1

Experimental study of square and rectangular CFDST sections with stainless steel outer 1

tubes under axial compression 2

Fangying Wang1; Ben Young, F.ASCE2; Leroy Gardner3 3

1Ph.D. Candidate, Dept. of Civil Engineering, The Univ. of Hong Kong, Pokfulam Rd., Hong Kong (corresponding author). 4

E-mail:christine.wang@connect.hku.hk 5

2 Professor, Dept. of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Hong Kong, China. E-6

mail: ben.young@polyu.edu.hk (Formerly, Dept. of Civil Engineering, The Univ. of Hong Kong, Pokfulam Rd., Hong 7

Kong, China. E-mail: young@hku.hk) 8

3 Professor, Dept. of Civil and Environmental Engineering, Imperial College London, London SW7 2AZ, U.K. E-mail: 9

leroy.gardner@imperial.ac.uk 10

Abstract: 11

A comprehensive experimental investigation into the axial compressive response of concrete-12

filled double skin tubular (CFDST) sections with stainless steel square and rectangular outer 13

tubes is presented. A total of 28 tests was carried out. The experimental setup and procedures 14

are described, and the test observations are fully reported. The test results are employed to 15

assess the applicability of the current European and North American design provisions for 16

composite carbon steel members to the design of the studied CFDST cross-sections. 17

Modifications to the current design codes are also considered—a higher buckling coefficient k 18

of 10.67 to consider the beneficial restraining effect of the concrete on the local buckling of 19

the stainless steel outer tubes and a reduction factor η to account for the effective compressive 20

strength of high strength concrete. Overall, the comparisons revealed that the existing design 21

rules may generally be safely applied to the prediction of the compressive resistance of CFDST 22

cross-sections with stainless steel outer tubes, while the modified design rules offered greater 23

accuracy and consistency. 24

25

Keywords: Cold-formed, Composite structures, CFDST, Stainless steel, Experiments, Testing. 26

2

INTRODUCTION 27

Concrete-filled double skin tubular (CFDST) sections consist of two metal tubes—an outer and 28

inner tube—with concrete infilled between the tubes. CFDST sections possess the high 29

strength, stiffness and ductility as other composite sections, and provide good fire resistance 30

since the concrete infill provides protection to the inner tube at elevated temperatures (Lu et al. 31

2010). CFDST sections share the constructability benefits of concrete filled tubular (CFT) 32

sections, with the steel tubes acting as permanent formwork, but will typically be lighter owing 33

to the absence of the inner core of concrete. 34

Stainless steel members have been utilised in construction increasingly year on year over the 35

past few decades for their excellent combination of corrosion resistance and mechanical 36

properties (Gardner 2005). There are multiple grades of stainless steel, with the austenitics 37

being the most commonly used in the construction industry, but lean duplex and ferritic 38

stainless steels, which contain less nickel, offer attractive alternatives due to their good 39

mechanical properties along with competitive cost that are appropriate for many applications 40

(Cashell and Baddoo 2014). In the studied form of construction, the metal tubes interact with 41

the sandwiched concrete, which leads to efficient material utilisation, and the presence of the 42

inner tube allows the stainless steel outer tube thickness to be reduced, thus improving the cost-43

effectiveness of the system. In this study, a novel type of CFDST section is therefore proposed, 44

employing carbon steel for the inner tube and stainless steel for the outer tube. 45

Previous experimental studies of CFDST members are scarce and most of which have focused 46

on CFDST sections employing circular or square carbon steel tubes and sandwiched concrete 47

grades up to 72 MPa (Wang et al. 2016). Investigations into CFDST members were first carried 48

out at Monash University, where Zhao and Grzebieta (2002) studied the compressive behavior 49

of CFDST members with square inner and outer cross-sections through eight stub column tests. 50

Further work on CFDST stub columns with rectangular inner and outer cross-sections was 51

3

described by Tao et al. (2004), where design formulae incorporating the confinement effect of 52

the sandwiched concrete were proposed. Tao and Han (2006) conducted two more stub column 53

tests on CFDST sections with rectangular hollow section (RHS) inner and outer tubes and the 54

load-deformation relationship of the composite section was predicted using a theoretical model. 55

The axial compressive behavior of rectangular stainless steel CFT sections was examined by 56

Ellobody and Young (2006), Young and Elloboday (2006), Uy et al. (2011), Lam et al. (2017) 57

and Li (2017); the significant influence of the slenderness of the metal tube on the compressive 58

strength and ductility of the studied CFT stub columns was highlighted in these studies. Uy et 59

al. (2011) found a substantial difference between the structural performance of stainless steel 60

CFT columns and carbon steel CFT columns, owing principally to the rounded stress-stain 61

response of the stainless steel material. Theofanous and Gardner (2009), Afshan and Gardner 62

(2013), Huang and Young (2013, 2014a), and Zhao et al. (2015, 2016) have studied the 63

structural performance of lean duplex and ferritic stainless steel RHS members, and the 64

influence of the particular characteristics of these stainless steel grades has been examined and 65

suitable design recommendations have been proposed. To date, investigations into CFDST 66

sections employing stainless steel as the outer tubes are very limited, while the behavior of 67

CFDST members with lean duplex or ferritic stainless steel outer tubes remains unexplored. 68

This paper presents an experimental program conducted on CFDST sections with carbon steel 69

inner tubes, lean duplex or ferritic stainless steel outer tubes, and three grades of concrete infill. 70

The test setup, procedures and observations are fully reported. The test results are employed to 71

evaluate the applicability of the European Code EN 1994-1-1 (CEN 2004a) and two American 72

Specifications AISC 360 (AISC 2016) and ACI 318 (ACI 2014) to the design of the CFDST 73

sections studied herein. Modifications to the design treatment in the areas of local buckling of 74

the outer tubes and the effective compressive strength of the concrete are also considered. 75

4

EXPERIMENTAL INVESTIGATION 76

Test specimens 77

Typical CFDST sections with cold-formed carbon steel SHS as the inner tubes and cold-formed 78

stainless steel (a) RHS and (b) SHS as the outer tubes are presented in Fig. 1. The stainless 79

steel grades employed in the present study were lean duplex stainless steel, grade EN 1.4062 80

(2202), which comprises only 2.6% nickel, and ferritic stainless steel, grade EN 1.4003 (410), 81

which contains an even lower nickel content of 0.4%. Lean duplex stainless steel RHS 82

150×80×3 mm (depth × width × thickness) and SHS 100×100×3 mm or ferritic stainless steel 83

RHS 100×80×4 and 120×80×3 mm were adopted as the outer tubes. The inner tubes were grade 84

S275 (ASTM A 36) carbon steel SHS 40×40×4, 40×40×1.5, 20×20×2.5, and 20×20×1.5 mm. 85

The nominal stub column length (L) was 2.5×Ho, which was deemed appropriately short to 86

prohibit global buckling, yet adequately long to avoid end effects. 87

The CFDST specimens were prepared by first precisely locating the inner tubes and outer 88

tubes concentrically, and then welding steel strips (10 mm deep and 2 mm thick) to the tubes 89

near both ends of the stub columns to fix their relative positions, as detailed in Fig. 2. Together, 90

the outer and inner tubes were wire cut flat and straight before casting concrete. The concrete 91

was compacted to reduce the volume of air voids. Strain visualization grids were painted onto 92

the specimen surfaces. Geometric measurements were carefully taken: the width and depth of 93

the cross-sections were measured using a Mitutoyo digital caliper; a Mitutoyo digital 94

micrometer was employed for measuring the thickness and the corner radii were measured 95

using Moore Wright radius gauges. The average measured values are presented in Table 1, 96

where B, H and t are the metal tube dimensions—width, height and thickness, which are 97

differentiated by subscripts (o for outer and i for inner) in the symbols, rint and rext are the 98

internal and external corner radii, and Ai, Ao and Ac correspond to the calculated cross-sectional 99

areas of the carbon steel inner tube, stainless steel outer tube and sandwiched concrete. 100

5

The CFDST test specimens were labelled such that the material, shape and dimensions of the 101

outer and inner tubes, as well as the grade of the concrete infill can be identified. For example, 102

the label LS100×3-NS40×4-C40R defines the following specimen: the first letter “L” refers to 103

lean duplex stainless steel (“F” is used for ferritic stainless steel); the second letter “S” means 104

SHS (“R” is used for an RHS); this is followed by the nominal dimensions of the SHS or RHS 105

outer tube –100×3 mm (Ho×to); for RHS, Ho×to is used. The hyphens in the label separate the 106

information of the outer tube, inner tube and concrete grade, so in this case the notation 107

“NS40×4” refers to the inner tube, where the letter “N” represents normal strength carbon steel 108

and the letter “S” indicates the SHS shape with the nominal dimensions of 40×4 mm. The term 109

after the second hyphen describes the sandwiched concrete, where the letter “C” followed by 110

the value of the concrete strength in MPa (40 MPa) designates the nominal concrete grade. For 111

repeated tests, the letter “R” is added as a suffix to the label. 112

Material properties 113

Longitudinal tensile coupon tests were carried out to obtain the material properties of the metal 114

tubes. Since cold-formed metal tubes undergo strength enhancement due to cold-working 115

during production, which is particularly pronounced in the corner areas of sections, coupons 116

were extracted from both the flat and corner regions of the tested tubes. The flat and corner 117

coupons were taken from the positions shown in Fig. 3(a) and (b) for the outer and inner tubes. 118

Each flat coupon was prepared with a 12.5 mm parallel width and a 50 mm gauge length, while 119

each corner coupon had a 4 mm parallel width and a 25 mm gauge length. For the corner 120

coupons, two 10.5 mm diameter holes were drilled and reamed at 17 mm from each end. The 121

flat coupons were gripped using a set of end-clamps, while a pair of steel rods was inserted into 122

the drilled holes of the corner coupons, through which the tensile force was applied. A contact 123

extensometer was attached to the coupons and a strain gauge was affixed to each side of the 124

coupons at mid-length. All the longitudinal tensile coupon tests were displacement controlled 125

6

and conducted in an MTS 50 kN testing machine. A constant displacement rate of 0.05 mm/min 126

was used in the elastic range of the stress–strain curves, while a higher rate of 0.4 mm/min was 127

used in the inelastic range; in the post-ultimate range, a rate of 0.8 mm/min was adopted, as 128

recommended in Huang and Young (2014b). 129

The static 0.2% proof stress σ0.2, the static ultimate tensile stress σu, the Young's modulus E, 130

the elongation at fracture εf, and the strain hardening exponents n and m, used in the compound 131

Ramberg-Osgood (R-O) material model (Mirambell and Real, 2000; Rasmussen, 2003; 132

Arrayago et al., 2015; Gardner and Yun, 2018), as determined from the coupon tests are 133

provided in Table 2. It can be observed that the process of cold-forming has resulted in a 134

moderate enhancement in both σ0.2 and σu in the corner regions, though this is accompanied by 135

a ductility reduction. The full stress-strain curves are presented in Fig. 4(a) and (b) for the outer 136

and inner tubes, respectively. 137

Concrete cylinder tests were performed to obtain the material properties of the concrete. Three 138

concrete grades—C40, C80, and C120 MPa—were produced in the laboratory using 139

commercially available materials. Their mix proportions are presented in Table 3. For each 140

batch of concrete, concrete cylinders were cast and cured together with the CFDST test 141

specimens. Two concrete cylinders were tested after 28 days of casting and the remainder were 142

tested at the days of the respective CFDST specimen tests. Table 4 summarizes the mean 143

measured strengths and the test number for each concrete grade. 144

Stub Column Tests 145

A total of 28 tests on the CFDST stub columns was performed, three for each of the eight series 146

and four repeated tests. Axial compressive force was applied to the CFDST stub columns in an 147

INSTRON 5000 kN capacity testing machine. Two reinforcing frames (see Fig. 5) were 148

clamped near the ends of the specimens to prevent localized failure due to end effects. The top 149

surface of the specimens was uneven due to concrete shrinkage; a thin layer (< 1 mm) of plaster 150

7

was thus utilised to fill the small gap. The plaster was then left to harden under an 151

approximately 2 kN applied load. This ensured that the inner tube, the outer tube and the 152

sandwiched concrete were loaded simultaneously during the tests. Three 50 mm range 153

transducers (LVDTs) were placed between the testing machine platens to measure the axial 154

shortening of the tested specimens; the layout of the LVDTs is illustrated in Fig. 6. A constant 155

0.4 mm/min displacement rate was used to drive the bottom end platen upwards in order to 156

apply load to the stub columns. All the stub column tests were stopped at a similar maximum 157

axial strain of approximately 0.05. 158

Localized strains were monitored in seven of the stub columns. These seven specimens cover 159

a variety of the key parameters, including the outer and inner tube slenderness, as well as the 160

concrete strength. For each of these specimens, 12 strain gauges were mounted to the outer 161

tube at 1/4, 1/2 and 3/4 points along the stub column lengths, in order to monitor the plate 162

deformations and strain development histories, as presented in Fig. 6. Of the 12 strain gauges, 163

three pairs of longitudinal and transverse strain gauges were affixed to the outer face of each 164

cross-section adjacent to the weld, while the other three pairs were positioned in the corner 165

region. 166

TEST OBSERVATIONS 167

Failure modes 168

The failure modes of the tested CFDST stub columns featured outward local buckling of the 169

stainless steel outer tube, crushing of the infill concrete, as well as local buckling of the carbon 170

steel inner tube. Photographs of typical failure modes are displayed in Fig. 7. The buckling 171

modes of both tubes were influenced by concrete shear failure, as shown for specimen 172

FR100×4-NS20×1.5-C40 and LS100×3-NS40×1.5-C40 in Fig. 7. Outward only local buckling 173

of the outer tubes was observed for all the tested specimens, as presented in Fig. 7 (a) and (c), 174

but, different failure modes were detected for the inner tubes, i.e. inward and outward local 175

8

buckling and inward only local buckling, as shown in Fig. 7 (b) and (d), respectively. The 176

outward only local buckling mode of the outer tube is due to the presence of the concrete, which 177

inhibits inward deformations, with concrete dilation under compression promoting positive 178

contact between the concrete and the outer tube. Local buckling of the outer tube is also 179

relatively insensitive to loss of support due to concrete failure since the cracking is very 180

localized in comparison to the local buckling half-wavelength of the plates. For the inner tube, 181

there was a trend of inward only local buckling for the inner tubes with high plate slenderness, 182

whereas both inward and outward local buckling was detected for the more compact inner 183

tubes. For the tested range of properties, neither the steel type nor the concrete compressive 184

strength appeared to have any significant influence on the failure mode. 185

Load versus axial deformation relationships 186

The load (P) versus average axial strain (ε) curves for all the stub column specimens are plotted 187

in Fig. 8, where P is the applied load recorded by the load actuator and ε is the average axial 188

strain, defined as the average axial shortening (Δ), calculated from the LVDT readings, divided 189

by the original specimen length (L). The experimental peak loads Pexp are presented in Table 190

1. In general, it may be observed that the concrete strength significantly influences the ductility 191

of the stub columns and their cross-sectional strengths. The ductility of the CFDST stub 192

columns was assessed through the ductility index (DI) given by Eq. (1), as proposed in Tao et 193

al. (2004), and widely adopted for concrete-filled tubular members in (Yang et al. 2008; 194

Jamaluddin et al. 2013; McCann et al. 2015). 195

DI = 85%

u

(1) 196

where Δ85% is the axial displacement when the load decreases to 85% of the ultimate load and 197

Δu is the axial displacement at ultimate load. Values of the ductility index obtained from each 198

of the stub column tests are presented in Table 1. A low DI value indicates that the load drops 199

9

off quickly beyond the peak load, whereas a high value indicates an ability to maintain at least 200

85% of Pexp with a considerable associated deformation. Values of DI for each test series are 201

plotted against the measured concrete cylinder strength in Fig. 9. Overall, it may be seen that 202

higher concrete strengths result in increased compressive resistance, but lower ductility. The 203

exception in Fig.9 (b) is caused by the shapes of the load versus average axial strain curves for 204

the C80 and C120 specimens, which resulted in higher DI values for the adopted definition of 205

ductility. However, as observed in Fig8 (c) and (d), the specimens with higher concrete 206

strengths (C80 and C120) still showed reduced ductility relative to their C40 counterparts. The 207

effect of the slenderness of the outer tube on ductility is also assessed through comparisons 208

among specimens with the same inner tubes and concrete grades but varying ho/to ratios, as 209

shown in Fig. 10. It may be observed that specimens with a more compact outer tube displayed 210

greater ductility, owing to the reduced susceptibility to local buckling and the improved 211

confinement afforded to the concrete. 212

Transverse to longitudinal strain ratios 213

The transverse to longitudinal strain ratios in the outer steel tubes of the tested specimens can 214

be used to assess the degree of confinement provided to the concrete (Uy et al. 2011); typical 215

examples are plotted against the normalised axial load in Fig. 11, where the strain ratios may 216

be seen to be approximately 0.3 in the early stages of loading. The ratios increase gradually 217

until the loads reach around 0.8 Pexp, and then grow sharply as the loads approach Pexp. This 218

can be explained with reference to the development of confinement in the CFDST stub columns 219

(Chan et al. 2015). The Poisson’s ratio of concrete (typically equal to about 0.2) is lower than 220

that of stainless steel (approximately 0.3) in the early (elastic) stages of loading, during which 221

the confinement afforded by the outer tube to the concrete core is negligible. As the load 222

increases, the concrete enters the plastic regime, and the effective Poisson’s ratio increases; 223

this causes greater lateral expansion of the concrete, increasing the contact pressure against the 224

10

outer tube, leading to increased confinement and enhanced transverse strains. Thus, increasing 225

ratios of transverse to longitudinal strain correspond to increasing levels of confinement to the 226

concrete core. 227

DISCUSSION AND ASSESSMENT OF CURRENT DESIGN CODES 228

General 229

In this section, the applicability of current design rules to the design of the studied CFDST 230

cross-sections is appraised. The experimental ultimate loads are compared with the resistance 231

predictions determined from the current European Code EN 1994-1-1 (EC4) (CEN 2004a) and 232

North American design provisions —AISC 360 (AISC 2016) and ACI 318 (ACI 2014) for 233

composite carbon steel members, as shown in Tables 5-7. For the slender cross-sections, the 234

effective width concept was employed to consider the effect of local buckling of the outer 235

tubes; note that the inner tubes were all fully effective in this study. Modifications to the 236

existing rules are also considered. In the comparisons presented, the measured material 237

properties and geometric dimensions of the test specimens have been employed, and all partial 238

safety factors have been taken to be equal to unity. The code limitations on steel strength and 239

concrete strength are often exceeded, but comparisons are still presented in order that possible 240

extension of the range of applicability of the codes can be assessed. 241

EN 1994-1-1 (EC4) 242

The compressive design resistance of rectangular or square carbon CFT sections in EC4 (CEN 243

2004b) is a simple summation of the steel tube and concrete contributions. Account is taken of 244

the higher resistance of the concrete, caused by confinement from the outer steel tube, by 245

adopting a concrete coefficient of 1.0, rather than 0.85 (CEN 2004b). The cross-section 246

capacity (PEC4) of a concrete-filled rectangular CFDST compression member is thus given by 247

Eq. (2). 248

EC4 0.2, 0.2,o o c c i iP A A f A (2) 249

11

where 0.2,o and 0.2,i correspond to the outer tube and inner tube 0.2% proof stresses, while fc 250

is the concrete cylinder compressive strength measured on the day of the corresponding stub 251

column tests. 252

A slenderness limit of Ho/to ≤ 52(235/fy)0.5 for the outer tube is also specified in EC4 (CEN 253

2004b), beyond which local buckling needs to be explicitly accounted for. In this study, the 254

limit has been modified for stainless steel to reflect the differences in material yield strength 255

and Young’s modulus, as given by Eq. (3), 256

0.5

o

0.2 ,

23552

210000o

o o

H E

t

(3) 257

It is worth noting that when the presence of the concrete is ignored in the classification of the 258

cross-section, the outer tubes of the LS100×3 series are class 4 (slender). However, when the 259

beneficial influence of the concrete infill in inhibiting local buckling is considered, i.e. 260

assessing the slenderness of the outer tube against the limit given by Eq. (3), these cross-261

sections are deemed to be non-slender. The outer tubes of the specimens in the LR150×3 and 262

FR120×3 series exceed the limit of Eq. (3) and are hence deemed to be slender, despite the 263

influence of the concrete, as shown in Table 5. In these cases, the effective width equations 264

provided in EN 1993-1-4 (CEN 2006a; Gardner and Theofanous 2008), as given by Eqs. (4) 265

and (5), are adopted for calculating the effective area of the outer tube: 266

2

0.772 0.079

p p

(4) 267

2

0.2, 0.2,

2

12(1 )( )o o

p o ocr o

h tk E

(5) 268

where ρ is the reduction factor for local buckling, p is the element slenderness, ν is the 269

Poisson’s ratio equal to 0.3, ho is the flat element height of the outer tube (replaced by bo for 270

the flat element width), k is the buckling coefficient, taken equal to 4 for plates with simply 271

supported boundary conditions in pure compression (CEN 2006b) and Eo is the outer tube 272

12

Young’s modulus. Table 5 presents the reduction factors to the width (ρb) and height (ρh) of 273

the stainless steel outer tubes for the LR150×3 and FR120×3 series, as well as the overall 274

effective areas. 275

AISC 360 276

The American Specification AISC 360 (AISC 2016) for the design of concrete-filled composite 277

members is also assessed herein. In AISC 360, concrete-filled composite cross-sections are 278

categorised into compact, noncompact and slender sections according to the width-to-thickness 279

ratio of the outer tube. The resulting classification influences the calculation of the axial 280

compressive strength. A compact section is able to reach the yield strength of the steel tube and 281

develop a concrete compressive strength of 0.85fc. A noncompact section confines the concrete 282

to a lesser extent, with 0.70fc being used in the design calculation, after which it is assumed 283

that the concrete volumetric dilation cannot be confined adequately since the noncompact steel 284

tube undergoes local buckling (Chen and Han 2007). A slender section can neither reach the 285

yield strength of the steel tube nor confine the concrete beyond 0.70 fc (Lai et al. 2014). 286

The limiting width-to-thickness ratios, i.e. p for compact/noncompact and r for 287

noncompact/slender, are tabulated in Table 6 for the outer tubes of all the tested sections. In 288

this study, all tested CFDST sections are classified as compact. Note that a local buckling 289

coefficient k = 10.67 is employed in AISC 360 to reflect the influence of the concrete in 290

restraining plate buckling (Uy and Bradford 1996). The cross-section capacities (PAISC) can be 291

thus predicted using Eq. (I2-9b) of AISC 360 (AISC 2016). It should be noted that the term for 292

the reinforcing bars is replaced by the inner tube. The structural behavior of the inner tube is 293

however different from that of the reinforcing bars. Reinforcing bars have little or no axial 294

resistance upon crushing of the concrete, whereas the inner tube still continues to sustain load 295

and can thus be treated as an independent term in the resistance function. Therefore, the 296

13

compressive cross-section strengths (PAISC) of the tested CFDST stub columns are calculated 297

from Eq. (6). 298

AISC 0.2, 0.2,0.85o o c c i iP A A f A (6) 299

ACI 318 300

The American Concrete Institute design guidelines ACI 318 (ACI 2014) for CFT sections are 301

also assessed herein. According to ACI 318 (ACI 2014), the cross-section resistance (PACI) is 302

determined from Eq. (7). 303

ACI 0.2, 0.2,0.85o o c c i iP A A f A (7) 304

It should be noted that the gross area of the outer tube can only be used provided that the 305

thickness of the outer tube satisfies to ≥ Ho(σ0.2,o/3Eo)0.5, as specified in Section 10.3.1.6 of ACI 306

318 (ACI 2014). The test specimens in the LR150×3 and FR120×3 series exceed the above 307

limit, as shown in Table 7. The compressive design resistance of the sections is therefore not 308

explicitly covered by ACI 318 but, in order to enable comparisons to be made, the effective 309

width expressions in the American Specification SEI/ASCE-8-02 (ASCE 2002) were utilised 310

in the calculations. The effective areas of the outer tubes were determined using the local 311

buckling reduction factors ρ, obtained from Eqs. (8)-(9), 312

1 0.22 / p

p

(8) 313

1.052 o n

p

o o

h F

t Ek

(9) 314

where p is the local slenderness, termed in SEI/ASCE-8-02 (ASCE 2002), Fn is the column 315

buckling stress, calculated using the iterative tangent modulus design approach, and the other 316

symbols are as previously defined. Taking k equal to 4 according to SEI/ASCE-8-02 (ASCE 317

2002), Fn equal to σ0.2,o due to the short length of the stub columns and ν = 0.3, the local 318

slenderness calculated using Eq. (9) is the same as that obtained from Eq. (5), and hence the 319

14

same symbol has been adopted herein. Table 7 presents the reduction factors and effective areas 320

of the stainless steel outer tubes for the LR150×3 and FR120×3 series. 321

Discussion and Design Recommendations 322

The ratio of test-to-design strength (Pexp/Pcode) for each of the tested CFDST specimens is 323

presented in Tables 5-7. The comparisons indicate that the unmodified design models (leading 324

to the capacity predictions PEC4, PAISC and PACI), which were developed for carbon steel CFT 325

sections, offer generally conservative strength predictions for the studied CFDST sections. The 326

predicted axial capacities determined according to EC4 (PEC4) show the best agreement with 327

the test strengths, with the mean value of Pexp/PEC4 = 1.1, owing mainly to the higher adopted 328

concrete coefficient. Of the North American provisions, AISC 360 (AISC 2016) yielded 329

slightly more accurate axial capacity predictions (PAISC) than ACI 318 (ACI 2014), due to 330

consideration of the beneficial effect of the concrete infill on the local buckling behavior of the 331

outer tube; this is discussed further below. 332

The ratios of test-to-predicted ultimate loads (Pexp/Pcode) are plotted against the concrete 333

cylinder strength in Fig. 12. The comparisons reveal that EC4 (CEN 2004b) provides less 334

conservative predictions for specimens with high strength concrete (C80 and C120) than their 335

counterparts with normal strength concrete (C40), particularly for sections within the specified 336

code slenderness limits. This observation has previously been made for concrete-filled tubes; 337

to remedy this, an effective compressive strength, as defined in EN 1992-1-1 (CEN 2004a), is 338

used for concrete strengths greater than 50 MPa and below 90 MPa. The effective strength is 339

determined by multiplying the concrete strength by a reduction factor η, as given by Eq. (10). 340

For concrete strengths beyond 90 MPa, a constant reduction factor η of 0.8, as proposed by 341

Liew et al. (2016), is employed herein to determine the effective compressive strength for 342

sections falling within the specified code slenderness limits. The values of η, as calculated from 343

Eq. (10), are shown in Table 5 for the specimens tested in the present study. 344

15

1.0 ( 50) 200 50 MPa 90 MPa

0.8 90 MPa

c c

c

f f

f

(10) 345

The resulting ratios of test-to-modified predicted strengths (Pexp/Pcode*) are presented in Tables 346

5-7. The inclusion of η leads to more consistent resistance predictions across the different 347

concrete strengths for EC4 and ACI 318, as highlighted in Fig. 12. However, it was found that 348

the design rules incorporating the effective compressive strength of concrete results in more 349

conservative and scattered predictions for AISC 360, particularly for the specimens with 350

LR150×3 and FR120×3 sections as the outer tubes. This is due to the influence of the different 351

concrete grades on the axial capacity of these sections not being as significant as that on the 352

specimens with the more compact sections, i.e., those with LS100×3 and FR100×4 sections as 353

the outer tubes. 354

The structural behavior of concrete-filled tubular members and hollow tubular members is 355

fundamentally different. As observed in the experiments, the presence of the concrete infill 356

alters the local buckling mode of the outer steel tube by restricting it from buckling inwards 357

(Lai et al. 2014). Uy and Bradford (1996) conducted a semi-analytical investigation using the 358

finite strip method into the elastic local buckling of steel plates in composite steel-concrete 359

members. It was shown that the buckling coefficient k increases from 4 for conventional (two-360

way) local buckling of simply-supported plates to 10.30 for outward only buckling. A further 361

theoretical study (Bradford et al. 1998) using the Rayleigh-Ritz method, indicated k to be 10.67, 362

which is about 2.67 times that of the unfilled case. 363

Modification to the current design rules in EC4 and ACI 318, taking the buckling coefficient k 364

as 10.67, rather than 4, in calculating the effective areas of the outer tubes is therefore 365

considered herein. In AISC 360 (AISC 2016), this beneficial effect of the presence of the 366

concrete infill is already considered in the cross-section slenderness limits. Concrete-filled 367

columns with compact sections reach their yield load before the development of local buckling 368

16

in the outer tube and thus the outer tube is fully effective. Theoretically the noncompact section 369

limit of 1.40(E/Fy)0.5 given in AISC 360 (AISC 2016) for hollow section could be increased by 370

2.67times, to 2.29(E/Fy)0.5. Based on available experimental data and other theoretical studies, 371

the constant has been increased to 2.26 in AISC 360 (Leon et al. 2007). 372

The modified axial capacity predictions, with k = 10.67, from EC4 and ACI 318 for the tested 373

specimens are shown in Tables 5 and 7, respectively. The local buckling reduction factors ρ 374

are now almost equal to unity for all the series, which indicates that the areas of the outer tubes 375

are essentially fully effective. The comparisons show that the mean ratios of test-to-modified 376

design strengths (Pexp/Pcode^) are equal to 1.07 and 1.15, with coefficients of variation (COVs) 377

of 0.062 and 0.049 for EC4 and ACI 318, respectively. This illustrates that the modified design 378

rules yield improved consistency and accuracy in the prediction of the compressive resistance 379

of CFDST members. 380

Some unconservative predictions again arise for the higher concrete strengths (C80 and C120) 381

though, as shown in Fig. 13. Therefore, the reduction factor η is employed as before. The 382

resulting ratios of test-to-predicted modified design strengths (Pexp/Pcode^*) are plotted against 383

the measured concrete cylinder strength in Fig. 13 and the overall mean ratios of Pexp/Pcode^* 384

are shown in Tables 5-7. The results reveal that the modified design rules incorporating both 385

the effective compressive strength of concrete and k = 10.67 provide safe-sided predictions 386

with very good consistency for CFDST with concrete grades extending to C120. 387

CONCLUSIONS 388

An experimental investigation into the behavior of concrete-filled double skin tubular 389

(CFDST) stub columns has been presented in this paper. The stub column test results, together 390

with the measured material properties and geometric properties, have been reported. The test 391

strengths were compared with the capacity predictions for conventional concrete-filled carbon 392

steel tubular columns given in the European Code EN 1994-1-1 and two American 393

17

Specifications (AISC 360 and ACI 318). Overall, it has been found that EC4 provides good 394

resistance predictions for the tested specimens, which featured steel sections of relatively 395

stocky proportions, while the predictions from the American Specifications AISC 360 (AISC 396

2016) and ACI 318 (ACI 2014) were on the safe side but rather conservative. The effect of 397

modifications to EC4 and ACI 318 to consider outward only local buckling of the outer tube, 398

by taking the buckling coefficient k as 10.67 instead of 4, was assessed. Concrete strengths 399

were also adjusted, by applying a reduction factor η to high strength material. Comparisons 400

revealed that modifying the existing design rules by incorporating the revised buckling 401

coefficient results in more accurate and consistent capacity predictions, while the approach of 402

using effective concrete strengths allows the rules in EC4 and ACI 318 to be safely extended 403

to the design of CFDST stub columns with concrete compressive cylinder strengths up to 120 404

MPa. 405

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489

490

(a) RHS outer and SHS inner tubes (b) SHS outer and SHS inner tubes 491

Fig. 1. Definition of symbols for CFDST specimens. 492

21

493

Fig. 2. Fabrication of the tubes prior to casting. 494

495

Fig. 3. Locations of coupons within the cross-sections.496

497

Fig. 4. Full measured stress–strain curves from longitudinal tensile coupons. 498

22

499

Fig. 5. Test set-up for CFDST stub column specimens. 500

501

Fig. 6. Arrangement of strain gauges and LVDTs. 502

503

23

504

Fig. 7. Failure modes of stub columns (FR100×4-NS20×1.5-C40 (a, b) LS100×3-NS40×1.5-505

C40 (c, d)). 506

(a) (b)

(c) (d)

24

(e) (f)

(g) (h) Fig. 8. Load-average axial strain curves for CFDST specimens. 507

(a) Outer tube LR150×3 (b) Outer tube LS100×3

(c) Outer tube FR120×3 (d) Outer tube FR100×4

Fig. 9. Influence of concrete strength on ductility 508

25

(a) Concrete grade C40 (b) Concrete grade C80

(c) Concrete grade C120

Fig. 10. Effect of slenderness ratio on ductility 509

  510

Fig. 11. Typical curves of normalized axial load to transverse-to-longitudinal strain ratios. 511

0.0

0.3

0.6

0.9

1.2

0 0.3 0.6 0.9 1.2

Nor

mal

ised

axi

al lo

ad

P/P

exp

Average transverse-to-longitudinal strain ratio

FR100×4-NS20×1.5-C80

LS100×3-NS40×4-C120

26

(a) EC4

(b) AISC 360 (c) ACI 318

Fig. 12. Variation of Pexp/Pcode ratio with concrete strength. 512

(a) EC4 (b) ACI 318

Fig. 13. Variation of Pexp/Pcode ratio with concrete strength with k = 10.67. 513

0.80

1.00

1.20

1.40

0 40 80 120 160

Pex

p/P

code

fc (MPa)

EC4EC4*

0.80

1.00

1.20

1.40

0 40 80 120 160

Pex

p/P

code

fc (MPa)

AISCAISC*

0.80

1.00

1.20

1.40

0 40 80 120 160

Pex

p/P

code

fc (MPa)

ACIACI*

0.80

1.00

1.20

1.40

0 40 80 120 160

Pex

p/P

code

fc (MPa)

EC4^EC4^*

0.80

1.00

1.20

1.40

0 40 80 120 160

Pex

p/P

code

fc (MPa)

ACI^ACI^*

27

Table 1. Average measured dimensions and key results of CFDST stub columns

Specimen Length

L (mm)

Inner tube dimensions Outer tube dimensions Cross-section areas Ultimate test

strength

Ductility index

Bi (mm)

Hi

(mm)

ti

(mm) Hi/ti

rint,i

(mm)

rext,i

(mm) Ho

(mm) Bo

(mm) to

(mm) Ho/to

rint,o

(mm) rext,o

(mm)

Outer tube

Inner tube

Concrete

Ao

(mm2) Ai

(mm2) Ac

(mm2) Pexp

(kN) DI

LR150×3-NS20×2.5-C40 375 19.9 19.9 2.58 7.7 2.4 4.6 150.3 79.8 3.10 48.6 6.1 8.9 1351 166 10204 1223.4 2.00

LR150×3-NS20×2.5-C40R 375 19.9 19.9 2.59 7.7 2.4 4.6 150.5 79.8 3.10 48.6 6.1 8.9 1353 166 10212 1254.9 2.30

LR150×3-NS20×2.5-C80* 375 19.9 19.9 2.59 7.7 2.4 4.6 150.4 79.8 3.10 48.5 6.1 8.9 1353 167 10207 1681.3 1.15

LR150×3-NS20×2.5-C120 375 19.9 19.9 2.57 7.7 2.4 4.6 150.3 79.8 3.10 48.4 6.1 8.9 1353 165 10196 1996.4 1.05

LR150×3-NS20×1.5-C40 375 20.0 20.0 1.55 12.9 2.0 3.4 150.3 79.7 3.10 48.6 6.1 8.9 1349 107 10178 1216.4 2.45

LR150×3-NS20×1.5-C80 375 20.0 20.0 1.52 13.2 2.0 3.4 150.3 79.9 3.10 48.5 6.1 8.9 1353 106 10192 1577.0 1.17

LR150×3-NS20×1.5-C120 375 20.0 20.0 1.50 13.3 2.0 3.4 150.3 79.8 3.10 48.5 6.1 8.9 1352 104 10183 2019.4 1.05

LS100×3-NS40×4-C40 250 40.0 40.0 3.84 10.4 3.9 7.4 100.3 100.0 3.15 31.8 3.6 6.1 1202 523 7245 1419.5 1.54

LS100×3-NS40×4-C40R 250 40.0 40.0 3.86 10.4 3.9 7.4 100.2 100.0 3.16 31.7 3.6 6.1 1202 524 7228 1401.2 1.98

LS100×3-NS40×4-C80* 250 40.0 40.0 3.87 10.3 3.9 7.4 100.2 99.9 3.13 32.1 3.6 6.1 1191 526 7238 1464.0 2.42

LS100×3-NS40×4-C120* 250 40.0 40.0 3.86 10.4 3.9 7.4 100.2 100.0 3.14 31.9 3.6 6.1 1196 525 7242 1706.1 2.34

LS100×3-NS40×1.5-C40 250 40.4 40.4 1.42 28.4 3.0 4.0 100.3 99.9 3.18 31.6 3.6 6.1 1210 216 7155 1209.2 1.45

LS100×3-NS40×1.5-C80* 250 40.4 40.4 1.44 28.1 3.0 4.0 100.2 100.0 3.15 31.8 3.6 6.1 1200 218 7175 1322.5 2.23

LS100×3-NS40×1.5-C120 250 40.4 40.4 1.44 28.1 3.0 4.0 100.2 100.0 3.15 31.8 3.6 6.1 1199 218 7169 1516.2 1.11

FR120×3-NS20×2.5-C40 300 19.9 19.9 2.59 7.7 2.4 4.6 119.8 79.8 2.86 41.9 4.5 6.9 1086 167 8059 909.9 1.80

FR120×3-NS20×2.5-C80* 300 20.0 20.0 2.67 7.5 2.4 4.6 119.8 79.8 2.85 42.1 4.5 6.9 1081 172 8060 1161.3 1.74

FR120×3-NS20×2.5-C120 300 19.9 19.9 2.61 7.7 2.4 4.6 119.8 79.8 2.88 41.7 4.5 6.9 1092 168 8056 1469.3 1.05

FR120×3-NS20×1.5-C40 300 20.3 20.3 1.52 13.3 2.0 3.4 119.8 79.8 2.87 41.7 4.5 6.9 1091 107 8029 855.9 2.15

FR120×3-NS20×1.5-C40R 300 20.2 20.2 1.53 13.2 2.0 3.4 119.8 79.7 2.88 41.6 4.5 6.9 1092 107 8021 864.4 1.77

FR120×3-NS20×1.5-C80* 300 20.2 20.2 1.54 13.1 2.0 3.4 119.8 79.9 2.87 41.7 4.5 6.9 1091 108 8037 1154.9 1.42

FR120×3-NS20×1.5-C120 300 20.2 20.2 1.53 13.2 2.0 3.4 119.8 79.8 2.86 41.8 4.5 6.9 1087 107 8035 1408.5 1.18

FR100×4-NS20×2.5-C40 250 20.3 20.3 1.55 13.1 2.4 4.6 99.9 79.8 3.83 26.1 5.0 9.1 1269 167 6258 1030.4 2.44

FR100×4-NS20×2.5-C80 250 20.3 20.3 1.52 13.4 2.4 4.6 100.0 79.8 3.79 26.4 5.0 9.1 1255 171 6272 1235.2 2.34

FR100×4-NS20×2.5-C120 250 20.2 20.2 1.50 13.4 2.4 4.6 100.0 79.8 3.79 26.4 5.0 9.1 1256 170 6275 1398.4 1.93

FR100×4-NS20×1.5-C40 250 20.2 20.2 1.51 13.4 2.0 3.4 99.9 79.8 3.78 26.4 5.0 9.1 1253 107 6253 1015.0 2.32

FR100×4-NS20×1.5-C40R 250 20.2 20.2 1.55 13.1 2.0 3.4 99.9 79.7 3.80 26.3 5.0 9.1 1258 109 6240 998.7 3.22

FR100×4-NS20×1.5-C80* 250 20.2 20.2 1.49 13.5 2.0 3.4 100.0 79.9 3.79 26.4 5.0 9.1 1257 105 6257 1191.4 1.96

FR100×4-NS20×1.5-C120 250 20.2 20.2 1.55 13.1 2.0 3.4 100.0 79.8 3.80 26.3 5.0 9.1 1259 109 6252 1358.5 2.12

Note: * Specimen chosen for attaching strain gauges in the stub column tests.

28

Table 2. Measured material properties of metal tubes from coupon tests

Section

Flat coupons Corner coupons Comparison u E εf

n m u

u E εf n m u

0.2,

0.2,

c

f

,

,

f c

f f

(MPa) (MPa) (GPa) (%) (MPa) (MPa) (GPa) (%)

LS100×3 556 709 209 38 6 4 1.28 784 906 195 17 5 4 1.15 1.4 0.44 LR150×3 475 712 206 41 4 3 1.50 754 869 196 20 4 4 1.15 1.6 0.50 FR100×4 439 466 214 25 6 4 1.06 587 620 211 11 5 4 1.06 1.3 0.46 FR120×3 401 442 205 28 7 4 1.10 546 580 198 13 5 4 1.06 1.4 0.45 NS20×1.5 357 401 204 13 6 4 1.12 377 428 195 9 9 4 1.13 1.1 0.68 NS20×2.5 468 504 213 9 6 4 1.08 474 515 212 10 8 4 1.08 1.0 1.16 NS40×1.5 324 384 211 22 16 4 1.18 412 461 207 6 11 4 1.12 1.3 0.29 NS40×4 404 455 210 13 3 4 1.13 463 529 206 12 6 4 1.14 1.1 0.96

Table 3. Concrete mix design

Concrete grade Mix proportions (relative to the weight of cement)

Cement Water Fine aggregate 10 mm aggregate Condensed silica fume Super plasticizer C40 1.0 0.56 1.67 2.51 0.00 0.004 C80 1.0 0.32 1.25 1.88 0.00 0.020 C120 1.0 0.21 1.02 1.53 0.09 0.053

Table 4. Measured concrete cylinder strengths

Nominal concrete

strength (MPa)

Average concrete strength at

28-day (MPa)

COV

Number of cylinder tests

Average concrete strength at days

of stub column tests (MPa)

COV

Number of cylinder tests

C40 39.5 0.029 2 41.8 0.019 3 C80 78.4 0.006 2 81.6 0.005 3 C120 101.9 0.049 2 115.9 0.029 4

29

Table 5. Test strengths and design predictions from EC4 of CFDST stub columns.

Specimen 0.5235 /52 y

o

o

fH

t

Reduction factor Effective area of outer tube

Concrete strength

reduction factor

Pexp/PEC4 Pexp/PEC4* Pexp/PEC4^ Pexp/PEC4^* k = 4 k = 10.67 k = 4 k = 10.67

ρb ρh ρb ρh Ao,eff (mm2) Ao,eff (mm2)

LR150×3-NS20×2.5-C40 No 1.00 0.65 1.00 0.99 1064 1342 1.00 1.21 1.21 1.07 1.07 LR150×3-NS20×2.5-C40R No 1.00 0.65 1.00 0.99 1065 1344 1.00 1.24 1.24 1.10 1.10 LR150×3-NS20×2.5-C80 No 1.00 0.65 1.00 0.99 1066 1345 1.00 1.19 1.19 1.08 1.08 LR150×3-NS20×2.5-C120 No 1.00 0.65 1.00 0.99 1067 1346 1.00 1.13 1.13 1.05 1.05 LR150×3-NS20×1.5-C40 No 1.00 0.65 1.00 0.99 1063 1340 1.00 1.26 1.26 1.10 1.10 LR150×3-NS20×1.5-C80 No 1.00 0.65 1.00 0.99 1067 1346 1.00 1.15 1.15 1.05 1.05 LR150×3-NS20×1.5-C120 No 1.00 0.65 1.00 0.99 1066 1344 1.00 1.17 1.17 1.09 1.09 LS100×3-NS40×4-C40 Yes --- --- --- --- 1202 1202 1.00 1.20 1.20 1.20 1.20 LS100×3-NS40×4-C40R Yes --- --- --- --- 1202 1202 1.00 1.18 1.18 1.18 1.18 LS100×3-NS40×4-C80 Yes --- --- --- --- 1191 1191 0.84 1.00 1.07 1.00 1.07 LS100×3-NS40×4-C120 Yes --- --- --- --- 1196 1196 0.80 0.99 1.10 0.99 1.10 LS100×3-NS40×1.5-C40 Yes --- --- --- --- 1210 1210 1.00 1.16 1.16 1.16 1.16 LS100×3-NS40×1.5-C80 Yes --- --- --- --- 1200 1200 0.84 1.00 1.07 1.00 1.07 LS100×3-NS40×1.5-C120 Yes --- --- --- --- 1199 1199 0.80 0.97 1.08 0.97 1.08 FR120×3-NS20×2.5-C40 No 1.00 0.80 1.00 1.00 963 1086 1.00 1.14 1.14 1.07 1.07 FR120×3-NS20×2.5-C80 No 1.00 0.79 1.00 1.00 957 1081 1.00 1.04 1.04 0.99 0.99 FR120×3-NS20×2.5-C120 No 1.00 0.80 1.00 1.00 971 1092 1.00 1.05 1.05 1.01 1.01 FR120×3-NS20×1.5-C40 No 1.00 0.80 1.00 1.00 970 1091 1.00 1.12 1.12 1.05 1.05 FR120×3-NS20×1.5-C40R No 1.00 0.80 1.00 1.00 972 1092 1.00 1.13 1.13 1.07 1.07 FR120×3-NS20×1.5-C80 No 1.00 0.80 1.00 1.00 970 1091 1.00 1.07 1.07 1.02 1.02 FR120×3-NS20×1.5-C120 No 1.00 0.80 1.00 1.00 965 1087 1.00 1.04 1.04 1.00 1.00 FR100×4-NS20×2.5-C40 Yes --- --- --- --- 1269 1269 1.00 1.15 1.15 1.15 1.15 FR100×4-NS20×2.5-C80 Yes --- --- --- --- 1255 1255 0.84 1.08 1.16 1.08 1.16 FR100×4-NS20×2.5-C120 Yes --- --- --- --- 1256 1256 0.80 1.03 1.15 1.03 1.15 FR100×4-NS20×1.5-C40 Yes --- --- --- --- 1253 1253 1.00 1.19 1.19 1.19 1.19 FR100×4-NS20×1.5-C40R Yes --- --- --- --- 1258 1258 1.00 1.17 1.17 1.17 1.17 FR100×4-NS20×1.5-C80 Yes --- --- --- --- 1257 1257 0.84 1.08 1.17 1.08 1.17 FR100×4-NS20×1.5-C120 Yes --- --- --- --- 1259 1259 0.80 1.03 1.16 1.03 1.16

Mean 1.11 1.14 1.07 1.10

COV 0.073 0.051 0.062 0.055 Note: PEC4* = modified predicted strength incorporating effective compressive strength of concrete; PEC4^ = modified predicted strength incorporating a higher buckling coefficient k = 10.67; PEC4^* = modified predicted strength incorporating both the effective compressive strength of concrete and k = 10.67.

30

Table 6. Test strengths and design predictions from AISC-360 of CFDST stub columns.

Specimen label

Limiting ratios

ho/to Classification

Concrete strength reduction factor

Pexp/PAISC Pexp/PAISC* Compact/noncompact

p Noncompact/slender

r

LR150×3-NS20×2.5-C40 47.1 62.5 42.6 Compact 1.00 1.13 1.13 LR150×3-NS20×2.5-C40R 47.1 62.5 42.6 Compact 1.00 1.16 1.16 LR150×3-NS20×2.5-C80 47.1 62.5 42.5 Compact 0.84 1.18 1.28 LR150×3-NS20×2.5-C120 47.1 62.5 42.5 Compact 0.80 1.16 1.31 LR150×3-NS20×1.5-C40 47.1 62.5 42.6 Compact 1.00 1.17 1.17 LR150×3-NS20×1.5-C80 47.1 62.5 42.5 Compact 0.84 1.14 1.24 LR150×3-NS20×1.5-C120 47.1 62.5 42.5 Compact 0.80 1.20 1.36 LS100×3-NS40×4-C40 43.8 58.1 27.6 Compact 1.00 1.25 1.25 LS100×3-NS40×4-C40R 43.8 58.1 27.5 Compact 1.00 1.23 1.23 LS100×3-NS40×4-C80 43.8 58.1 27.8 Compact 0.84 1.06 1.13 LS100×3-NS40×4-C120 43.8 58.1 27.7 Compact 0.80 1.07 1.18 LS100×3-NS40×1.5-C40 43.8 58.1 27.3 Compact 1.00 1.21 1.21 LS100×3-NS40×1.5-C80 43.8 58.1 27.6 Compact 0.84 1.07 1.14 LS100×3-NS40×1.5-C120 43.8 58.1 27.6 Compact 0.80 1.05 1.16 FR120×3-NS20×2.5-C40 51.2 67.9 36.8 Compact 1.00 1.14 1.14 FR120×3-NS20×2.5-C80 51.2 67.9 36.9 Compact 0.84 1.08 1.18 FR120×3-NS20×2.5-C120 51.2 67.9 36.5 Compact 0.80 1.12 1.28 FR120×3-NS20×1.5-C40 51.2 67.9 36.6 Compact 1.00 1.12 1.12 FR120×3-NS20×1.5-C40R 51.2 67.9 36.5 Compact 1.00 1.14 1.14 FR120×3-NS20×1.5-C80 51.2 67.9 36.6 Compact 0.84 1.12 1.22 FR120×3-NS20×1.5-C120 51.2 67.9 36.7 Compact 0.80 1.11 1.27 FR100×4-NS20×2.5-C40 49.9 66.3 21.5 Compact 1.00 1.20 1.20 FR100×4-NS20×2.5-C80 49.9 66.3 21.8 Compact 0.84 1.16 1.24 FR100×4-NS20×2.5-C120 49.9 66.3 21.7 Compact 0.80 1.12 1.24 FR100×4-NS20×1.5-C40 49.9 66.3 21.8 Compact 1.00 1.25 1.25 FR100×4-NS20×1.5-C40R 49.9 66.3 21.7 Compact 1.00 1.23 1.23 FR100×4-NS20×1.5-C80 49.9 66.3 21.7 Compact 0.84 1.16 1.25 FR100×4-NS20×1.5-C120 49.9 66.3 21.7 Compact 0.80 1.12 1.25 Mean 1.15 1.21 COV 0.048 0.050

Note: PAISC* = modified predicted strength incorporating effective compressive strength of concrete; PAISC* = modified predicted strength incorporating the effective compressive strength of concrete.

31

Table 7. Test strengths and design predictions from ACI 318 of CFDST stub columns.

Specimen label Thickness limit

tmin

(mm)

minot t

Reduction factor Effective area of outer tubePexp/PACI Pexp/PACI* Pexp/PACI^ Pexp/PACI^* k = 4 k = 10.67 k = 4 k = 10.67

ρb ρd ρb ρd Ao,eff (mm2) Ao,eff (mm2)

LR150×3-NS20×2.5-C40 4.2 No 1.00 0.74 1.00 1.00 1138 1351 1.25 1.25 1.13 1.13 LR150×3-NS20×2.5-C40R 4.2 No 1.00 0.74 1.00 1.00 1139 1353 1.28 1.28 1.16 1.16 LR150×3-NS20×2.5-C80 4.2 No 1.00 0.74 1.00 1.00 1140 1353 1.27 1.27 1.18 1.18 LR150×3-NS20×2.5-C120 4.2 No 1.00 0.74 1.00 1.00 1141 1353 1.23 1.23 1.16 1.16 LR150×3-NS20×1.5-C40 4.2 No 1.00 0.74 1.00 1.00 1136 1349 1.29 1.29 1.17 1.17 LR150×3-NS20×1.5-C80 4.2 No 1.00 0.74 1.00 1.00 1141 1353 1.23 1.23 1.14 1.14 LR150×3-NS20×1.5-C120 4.2 No 1.00 0.74 1.00 1.00 1140 1352 1.28 1.28 1.20 1.20 LS100×3-NS40×4-C40 3.0 Yes --- --- --- --- 1141 1202 1.25 1.25 1.25 1.25 LS100×3-NS40×4-C40R 3.0 Yes --- --- --- --- 1143 1202 1.23 1.23 1.23 1.23 LS100×3-NS40×4-C80 3.0 Yes --- --- --- --- 1126 1191 1.06 1.13 1.06 1.13 LS100×3-NS40×4-C120 3.0 Yes --- --- --- --- 1133 1196 1.07 1.18 1.07 1.18 LS100×3-NS40×1.5-C40 3.0 Yes --- --- --- --- 1155 1210 1.21 1.21 1.21 1.21 LS100×3-NS40×1.5-C80 3.0 Yes --- --- --- --- 1139 1200 1.07 1.14 1.07 1.14 LS100×3-NS40×1.5-C120 3.0 Yes --- --- --- --- 1138 1199 1.05 1.16 1.05 1.16 FR120×3-NS20×2.5-C40 3.1 No 1.00 0.87 1.00 1.00 1007 1086 1.18 1.18 1.14 1.14 FR120×3-NS20×2.5-C80 3.1 No 1.00 0.87 1.00 1.00 1001 1081 1.12 1.12 1.08 1.08 FR120×3-NS20×2.5-C120 3.1 No 1.00 0.87 1.00 1.00 1015 1092 1.15 1.15 1.12 1.12 FR120×3-NS20×1.5-C40 3.1 No 1.00 0.87 1.00 1.00 1014 1091 1.17 1.17 1.12 1.12 FR120×3-NS20×1.5-C40R 3.1 No 1.00 0.87 1.00 1.00 1016 1092 1.18 1.18 1.14 1.14 FR120×3-NS20×1.5-C80 3.1 No 1.00 0.87 1.00 1.00 1014 1091 1.15 1.15 1.12 1.12 FR120×3-NS20×1.5-C120 3.1 No 1.00 0.87 1.00 1.00 1009 1087 1.14 1.14 1.11 1.11 FR100×4-NS20×2.5-C40 2.6 Yes --- --- --- --- 1269 1269 1.20 1.20 1.20 1.20 FR100×4-NS20×2.5-C80 2.6 Yes --- --- --- --- 1255 1255 1.16 1.24 1.16 1.24 FR100×4-NS20×2.5-C120 2.6 Yes --- --- --- --- 1256 1256 1.12 1.24 1.12 1.24 FR100×4-NS20×1.5-C40 2.6 Yes --- --- --- --- 1253 1253 1.25 1.25 1.25 1.25 FR100×4-NS20×1.5-C40R 2.6 Yes --- --- --- --- 1258 1258 1.23 1.23 1.23 1.23 FR100×4-NS20×1.5-C80 2.6 Yes --- --- --- --- 1257 1257 1.16 1.25 1.16 1.25 FR100×4-NS20×1.5-C120 2.6 Yes --- --- --- --- 1259 1259 1.12 1.25 1.12 1.25

Mean 1.18 1.21 1.15 1.18 COV 0.060 0.042 0.049 0.044

Note: PACI* = modified predicted strength incorporating effective compressive strength of concrete; PACI^ = modified predicted strength incorporating a higher buckling coefficient k = 10.67; PACI^* = modified predicted strength incorporating both the effective compressive strength of concrete and k = 10.67.