicated for the case of circular specimens and, therefore, a special technique was developed which is illustrated in Figs. 4b and 7. To this end, using a high-precision waterjet cutter (with a linear positional accuracy of 0.0762 mm), a measurement ring (Fig. 7a) was first cut at the laboratory with an outer radius of 435 mm and twenty radial measurement stations (ST01 to ST20). A light-weight laser holder was then fabricated to which an ILD1302-200 laser-based distance measurement sensor with an accuracy of 0.4 mm and a resolution of 0.04 mm was mounted. As shown in Fig. 7a, the laser holder could be connected to each measurement station using four smalldiameter bolts. These bolts were equipped with levelling nuts in order to level the laser at each station. After fixing the circular specimen and the ring at the desired height (Fig. 4b), the radial distance (ri) at each station (STi) was determined as ri ¼ 435-ai-bi where, as shown in Fig. 7a, ai is the distance between the outer end of the ring and the laser (measured using a calliper) and bi is the distance recorded by the laser. It should be emphasised that the specimen could be positioned at any location inside the ring and needed not to be centred. After

Table 2 Material properties obtained from the coupon tests. Coupon

t (mm)

E (GPa)

s0.01 (MPa)

s0.2 [fy] (MPa)

fu (MPa)

fu/fy

εf (%)

n

A3-L1 A3-L2 A3-T1 A3-T2 Mean A5-L1 A5-L2 A5-T1 A5-T2 Mean

3 3 3 3 3 5 5 5 5 5

202.2 200.0 201.9 203.6 201.9 192.8 189.3 187.1 201.0 192.6

161 165 179 181 172 184 181 195 191 188

261 271 261 260 263 264 265 283 273 271

613 622 600 588 606 584 580 580 583 582

2.3 2.3 2.3 2.3 2.3 2.2 2.2 2.0 2.1 2.1

68 62 70 69 67 72 73 73 73 73

6.2 6.0 7.9 8.3 7.1 8.3 7.9 8.0 8.4 8.1

Please cite this article as: S. Kazemzadeh Azad et al., Axial slenderness limits for austenitic stainless steel-concrete composite columns, Journal of Constructional Steel Research, https://doi.org/10.1016/j.jcsr.2019.105856

S. Kazemzadeh Azad et al. / Journal of Constructional Steel Research xxx (xxxx) xxx

5

Fig. 3. Stress-strain curves obtained from the coupon tests.

(i.e. d), maximum diameter (dmax), and minimum diameter (dmin) at the section. The diameters were then used to calculate out of roundness as per EN 1090-2 [46]:


  ðdmax  2tÞ  ðdmin  2tÞ  100 O % ¼ ðd  2tÞ

(1)

Fig. 4. Imperfection measurement methods used for (a) box and I-sections and (b) circular sections.

It is worth noting that the measurement method was rather laborious and required hundreds of manual adjustments and recordings for each specimen. Nevertheless, it was deemed fruitful since imperfection measurements for longitudinally welded circular sections in general, and for stainless steel ones in particular, are quite rare in the literature. Although automated measurement techniques have been developed [48], such approaches typically require special facilities and equipment which were not employed in this study. The developed approach however works on the same principles with a reasonable accuracy. As representative cases, imperfections for half of the specimens, namely A-C300, A-C420, and A-C540 were measured. A MATLAB code was again developed for analysing and post-processing of the data. For instance, the results obtained at the five equally-spaced sections (S1 to S5) along specimen A-C540 are depicted in Fig. 6c. The numerical values for all the measurements are summarised in Table 3. An average value of d/140 can be considered as the maximum amplitude of local imperfections for the studied circular sections. The effect of this amplitude on numerical modelling of circular sections is further discussed in Section 4.1.4. The average of maximum out of roundness is about 2.2% which compares well with the fabrication tolerances recommended in EN 1090-2 [46], i.e. 1.4%, 2%, and 3% for Class A (excellent quality), Class B (high quality), and Class C (normal quality) cylindrical shells, respectively.

Fig. 5. Definition of local imperfections and reference geometry: (a) box; and (b) Isection.

2.4. Test setup and instrumentation

completing the radial measurements at all twenty stations, the results were plotted using the obtained polar coordinates (ri,qi) as shown in Fig. 7b. The measured points were connected using a cubic spline data interpolation. In order to determine local imperfections, it is necessary to first define a reference circle. The diameter of this reference circle shall be equal to the nominal diameter of the specimen (d) under consideration. However, the location of centre for the circle is not known a priori and can drastically affect the results. Consequently, an optimisation routine [47] was used in order to determine the location of centre which would minimise the recorded maximum imperfection (minimise d in Fig. 7c). After determining the location of centre for the reference circle (black dot in Fig. 7c), a straight line passing through the centre was rotated 360 in order to find the maximum imperfection

The columns were tested using an Amsler Testing Machine with a capacity of 5000 kN. The utilised test setup is depicted in Fig. 8. Reusable carbon steel end-plates were first connected to both ends of each specimen using high-strength gypsum with 0.24% expansion and 70 MPa compressive strength at 24 h. It should be noted that the specimen ends were all ground flat by the fabricator prior to delivery to the lab. For specimens with smaller width/diameter than the machine platens, 32 mm-thick end-plates were used, whereas for larger columns, 60 mm-thick end-plates were used in order to uniformly distribute the applied force to the column section (Fig. 8b). As schematically depicted in Fig. 8a, after placing each specimen into the machine, the top crosshead was first lowered down to fix the column in place and then the loading was initiated by upward movement of the bottom hydraulic ram. The quasi-static loading rate was 0.008 mm/s which corresponds to a strain rate of 0.5  105 to 2.5  105 s1 for the studied specimens. The platens

Please cite this article as: S. Kazemzadeh Azad et al., Axial slenderness limits for austenitic stainless steel-concrete composite columns, Journal of Constructional Steel Research, https://doi.org/10.1016/j.jcsr.2019.105856

6

S. Kazemzadeh Azad et al. / Journal of Constructional Steel Research xxx (xxxx) xxx

Fig. 6. Measured local imperfections for three specimens (all dimensions in mm). Imperfections are drastically magnified.

Table 3 Measured local imperfections. Specimen

Parameter

Maximum Imperfection at Section S1

S2

S3

S4

S5

Magnitude

Normalised

A-B200 A-B350 A-B500 A-I100

A-C300

d (mm) d (mm) d (mm) dfl (mm) dw (mm) dfl (mm) dw (mm) d (mm)

A-C420

d (mm)

A-C540

d (mm)

0.27 0.77 1.20 1.73 0.27 3.24 0.34 2.41 1.9 3.15 2.6 2.28 1.3

0.16 0.31 0.70 1.53 0.15 3.07 0.06 2.16 1.2 2.66 2.4 2.47 1.5

0.10 0.22 0.46 1.48 0.19 2.57 0.07 2.01 1.2 2.71 2.4 3.25 1.9

0.16 0.47 0.67 1.34 0.06 2.43 0.09 2.40 2.1 2.88 2.3 2.69 1.6

0.29 1.01 0.95 1.39 0.26 3.29 0.28 2.20 1.8 3.19 2.2 2.76 1.5

0.29 1.01 1.20 1.73 0.27 3.29 0.34 2.41 2.1 3.19 2.6 3.25 1.9

b/688 b/348 b/417 bf/118 hw/748 bf/123 hw/1203 d/125 e d/132 e d/166 e

A-I200

O (%) O (%) O (%)

Maximum Imperfection

Fig. 7. Measurement of local imperfections and definition of reference geometry for circular sections. Fig. 8. Utilised test setup.

of the machine were restrained against rotation. Shortening of each specimen was measured using four linear variable differential transformers (LVDTs). As illustrated in Fig. 8a, LVDT1 and LVDT2 (located at the front) were used for measuring the upward displacement of the bottom end of the column whereas LVDT3 and LVDT 4 (located at the back) were used for measuring that of the top end. It is worth noting that the top end was nominally fixed and, therefore, the measurements from LVDT3 and LVDT4 were very small and limited only to the initial stages of loading where small penetration of the column into the gypsum

occurred for some specimens. Although negligible in the general column behaviour, initial elastic tests revealed that considering these small penetrations by measuring them via LVDT3 and LVDT4 can significantly enhance the accuracy of the measured elastic stiffness of the column when compared to theoretical and finite element results. Consequently, the axial shortening of the column (D) was calculated as the difference between the average recordings of LVDT1 and LVDT2 and the average recordings of LVDT3 and LVDT4.

Please cite this article as: S. Kazemzadeh Azad et al., Axial slenderness limits for austenitic stainless steel-concrete composite columns, Journal of Constructional Steel Research, https://doi.org/10.1016/j.jcsr.2019.105856

S. Kazemzadeh Azad et al. / Journal of Constructional Steel Research xxx (xxxx) xxx

General purpose single element strain gauges were used throughout the experiments to capture the distribution of longitudinal strain on each specimen and to pinpoint the occurrence of local buckling. The typical location of strain gauges on each specimen type is schematically summarised in Fig. 9. Eight strain gauges were used for the box and I-section columns whereas nine were used for the circular cases. The strain gauges were distributed along each specimen to capture the behaviour with a reasonable accuracy. It should be noted that, for a few specimens, the arrangement of strain gauges was slightly altered due to space limitations. Results were recorded by connecting all the instrumentation to a data acquisition system. 3. Experimental results 3.1. Box CFSST sections 3.1.1. Failure modes The studied austenitic box CFSST columns exhibited local buckling (prior to or after yielding considering the slenderness of the section) first observed as a slight outward bulging of the plates which increased significantly with loading. The test was terminated when the column was considered failed due to weld fracture or rapid reduction of column resistance below 80% of its maximum achieved load. These stages are shown in Fig. 10 for specimen AB450. A rather similar failure mode was observed for the other specimens as shown in Fig. 11. For columns with a considerable post-local buckling (or post-buckling) reserve strength, the test had to be continued for a significant duration after the initiation of local buckling to reach failure. For most specimens, such as A-B500, local buckling occurred on all four sides at almost the same height (Fig. 11c). On the other hand, some specimens such as A-B250, exhibited local buckling at slightly different heights on each side (Fig. 11a). Local buckling occurred mostly closer to the top or bottom end of each specimen where the magnitude of measured geometrical imperfections was higher (Table 3). This is related to the higher

7

welding-induced distortions near the end stiffeners. Because of the large ductility of the austenitic material (Fig. 3), very large out-ofplane deformations were observed during the tests, such as those depicted in Fig. 11, prior to failure. This issue was also highlighted in the review study of Han et al. [31]. 3.1.2. Axial behaviour Recorded axial load (P) versus average axial strain (ε) curves for all the box CFSST specimens are plotted in Fig. 12, where ε was calculated as D/L. In this paper, compression is considered positive. As highlighted in Fig. 12a, in each subplot, the yield load is shown with a horizontal dashed line (Y) whereas the instants of local buckling (B) and failure (F) are pinpointed with a filled blue and hollow red circle, respectively. The yield load (Py) was calculated as the area of the stainless steel section, A, times the mean fy value obtained from the coupon tests (Table 2). The instant of failure was determined based on the column failure definition of Section 3.1.1. The instant of local buckling was determined based on the recorded strain histories. To this end, the strain gauge outputs were combined with the recorded average axial stress values (i.e. axial load divided by the stainless steel area) to reach to stress-strain curves such as those depicted in Fig. 13. The numbering of strain gauges in these plots is based on Fig. 9a. The instant of local buckling was then detected as the point after which abrupt changes in the strain history of one or more gauges were detected. This was accompanied by the initiation of outward bulging during the experiments. In order to aid the detection process, the average material response was also added to the stressstrain plots (as a dashed line in Fig. 13) based on the coupon test results (Fig. 3). For instance, the buckling stress for specimen AB400 was detected as 161 MPa in Fig. 13b (corresponding to an axial load of 1285 kN in Fig. 12e) based on the sudden increase in the strain history of SG7 and SG8 after this stress level accompanied by a reduction of strain in the other gauges. This is in line with the experimental observations since local buckling and concentration of deformation occurred at the top region of A-B400 (Fig. 11b) where strain gauges SG7 and SG8 where located in the concave part

Fig. 9. Typical location and numbering of strain gauges.

Please cite this article as: S. Kazemzadeh Azad et al., Axial slenderness limits for austenitic stainless steel-concrete composite columns, Journal of Constructional Steel Research, https://doi.org/10.1016/j.jcsr.2019.105856

8

S. Kazemzadeh Azad et al. / Journal of Constructional Steel Research xxx (xxxx) xxx

Fig. 10. Progress of test for specimen A-B450.

Fig. 11. Typical failure modes for the studied austenitic box CFSST columns.

Fig. 12. Recorded axial load versus average axial strain curves for all box CFSST specimens.

of the buckling wave (with compression on the outer fibre) and, thus, exhibited a sudden increase of strain. Results for the box specimens are summarised in Fig. 12h where the recorded axial loads are normalised with respect to Py of each specimen. Specimens A-B200 and A-B250 reached the yield limit (compact) whereas the other specimens did not (slender). For the compact specimens the load reduction after the ultimate load is much smoother compared to the sharp decrease of resistance observed for the slender specimens after the ultimate load.

Furthermore, the ductility of the section reduces with an increase in the slenderness value (b/t). Stiffer plate edges in corners of box sections allow for the redistribution of stresses after local buckling, enabling the section to retain a portion of its strength and stiffness and to benefit more efficiently from the characteristics of its material type [34]. Consequently, the ductility and residual strength were found to be rather high for the studied austenitic box CFSST sections compared to other similar slenderness tests on carbon steel filled sections

Please cite this article as: S. Kazemzadeh Azad et al., Axial slenderness limits for austenitic stainless steel-concrete composite columns, Journal of Constructional Steel Research, https://doi.org/10.1016/j.jcsr.2019.105856

S. Kazemzadeh Azad et al. / Journal of Constructional Steel Research xxx (xxxx) xxx

9

Fig. 13. Detection of local buckling for box CFSST specimens.

where only the steel tube was loaded [7,33]. The studied box columns were able to reach average axial strains (ε) of 1.6%e4.8% prior to failure. The test results are also summarised in Table 4 where Plb, Pu, slb, su, and εf are the local buckling load, ultimate load, local buckling stress, ultimate stress, and average axial strain at failure, respectively. Furthermore, h, calculated as ðPu  Plb Þ, represents the amount of post-buckling reserve strength that the section exhibited, reported in terms of the percentage of Py. The post-buckling reserve strength is rather high for slender sections and becomes negligible when compact sections are approached. This can also be clearly observed in Fig. 12 where for compact sections (e.g. A-B200) the buckling almost coincided with the ultimate load whereas for slender sections (e.g. A-B400) the column continued to carry a significant amount of additional load even after local buckling. It should be noted that the last column of Table 4 (be/b) is discussed in Section 5.

3.2. Circular CFSST sections 3.2.1. Failure modes For all the austenitic circular CFSST columns, the local buckling mode was characterised by the formation of a uniform outward ring bulge. Unlike the box sections where predominantly weld fracture marked failure, the test for the circular columns was typically terminated due to the abrupt reduction of column resistance below 80% of its maximum achieved load (i.e. 0.8Pu). The formation of the ring bulge was rather rapid, compared to the slower progress of buckling-induced bulging in the box sections, and the localisation of deformations was restricted to a very narrow band along the height of each circular column (Fig. 14). Furthermore, the circular columns failed shortly after experiencing local buckling, indicating negligible post-buckling reserve strength. The lack of post-buckling reserve strength for filled circular members was also demonstrated in the theoretical study of Bradford et al. [49]. As shown in Fig. 15aeb, for most specimens, local buckling occurred near the top or bottom end; the exception was specimen A-C540 (Fig. 15c) in which the local buckling occurred at the midheight where higher amplitudes of imperfection were recorded due to the girth welding (Table 3).

3.2.2. Axial behaviour The P-ε responses recorded for the circular CFSST specimens are plotted in Fig. 16 along with the yield load and instants of buckling and failure. The instant of local buckling was again determined based on the recorded strain histories, such as those depicted in Fig. 17, where the numbering of strain gauges is based on Fig. 9b. A rather different strain history can be observed in Fig. 17c for SG5 of specimen A-C540 with an abrupt reduction of strain, going from compression (þ) to tension (). The reason is that, as it can be seen in Fig. 15c, the strain gauge SG5 was located exactly on the convex part of the buckling wave, with tension on the outer fibre, and, therefore, exhibited a sudden reduction of compressive strain after reaching the local buckling stress of 250 MPa. Normalised results, i.e. P/Py versus ε responses, for all the circular specimens are summarised in Fig. 16f. Only specimens A-C480 and A-C540 were not able to reach their yield capacity and thus can be categorised as slender. Similar to the box sections, lower ductility and sharper loss of resistance after ultimate load can be observed for circular sections with higher section slenderness values. In general, the circular specimens exhibited lower ductilities compared to the box counterparts, reaching only to average axial strains (ε) of 0.4%e0.8% prior to failure. A similar behaviour was observed in the slenderness tests of O'Shea and Bridge [35] on carbon steel filled circular sections where only the steel tube was loaded. As mentioned earlier, the redistribution of stresses in a box section as a result of stiffer plate edges enables the section to experience post-buckling strength and to benefit more efficiently from the characteristics of its material type [34]. However, no such mechanism exists in circular sections which in turn limits their ability to exhibit post-buckling strength and to exploit the high ductility characteristics of the austenitic material. Consequently, the column resistance in the circular CFSSTs dropped below 0.8Pu much earlier than the occurrence of any material fracture. Therefore, not much improvement can be observed in terms of ductility when the austenitic circular tests of the present study are compared with the carbon steel circular tests of O'Shea and Bridge [35]. It is however necessary to note that selecting a different failure criterion might affect this observation. A summary of the experimental results for the circular specimens is also presented in Table 5. As noted earlier, the postbuckling reserve strength (h) is very small (<1% of Py) for both

Table 4 Summary of experimental results for the box CFSST specimens. Specimen

b/t

Py (kN)

Plb (kN)

Pu (kN)

slb (MPa)

su (MPa)

Plb/Py

Pu/Py [Ae/A]

h (% of Py)

εf (%)

be/b

A-B200 A-B250 A-B300 A-B350 A-B400 A-B450 A-B500

40 50 60 70 80 90 100

1084 1355 1626 1897 2168 2439 2710

1160 1285 1260 1267 1288 1278 1160

1168 1348 1457 1554 1714 1655 1677

290 257 210 181 161 142 116

292 270 243 222 214 184 168

1.07 0.95 0.77 0.67 0.59 0.52 0.43

1.08 0.99 0.90 0.82 0.79 0.68 0.62

0.8 4.7 12.1 15.1 19.6 15.5 19.1

4.6 4.8 2.6 2.5 1.9 2.6 1.6

1.08 0.99 0.90 0.82 0.79 0.68 0.62

Please cite this article as: S. Kazemzadeh Azad et al., Axial slenderness limits for austenitic stainless steel-concrete composite columns, Journal of Constructional Steel Research, https://doi.org/10.1016/j.jcsr.2019.105856

10

S. Kazemzadeh Azad et al. / Journal of Constructional Steel Research xxx (xxxx) xxx

Fig. 14. Progress of test for specimen A-C300.

Fig. 15. Typical failure modes for the studied austenitic circular CFSST columns.

Fig. 16. Recorded axial load versus average axial strain curves for all circular CFSST specimens.

compact and slender circular specimens. Therefore, in contrast to the box specimens, local buckling almost coincided with the ultimate load for all the circular specimens (Fig. 16). Although the largest possible columns were tested considering the limitations of

the testing facility, the studied circular specimens did not exhibit Pu/Py values below 0.9. Finite element simulations of Section 4 are used to extend the range of specimens and to substantiate the results.

Please cite this article as: S. Kazemzadeh Azad et al., Axial slenderness limits for austenitic stainless steel-concrete composite columns, Journal of Constructional Steel Research, https://doi.org/10.1016/j.jcsr.2019.105856

S. Kazemzadeh Azad et al. / Journal of Constructional Steel Research xxx (xxxx) xxx

11

Fig. 17. Detection of local buckling for circular CFSST specimens.

Table 5 Summary of experimental results for the circular CFSST specimens. Specimen

d/t

Py (kN)

Plb (kN)

Pu (kN)

slb (MPa)

su (MPa)

Plb/Py

Pu/Py [Ae/A]

h (% of Py)

εf (%)

de/d

A-C300 A-C360 A-C420 A-C480 A-C540

100 120 140 160 180

736 885 1034 1182 1331

803 925 1069 1164 1265

810 927 1077 1170 1270

287 275 272 259 250

289 276 274 260 251

1.09 1.05 1.03 0.98 0.95

1.10 1.05 1.04 0.99 0.95

0.9 0.2 0.8 0.5 0.4

0.8 0.6 0.4 0.4 0.4

1.10 1.05 1.04 0.99 0.95

3.3. Partially-encased I-Sections 3.3.1. Failure modes Local buckling initiated as a small outward bulging in the flanges of the studied austenitic partially-encased I-sections. As shown in Fig. 18, the out-of-plane deformations exacerbated with the continuation of the test. Unlike the studied box and circular specimens, for most I-sections, the test was terminated when a rigidbody movement of the concrete infill was observed (which was typically prior to any weld fracture or excessive reduction in resistance) to avoid any complications in the test procedure. This was related to the fact that the concrete infill in the partiallyencased I-sections was not mechanically connected to the stainless steel section in order to prevent any concrete-related enhancement in the local stability. Consequently, excessive deformations in the section led to the above-mentioned rigid-body movements in some cases. It is believed that the lower bond strength between stainless steel and concrete [31] (compared to carbon steel and concrete) was also influential since such rigidbody movements were not observed in similar previous studies on carbon steel partially-encased I-sections [7,33]. It should be emphasised that the issue did not have any detrimental effect on the recorded local buckling and ultimate loads as they took place earlier than the termination of the test. Based on the distribution of imperfections, local buckling occurred at different locations (at the mid-height or near the ends)

along the flanges of the I-section specimens (Fig. 19). One, or in some cases, two buckling waves formed along each flange edge. It should be noted that the I-sections with slender flanges, such as AI200, exhibited a notable post-buckling reserve strength prior to reaching their ultimate load.

3.3.2. Axial behaviour The recorded axial responses (P-ε) for all the partially-encased Isection columns are plotted in Fig. 20. In each subplot, the yield load and instant of buckling are also indicated. Unlike the plots for other specimen types, the instant of failure is not marked in Fig. 20 since, as discussed in the previous section, the test was terminated before any weld fracture or excessive reduction in resistance for most cases. An exception was specimen A-I50 which was loaded until failure and exhibited a rather high average axial strain (ε) of 4.3%. Similar to Sections 3.1 and 3.2, the instant of local buckling was determined based on the recorded strain histories, such as those depicted in Fig. 21, where the numbering of strain gauges is based on Fig. 9c. For specimen A-I50, however, the buckling occurred at strain values higher than the maximum reliable limit of the utilised strain gauges and, therefore, the buckling instant for this specimen was determined based on visual observation. All the normalised axial responses (P/Py versus ε) for the studied I-sections are plotted in Fig. 20e. As it can be seen, specimen A-I50 exceeded its yield capacity and can be categorised as compact. Specimen A-I100 almost reached Py whereas the slender specimens

Fig. 18. Progress of test for specimen A-I150.

Please cite this article as: S. Kazemzadeh Azad et al., Axial slenderness limits for austenitic stainless steel-concrete composite columns, Journal of Constructional Steel Research, https://doi.org/10.1016/j.jcsr.2019.105856

12

S. Kazemzadeh Azad et al. / Journal of Constructional Steel Research xxx (xxxx) xxx

Fig. 19. Typical failure modes for the studied austenitic partially-encased I-sections.

Fig. 20. Recorded axial load versus average axial strain curves for all partially-encased I-sections.

Fig. 21. Detection of local buckling for partially-encased I-sections.

A-I150 and A-I200 did not attain their yield limit. The experimental results are also summarised in Table 6. Similar to box sections, the post-buckling reserve strength (h) is considerable for slender flanges and becomes negligible when compact flanges are approached.

4. Numerical investigation In order to extend the range of studied sections and to further substantiate the obtained results, a comprehensive numerical investigation was also conducted as a part of the present study.

Please cite this article as: S. Kazemzadeh Azad et al., Axial slenderness limits for austenitic stainless steel-concrete composite columns, Journal of Constructional Steel Research, https://doi.org/10.1016/j.jcsr.2019.105856

S. Kazemzadeh Azad et al. / Journal of Constructional Steel Research xxx (xxxx) xxx

13

Table 6 Summary of experimental results for the partially-encased I-sections. Specimen

b/t

Py (kN)

Plb (kN)

Pu (kN)

slb (MPa)

su (MPa)

Plb/Py

Pu/Py [Ae/A]

h (% of Py)

be/b

A-I50 A-I100 A-I150 A-I200

10 20 30 40

427 833 1240 1646

496 787 737 735

502 817 1003 1117

315 256 161 121

319 266 219 184

1.16 0.94 0.59 0.45

1.18 0.98 0.81 0.68

1.4 3.6 21.5 23.2

1.26 0.97 0.71 0.52

Details of the investigation are outlined in this section. 4.1. Modelling details 4.1.1. General All numerical simulations were carried out using the FE package ABAQUS 6.14-1 [50]. The stainless steel sections were modelled using general-purpose four-node S4R shell elements. The Simpson rule was employed in the shell elements with 9 through-thickness integration points in order to accurately capture the stress gradient through the plates. The concrete infill, on the other hand, was modelled using eight-node C3D8R brick elements. Both element types used reduced integration and hourglass control schemes to avoid numerical issues such as locking and zero-energy modes. Based on the results of a sensitivity analysis, a reasonable mesh size of b/15 for square specimens, d/20 for circular specimens, and bf/15 for I-section specimens at the section level and L/100 along all members was found to be suitable. This is comparable to the meshing used previously by Tao et al. [26] and Kazemzadeh Azad et al. [51]. As discussed in Section 2.1, during the experiments, the axial loading was applied only to the stainless steel section (and not the concrete infill) in order to have an isolated investigation on the local stability of the stainless steel section. In line with this, in each numerical model, all degrees of freedom at the top and bottom ends of the stainless steel section were restrained except the vertical translation of the top end which was used for imposing shortening to the specimen. In order to secure the concrete infill and avoid any numerical issues, the translational degrees of freedom at the bottom corners of the concrete infill were also restrained. Compared to carbon steel sections, the surface of stainless steel sections is generally smoother since it can be free of rust. As a result, lower bond strength and coefficient of friction are typically expected for stainless steel-concrete composite members (compared to carbon steel counterparts) as demonstrated in the recent experimental study of Tao et al. [52]. Considering that the main aim of the present study was to recommend reliable and conservative axial slenderness limits, it was decided to neglect the effect of bond strength and friction between the concrete infill and stainless steel section in the numerical simulations. Consequently, a surface-to-surface interaction with a coefficient of friction of zero was defined in the FE models between the concrete infill and stainless steel section which allowed for the concrete to act as an internal restraint but did not transfer any vertical load to the infill. The procedure ensured that the proposed slenderness limits were conservative, and the recommendations were not dependant on the surface condition and level of bond strength. As mentioned in Section 2.1, during the experiments, recesses were included in the concrete infill to ensure that the load was applied only to the stainless steel section. Consequently, stiffeners were added to each specimen to prevent the occurrence of premature local buckling near the recesses, where the stainless steel section did not have an internal restraint. On the other hand, in the simulations, the length of the concrete was made equal to that of the stainless steel section (i.e. without the recesses) since the load could be applied directly to the stainless steel section. Therefore, the need for the stiffeners was eliminated and they were not

included in the numerical models. For each model, the analysis was continued until an average axial strain (ε) of 2% was reached. This limit was selected based on the experimental results and ensured that the local buckling and ultimate loads were captured during each simulation. Both material and geometrical nonlinear effects were included in the analysis. 4.1.2. Stainless steel material modelling A von Mises plasticity constitutive model with isotropic hardening was utilised in all simulations for modelling stainless steel behaviour. The average coupon test results of Fig. 3 were used to construct true stress versus true plastic strain curves which were required for the definition of the constitutive model in the FE software. 4.1.3. Concrete material modelling As discussed earlier, only the stainless steel section was axially loaded in the studied specimens. The concrete infill therefore acted only as a means of preventing the inward buckling of the stainless steel section. Consequently, the concrete was modelled as an elastic material (with linear behaviour and no damage criterion) assuming that it had sufficient stiffness and strength to act as an internal restraint. This assumption was in line with the experimental observations. Furthermore, a recent study by Huang et al. [33], demonstrated that modelling the concrete infill as a linear-elastic material or using the Concrete Damaged Plasticity (CDP) model of ABAQUS [50] did not affect the results at all when axial compression was only applied to the steel section of box CFST and partiallyencased I-section columns. 4.1.4. Geometrical imperfections Only local geometrical imperfections were considered in the numerical simulations since the study was focused on the local stability of stainless steel-concrete composite sections. In all models, the shape of local imperfections was assumed to be identical to the first buckling mode obtained from an eigenvalue analysis (Fig. 22). The amplitude of local imperfections for box and I-sections was selected as b/450 and bf/120, respectively, based on the imperfection measurements summarised in Section 2.3.1. However, for circular sections, the analysis results were found to be very different from the experimental results when the amplitude of local imperfections was selected as d/140; i.e. the maximum amplitude of local imperfections measured in Section 2.3.2. A careful examination of the results revealed that the reason is the notable difference that exists between the imposed imperfection shape in the numerical model (i.e. the first eigenmode) and the actual imperfection pattern for the circular sections. For the case of box and I-sections, the first eigenmode resembles to a reasonable extent the actual imperfection pattern of the section, however, for circular sections, the first eigenmode (illustrated in Fig. 22b) imposes a uniform axisymmetric outward bulging to critical sections of the column which affects the resistance drastically more than the actual imperfection pattern (such as Fig. 6c which contains both outward and inward imperfections) even if both patterns have the same amplitude. In order to further elaborate the issue, an imperfection

Please cite this article as: S. Kazemzadeh Azad et al., Axial slenderness limits for austenitic stainless steel-concrete composite columns, Journal of Constructional Steel Research, https://doi.org/10.1016/j.jcsr.2019.105856

14

S. Kazemzadeh Azad et al. / Journal of Constructional Steel Research xxx (xxxx) xxx

Fig. 22. Assumed local imperfection shape for (a) box, (b) circular, and (c) I-section specimens.

sensitivity study was conducted considering the tested circular sections. Results for two cases, namely A-C300 and A-C540, are depicted in Fig. 23 as representatives. In this figure, the solid line is the response of the column when the average measured geometry (Section 2.3.2) was directly used in the numerical model. The dashed lines, on the other hand, represent the results for cases where the first eigenmode was imposed as the imperfection pattern, however, with different amplitudes, namely d/140, 0.2t, and 0.01t. The amplitude of d/140, is the maximum amplitude of local imperfections measured in Section 2.3.2. The amplitudes of 0.2t and 0.01t are the values suggested in the literature. Studies on the imperfections of stainless steel circular sections are very limited in the literature. Based on the results of sensitivity analyses, Gardner and Nethercot [53], and more recently, Zhao et al. [54] proposed the amplitudes of 0.2t and 0.01t to be used in the numerical simulation of stainless steel circular sections when the first eigenmode is imposed as the imperfection pattern to the models. Results summarised in Fig. 23 clearly demonstrate that the numerical results obtained with the eigenmode method approach to those obtained using the average measured geometry method when the amplitude of 0.01t is used. The same conclusion was reached for the other studied circular sections. The results suggested that a uniform axisymmetric outward bulging of amplitude 0.01t, has the same effect on the local stability of the studied circular sections as the measured irregular imperfection pattern of the specimen. Consequently, it was decided to use this amplitude for all the circular models.

4.1.5. Residual stresses The residual stresses of fabricated stainless steel sections are not much explored in the literature. The most comprehensive study was conducted recently by Yuan et al. [55] on stainless steel welded box and I-sections where predictive patterns were provided. These patterns were also used in the present paper for introducing residual stresses to box and I-section models, as shown in Fig. 24a,c, where hw is the web height. Generally, for these welded sections, only longitudinal membrane residual stresses are dominant [56]. It is worth noting that the sections studies by Yuan et al. [55] were fabricated from water jet cut plates whereas the plates considered in the present study were laser cut. Although, the heat input due to laser cutting can be higher than that of water jet cutting, the predictive patterns of Yuan et al. [55] were still used here since there are no studies particularly on laser cut welded stainless steel sections. Residual stresses were also included in the circular models. It is worth clarifying that circular sections with small diameters are generally mass-produced via an automated manufacturing process using a series of rollers and through gradual cold rolling and automated seam welding, which is sometimes accompanied by special cooling systems. On the other hand, larger diameter circular sections (such as those studied herein) are generally fabricated individually by manually rolling flat plates and longitudinal welding them. As a consequence, manufactured circular sections can have different residual stress patterns compared to fabricated circular sections [57]. Residual stress studies on circular sections in

Fig. 23. Imperfection sensitivity analysis for circular sections.

Please cite this article as: S. Kazemzadeh Azad et al., Axial slenderness limits for austenitic stainless steel-concrete composite columns, Journal of Constructional Steel Research, https://doi.org/10.1016/j.jcsr.2019.105856

S. Kazemzadeh Azad et al. / Journal of Constructional Steel Research xxx (xxxx) xxx

15

Fig. 24. Longitudinal membrane residual stress patterns used for (a) box, (b) circular, and (c) I-section models and the transverse bending residual stress pattern used for (d) circular models.

general, and on stainless steel ones in particular, are very limited in the literature. Zheng et al. [58] recently proposed a residual stress pattern for manufactured austenitic stainless steel circular sections, however, as noted above, the study was focused on mass-produced small diameter (d < 127 mm) sections. Considering that there are no studies on the residual stresses of fabricated stainless steel circular sections with larger diameters (such as those investigated in the present paper), it was decided to use the pattern proposed by Ross and Chen [59] for fabricated carbon steel circular sections. In addition to the welding-induced longitudinal membrane residual stresses (Fig. 24b), the pattern includes forming-induced transverse bending residual stresses with a through-thickness stress gradient (Fig. 24d). The applied residual stress patterns for all the specimen types are depicted in Fig. 25. It is worth noting that the transverse bending pattern for the circular sections (Fig. 24d) was applied in the numerical models by imposing different residual stress values to the 9 through-thickness integration points of the shell elements (Fig. 25b).

Table 7 Summary of verification results. Specimen

b/t or d/t

Pu (kN)

P FEM (kN) u

Pu/P FEM u

A-B200 A-B250 A-B300 A-B350 A-B400 A-B450 A-B500 A-C300 A-C360 A-C420 A-C480 A-C540 A-I50 A-I100 A-I150 A-I200 Mean SDa

40 50 60 70 80 90 100 100 120 140 160 180 10 20 30 40

1168 1348 1457 1554 1714 1655 1677 810 927 1077 1170 1270 502 817 1003 1117

1145 1314 1409 1527 1625 1659 1725 784 900 1037 1168 1287 485 775 975 1163

1.02 1.03 1.03 1.02 1.05 1.00 0.97 1.03 1.03 1.04 1.00 0.99 1.04 1.05 1.03 0.96 1.02 0.03

a

Standard Deviation.

4.2. Verification In order to verify the adopted modelling techniques, the experimented specimens were analysed following the details outlined in the previous sections. All the verification results are summarised in Table 7 and, as representatives, the axial responses obtained from six of the models are compared with the test results in Fig. 26. The obtained failure modes for these specimens are also depicted in Fig. 27. Based on the table, a reasonable agreement can be seen between the ultimate loads obtained from the analyses (P FEM u ) and those recorded during the tests (Pu). Results summarised in Fig. 26 demonstrate that the initial stiffness, ultimate load, and the trend of the P-D curve were all well captured in the simulations. Furthermore, the failure modes obtained from the FE analyses (Fig. 27) were comparable to those observed during the tests (Figs. 11, Figure 15, and Fig. 19). The obtained results as a whole demonstrated the reliability of the utilised FE modelling techniques for further investigating the local and post-local buckling behaviour

of stainless steel-concrete composite columns. 4.3. Parametric study Following the verification of the numerical modelling approach, a comprehensive parametric study was conducted in order to extend the range of studied sections and to further substantiate the experimental results. The studied models and the obtained numerical results are summarised in Table 8. The ranges of width (or diameter)-to-thickness ratios were selected such that they would cover a wide range of practical columns while adhering to the maximum allowed slenderness values stipulated by international design standards on carbon steel-concrete composite columns [36,60]. In line with the experimental programme, concrete-filled box and circular sections as well as partially-encased I-sections were included in the parametric study. The same material

Fig. 25. Applied residual stress patterns in the numerical models: (a) longitudinal membrane; and (b) transverse bending (only for circular models).

Please cite this article as: S. Kazemzadeh Azad et al., Axial slenderness limits for austenitic stainless steel-concrete composite columns, Journal of Constructional Steel Research, https://doi.org/10.1016/j.jcsr.2019.105856

16

S. Kazemzadeh Azad et al. / Journal of Constructional Steel Research xxx (xxxx) xxx

Fig. 26. Comparison of numerical and experimental results for selected (a) box, (b) circular, and (c) I-section specimens.

Fig. 27. FE failure modes obtained for (a) A-B200, (b) A-B500, (c) A-C300, (d) A-C540, (e) A-I50, and (f) A-I200. The von Mises stress contours are shown.

Table 8 Summary of parametric study. Type

Specimen

b or d (mm)

b/t or d/t

Py (kN)

Pu (kN)

Pu/Py [Ae/A]

be/b or de/d

Box

A-B150 A-B225 A-B275 A-B325 A-B375 A-B425 A-B475 A-B550 A-B600 A-B650 A-C270 A-C330 A-C390 A-C450 A-C510 A-C570 A-C630 A-C690 A-I65 A-I85 A-I115 A-I135 A-I165 A-I185 A-I215 A-I235

150 225 275 325 375 425 475 550 600 650 270 330 390 450 510 570 630 690 65 85 115 135 165 185 215 235

30 45 55 65 75 85 95 110 120 130 90 110 130 150 170 190 210 230 13 17 23 27 33 37 43 47

813 1220 1491 1762 2033 2304 2575 2981 3252 3523 662 811 959 1108 1257 1405 1554 1703 549 711 955 1118 1362 1524 1768 1931

883 1249 1346 1463 1564 1632 1681 1796 1815 1868 709 843 969 1101 1234 1356 1476 1601 585 705 857 940 1046 1111 1230 1325

1.09 1.02 0.90 0.83 0.77 0.71 0.65 0.60 0.56 0.53 1.07 1.04 1.01 0.99 0.98 0.96 0.95 0.94 1.07 0.99 0.90 0.84 0.77 0.73 0.70 0.69

1.09 1.02 0.90 0.83 0.77 0.71 0.65 0.60 0.56 0.53 1.07 1.04 1.01 0.99 0.98 0.96 0.95 0.94 1.10 0.99 0.85 0.76 0.65 0.59 0.54 0.53

Circular

I-Section

Please cite this article as: S. Kazemzadeh Azad et al., Axial slenderness limits for austenitic stainless steel-concrete composite columns, Journal of Constructional Steel Research, https://doi.org/10.1016/j.jcsr.2019.105856

S. Kazemzadeh Azad et al. / Journal of Constructional Steel Research xxx (xxxx) xxx

properties and thicknesses used for the verification were considered in the parametric study. The yield strength (Py) in Table 8 was calculated using the average fy obtained from the coupon tests (Table 2). Results of the parametric study are discussed in the following section.

when compact sections are approached. The normalised elastic local buckling load (P el lb /Py) is also plotted in the figure as a dashed line:

"

P el lb

5. Discussion of results All the experimental and numerical results obtained in the present study are thoroughly discussed and synthesised in this section in order to propose slenderness limits and effective width/ dimeter formulae for austenitic box and circular CFSSTs as well as partially-encased I-sections under axial compression. 5.1. Box CFSST sections All the experimental and numerical results obtained in the present study for austenitic concrete-filled box sections are summarised in Fig. 28. In each subplot, two horizontal axes are used. The p bottom ffiffiffiffiffiffiffiffiffi horizontal axis normalises the results based on ðb=tÞ fy=E which is used by some international design standards, including the American AISC 360 [60], to define slenderness limits. The top horizontal axis, on the other hand, normalises the results pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi based on the plate element slenderness, le ¼ ðb=tÞ fy=250, which is used by the Australian/New Zealand Standard AS/NZS 2327 [36] to define slenderness limits. Using two horizontal axes facilitates the results to be investigated simultaneously in two common systems. The normalised local buckling load (Plb/Py) as well as the normalised ultimate load (Pu/Py) obtained from the experiments on box CFSSTs are depicted in Fig. 28a. A vertical line connects the buckling and ultimate loads of each specimen, representing the amount of post-buckling reserve strength (h) in terms of the percentage of Py. As discussed earlier, the post-buckling reserve strength is rather high for slender sections and becomes negligible

17

¼ Af el lb

kp2 E ¼A   12 1  n2 ðb=tÞ2

# (2)

where n is the Poisson's ratio and k is the buckling coefficient which is taken as 10.3 for concrete-filled box sections [61]. As can be seen in the figure, the experimental buckling loads are notably lower than the theoretical predictions even for rather slender members. This can be attributed to ignoring the effects of imperfections, residual stresses, material nonlinearity, and connecting plates in the theoretical formula. A similar issue was observed in the experimental study of Uy [7] on mild steel columns and numerical study of Kazemzadeh Azad et al. [51] on stainless steel members. The concept of effective width (be) is commonly used by international design standards as a convenient approach to exploit the post-buckling strength of thin-walled members. The average ultimate stress acting on the full width of a plate is considered to be equivalent to the yield stress acting on the effective width of the plate; i.e. be/b ¼ Pu/Py for a box section. The effective width ratios (be/b) for all the experimental and numerical cases are plotted in Fig. 28b. The axial slenderness limit is considered the width-tothickness limit below which the plate can reach its yield capacity under compression; i.e. the full plate width is effective (be/b ¼ 1.0). It should be mentioned that be/b > 1.0 is generally due to strain hardening which is typically ignored in design standards. Since there are currently no codified slenderness limits for stainless steelconcrete composite members, the results are compared with the axial slenderness limits of Australian (AS/NZS 2327 [36]), American (AISC 360 [60]), and European (Eurocode 4 [62]) design standards for carbon steel box CFSTs. These codified limits are shown with

Fig. 28. Summary of experimental and numerical results for austenitic concrete-filled box sections.

Please cite this article as: S. Kazemzadeh Azad et al., Axial slenderness limits for austenitic stainless steel-concrete composite columns, Journal of Constructional Steel Research, https://doi.org/10.1016/j.jcsr.2019.105856

18

S. Kazemzadeh Azad et al. / Journal of Constructional Steel Research xxx (xxxx) xxx

vertical dashed lines in the figure. The results obtained in the pffiffiffiffiffiffiffiffiffi present study suggest an axial slenderness limit of b/t ¼ 1.80 E=fy (or le ¼ 50) for austenitic box CFSSTs, shown in Fig. 28b with a red vertical solid line, below which the full width of the plate would be effective. As it can be seen, the current pffiffiffiffiffiffiffiffiffilimit of AS/NZS 2327 [36] and AISC 360 [60], i.e. b/t ¼ 2.26 E=fy (or le ¼ 64), is unconservative for austenitic box CFSSTs, whereas the limit of Eurocode 4 [62] (i.e. le ¼ 51) seems to be reasonable. Effective width formulae are typically used by design standards to predict the trend of be/b. Main approaches are compared with the experimental and numerical results of the present study in Fig. 28ced. Based on a previous edition of the Australian Standard AS 4100 [63], the variation of be/b can be described using the
rma
n's formula: following relation, which is a variant of von Ka

rffiffiffiffiffiffiffiffiffiffiffiffiffi .

be =b ¼ a

f el lb fy

(3)

where the elastic local buckling stress is calculated using Eq. (2) and a is a reduction factor depending on the manufacturing process. For lightly-welded (LW) box sections a is equal to 0.74 whereas for heavily-welded (HW) box sections it is equal to 0.65 [63]. As shown in Fig. 28c, the be/b curve for the LW case provides reasonable predictions for very slender members, however, gives unconservative predictions for less slender members. The results suggest that the tested specimens could be better categorised as heavilywelded sections since the HW curve provides mostly conservative results for the full dataset. Another common approach for predicting the trend of be/b is Winter's formula:

be = b ¼

rffiffiffiffiffiffiffiffiffiffiffiffiffi rffiffiffiffiffiffiffiffiffiffiffiffiffi .
.  el f el lb fy 1  b f lb fy

(4)

where b is a coefficient which was calibrated as 0.25 in the present study. As depicted in Fig. 28c, the Winter's curve can represent the full dataset with a higher accuracy compared to von Karman's LW and HW curves. The issue with all three of the above approaches is that they converge to different slenderness limits than that proposed in the present study (Fig. 28c). Different approaches are utilised by current design standards to provide effective width formulae which are consistent with their codified slenderness limits. These include modifying the k value in Eq. (2) and modifying/adding terms in/to Eq. (3) or (4). In line with this, the Australian/New Zealand Standard
rma
n's formula as follows AS/NZS 2327 [36] uses a modified von Ka which ensures that the be/b curve will converge to the codified limit:

be = b ¼ le =le

(5)

where le is the codified slenderness limit. As shown in Fig. 28d (Calibrated AS/NZS 2327 curve), the approach can be conservatively and easily applied to austenitic box CFSSTs using the proposed slenderness limit of le ¼ 50. Similarly, the recent edition of the US specification AISC 360 [60] provides a modified Winter's formula which ensures that the be/b curve will converge to the codified slenderness limit:


 
 be le le ¼ c2 1  c1 c2 b le le

(6)

where c1 is an adjustment factor and c2 is calculated as follows:

c2 ¼

1

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1  4c1 2c1

(7)

The calibrated c1 values are presented in AISC 360 [60] for different bare carbon steel members. Investigation of the results suggested that the dataset of the present study for austenitic box CFSSTs can be best represented using c1 ¼ 0.22 (which leads to c2 ¼ 1.49) and the proposed slenderness limit of le ¼ 50 in Eq. (6) as shown in Fig. 28d (Calibrated AISC 360 curve). 5.2. Circular CFSST sections Results for all the investigated austenitic concrete-filled circular sections are summarised in Fig. 29. Similar to the previous section, two horizontal axes are used in each subplot, however, they have been modified to (d/t)(fy/E) and le ¼ (d/t)(fy/250) based on the approaches used by AISC 360 [60] and AS/NZS 2327 [36] for circular sections, respectively. The vertical axis in the figure is the effective diameter ratio, i.e. de/d ¼ Pu/Py for a circular section. The theoretical elastic local buckling load for the range of d/t studied herein can be obtained as follows:

" # 2E el ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi q P el ¼ Af ¼ A lb lb   k 1  n2 ðd=tÞ

(8)

where k can be taken as 1.0 for filled circular sections [49]. Nevertheless, as demonstrated by previous research [34,49,60], the theoretical formula overestimates the buckling load of circular columns significantly (of the order of several hundred percent). A similar issue was observed in the present study when the theoretical buckling curve fell outside the axis limits used in the plots of Fig. 29. It is also worth noting that, as discussed in Section 3.2, the post-buckling reserve strength of the studied circular sections was negligible. The codified slenderness limits of the American [60], Australian [36], and European [62] standards for carbon steel circular CFSSTs are compared with the results of the present study in Fig. 29a. In contrast to the results of box sections, the reduction in de/d with an increase in the section slenderness is much more gradual and has a gentle slope. Although the results summarised in Fig. 29a suggest a higher limit, it was decided to conservatively propose the axial slenderness limit for austenitic circular CFSSTs as d/t ¼ 0.15E/fy (or le ¼ 120). The proposed limit, shown in the figure with a red vertical solid line, is identical to the limit stipulated in AISC 360 [60] and AS/NZS 2327 [36] for carbon steel circular CFSSTs. The reasons for not recommending a higher limit are as follows: (i) circular sections are in general rather sensitive to the amplitude of imperfections [34] and, therefore, suggesting a conservative limit was considered to be beneficial; and (ii) the axial slenderness limits previously developed for stainless steel sections have mostly been lower than those of the counterpart carbon steel sections (compare for instance those stipulated in Refs. [60,64]). This is related to the differences in the nonlinearity, proportionality limit, and manufacturing processes associated with the two material types. In line with this, it was decided not to propose a limit for austenitic circular CFSSTs which would be higher than that of carbon steel circular CFSTs. Nevertheless, the axial slenderness limit for both circular CFST and CFSSTs might be further relaxed on the basis of future studies. Effective diameter formulae for circular sections are less explored in the literature compared to the effective width formulae for box sections. Based on the study of Bradford et al. [49], AS/NZS 2327 [36] uses the following expression to predict the trend of de/ d for carbon steel circular CFSTs:

Please cite this article as: S. Kazemzadeh Azad et al., Axial slenderness limits for austenitic stainless steel-concrete composite columns, Journal of Constructional Steel Research, https://doi.org/10.1016/j.jcsr.2019.105856

S. Kazemzadeh Azad et al. / Journal of Constructional Steel Research xxx (xxxx) xxx

19

Fig. 29. Summary of experimental and numerical results for austenitic concrete-filled circular sections.

i hqffiffiffiffiffi de = d ¼ min le =le ; ð3le =le Þ2

(9)

where le is the codified slenderness limit, proposed as le ¼ 120 in the present paper for the austenitic counterpart. As shown in Fig. 29b (Calibrated AS/NZS 2327 curve), the approach provides rather conservative estimations compared to the results obtained herein. The US specification AISC 360 [60] also provides the following relation to be used for bare carbon steel circular sections:

de 0:038 E ¼ þ 0:67 d=t fy d

(10)

which can be rewritten in the following general form:

de c1 ¼ þ c2 d le

(11)

with the adjustment factors c1 and c2; and le ¼ (d/t)(fy/250) as defined earlier for circular sections. As shown in Fig. 29b (Calibrated AISC 360 curve), the factors were calibrated based on the results of the present study (as c1 ¼ 25 and c2 ¼ 0.8) such that the curve would represent the dataset with a reasonable accuracy and also converge to the proposed slenderness limit of le ¼ 120.

pffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi on ðb=tÞ fy=E and le ¼ ðb=tÞ fy=250, similar to the case of box sections. According to Fig. 30a, the post-buckling reserve strength is rather high for slender sections and becomes negligible when compact sections are approached. It is worth noting that, prior to the 1970s, outstand (or unstiffened) plate elements (such as the flanges of the I-sections studied herein) were considered to have a negligible post-buckling reserve strength, however, later studied revealed that such plate elements can also exhibit notable postbuckling capacities [65,66]. The normalised elastic local buckling load (P el lb /Py) is also plotted in the figure as a dashed line using Eq. (2) considering k ¼ 2.0 [61]. Again, the experimental buckling loads are much lower than the theoretical predictions. The variation of the effective width ratio (be/b) for the studied Isections is plotted in Fig. 30b against the codified slenderness limits of Eurocode 4 [62] and AS/NZS 2327 [36]. It is important to mention that, in general, Pu/Py is equal to Ae/A, where Ae is the effective area. For the case of box sections, however, Ae/A is equal to be/b since the plate elements are under nominally identical conditions; i.e. Pu/ Py ¼ Ae/A ¼ 4bet/4bt ¼ be/b. Similarly, for circular sections, Pu/ Py ¼ de/d. However, for a partially-encased I-section, the web buckling is restrained (i.e. the web is fully active) and the variation of the effective width is only applicable to the flanges. Therefore:

5.3. Partially-encased I-Sections

Pu Ae hw tw þ 4be t ¼ ¼ hw tw þ 4bt Py A

Summary of results for the studied austenitic partially-encased I-sections is presented in Fig. 30. The horizontal axes are based

where tw is the web thickness. Substituting the web dimensions used in the present study (Fig. 2) and back-calculating be/b leads to:

(12)

Fig. 30. Summary of experimental and numerical results for austenitic partially-encased I-sections.

Please cite this article as: S. Kazemzadeh Azad et al., Axial slenderness limits for austenitic stainless steel-concrete composite columns, Journal of Constructional Steel Research, https://doi.org/10.1016/j.jcsr.2019.105856

20

S. Kazemzadeh Azad et al. / Journal of Constructional Steel Research xxx (xxxx) xxx

  be = b z 1:5 Pu Py  0:5

(13)

Eq. (13) was used for calculating the effective width ratio for Isections in Table 6, Table 8, and Fig. 30bec. A similar approach was used by other researchers [67,68]. As shown in pFig. ffiffiffiffiffiffiffiffiffi30b, the results suggest an axial slenderness limit of b/t ¼ 0.65 E=fy (or le ¼ 18) for austenitic partially-encased I-sections. The proposed limit is lower than those in use by Eurocode 4 [62] and AS/NZS 2327 [36] for carbon steel partially-encased I-sections. As discussed in Section 5.1, the modified version of von
rma
n's formula (Eq. (5)), used by AS/NZS 2327 [36], ensures that Ka the be/b curve will converge to the codified limit. As shown in Fig. 30c (Calibrated AS/NZS 2327 curve), the approach is applicable to austenitic partially-encased I-sections as well using the proposed slenderness limit of le ¼ 18. The modified Winter's formula (Eq. (6)) of the US specification AISC 360 [60] is also compared with the dataset of the present study in Fig. 30c (Calibrated AISC 360 curve). Although the formula is mainly intended for bare carbon steel members in the specification, the figure demonstrates that it can capture the trend of be/b for austenitic partially-encased I-sections rather accurately using c1 ¼ 0.18 (which leads to c2 ¼ 1.31) and the proposed slenderness limit of le ¼ 18. 5.4. A discussion on definition of slenderness limit As noted in Section 5.1, the axial slenderness limit in the present study is considered the width (or diameter)-to-thickness limit below which the plate element can reach its yield capacity. Based on this classic definition, only one slenderness limit (le ) is needed for members under axial compression. A possible application of this concept to the design of composite members under axial load, originally developed by Uy [6], is schematically depicted in Fig. 31a. Based on this approach, members with (le  le ) can reach their full axial capacity (P1) where the forces in steel and concrete would reach for instance to Afy and 0.85Acfc (or Acfc as per some design standards), respectively, where Ac is the area of concrete infill. For members with higher slenderness values, only a reduction in the steel resistance is incorporated where it attains Aefy with Ae (A) determined readily from effective width formulae. This is consistent with the approach used by most international design standards for determining the section capacity of bare steel members under compression. In 2010, however, the US specification AISC 360 [69] started to define two axial slenderness limits only for composite members based on the work of Lai et al. [70,71]: i.e. compact/noncompact (denoted herein as le1 ) and noncompact/slender (le2 ). It is worth noting that, for all other bare steel members, the specification still defines only one axial slenderness limit. The two limits are schematically illustrated in Fig. 31b for the case of box CFSTs. Members

with (le  le1 ) can reach their full axial capacity (P1) similar to the previous approach (Fig. 31a). For members with higher slenderness values than le1 , the capacity starts to reduce quadratically until it reaches to P2 at le ¼ le2 . Interestingly, at this limit, the steel resistance is still set as Afy while the concrete resistance is reduced to 0.7Acfc due to volumetric dilation. After le2, the steel resistance can only reach to the theoretical elastic buckling capacity of Af lbel (Eq. (2)) while the concrete remains at the resistance level of 0.7Acfc. There are a number of important issues related with this new approach:  Although the first limit of le1 matches well with the previous slenderness tests on CFSTs [5,33,72], the second limit of le2 is indeed obtained simply by equating the elastic buckling load of Eq. (2) to Afy. The equation is purely theoretical and does not consider the effects of imperfections, residual stresses, and connecting plates at all. Nevertheless, the new approach states that the steel would still reach to its yield strength (fy) simply if le is less than the theoretical limit of le2 [60,69e71]. The results of the present study as well as other previous slenderness tests [5,33,72] have clearly demonstrated that it is not possible for the steel tube of a concrete-filled box section to reach to its yield capacity simply by keeping le  le2 (¼ 85). The common consensus in all these studies is that the reduction of steel resistance below Afy starts much earlier than the theoretical limit of le2 (¼ 85). If the theoretical limit was simply applicable, then there would be no need for conducting any experiments or numerical studies.

Fig. 32. Comparison of the results reported in the literature with the theoretical elastic local buckling curve for concrete-filled box sections.

Fig. 31. Different approaches regarding the definition of axial slenderness limit for box CFST members.

Please cite this article as: S. Kazemzadeh Azad et al., Axial slenderness limits for austenitic stainless steel-concrete composite columns, Journal of Constructional Steel Research, https://doi.org/10.1016/j.jcsr.2019.105856

S. Kazemzadeh Azad et al. / Journal of Constructional Steel Research xxx (xxxx) xxx Table 9 Summary of recommendations for axial slenderness limits of austenitic stainless steel-concrete composite columns. Type

Aust. Notation*

Box CFSST

le ¼ 50 le ¼ 120 le ¼ 18

US Notation pffiffiffiffiffiffiffiffiffi b/t ¼ 1.8 E=fy

EU Notation pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi b/t ¼ 52 235=fy

d/t ¼ 0.15(E/fy) d/t ¼ 128 (235/fy) pffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi b/t ¼ 0.65 E=fy bf /t ¼ 37 235=fy pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi * Full section effectiveness if le ¼ ðb =tÞ  fy =250 (for box and I-sections) or le ¼ (d/t)(fy/250) (for circular) is less than le . Circular CFSST

Partially-Encased I

 The new approach states that, after le2, the steel tube would elastically buckle and therefore its resistance is conservatively capped to Af lbel which is again calculated from the theoretical Eq. (2) [60,69e71]. However, it is well-known that Eq. (2) overestimates the local buckling load significantly as it is purely theoretical and ignores the effects of imperfections, residual stresses, and connecting plates. AISC 360 refers to the work of Lai et al. [71] in which they conducted a series of FE analyses and concluded that Eq. (2) is rather conservative and can be safely applied to box CFSTs. The FE results of Lai et al. [71] are compared in Fig. 32 with the test results of the present study and those available in the literature within the applicable range. In all FE models of Lai et al. [71] and the tests of Uy [72] (represented by grey diamonds), both concrete and steel were loaded while the rest of the results were obtained from tests on concrete-filled box members where only the steel was loaded. Except the results of the present study, all data are from carbon steel box CFSTs. It can clearly be seen from the figure that, while the FE results of Lai et al. [71] stay well above the theoretical elastic buckling curve, all test data fall significantly below the theoretical predictions of Eq. (2) regardless of the loading approach or the material type. This demonstrates the overestimation associated with Eq. (2). The discrepancy between the test and FE results is drastic. Regardless of the above issues, Lai et al. [70,71] demonstrated that the new approach with two slenderness limits predicts the axial capacity of CFST columns very reasonably and conservatively. The above-discussed overestimations might have simply been counterbalanced by the utilised concrete resistance which reduces from 0.85Acfc to 0.7Acfc for members with le > le1 . However, this raises the question of why the steel resistance in the new approach is not consistent with the previous findings in the literature. It is out of the scope of this paper to further investigate the new AISC 360 approach, however, this discussion was deemed necessary since (i) there was (and still is) a lack of discussion on the topic; (ii) the use of two slenderness limits in the new approach has become a source of confusion and inconsistency between different studies as to what is an axial slenderness limit for composite members; and

21

(iii) to clarify explicitly which definition was used in the present study. It is worth mentioning that, in Section 5, the limits reported for AISC 360 [60] are all compact/noncompact (le1 ) limits. A set of tests on composite columns is underway by the authors to further investigate if the use of two slenderness limits is necessary for stainless steel CFSSTs as well. It is worth noting that, while the next edition of AS/NZS 2327 [73] also presents two axial slenderness limits for CFSTs, the strength calculations are solely based on the first limit (similar to the approach schematically shown in Fig. 31a). 5.5. Summary of recommendations The recommended axial slenderness limits and effective width/ diameter formulae for austenitic stainless steel-concrete composite sections investigated in the present study are summarised in Table 9 and Table 10. The recommended limits are presented in Table 9 in three common notations; i.e. Australian, American, and European. The limits are notably higher than the corresponding limits for bare stainless steel sections. It is also worth noting that the recommended slenderness limits compare well with the recent findings of Kazemzadeh Azad et al. [51] where austenitic coldformed concrete-filled square and circular CFSSTs were numerically investigated. Two alternatives are presented in Table 10 for the effective width/diameter formulae. The first alternative provides conservative predictions while the second alternative represents the obtained results more accurately. 6. Conclusions The local and post-local buckling behaviour of austenitic stainless steel-concrete composite columns were investigated experimentally and numerically in the present study. The following can be concluded from the study:  Average values of b/450 and bf/120 were found to be the maximum amplitude of local imperfections for walls of the studied fabricated box sections and flanges of the studied fabricated I-sections. For the studied fabricated circular sections, an average value of d/140 was found to best represent the measurement results, however, it was demonstrated through a sensitivity analysis that a lower value (0.01t) shall be considered in numerical models as the amplitude of imperfections of circular columns if the first eigenmode is used as the initial imperfection pattern.  Rather high post-buckling reserve strengths were observed for slender box and I-sections. In contrast, the post-buckling reserve strength of circular sections was found to be negligible due to the lack of a stress redistribution mechanism.  All the obtained experimental and numerical results were synthesised to recommend axial slenderness limits and effective

Table 10 Summary of recommendations for effective width or diameter formulae. Effective Width/Diameter Formula*

Type Box CFSST

Alt.1 Alt. 2

Circular CFSST

Partially-Encased I

qffiffiffiffiffiffiffiffiffiffiffiffi le =le ; ð3le =le Þ2 

Alt.1

de =d ¼ min½

Alt. 2

de 25 ¼ þ 0:8 d le

Alt.1

be =b ¼ le =le
 
 be le le ¼ 1:31 1  0:18 1:31 b le le

Alt. 2 *

be =b ¼ le =le  

be le le 1  0:22 1:49 ¼ 1:49 b le le

Plate Element Slenderness pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi le ¼ (b/t) fy =250

le ¼ (d/t)(fy/250)

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

le ¼ (b/t) fy =250

See Table 9 for le values.

Please cite this article as: S. Kazemzadeh Azad et al., Axial slenderness limits for austenitic stainless steel-concrete composite columns, Journal of Constructional Steel Research, https://doi.org/10.1016/j.jcsr.2019.105856

22

S. Kazemzadeh Azad et al. / Journal of Constructional Steel Research xxx (xxxx) xxx

width/diameter formulae for the studied sections. The proposed limits in the Australian notation (le ) are 50, 120, and 18 for austenitic concrete-filled box, concrete-filled circular, and partially-encased I-section columns, respectively. The equivalent form of these limits in the American and European notations as well as the recommended effective width/diameter formulae are summarised in Tables 9 and 10.  A discussion on the use of two slenderness limits in AISC 360 (instead of the classic approach of using one) for composite members under axial compression was presented in the paper. The implications of this new approach were explained on the basis of the experimental results of the present study and those in the literature and the need for further discussion on the definition of “axial slenderness limit” for composite members was highlighted. As a final note, it should be mentioned that the use of duplex stainless steel has also become popular in the recent decade in structural applications. In line with this, another set of experiments on duplex and lean duplex stainless steel-concrete composite members is underway by the authors in order to investigate their local stability. Acknowledgments The study was supported by the Australian Research Council (ARC) under the Discovery Project scheme (Project ID: DP180100418). The support provided to the first author through the University of Sydney International Scholarship (USydIS) is also gratefully acknowledged. The stainless steel material used in the experimental programme was generously donated by Outokumpu and Stirlings Australia. Special thanks to Mr. Con Logos from Outokumpu as well as Mr. David Pruden from Stirlings Australia for the technical support and assistance in delivering the material. The authors would like to thank Mr. Zhichao Huang for his help during the experiments. Assistance from Dr. Mohanad Mursi and the technical staff of the J. W. Roderick Laboratory of the Centre for Advanced Structural Engineering (CASE) of the University of Sydney is also gratefully acknowledged. References [1] W.P. Moore, An overview of composite construction in the United States, in: Proc. International Conference on Composite Construction, 1987. Henniker, NH. [2] O. Faber, Savings to be effected by the more rational design of cased stanchions as a result of recent full-size tests, Struct. Eng. 34 (3) (1956) 88e109. [3] R.W. Furlong, Strength of steel-encased concrete beam columns, J. Struct. Div. ASCE 93 (5) (1967) 113e124. [4] T. Chicoine, R. Tremblay, B. Massicotte, J.M. Ricles, L.W. Lu, Behavior and strength of partially encased composite columns with built-up shapes, J. Struct. Eng. ASCE 128 (3) (2002) 279e288. [5] R.Q. Bridge, M.D. O'Shea, Behaviour of thin-walled steel box sections with or without internal restraint, J. Constr. Steel Res. 47 (1) (1998) 73e91. [6] B. Uy, Strength of concrete filled steel box columns incorporating local buckling, J. Struct. Eng. ASCE 126 (3) (2000) 341e352. [7] B. Uy, Local and postlocal buckling of fabricated steel and composite cross sections, J. Struct. Eng. ASCE 127 (6) (2001) 666e677. [8] N.E. Shanmugam, B. Lakshmi, State of the art report on steeleconcrete composite columns, J. Constr. Steel Res. 57 (10) (2001) 1041e1080. [9] L.H. Han, W. Li, R. Bjorhovde, Developments and advanced applications of concrete-filled steel tubular (CFST) structures: Members, J. Constr. Steel Res. 100 (2014) 211e228. [10] E.W. Hammer, R.E. Petersen, Column curves for type 301 stainless steel, J. Frankl. Inst. 261 (2) (1956) 257e260. [11] J. Dubuc, V. Krivobok, G. Welter, Studies of type 301 stainless steel columns, in: Proc. ASTM 2nd Pacific Area National Meeting, 1956. Los Angeles, CA. [12] A.L. Johnson, G. Winter, Behaviour of stainless steel columns and beams, J. Struct. Div. ASCE 92 (5) (1966) 97e118. [13] L. Gardner, A New Approach to Structural Stainless Steel Design, Ph.D. Thesis, Structures Section, Department of Civil and Environmental Engineering, Imperial College, London, UK, 2002. [14] N.R. Baddoo, Stainless steel in construction: a review of research, applications,

challenges and opportunities, J. Constr. Steel Res. 64 (11) (2008) 1199e1206. [15] G. Gedge, Structural uses of stainless steel d buildings and civil engineering, J. Constr. Steel Res. 64 (11) (2008) 1194e1198. [16] B. Rossi, Discussion on the use of stainless steel in constructions in view of sustainability, Thin-Walled Struct. 83 (2014) 182e189. [17] AS/NZS 4673, Cold-Formed Stainless Steel Structures, Standards Australia/ Standards New Zealand, Sydney, Australia/Wellington, New Zealand, 2001. [18] Eurocode 3, Design of Steel Structures - Part 1-4: General Rules - Supplementary Rules for Stainless Steels, EN 1993-1-4:2006, European Standard,
Europe
en de Normalisation, Brussels, Belgium, 2006. Comite [19] SCI, Design Manual for Structural Stainless Steel, fourth ed., Steel Construction Institute, Berkshire, UK, 2017. [20] A. Roufegarinejad, B. Uy, M.A. Bradford, Behaviour and design of concrete filled steel columns utilizing stainless steel cross sections under combined actions, in: Proc. 18th Australasian Conference on the Mechanics of Structures and Materials, 2004, pp. 159e165. Perth, Australia. [21] B. Young, E. Ellobody, Experimental investigation of concrete-filled coldformed high strength stainless steel tube columns, J. Constr. Steel Res. 62 (5) (2006) 484e492. [22] E. Ellobody, B. Young, Design and behaviour of concrete-filled cold-formed stainless steel tube columns, Eng. Struct. 28 (5) (2006) 716e728. [23] M.A. Dabaon, M.H. El Boghdadi, M.F. Hassanein, Experimental investigation on concrete-filled stainless steel stiffened tubular stub columns, Eng. Struct. 31 (2) (2009) 300e307. [24] D. Lam, L. Gardner, Structural design of stainless steel concrete filled columns, J. Constr. Steel Res. 64 (11) (2008) 1275e1282. [25] B. Uy, Z. Tao, L.H. Han, Behaviour of short and slender concrete-filled stainless steel tubular columns, J. Constr. Steel Res. 67 (3) (2011) 360e378. [26] Z. Tao, B. Uy, F.Y. Liao, L.H. Han, Nonlinear analysis of concrete-filled square stainless steel stub columns under axial compression, J. Constr. Steel Res. 67 (11) (2011) 1719e1732. [27] D. Lam, L. Gardner, M. Burdett, Behaviour of axially loaded concrete filled stainless steel elliptical stub columns, Adv. Struct. Eng. 13 (3) (2010) 493e500. [28] D. Li, B. Uy, F. Aslani, C. Hou, Behaviour and design of spiral-welded stainless steel tubes subjected to axial compression, J. Constr. Steel Res. 154 (2019) 67e83. [29] D. Lam, J. Yang, A. Mohammed, Axial behaviour of concrete filled lean duplex stainless steel square hollow sections, in: Proc. 8th European Conference on Steel and Composite Structures (Eurosteel 2017), 2017. Copenhagen, Denmark. [30] B. Xing, B. Young, Experimental investigation of concrete-filled lean duplex stainless steel RHS stub columns, in: Proc. 16th International Symposium on Tubular Structures, ISTS 2017, Melbourne, Australia, 2017. [31] L.H. Han, C.Y. Xu, Z. Tao, Performance of concrete filled stainless steel tubular (CFSST) columns and joints: summary of recent research, J. Constr. Steel Res. 152 (2019) 117e131. [32] AS/NZS 1554, 6, Structural Steel Welding - Part 6: Welding Stainless Steels For Structural Purposes, Standards Australia/Standards New Zealand, Sydney, Australia/Wellington, New Zealand, 2012. [33] Z. Huang, D. Li, B. Uy, H.T. Thai, C. Hou, Local and post-local buckling of fabricated high-strength steel and composite columns, J. Constr. Steel Res. 154 (2019) 235e249. [34] R.D. Ziemian, Guide to Stability Design Criteria for Metal Structures, sixth ed., John Wiley & Sons, Hoboken, NJ, 2010. [35] M.D. O'Shea, R.Q. Bridge, Local buckling of thin-walled circular steel sections with or without internal restraint, J. Constr. Steel Res. 41 (2) (1997) 137e157. [36] AS/NZS 2327, Composite Structures d Composite Steel-Concrete Construction in Buildings, Standards Australia/Standards New Zealand, Sydney, Australia/ Wellington, New Zealand, 2017. [37] AS 3600, Concrete Structures, Standards Australia, Sydney, Australia, 2018. [38] AS 1391, Metallic Materials d Tensile Testing at Ambient Temperature, Standards Australia, Sydney, Australia, 2007. [39] Y. Huang, B. Young, The art of coupon tests, J. Constr. Steel Res. 96 (2014) 159e175. [40] BS EN 10088, Stainless Steels, BS EN 10088:2014, British Standards Institution, London, UK, 2014. [41] AS 1012, Methods of Testing Concrete, Standards Australia, Sydney, Australia, 2014. [42] H.X. Yuan, Y.Q. Wang, L. Gardner, Y.J. Shi, Localeoverall interactive buckling of welded stainless steel box section compression members, Eng. Struct. 67 (2014) 62e76. [43] H.X. Yuan, Y.Q. Wang, Y.J. Shi, L. Gardner, Stub column tests on stainless steel built-up sections, Thin-Walled Struct. 83 (2014) 103e114. €z, Computational modeling of cold-formed steel: char[44] B.W. Schafer, T. Peko acterizing geometric imperfections and residual stresses, J. Constr. Steel Res. 47 (3) (1998) 193e210. [45] AS/NZS 5131, Structural Steelwork d Fabrication and Erection, Standards Australia/Standards New Zealand, Sydney, Australia/Wellington, New Zealand, 2016. [46] EN 1090-2, Execution of Steel Structures and Aluminium Structures d Part 2: Technical requirements for Steel Structures - EN 1090-2:2008, European Stan
Europe
en de Normalisation, Brussels, 2008. dard, Comite [47] S. Kazemzadeh Azad, O. Hasançebi, S. Kazemzadeh Azad, Upper bound strategy for metaheuristic based design optimization of steel frames, Adv. Eng. Software 57 (2013) 19e32. [48] X. Zhao, M. Tootkaboni, B.W. Schafer, Laser-based cross-section measurement

Please cite this article as: S. Kazemzadeh Azad et al., Axial slenderness limits for austenitic stainless steel-concrete composite columns, Journal of Constructional Steel Research, https://doi.org/10.1016/j.jcsr.2019.105856

S. Kazemzadeh Azad et al. / Journal of Constructional Steel Research xxx (xxxx) xxx

[49] [50] [51]

[52] [53]

[54]

[55] [56] [57] [58]

[59] [60]

of cold-formed steel members: model reconstruction and application, ThinWalled Struct. 120 (2017) 70e80. M.A. Bradford, H.Y. Loh, B. Uy, Slenderness limits for filled circular steel tubes, J. Constr. Steel Res. 58 (No. 2) (2002) 243e252. mes, Simulia, Providence, RI, ABAQUS 6.14-1 Documentation, Dassault Syste 2014. S. Kazemzadeh Azad, B. Uy, D. Li, C. Hou, A numerical study on local and postlocal buckling of stainless steel-concrete composite columns, in: Proc. 9th International Conference on Advances in Steel Structures (ICASS’2018), 2018. Hong Kong. Z. Tao, T.Y. Song, B. Uy, L.H. Han, Bond behavior in concrete-filled steel tubes, J. Constr. Steel Res. 120 (2016) 81e93. L. Gardner, D.A. Nethercot, Numerical modeling of stainless steel structural components - a consistent approach, J. Struct. Eng. ASCE 130 (10) (2004) 1586e1601. O. Zhao, L. Gardner, B. Young, Structural performance of stainless steel circular hollow sections under combined axial load and bending e Part 1: experiments and numerical modelling, Thin-Walled Struct. 101 (2016) 231e239. H.X. Yuan, Y.Q. Wang, Y.J. Shi, L. Gardner, Residual stress distributions in welded stainless steel sections, Thin-Walled Struct. 79 (2014) 38e51. M. Abambres, W.M. Quach, Residual stresses in steel members: a review of available analytical expressions, Int. J. Struct. Integ. 7 (1) (2016) 70e94. H.G.L. Prion, P.C. Birkemoe, Beam-column behavior of fabricated steel tubular members, J. Struct. Eng. ASCE 118 (5) (1992) 1213e1232. B. Zheng, G. Shu, Q. Jiang, Experimental study on residual stresses in cold rolled austenitic stainless steel hollow sections, J. Constr. Steel Res. 152 (2019) 94e104. D.A. Ross, W.F. Chen, Tests of Fabricated Tubular Columns, vol. 477, Fritz Laboratory, Lehigh University, Bethlehem, PA, 1976. Report No. AISC, Specification for Structural Steel Buildings, ANSI/AISC 360-16, American Institute of Steel Construction, Chicago, IL, 2016.

23

[61] B. Uy, M.A. Bradford, Elastic local buckling of steel plates in composite steelconcrete members, Eng. Struct. 18 (3) (1996) 193e200. [62] Eurocode 4, Design of Composite Steel and Concrete Structures e Part 1-1: General Rules and Rules for Buildings, EN 1994-1-1:2004, European Standard,
Europe
en de Normalisation, Brussels, Belgium, 2004. Comite [63] AS 4100, Steel Structures, Standards Australia, Sydney, Australia, 1990. [64] N.R. Baddoo, AISC Steel Design Guide 27: Structural Stainless Steel, American Institute of Steel Construction, Chicago, IL, 2013. €z, G. Winter, Unstiffened compression elements, [65] V. Kalyanaraman, T. Peko J. Struct. Div. ASCE 103 (9) (1977) 1833e1848. [66] M.R. Bambach, K.J.R. Rasmussen, Effective widths of unstiffened elements with stress gradient, J. Struct. Eng. ASCE 130 (10) (2004) 1611e1619. [67] R. Tremblay, B. Massicotte, I. Filion, R. Maranda, Experimental study on the behaviour of partially encased composite columns made with light welded H steel shapes under compressive axial loads, in: Proc. Structural Stability Research Council: Annual Technical Session and Meeting, 1998. Atlanta, GA. [68] Y. Song, J. Li, Y. Chen, Local and post-local buckling of normal/high strength steel sections with concrete infill, Thin-Walled Struct. 138 (2019) 155e169. [69] AISC, Specification for Structural Steel Buildings, ANSI/AISC 360-10, American Institute of Steel Construction, Chicago, IL, 2010. [70] Z. Lai, A.H. Varma, Noncompact and slender circular CFT members: experimental database, analysis, and design, J. Constr. Steel Res. 106 (2015) 220e233. [71] Z. Lai, A.H. Varma, K. Zhang, Noncompact and slender rectangular CFT members: experimental database, analysis, and design, J. Constr. Steel Res. 101 (2014) 455e468. [72] B. Uy, Local and post-local buckling of concrete filled steel welded box columns, J. Constr. Steel Res. 47 (1) (1998) 47e72. [73] AS/NZS 2327: 2019 (Draft), Composite structures d Composite steel-concrete Construction in Buildings, Standards Australia/Standards New Zealand, Sydney, Australia/Wellington, New Zealand, 2019.

Please cite this article as: S. Kazemzadeh Azad et al., Axial slenderness limits for austenitic stainless steel-concrete composite columns, Journal of Constructional Steel Research, https://doi.org/10.1016/j.jcsr.2019.105856