Wang et al. (2019) - Experimental study of square and ...
Transcript of Wang et al. (2019) - Experimental study of square and ...
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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:[email protected] 5
2 Professor, Dept. of Civil and Environmental Engineering, The Hong Kong Polytechnic University, Hong Kong, China. E-6
mail: [email protected] (Formerly, Dept. of Civil Engineering, The Univ. of Hong Kong, Pokfulam Rd., Hong 7
Kong, China. E-mail: [email protected]) 8
3 Professor, Dept. of Civil and Environmental Engineering, Imperial College London, London SW7 2AZ, U.K. E-mail: 9
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
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Keywords: Cold-formed, Composite structures, CFDST, Stainless steel, Experiments, Testing. 26
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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.