Structures 27 (2020) 1623–1636

Contents lists available at ScienceDirect

Structures
journal homepage: www.elsevier.com/locate/structures

Behaviour of grout-filled double-skin tubular steel stub-columns: Numerical T

modelling and design considerations
Nikolaos I. Tziavosa, , Michaela Gkantoub, Marios Theofanousc, Samir Dirarc,
⁎

Charalampos Baniotopoulosc
a
Centre for Smart Infrastructure and Construction, Department of Engineering, University of Cambridge, UK
b
Department of Civil Engineering, Liverpool John Moores University, UK
c
Department of Civil Engineering, University of Birmingham, UK

ARTICLE INFO ABSTRACT

Keywords: The use of grout-filled double-skin tubular (GFDST) sections in civil, bridge and offshore engineering applica­
Composite columns tions is rapidly increasing. The design of such composite members is not directly covered by design codes,
Double skin despite recent research studies investigating their performance, proposing design equations or modifying ex­
Grout-filled isting codified methods. Aiming to extend the available pool of structural performance data, the current study
Finite element modelling
reports the results of an extensive numerical investigation on GFDST stub-columns. Finite element (FE) models,
are developed and validated against published test data. A parametric investigation is conducted to evaluate the
effect of key parameters, including cross-sectional slenderness, hollow ratio and the effect of concrete infill on
the capacity of GFDST members. The numerically obtained load capacities along with collated test data are
utilised to assess the applicability of design strength predictions based on European Code (EC4), the American
Concrete Institute (ACI) and the analytical models proposed by Han et al. and Yu et al. Overall, the modified Yu
et al. provided strength predictions with low scatter, whereas ACI yielded overly conservative predictions
particularly for smaller hollow ratios.

1. Introduction connections [11] or as a remediation solution for lifetime extension as

many offshore structures in the North Sea are close to end-of-life [12].
Concrete-filled tubular members are extensively employed in the Tubular double-skin filled members combining carbon and stainless
construction of bridges, high-rise buildings, transmission towers and steel [13,14] are also used in submarine pipelines [13]. For offshore
offshore structures [1,2]. The surrounding tube provides confinement applications, GFDSTs with circular hollow sections (CHSs) are the
to the concrete core thus increasing its strength and ductility, whilst the configuration attracting more interest, as they provide the highest level
concrete infill prolongs the occurrence of local buckling of the steel of confinement on the sandwiched grout core [9,15].
tube [3,4]. Hence, they possess superior stiffness, strength and ductility To better understand the response of this type of composite mem­
compared to their bare steel or reinforced concrete counterparts re­ bers, several researchers have experimentally investigated the strength
sulting in smaller section sizes and larger lettable areas in the lower of CFDST stub-columns and beam-columns with CHS tubes [6,16–21].
stories of multi-storey buildings [5]. In recent years, concrete-filled The performance of different cross section shapes has also been eval­
double skin tubular (CFDST) sections – where concrete is used to fill the uated in experimental studies, including CFDST with square hollow
annulus of two steel hollow sections, are attracting more interest, of­ sections [22], rectangular hollow sections [23] and a combination of
fering a lighter-weight alternative with enhanced stiffness, greater CHS and square hollow sections [16]. Han et al. [24] tested CFDST
bending capacity, along with improved fire and seismic resistance beam-columns with CHS and square cross-section under cyclic loads,
[6–10]. whereas impact [25] and torsional tests [26] are also reported in the
In offshore construction, the infill material is typically a cement- literature. Alternatives to carbon steel have been considered for struc­
based grout, resulting in grout-filled double skin tubular (GFDST) tural applications in corrosive environments such as stainless steel
members. Such members are typically employed in oil and gas jacket [27–29] and aluminium [30], while the use of alternative cementitious
platforms and offshore wind turbine foundations to form grouted composites such as rubberised concrete [31] has been urged by the

⁎
Corresponding author.
E-mail address: nt431@cam.ac.uk (N.I. Tziavos).

https://doi.org/10.1016/j.istruc.2020.07.021
Received 22 March 2020; Received in revised form 10 June 2020; Accepted 9 July 2020
Available online 07 August 2020
2352-0124/ © 2020 Institution of Structural Engineers. Published by Elsevier Ltd. All rights reserved.
N.I. Tziavos, et al. Structures 27 (2020) 1623–1636

Nomenclature fcu Compressive strength of cubic sample

fc Compressive cylinder strength
Ag Cross sectional area of grout core fcc Confined compressive strength
Ak Cross sectional area of hollow part fc Unconfined compressive strength
Aso Cross sectional area of outer steel tube L Stub-column length
Asi Cross sectional area of inner steel tube a Steel ratio
Do External tube diameter an Nominal steel ratio
Di Internal tube diameter to External tube thickness
Dg Grout core diameter ti Internal tube thickness
fsyo External steel yield strength c Post-peak confinement factor
fsyi Internal steel yield strength c Strength reduction factor
fsy Steel yield strength cc Strain corresponding to confined compressive strength
frp Lateral confining pressure ¯ Relative slenderness
fgt Grout tensile strength ξ Confinement factor
χ Hollow ratio, = D i 2t
D
fgc Compressive strength of grout o o

need to minimise carbon emissions. Along with the aforementioned 1994-1-1 (EC4) [36], American Concrete Institute (ACI) [37] and the
studies and to enhance the design practice of double-skinned composite analytical models proposed by Han et al. [8] and Yu et al. [38].
members, researchers have conducted numerical investigations on the
influence of material and geometrical parameters to generate new data
2. Numerical modelling
and assess existing design methods [10,13,32–35].
Tests on GFDST members are scarce; Li et al. [12] reported 8 tests
The general-purpose FE software Abaqus [39] was employed for the
on stub-columns, 4 beam-columns and 2 on GFDST beams. Although
numerical computations. In order to verify the accuracy of the nu­
the behaviour of the grout is often treated in a similar manner to that of
merical simulations, the numerical model was validated against test
concrete, for GFDSTs the grouted annulus is often very small resulting
data reported in two experimental studies [6,12], which are briefly
in higher hollow ratio (χ) values. Hollow ratio is the ratio of the in­
discussed in Section 2.1. Sections 2.2 and 2.3 provide a detailed de­
ternal steel diameter to the internal diameter of the external steel tube
scription on the numerical modelling assumptions, including the type of
and is a commonly used metric in CFDSTs to provide information on the
analyses, the adopted boundary conditions, interaction properties and
cross-sectional geometry. Typical hollow ratios in previous experi­
the employed material models for the steel and the infill.
mental studies range from 0.2 to 0.7, whereas in offshore construction
of GFDST, members with hollow ratios greater than 0.8 are often em­
ployed. The ultimate strength of GFDST stub columns, is a function of 2.1. Selected experimental tests
the steel yield strength (fsy), the grout material compressive strength
(fgc) and the steel cross sectional properties (diameter to thickness ratio, The experiments on stub columns reported by Tao et al. [6] and Li
D/t). et al. [12] are used herein to validate the FE models. The infill material
The present paper aims to fill this gap of limited available data on in the tests reported in [6] is concrete with a compressive strength of
the structural performance of GFDST cross-sections across a range of 47.4 N/mm2, whereas a grout infill with a compressive strength of 51.1
hollow ratios by generating new data on the compressive capacity of and 54.8 N/mm2 was used in the tests reported in [12]. A total of 7
GFDST stub columns by means of numerical modelling. Initially, the cross-section geometries were considered, with duplicate tests per­
developed FE models are validated against experiments and subse­ formed for each configuration thereby resulting in 14 experimental
quently a parametric study is carried out, investigating the effect of tests. The hollow ratio of the selected experimental tests ranges from
cross-sectional slenderness in small and large-diameter GFDST stub- 0.28 to 0.84. The dimensions of each specimen and the corresponding
columns. The hollow ratios for the developed FE models range from 0.4 material properties are reported in Table 1, where L is the length of the
to 0.9. The numerically obtained strengths are subsequently compared specimen and Do, to, Di, ti, the diameter and thickness of the external
with design strength predictions obtained from European Code EN and internal steel tube respectively. A typical GFDST cross-section is
shown in Fig. 1, where Aso and Asi are the cross-sectional areas of the

Table 1
Dimensions and material properties of circular double skin stub-column specimens used in the validation study.
Dimensions (mm) Material properties

Source Test ID Do to Di ti L fsyo (N/mm2) fsyi (N/mm2) fcu (N/mm2) Pu, test (kN)

[6] cc2a 180 3 48 3 540 275.9 396.1 47.4 1790

cc2b 180 3 48 3 540 275.9 396.1 47.4 1791
cc3a 180 3 88 3 540 275.9 370.2 47.4 1648
cc3b 180 3 88 3 540 275.9 370.2 47.4 1650
cc4a 180 3 140 3 540 275.9 342 47.4 1435
cc4b 180 3 140 3 540 275.9 342 47.4 1358
cc5a 114 3 58 3 342 294.5 374.5 47.4 904
cc5b 114 3 58 3 342 294.5 374.5 47.4 898
[12] GC1-1 140 2.5 114 2 420 307 321 51.1 751.80
GC1-2 140 2.5 114 2 420 307 321 51.1 698.86
GC2-1 140 2.5 76 1.6 420 307 321 51.1 935.81
GC2-2 140 2.5 76 1.6 420 307 321 51.1 928.62
GCL-1 450 8 400 8 700 365 363 54.8 8867.92
GCL-2 450 8 400 8 700 365 363 54.8 8735.85

1624
N.I. Tziavos, et al. Structures 27 (2020) 1623–1636

Fig. 4. Exemplary stress-strain curve for confined concrete.

outer and the inner tube respectively, Ag the cross-sectional area of the
grout and Ak the area of the hollow part. The average yield strength of
the external (fsyo) and internal steel tubes (fsyi), as obtained from tensile
Fig. 1. Geometric properties and notation for GFDST members.
coupon tests, along with the cubic compressive strength (fcu) and the
recorded ultimate compressive strength (Pu,test) are also reported in
Table 1.

2.2. Modelling assumptions

The loading and support conditions used in the experimental set-up

were reflected in the boundary conditions and constraints adopted in
the FE models. The boundary conditions were applied to two reference
points, one on each end of the member, to which the degrees of freedom
of the nodes of top and bottom cross-section of the model were tied. For
each of the modelled tests the employed boundary conditions and
constraints are shown in Fig. 3a. Translation along the z-axis (i.e. par­
allel to the member axis) was allowed at the top reference points, with
all remaining degrees of freedom restrained at both reference points.
Fig. 2. Comparison between internal and kinetic energy for specimen cc4a, b. The FE models were based on the reported dimensions [6,12] and the
steel and grout parts were discretised using linear solid elements with
reduced integration (C3D8R). A mesh convergence study has been in­
itially performed and a minimum of three elements have been used
along the thickness of the steel plates and grout [40], respectively, as
shown in Fig. 3b, to produce accurate and computationally efficient
results.
A quasi-static explicit solution scheme was selected in order to avoid
convergence difficulties arising during the conventional implicit ana­
lysis due to the non-monotonic nature of the concrete response [41].
This approach alleviates convergence issues, however it is sensitive to
the selected loading rate requiring engineering judgment on the com­
putational results.
In this case, the step time was set at 10 s and a sufficiently small
time increment was selected (10−4) through a sensitivity analysis, en­
suring that the inertia effects and artificial strain energy were negligible
during the simulations. This was subsequently verified by ensuring that
the kinetic energy remained smaller than 2% of the internal strain en­
ergy throughout the analysis. As an example this is illustrated in Fig. 2.
The load was applied using displacement control with a smooth am­
plitude function. Contact at the steel-grout interfaces was modelled
using the general contact algorithm. In the normal direction, a hard
contact formulation was chosen and a friction coefficient (μ) of 0.4 was
assigned for the tangential direction [41].
Geometric imperfections and residual stresses are known to affect
the response of axially loaded compressive tubular members. However,
in GFDST members their influence is considerably reduced due to the
Fig. 3. a) Boundary conditions on stub column finite element model and b) presence of the infill material providing lateral restraint, which lessens
Typical mesh discretisation.
the sensitivity of the tubes to local buckling and can therefore be ig­
nored in the numerical analysis. This is in line with past studies [27]

1625
N.I. Tziavos, et al. Structures 27 (2020) 1623–1636

Fig. 5. Comparison of axial load-shortening curves for experimental and FE models for stub-columns.

and as shown in Section 3, this assumption did not have any implication true = eng (1 + eng ) (1)
on the accuracy of the FE models. Fig. 3
true
true = ln(1 + eng )
E (2)
2.3. Material modelling
Typical cement-based grouts exhibit similar behaviour to concrete
For the steel tubulars the von Mises yield criterion with an isotropic in compression, although a larger scatter is to be expected in test results
hardening behaviour was used. The behaviour of the steel tubes was particularly for higher strength material. For this purpose, for the
defined with a multi-linear stress-strain curve employing the yield and subsequent analyses an analytical concrete model has been employed to
ultimate stress values and corresponding strains, which were experi­ describe the behaviour of the infill material in compression. In addition,
mentally obtained and reported in [12]. Cold-formed steel tubes were to account for the restraint on the core from the steel tubes, a confined
used in the experiments conducted by Tao et al. [6]. The yield strength concrete model described in Ref. [15] was selected. An exemplary
for each steel section is given in Table 1, whereas the Poisson’s ratio (ν) stress-strain curve when using the aforementioned analytical model is
was set at 0.3. The engineering stress (σeng) and strain (εeng) values depicted in Fig. 4 comprising three stages and is described herein. The
were converted to true stress (σtrue) and strain (εtrue) following Eqs. (1) first part of the confined stress-strain curve (AB) is described by Eq. (1),
and (2): which was suggested by Mander et al. [42].

1626
N.I. Tziavos, et al. Structures 27 (2020) 1623–1636

Table 2 uniaxial compressive stress fb0/fc0 was taken equal to 1.16 and finally
Comparison of ultimate strength of FE models against test results. the ratio of the second stress invariant on the tensile meridian to that on
Source Test ID Pu, test (kN) Pu, FE (kN) Pu, test/FE
the compressive meridian at initial yield was set equal to 0.725 as per
[45]. The tensile strength of the grout was estimated from Eq. (13) as
Tao et al. [6] cc2a 1790 1780.19 1.005 suggested in [46] and a stress-displacement curve was defined for the
cc2b 1791 1780.19 1.006
tensile response of the infill material.
cc3a 1648 1668.61 0.987
cc3b 1650 1668.61 0.988 fgt = 0.3(fck ) 2/3
cc4a 1435 1311.05 1.094
(13)
cc4b 1358 1311.05 1.035
cc5a 904 854.54 1.057
cc5b 898 854.54 1.050 3. Validation
Li et al. [12] GC1-1 751.80 731.10 1.028
GC1-2 698.86 731.10 0.956
The FE models were verified against the experimental tests reported
GC2-1 935.81 933.60 1.002
GC2-2 928.62 933.60 0.995 in Refs. [6,12]. The comparison between the tests and the numerical
GCL-1 8867.92 8622.52 1.028 models was based on the load-displacement response, the observed
GCL-2 8735.85 8622.52 1.013 failure modes and the ultimate axial capacity. In Fig. 5 the experimental
Average 1.017 and the numerical load – axial displacement response is compared. The
COV 0.033 initial stiffness has been accurately simulated in all the examined cases,
demonstrating that the elastic constants and boundary conditions were
accurately modelled. In all the models the ultimate load is also well
fcc ( cc/ cc ) captured. The ultimate load (Pu, test), is compared with the numerically-
c = , c < cc
1 + ( c/ cc ) (3) obtained one (Pu, FE) in Table 2, showing very good agreement, with an
average ratio of 1.017 and a COV of 0.033. Typical buckling modes in
Ec
where = filled double-skin members include outward buckling of the external
Ec (fcc / cc ) (4) tube, inward/outward buckling of the internal tube and crushing/
and f’cc, ε’cc are the confined compressive strength and corresponding cracking of the infill medium. This is confirmed in Fig. 6, where a
strain, εc the compressive strain and Ec the Young’s modulus. In this comparison of the experimental and numerical failure modes is made.
study the experimentally defined Young’s modulus, reported in [12] is The observed outward buckling of the external and internal steel tubes
used in the numerical models. and grout/concrete crushing is accurately captured for different
models. As shown in Fig. 5, the post-peak behaviour which was re­
fcc = c fc + k1frp (5) corded in some of the experiments has not been very well captured by
the numerical model, which is possibly attributed to the employed
frp
cc = c 1 + k2 analytical concrete model and the plateau it forms until it reaches the
c fc (6) ultimate strain, as illustrated in Fig. 4 and was also suggested by Thai
et al. [47]. It is considered that this did not have any impact on the
For the constants k1 and k2, values of 4.1 and 20.5 as suggested in
primary focus of this study, as the ultimate load has been captured with
Richart et al. [43] were used, whereas ε’c is the unconfined concrete
great precision. Overall, it is demonstrated that from the validation
strain at f’c and γc a strength reduction factor to account for material
study the numerical models provide an accurate representation of the
imperfections and Dg is the diameter of the grout core. The lateral
real conditions and a precise prediction of the experimentally observed
confining pressure (frp), on the grout is obtained from Eq. (9) as it sa­
ultimate load and corresponding failure modes which are subsequently
tisfies the cross-sections under investigation.
used for the analytical assessment.
c fc 28
c = 0.002 + , 28 c fc 82
54000 (7) 4. Parametric study

c = 1.85Dg 0.135, 0.85 c 1.0 (8) Upon successful validation, the numerical models were utilised to
conduct an extensive parametric analysis, aiming to investigate the
D effect of key parameters on the structural response of GFDST stub-col­
frp = 0.006241 0.0000357 f , 47 < D / t 150
t syo (9) umns. The validated models included two cross-sections with external
The second (BC) and third (CD) stages of the stress-strain curve are diameters equal to 140 mm and 450 mm. Using these models as a basis,
described by Eqs. (10) and (11) respectively. two groups were considered; one with a small (group GCS) and one
with a large diameter (group GCL). In order to get an accurate re­
= cu c presentation of the cross-sectional response, for the numerical models
c c f cc + (fcc c f cc ), cc < c cu
cu cc (10) the length of the stub-columns was taken equal to 3 times the external
diameter. The effect of the diameter-to-thickness ratio was examined
c = c f cc , c > cu (11) and four cross-sectional slenderness values equal to 50, 60, 70 and 80
where βc accounts for any confinement after the peak load was reached (abbreviated as Dt50, Dt60, Dt70 and Dt80) were investigated for each
and was expressed in [44] as follows: of the GCS and GCL groups. For the parametric study, the external and
internal steel tubes were set to have equal D/t ratios on all FE models
2
D D and the hollow ratio effect is further investigated in the remaining
= 0.0000339 + 0.010085 + 1.3491
c
t t (12) sections.
Subsequently, the analytical compressive stress-strain curve was
converted to true values and employed in the finite element model with 4.1. Cross-sectional slenderness
the Concrete Damaged Plasticity model. In this study, following a
sensitivity analysis, a dilation angle equal to 20° was found to result in For each one of the D/t values, six hollow ratio values ranging from
good agreement with the experimental tests. For the remaining para­ 0.4 to 0.9 with a step of 0.1 were considered. By maintaining a constant
meters, the eccentricity was set equal to 0.1, the ratio of equibiaxial to diameter to thickness ratio for both the external and the internal steel

1627
N.I. Tziavos, et al. Structures 27 (2020) 1623–1636

Fig. 6. Failure mode comparison between experiments and FE models for tests a) GC1-2, b) GC2-1, c) GCL-1, d) cc3a and infill material crushing for GCL-1 and cc3a.

tube, the same hollow ratio value χ can be achieved by either varying outer steel tube geometric properties are constant for the examined
the diameter and the thickness of the outer tube and keeping the inner hollow ratios. As anticipated, a smaller hollow ratio that corresponds to
tube dimensions constant or vice versa. Both cases have been in­ a larger grout thickness increases the axial capacity the GFDST stub-
vestigated and are designated as I (followed by the χ value) or O (fol­ column. This is more pronounced in Fig. 7a where the outer tube has
lowed by the χ value), depending on whether the inner or outer tube been modified indicating that the influence of the external steel tube is
dimensions have been modified. Adopting the same assumptions de­ higher. In most cases, the overall response does not present a sudden
scribed in Section 2, a total of 96 nonlinear analyses were carried out loss of strength but rather a stable ductile post-peak response, which is
and the results are reported in this section. similar to the behaviour reported in the experiments (see Fig. 5).
The full load-displacement path was captured during the analysis In Fig. 8 and Fig. 9 the numerically obtained failure loads are nor­
and typical cases for a small scale and a large scale stub column with D/ malised against the squash load (Fy), and are plotted against the hollow
t = 60 are shown in Fig. 7a and Fig. 7b respectively. Note that for the ratio for the small (GCS group) and large diameter (GCL group) FE
cases with flat load-displacement post-elastic response, where a clear models respectively. The squash load is defined as the sum of three
peak value was not observed, the maximum load that was recorded terms, which are the products of the yield strength and the cross section
during the simulation was considered to be the ultimate load. In both of the two steel tubes and the product of the compressive strength of the
cases, the effect of the change in the hollow ratio value is evident. In grout with the cross section of the grout. For each group two cases were
Fig. 7a the inner steel tube has been kept constant, while in Fig. 7b, the investigated, one with a constant outer steel tube and one with a

1628
N.I. Tziavos, et al. Structures 27 (2020) 1623–1636

Fig. 7. Typical load-displacement curves from parametric models for a) varying external tube and b) varying internal tube.

Fig. 9. Effect of steel tube cross section on the axial compressive strength of FE
Fig. 8. Effect of steel tube cross section on the axial compressive strength of FE models in group GCL for a) constant external tube and b) constant inner tube.
models in group GCS for a) constant external tube and b) constant inner tube.

4.2. Effect of grout thickness

constant inner steel tube. As previously observed in Fig. 7, an increase
in the value of hollow ratio, decreases the normalised compressive For the GCS group with D/t = 80, the axial stresses for increasing
strength of the stub column for all the considered models of the GCS grout thickness are visualised in Fig. 10. The grout thicknesses at
group (Fig. 8a, b). The same conclusions are also drawn from the FE Fig. 10(a) to (d) were 6.35 mm, 24.51 mm, 38.13 mm and 85.81 mm
models in the GCL group specimens for constant outer and inner tubes, and the corresponding ultimate loads Pu were 436.99 kN, 871.11 kN,
as shown in Fig. 9a and b respectively. In particular, for GCS with 1260.64 kN, 3099, 45 kN respectively. In all cases, the bottom cross-
constant external tube, the normalised load was in the range of 1.28 to section shows the stress distribution in N/mm2 when the failure load
1.05 for hollow ratio equal to 0.4 and 0.9, respectively. The same ratios (Pu) was reached and the top cross section shows the stresses at
were equal to 1.29 to 1.02 for GCS with constant inner tube, 1.36 to P = 0.25Pu, during the elastic stage of the load-axial shortening curve.
1.03 for GCL with constant external tube and 1.29 to 1.04 for GCL with For the examined FE models, the stresses on the grout core indicate a
constant inner tube. In addition, no clear effect of the D/t value on the smooth transition along the thickness during the elastic stage. For ex­
normalised load was observed. ample for the models with intermediate thicknesses (see Fig. 10(b) and
(c)), the stresses appear to be in the range of 7 to 10 N/mm2 and 8 to
12 N/mm2 for 0.25 Pu, respectively. Similar are the conclusions for the

1629
N.I. Tziavos, et al. Structures 27 (2020) 1623–1636

Fig. 10. Distribution of stresses on concrete core for varying hollow ratio and constant D/t = 80.

specimens with higher and lower grout thickness. previously proposed design equations and code specifications and their
On the contrary, once the ultimate load is reached the distribution applicability to GFDST stub-columns. For this purpose, the design
of stresses from the inner to the outer steel tube, is significantly higher equations provided in EC4 [36] and in the ACI code [37] for concrete
for all models. For example as shown in Fig. 10(d), the concrete stresses filled members are modified to be applicable for double-skin tubular
closer to the inner tube are as low as 9 N/mm2 and reach values as high steel members and assessed herein. In addition, the analytical models
as 61 N/mm2 once closer to the external tube, demonstrating an in­ proposed in [8] and [38] are also evaluated. The accuracy of the
crease of 52 N/mm2 towards the outer tube. Similar is the range for all aforementioned four different design approaches to accurately predict
four cases of Fig. 10 with an axial stress range within 48–57 N/mm2. the resistance of double skin cross-sections in compression at ultimate
This is owing to the larger confinement that is provided on the grout limit state has been assessed.
core from the external steel tube when compared to the internal tube. In Sections 5.1–5.4, the design equations that were used, along with
This is also in agreement with findings presented in Section 4.1. the modifications made are presented in detail. The presently generated
Typical failure modes that were observed in the numerical models numerical data along with literature collated data are summarised and
are shown in Fig. 11. For sections with large hollow ratio values – compared to the design guidelines in section 5.5.
hence, small grout core thickness, the lateral restraint was less pro­
nounced, leading to local instabilities at locations where higher com­ 5.1. Eurocode 4 (EN 1994-1-1)
pressive steel stresses occurred, as shown in Fig. 11a. As it can be ob­
served in Fig. 11b and Fig. 11c, for Dt60 and Dt70 the compressive EN 1994-1-1 (EC4) [36] provides general rules for the design of
stresses led to a local instability in the external steel tube, resulting in a composite steel-concrete columns and composite structures in com­
failure mode similar to “elephant foot” buckling. For larger grout pression. Even though the plastic resistance of concrete-filled tubes in
thicknesses (Fig. 11d), material yielding was the prominent failure compression is detailed in Section 6.7.3.2 [36], the design of filled
mode. Finally, it is noted that the deformed shape of the model shown double-skin steel members is not currently covered by Eurocodes, thus a
in Fig. 11a corresponds to high applied deformations, well beyond the modification to existing methods was made. EC4 provides a design
ultimate load. It is believed that despite the symmetry in terms of equation for concrete-filled steel tubes with reinforcement by means of
geometry, loading and boundary conditions, a non-symmetric deformed a resistance function. The plastic resistance in compression Npl,Rd is the
shape can occur either as the result numerical instabilities/roundoff summation of the resistance of the components forming the cross-sec­
errors that start off as infinitesimal but propagate and accumulate tion under investigation. The latter has been modified for GFDSTs to
throughout the analysis thus becoming significant or due to the bi­ include the grout infill and the internal steel tube replaces the steel
furcation of the symmetric solution to non-symmetric ones. This sec­ reinforcement as per Eq. (14). Similar modifications to EC4 have been
ondary bifurcation has been observed experimentally [48] and dis­ employed by Wang et al. [27], for double-skinned sections formed by
cussed analytically [49] for circular tubes in compression and it is stainless and high strength steel tubes.
believed that it can occur for the type of structures studied herein, al­
beit, the presence of concrete infill makes the switching from an ax­ t o fsyo
PEC4 = a A sofsyo + A g fc 1 + + A sifsyi
isymmetric model to a non-axisymmetric one more difficult. c
Do fc (14)

5. Design predictions where fc is the compressive cylinder strength of the grout and, ηa ηc and
are given by Eqs. (15) and (16),
The data generated from the parametric study alongside experi­
= 0.25(3 + 2 ¯ ) 1.0 (15)
mental data collected from the literature, were employed to assess a

1630
N.I. Tziavos, et al. Structures 27 (2020) 1623–1636

Fig. 11. Typical failure modes from FE models for varying cross-sectional slenderness.

c = 4.9 18.5 ¯ + 17 ¯ 2 0 (16) et al. [27], for CFDST stub-columns with external stainless steel tube.

where is the relative slenderness as described in Eq. (17): 90 235 Eo,i

0.5

A seo,i = A so,i
Npl,Rk Do,i /t o,i fsyo,i 210000 (21)
¯=
Ncr (17) where, the subscripts (o, i) refer to the external and internal steel tube.
where Npl,Rk is the characteristic value of the plastic resistance to
compression given by Eq. (18) and evaluated as a sum of forces of the 5.2. American Concrete Institute (ACI)
constituent elements. For the grout core a unity coefficient has been
employed to take into consideration the confinement effects. ACI [37] which is the American code for the design of concrete
structures provides design formula for the evaluation of the ultimate
Npl,Rk = A so fsyo + A g fc + A sifsyi (18) strength of concrete-filled circular short columns. Incorporating the
The elastic critical buckling load (Ncr), is calculated with the elastic contribution of the inner tube, the compressive cross-sectional strength
effective stiffness (EIeff), according to Eq. (19), (PACI ) of concrete-filled tubes is modified to Eq. (22) as follows:

EIeff = Eso Iso + Esi Isi + K e Eg Ig (19) PACI = A sofsyo + 0.85A g fc + A sifsyi (22)

where Ke is a correction factor for the grout core equal to 0.6, E the
Young’s modulus and the second moment of area (I) for each of the 5.3. Han et al. [8]
components of the cross-section. According to EC 4, for circular hollow
steel sections if the local slenderness limit as defined in (20) is ex­ Han et al. carried out a series of experiments on CFDST stub col­
ceeded, local buckling ought to be accounted for, umns and proposed a new design Eq. (23) for the ultimate strength of
CFDST cross-sections, also considering the confinement offered to the
D/t 90(235/ fsy ) (20) core from the external steel tube and the influence of the hollow ratio:
For this reason for the subsequent EC4 calculation, the cross section PHan = A sco fscyo + A sifsyi (23)
of the steel tubes was modified to account for local buckling according
to Eq. (21) proposed in [50] and has been recently employed by Wang The first term corresponds to the compressive capacity of the

1631
N.I. Tziavos, et al. Structures 27 (2020) 1623–1636

Table 3
Comparisons of small diameter FE model with design strength predictions.
Group FE model ID D/t Do (mm) to (mm) Di (mm) ti (mm) L (mm) χ Pu, EC 4 Pu, ACI Pu, Han Pu, Yu, mod
Pu, FE Pu, FE Pu, FE Pu, FE

GCS1 I0.9-Dt50 50 140.0 2.80 120.9 2.41 420.0 0.9 1.125 1.080 1.031 1.015
I0.8-Dt50 107.5 2.15 0.8 1.126 1.156 1.060 1.031
I0.7-Dt50 94.0 1.88 0.7 1.110 1.206 1.067 1.027
I0.6-Dt50 80.6 1.61 0.6 1.118 1.273 1.092 1.043
I0.5-Dt50 67.2 1.34 0.5 1.103 1.306 1.093 1.037
I0.4-Dt50 53.7 1.07 0.4 1.094 1.337 1.096 1.034
O0.9-Dt50 131.9 2.63 114.0 2.28 395.8 0.9 1.089 1.046 0.998 0.983
O0.8-Dt50 148.4 2.96 445.3 0.8 1.085 1.114 1.021 0.994
O0.7-Dt50 169.6 3.39 508.9 0.7 1.079 1.176 1.042 1.002
O0.6-Dt50 197.9 3.95 593.7 0.6 1.073 1.233 1.061 1.010
O0.5-Dt50 237.5 4.75 712.5 0.5 1.071 1.290 1.084 1.022
O0.4-Dt50 296.8 5.93 890.6 0.4 1.063 1.333 1.099 1.028
GCS2 I0.9-Dt60 60 140.0 2.33 121.8 2.03 420.0 0.9 1.118 1.074 1.022 1.008
I0.8-Dt60 108.2 1.80 0.8 1.096 1.132 1.034 1.008
I0.7-Dt60 94.7 1.57 0.7 1.098 1.204 1.061 1.026
I0.6-Dt60 81.2 1.35 0.6 1.106 1.273 1.089 1.045
I0.5-Dt60 67.6 1.12 0.5 1.106 1.323 1.105 1.055
I0.4-Dt60 54.1 0.90 0.4 1.110 1.370 1.122 1.066
O0.9-Dt60 131.0 2.18 114 1.90 393.1 0.9 1.106 1.062 1.010 0.997
O0.8-Dt60 147.4 2.45 442.2 0.8 1.113 1.150 1.050 1.024
O0.7-Dt60 168.4 2.80 505.4 0.7 1.111 1.221 1.077 1.040
O0.6-Dt60 196.5 3.27 589.6 0.6 1.078 1.248 1.071 1.025
O0.5-Dt60 235.8 3.93 707.5 0.5 1.108 1.342 1.126 1.068
O0.4-Dt60 294.8 4.91 884.4 0.4 1.096 1.379 1.137 1.070
GCS3 I0.9-Dt70 70 140.0 2.00 122.4 1.74 420.0 0.9 1.183 1.094 1.031 1.019
I0.8-Dt70 108.8 1.55 0.8 1.156 1.157 1.046 1.024
I0.7-Dt70 95.2 1.36 0.7 1.145 1.220 1.067 1.036
I0.6-Dt70 81.6 1.16 0.6 1.146 1.283 1.090 1.053
I0.5-Dt70 68.0 0.97 0.5 1.151 1.341 1.114 1.071
I0.4-Dt70 54.4 0.77 0.4 1.157 1.390 1.134 1.086
O0.9-Dt70 130.3 1.86 114 1.62 391.1 0.9 1.153 1.066 1.005 0.993
O0.8-Dt70 146.6 2.09 440.0 0.8 1.151 1.152 1.042 1.020
O0.7-Dt70 167.6 2.39 502.9 0.7 1.153 1.232 1.079 1.046
O0.6-Dt70 195.5 2.79 586.7 0.6 1.152 1.297 1.109 1.067
O0.5-Dt70 234.7 3.35 704.1 0.5 1.148 1.358 1.133 1.083
O0.4-Dt70 293.3 4.19 880.1 0.4 1.133 1.393 1.143 1.085
GCS4 I0.9-Dt80 80 140.0 1.75 122.8 1.53 420.0 0.9 1.263 1.149 1.047 1.037
I0.8-Dt80 109.2 1.36 0.8 1.261 1.250 1.096 1.077
I0.7-Dt80 95.5 1.19 0.7 1.224 1.297 1.102 1.076
I0.6-Dt80 81.9 1.02 0.6 1.181 1.317 1.092 1.061
I0.5-Dt80 68.2 0.85 0.5 1.183 1.373 1.116 1.080
I0.4-Dt80 54.6 0.68 0.4 1.190 1.422 1.139 1.099
O0.9-Dt80 129.9 1.62 114.0 1.42 389.7 0.9 1.198 1.090 0.993 0.983
O0.8-Dt80 146.1 1.82 438.4 0.8 1.184 1.174 1.030 1.011
O0.7-Dt80 167.0 2.08 501.0 0.7 1.161 1.236 1.050 1.025
O0.6-Dt80 194.8 2.43 584.6 0.6 1.164 1.309 1.088 1.053
O0.5-Dt80 233.8 2.92 701.5 0.5 1.159 1.364 1.114 1.071
O0.4-Dt80 292.3 3.65 876.9 0.4 1.161 1.420 1.143 1.093

Average 1.136 1.244 1.076 1.040

COV 0.040 0.085 0.038 0.029

external steel tube alongside the sandwiched grout and the second term a=
A so
, an =
A so
to the compressive capacity of the internal steel tube. The cross-sec­ Ag A g,nom (28)
tional area A sco , is given from Eq. (24)
where the nominal cross-section of the sandwiched grout (Ag,nom) is:
A sco = A so + A g (24)
(Do 2t o) 2
A g,nom =
and fscyo for circular sections is given by Eq. (25), 4 (29)

fscyo = C1 2fsyo + C2 (1.14 + 1.02 ) fc (25)

5.4. Yu et al. [38]
where the coefficients C1, C2 and the confinement factor (ξ) are calcu­
lated according to Eqs. (26) and (27): Yu et al. proposed a unified equation for the estimate of ultimate
compressive strength of concrete-filled tubes in compression. To in­
a 1 + an
C1 = , C2 = clude the internal steel tube, the modification suggested in Hassanein
1+a 1+a (26)
and Kharoob [10] is used herein following Eq. (30),
fscyo
= an PYu, mod = (A so fsyo + A g fc ) 1 + 0.5 + A si fsyi
fc (27) 1+ (30)

where a and an are the steel ratio and the nominal steel ratio as follows: where the solid ratio, Ω is defined as per Eq. (31), Ak the hollow area as

1632
N.I. Tziavos, et al. Structures 27 (2020) 1623–1636

Table 4
Comparisons of large diameter FE model with design strength predictions.
Group FE model ID D/t Do (mm) to (mm) Di (mm) ti (mm) L (mm) χ Pu, EC 4 Pu, ACI Pu, Han Pu, Yu, mod
Pu, FE Pu, FE Pu, FE Pu, FE

GCL1 I0.9-Dt50 50 450.0 9.00 388.8 7.77 1350.0 0.9 1.101 1.052 1.010 0.990
I0.8-Dt50 345.6 6.91 0.8 1.121 1.145 1.061 1.021
I0.7-Dt50 302.4 6.04 0.7 1.111 1.201 1.077 1.021
I0.6-Dt50 259.2 5.18 0.6 1.113 1.265 1.102 1.032
I0.5-Dt50 216.0 4.32 0.5 1.116 1.322 1.124 1.042
I0.4-Dt50 172.8 3.45 0.4 1.128 1.383 1.153 1.060
O0.9-Dt50 462.9 9.25 400.0 8.00 1388.9 0.9 1.103 1.054 1.012 0.992
O0.8-Dt50 520.8 10.41 1562.5 0.8 1.118 1.141 1.057 1.017
O0.7-Dt50 595.2 11.90 1785.7 0.7 1.107 1.197 1.075 1.018
O0.6-Dt50 694.4 13.88 2083.3 0.6 1.100 1.250 1.093 1.020
O0.5-Dt50 833.3 16.66 2500.0 0.5 1.093 1.295 1.107 1.020
O0.4-Dt50 1041.7 20.83 3125.0 0.4 1.079 1.325 1.111 1.012
GCL2 I0.9-Dt60 60 450.0 7.50 391.5 6.52 1350.0 0.9 1.136 1.059 1.015 0.996
I0.8-Dt60 348.0 5.80 0.8 1.145 1.147 1.060 1.022
I0.7-Dt60 304.5 5.07 0.7 1.135 1.209 1.081 1.028
I0.6-Dt60 261.0 4.35 0.6 1.130 1.267 1.101 1.036
I0.5-Dt60 217.5 3.62 0.5 1.129 1.321 1.122 1.046
I0.4-Dt60 174.0 2.90 0.4 1.132 1.369 1.141 1.056
O0.9-Dt60 459.77 7.66 400.0 6.66 1379.3 0.9 1.146 1.068 1.024 1.004
O0.8-Dt60 517.24 8.62 1551.7 0.8 1.150 1.152 1.065 1.026
O0.7-Dt60 591.13 9.85 1773.4 0.7 1.140 1.214 1.087 1.032
O0.6-Dt60 689.65 11.49 2068.9 0.6 1.135 1.273 1.110 1.040
O0.5-Dt60 827.58 13.79 2482.8 0.5 1.134 1.326 1.132 1.048
O0.4-Dt60 1034.48 17.24 3103.4 0.4 1.129 1.368 1.147 1.051
GCL3 I0.9-Dt70 70 450.0 6.42 393.4 5.62 1350.0 0.9 1.200 1.085 1.008 0.990
I0.8-Dt70 349.7 4.99 0.8 1.198 1.175 1.054 1.019
I0.7-Dt70 306.0 4.37 0.7 1.182 1.240 1.079 1.030
I0.6-Dt70 262.2 3.74 0.6 1.170 1.297 1.100 1.040
I0.5-Dt70 218.5 3.12 0.5 1.166 1.350 1.121 1.051
I0.4-Dt70 174.8 2.49 0.4 1.195 1.464 1.217 1.135
O0.9-Dt70 457.5 6.53 400.0 5.71 1372.5 0.9 1.220 1.103 1.025 1.006
O0.8-Dt70 514.7 7.35 1544.1 0.8 1.163 1.140 1.024 0.989
O0.7-Dt70 588.2 8.40 1764.7 0.7 1.186 1.243 1.084 1.033
O0.6-Dt70 686.2 9.80 2058.8 0.6 1.176 1.303 1.108 1.044
O0.5-Dt70 823.5 11.76 2470.5 0.5 1.166 1.350 1.126 1.049
O0.4-Dt70 1029.4 14.70 3088.2 0.4 1.154 1.385 1.138 1.050
GCL4 I0.9-Dt80 80 450.0 5.62 394.8 4.93 1350.0 0.9 1.273 1.136 1.017 0.999
I0.8-Dt80 351.0 4.38 0.8 1.250 1.220 1.056 1.024
I0.7-Dt80 307.1 3.83 0.7 1.229 1.287 1.085 1.040
I0.6-Dt80 263.2 3.29 0.6 1.211 1.342 1.106 1.051
I0.5-Dt80 219.3 2.74 0.5 1.204 1.395 1.128 1.065
I0.4-Dt80 175.5 2.19 0.4 1.199 1.437 1.145 1.075
O0.9-Dt80 455.8 5.69 400.0 5.00 1367.5 0.9 1.279 1.141 1.021 1.004
O0.8-Dt80 512.8 1.82 1538.4 0.8 1.256 1.225 1.062 1.029
O0.7-Dt80 586.0 2.08 1758.2 0.7 1.231 1.289 1.088 1.041
O0.6-Dt80 683.7 2.43 2051.2 0.6 1.222 1.353 1.118 1.058
O0.5-Dt80 820.5 10.25 2461.5 0.5 1.185 1.373 1.114 1.045
O0.4-Dt80 1025.6 12.82 3076.9 0.4 1.196 1.437 1.151 1.070

Average 1.113 1.231 1.088 1.033

COV 0.014 0.088 0.042 0.025

Table 5 depicted in Fig. 1 and the rest as previously defined:

Comparisons of collated test data with design strength predictions.
Ag
=
Source Test ID
(31)
Pu, EC 4 Pu, ACI Pu, Han
Pu, Test
Pu, Yu, mod
A g + Ak
Pu, Test Pu, Test Pu, Test

[6] cc2a, cc2b, cc3a, cc3b, cc4a, 1.179 1.344 1.127 1.118
cc4b, 5.5. Assessment of design predictions
cc5a, cc5b, cc6a, cc6b, cc7a, cc7b
[8] DC-1, DC-2. DCc-0, DCc-1, DCc-2 1.074 1.171 0.970 0.971 In order to evaluate the suitability of design prediction methods, the
[12] GC1-1, GC1-2, GC2-1, GC2-2, 1.118 1.135 1.006 0.995
GCL-1, GCL-2
bearing capacity of the FE models is normalised against the analyti­
[20] 0-1-1-1, 0-1-1-2, 0-2-1-1, 0-2-1-2, 1.053 1.175 0.991 0.959 cally-obtained strength predictions (PEC4, PACI, PHan and PYu,mod) and is
0-2-1-2, shown in a tabulated format for the small (GCS) and large diameter
0-1-2-1, 0-1-2-2, 0-2-2-1, 0-2-2-2 (GCL) groups, in Table 3 and Table 4 respectively. Collated test data
[21] 1-1-2, 2-1-2, 1-1-1, 2-1-1, 1-2-2, 1.095 1.221 1.033 1.007
from the literature [6,8,12,20,21], are also employed for assessment
2-2-2,
1-2-1, 2-2-1 purposes and are shown in Table 5 in a similar format, by normalising
test results against design predictions. For both groups of the FE models
Average 1.113 1.230 1.041 1.025
COV 0.055 0.082 0.071 0.078 and collated data it is found that the strength predictions are on the safe
side with varying levels of conservatism and scatter as shown in Fig. 12,
where the ultimate sustained load is normalised with the predicted

1633
N.I. Tziavos, et al. Structures 27 (2020) 1623–1636

Fig. 12. Comparison of FE obtained compressive strength to design strength predictions for small diameter (group GCS) and large diameter (group GCL) models with
a) EC4, b) ACI, c) Han et al. [8], d) Yu et al. [38]

capacity from each design method and presented against the examined results in good predictions close to unity with reduced conservatism
hollow ratios. EC4 yielded safe predictions with similar trends for both (Fig. 12d) and a coefficient of variation of 0.029 (GCS group) and 0.025
groups, with an average of 1.136 and 1.113 for GCS and GCL groups (GCL group). Overall, it is shown that the modified Yu et al. strength
respectively. An increasing conservatism with increasing hollow ratio predictions are of lower conservatism. Nevertheless, Han et al. and EC4
values is observed to be consistent for small and large-diameter models methods can also be used for design purposes of GFDST members as the
(Fig. 12a). The conservatism for high slenderness is possibly attributed vast majority of the models are on the safe side.
to the local buckling limit suggested in [36], which is currently not In Fig. 13, the ultimate capacity obtained from the collated test data
explicitly defined for double skin filled tubular members, but for hollow or the presented FE models is normalised against the plastic resistance
steel members. In this case local buckling limit was taken equal to class design predictions from EC4 and ACI. In this case buckling of the
3 hollow sections, which does not account for the lateral restraint from slender cross-sections is not considered, thus allowing to examine the
the infill material. applicability of the class 3 limit for GFDST stub-columns. The current
The design predictions from ACI were found to be the most con­ limits for local buckling are also plotted for each design method.
servative amongst the design methods. Particularly for smaller hollow In Fig. 13a, it is shown that strength predictions are on the safe side
ratios (0.4–0.6) a high level of conservatism is shown, whereas this for GCS, GCL groups and also for the experimental data, hence it is
reduces for models with large hollow ratios (Fig. 12b). In addition, for suggested that further investigations are required to define a more
all the investigated models a high scatter was observed when this appropriate slenderness limit for GFDST stub-columns, considering the
method was employed, which can be associated with the fact that ACI lateral restraint provided by the infill material. This could potentially
does not account for confinement effects. Similar findings were also result in strength predictions with less conservatism. The ACI model,
reported for CFDST stub-columns with external stainless steel tubes in despite the ease of use resulted in very large scatter and conservatism
Wang et al. [27]. Predictions obtained from Han et al. [8] were also for all the investigated data (Fig. 13b). Considering local buckling im­
found on the safe side with a small scatter and an average of 1.076 for proved the results as shown in Fig. 12b, however further fine tuning of
GCS and 1.088 for GCL models (Fig. 12c). Strength predictions for the model is required in order to consider confinement effects for
models with hollow ratios of 0.8 and 0.9 are closer to unity and overall varying cross-sections and strain hardening of steel tubes, to allow for
with less conservatism compared to EC4 and ACI. Yu et al. [38] model less conservative results.

1634
N.I. Tziavos, et al. Structures 27 (2020) 1623–1636

Declaration of Competing Interest

The authors declare that they have no known competing financial

interests or personal relationships that could have appeared to influ­
ence the work reported in this paper.

References

[1] Espinos A, Romero ML, Serra E, Hospitaler A. Experimental investigation on the fire
behaviour of rectangular and elliptical slender concrete-filled tubular columns.
Thin-Walled Struct 2015;93:137–48. https://doi.org/10.1016/j.tws.2015.03.018.
[2] Portolés JM, Romero ML, Bonet JL, Filippou FC. Experimental study of high
strength concrete-filled circular tubular columns under eccentric loading. J Constr
Steel Res 2011;67:623–33. https://doi.org/10.1016/j.jcsr.2010.11.017.
[3] Han LH, Li W, Bjorhovde R. Developments and advanced applications of concrete-
filled steel tubular (CFST) structures: members. J Constr Steel Res
2014;100:211–28. https://doi.org/10.1016/j.jcsr.2014.04.016.
[4] Vernardos S, Gantes C. Experimental behavior of concrete-filled double-skin steel
tubular (CFDST) stub members under axial compression: a comparative review.
Structures 2019;22:383–404. https://doi.org/10.1016/j.istruc.2019.06.025.
[5] Giakoumelis G, Lam D. Axial capacity of circular concrete-filled tube columns. J
Constr Steel Res 2004;60:1049–68. https://doi.org/10.1016/j.jcsr.2003.10.001.
[6] Tao Z, Han LH, Zhao XL. Behaviour of concrete-filled double skin (CHS inner and
CHS outer) steel tubular stub columns and beam-columns. J Constr Steel Res
2004;60:1129–58. https://doi.org/10.1016/j.jcsr.2003.11.008.
[7] Zhao XL, Tong LW, Wang XY. CFDST stub columns subjected to large deformation
axial loading. Eng Struct 2010;32:692–703. https://doi.org/10.1016/j.engstruct.
2009.11.015.
[8] Han LH, Li YJ, Liao FY. Concrete-filled double skin steel tubular (CFDST) columns
subjected to long-term sustained loading. Thin-Walled Struct 2011;49:1534–43.
https://doi.org/10.1016/j.tws.2011.08.001.
[9] Hu HT, Su FC. Nonlinear analysis of short concrete-filled double skin tube columns
subjected to axial compressive forces. Mar Struct 2011;24:319–37. https://doi.org/
Fig. 13. Comparison of collated experimental data and FE models against 10.1016/j.marstruc.2011.05.001.
strength predictions from a) EC4 and b) ACI. [10] Hassanein MF, Kharoob OF. Compressive strength of circular concrete-filled double
skin tubular short columns. Thin-Walled Struct 2014;77:165–73. https://doi.org/
10.1016/j.tws.2013.10.004.
[11] Tziavos NI, Hemida H, Dirar S, Papaelias M, Metje N, Baniotopoulos C. Structural
6. Conclusions
health monitoring of grouted connections for offshore wind turbines by means of
acoustic emission: an experimental study. Renew Energy 2020;147:130–40. https://
A comprehensive numerical investigation on the behaviour of tub­ doi.org/10.1016/j.renene.2019.08.114.
ular GFDST stub-columns was presented in this paper. The numerical [12] Li W, Wang D, Han LH. Behaviour of grout-filled double skin steel tubes under
compression and bending: experiments. Thin-Walled Struct 2017;116:307–19.
models have been validated against experimental data from the litera­ https://doi.org/10.1016/j.tws.2017.02.029.
ture, replicating the experimentally observed the load-displacement [13] Wang FC, Han LH. Analytical behavior of carbon steel-concrete-stainless steel
performance, the failure modes and the load capacity. A detailed de­ double-skin tube (DST) used in submarine pipeline structure. Mar Struct
2019;63:99–116. https://doi.org/10.1016/j.marstruc.2018.09.001.
scription of the numerical considerations and assumptions was given [14] Patel VI, Liang QQ, Hadi MNS. Numerical analysis of circular double-skin concrete-
and a parametric study, aiming to generate additional structural per­ filled stainless steel tubular short columns under axial loading. Structures
formance data and to evaluate the influence of key parameters has been 2020;24:754–65. https://doi.org/10.1016/j.istruc.2020.02.001.
[15] Liang QQ, Fragomeni S. Nonlinear analysis of circular concrete-filled steel tubular
carried out. The following conclusions were drawn: short columns under axial loading. J Constr Steel Res 2009;65:2186–96. https://
doi.org/10.1016/j.jcsr.2009.06.015.
• It was shown that the compressive capacity of GFDST stub-columns [16] Han LH, Tao Z, Huang H, Zhao XL. Concrete-filled double skin (SHS outer and CHS
inner) steel tubular beam-columns. Thin-Walled Struct 2004;42:1329–55. https://
increases as the hollow ratio decreases. In most cases the GFDST
doi.org/10.1016/j.tws.2004.03.017.
stub-columns failed in a ductile manner once the peak load was [17] Uenaka K, Kitoh H, Sonoda K. Concrete filled double skin circular stub columns
reached. under compression. Thin-Walled Struct 2010;48:19–24. https://doi.org/10.1016/j.

• An investigation on the distribution of stresses laterally across the tws.2009.08.001.

[18] Wei S, Mau ST, Vipulanandan C, Mantrala SK. Performance of new sandwich tube
cross section of the examined models, showed that higher stresses under axial loading: Experiment. J Struct Eng 1995;121:1806–14. https://doi.org/
occur close to the external steel tube for GFDSTs at ultimate capa­ 10.1061/(ASCE)0733-9445(1995)121:12(1806).
city. This suggests that the confinement effect offered by the internal [19] Essopjee Y, Dundu M. Performance of concrete-filled double-skin circular tubes in
compression. Compos Struct 2015;133:1276–83. https://doi.org/10.1016/j.
steel tube may be less pronounced for double skin sections. compstruct.2015.08.033.
• The modified design method of EC4 showed good strength predic­ [20] Ekmekyapar T, Alwan OH, Hasan HG, Shehab BA, AL-Eliwi BJM. Comparison of
classical, double skin and double section CFST stub columns: experiments and de­
tions for both groups and is suggested that it may be employed for
sign formulations. J Constr Steel Res 2019;155:192–204. https://doi.org/10.1016/
the design of GFDST stub-columns, however further studies are re­ j.jcsr.2018.12.025.
quired to define an appropriate slenderness limit. On the contrary, [21] Ekmekyapar T, Ghanim HH. The influence of the inner steel tube on the com­
ACI yielded the higher levels of conservatism, especially for hollow pression behaviour of the concrete filled double skin steel tube (CFDST) columns.
Mar Struct 2019;66:197–212. https://doi.org/10.1016/j.marstruc.2019.04.006.
ratios between 0.4 and 0.6.
•
[22] Zhao XL, Grzebieta R. Strength and ductility of concrete filled double skin (SHS
Han et al. and the modified Yu et al. models produced good strength inner and SHS outer) tubes. Thin-Walled Struct 2002;40:199–213. https://doi.org/
predictions with lower conservatism. Overall, Yu et al. results were 10.1016/S0263-8231(01)00060-X.
[23] Tao Z, Han LH. Behaviour of concrete-filled double skin rectangular steel tubular
superior to other methods with the smallest coefficient of variation
beam-columns. J Constr Steel Res 2006;62:631–46. https://doi.org/10.1016/j.jcsr.
for all groups. It should be noted that both models were specifically 2005.11.008.
developed for double skin filled stub-columns. [24] Han LH, Huang H, Tao Z, Zhao XL. Concrete-filled double skin steel tubular
(CFDST) beam-columns subjected to cyclic bending. Eng Struct 2006;28:1698–714.
https://doi.org/10.1016/j.engstruct.2006.03.004.
[25] Aghdamy S, Thambiratnam DP, Dhanasekar M, Saiedi S. Effects of load-related
parameters on the response of concrete-filled double-skin steel tube columns

1635
N.I. Tziavos, et al. Structures 27 (2020) 1623–1636

subjected to lateral impact. J Constr Steel Res 2017;138:642–62. https://doi.org/ Standardization (CEN), Brussels, 2004.
10.1016/j.jcsr.2017.08.015. [37] ACI 318, Building Code Requirements for Structural Concrete and Commentary,
[26] Huang H, Han LH, Zhao XL. Investigation on concrete filled double skin steel tubes Farmington Hills, Michigan, USA, 2014.
(CFDSTs) under pure torsion. J Constr Steel Res 2013;90:221–34. https://doi.org/ [38] Yu M, Zha X, Ye J, Li Y. A unified formulation for circle and polygon concrete-filled
10.1016/j.jcsr.2013.07.035. steel tube columns under axial compression. Eng Struct 2013;49:1–10. https://doi.
[27] Wang F, Young B, Gardner L. Compressive testing and numerical modelling of org/10.1016/j.engstruct.2012.10.018.
concrete-filled double skin CHS with austenitic stainless steel outer tubes. Thin- [39] ABAQUS, ABAQUS/standard User's Manual. Version 2019, Dassault Systemes
Walled Struct 2019;141:345–59. https://doi.org/10.1016/j.tws.2019.04.003. Simulia Corp., USA, 2019.
[28] Wang F, Young B, Gardner L. CFDST sections with square stainless steel outer tubes [40] Wang J, Afshan S, Gkantou M, Theofanous M, Baniotopoulos C, Gardner L. Flexural
under axial compression: experimental investigation, numerical modelling and behaviour of hot-finished high strength steel square and rectangular hollow sec­
design. Eng Struct 2020;207:110189https://doi.org/10.1016/j.engstruct.2020. tions. J Constr Steel Res 2016;121:97–109. https://doi.org/10.1016/j.jcsr.2016.01.
110189. 017.
[29] Wang F, Young B, Gardner L. Experimental study of square and rectangular CFDST [41] Tziavos NI, Hemida H, Metje N, Baniotopoulos C. Non-linear finite element analysis
sections with stainless steel outer tubes under axial compression. J Struct Eng of grouted connections for offshore monopile wind turbines. Ocean Eng
(United States) 2019;145.. https://doi.org/10.1061/(ASCE)ST.1943-541X. 2019;171:633–45. https://doi.org/10.1016/j.oceaneng.2018.11.005.
0002408. [42] Mander JB, Priestley MJ, Park R. Theoretical stress-strain model for confined
[30] Zhou F, Young B. Concrete-filled double-skin aluminum circular hollow section stub concrete. J Struct Eng 1988;114(8):1804–26https://doi:10.1061/(ASCE)0733-
columns. Thin-Walled Struct 2018;133:141–52. https://doi.org/10.1016/j.tws. 9445(1988)114:8(1804.
2018.09.037. [43] Richart FE, Brandtzaeg A, Brown RL. A study of the failure of concrete under
[31] Elchalakani M, Hassanein MF, Karrech A, Fawzia S, Yang B, Patel VI. Experimental combined compressive stresses. Champaign: University of Illinois at Urbana; 1973.
tests and design of rubberised concrete-filled double skin circular tubular short [44] Hu HT, Huang CS, Wu MH, Wu YM. Nonlinear analysis of axially loaded concrete-
columns. Structures 2018;15:196–210. https://doi.org/10.1016/j.istruc.2018.07. filled tube columns with confinement effect. J Struct Eng 2003;129:1322–9.
004. https://doi.org/10.1061/(ASCE)0733-9445(2003)129:10(1322).
[32] Pagoulatou M, Sheehan T, Dai XH, Lam D. Finite element analysis on the capacity of [45] Tao Z, Bin Wang Z, Yu Q. Finite element modelling of concrete-filled steel stub
circular concrete-filled double-skin steel tubular (CFDST) stub columns. Eng Struct columns under axial compression. J Constr Steel Res 2013;89:121–31. https://doi.
2014;72:102–12. https://doi.org/10.1016/j.engstruct.2014.04.039. org/10.1016/j.jcsr.2013.07.001.
[33] Hassanein MF, Elchalakani M, Karrech A, Patel VI, Yang B. Behaviour of concrete- [46] CEB-FIP CE. Model code 2010. Comite Euro-International du beton, 2010.
filled double-skin short columns under compression through finite element mod­ [47] Thai HT, Uy B, Khan M, Tao Z, Mashiri F. Numerical modelling of concrete-filled
elling: SHS outer and SHS inner tubes. Structures 2018;14:358–75. https://doi.org/ steel box columns incorporating high strength materials. J Constr Steel Res
10.1016/j.istruc.2018.04.006. 2014;102:256–65. https://doi.org/10.1016/j.jcsr.2014.07.014.
[34] Xing Ding F, Jun Wang W, Ren LuD, Mei Liu X. Study on the behavior of concrete- [48] Bardi FC, Kyriakides S. Plastic buckling of circular tubes under axial compression-
filled square double-skin steel tubular stub columns under axial loading. Structures part I: experiments. Int J Mech Sci 2006;48:830–41. https://doi.org/10.1016/j.
2020;23:665–76. https://doi.org/10.1016/j.istruc.2019.12.008. ijmecsci.2006.03.005.
[35] Duarte APC, Silva BA, Silvestre N, de Brito J, Júlio E, Castro JM. Finite element [49] Bardi FC, Kyriakides S, Yun HD. Plastic buckling of circular tubes under axial
modelling of short steel tubes filled with rubberized concrete. Compos Struct compression-part II: Analysis. Int J Mech Sci 2006;48:842–54. https://doi.org/10.
2016;150:28–40. https://doi.org/10.1016/J.COMPSTRUCT.2016.04.048. 1016/j.ijmecsci.2006.03.002.
[36] EN 1994-1-1, Eurocode 4, Design of Composite Steel and Concrete Structures, Part [50] Chan TM, Gardner L. Compressive resistance of hot-rolled elliptical hollow sections.
1.1: General Rules and Rules for Buildings, European Committee for Eng Struct 2008;30:522–32. https://doi.org/10.1016/j.engstruct.2007.04.019.

1636