Two different schemes called “ties and longitudinal stiffeners” were proposed for improving the performance of stainless steel square thin walled tubes. An analytical study using finite element models loaded axially has been conducted. Both geometric and material nonlinearities were considered. Those models were verified against the results obtained from previous researches. The analytical study compared between unstiffened, ties stiffened and longitudinally stiffened stainless steel square thin walled tubes. The studied parameters were square thin walled tube width-to-thickness ratio (W/t) and the axial spacing of stiffening along the length. It was observed that the axial load strength can be enhanced by proposed ties stiffening schemes.

1. http://www.iaeme.com/IJCIET/index.asp 45 editor@iaeme.com
International Journal of Civil Engineering and Technology (IJCIET)
Volume 6, Issue 11, Nov 2015, pp. 45-54, Article ID: IJCIET_06_11_006
Available online at
http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=6&IType=11
ISSN Print: 0976-6308 and ISSN Online: 0976-6316
© IAEME Publication
___________________________________________________________________________
AXIAL BEHAVIOR OF STAINLESS STEEL
SQUARE THIN-WALLED TUBES
STIFFENED INTERNALLY
Mona M. Fawzy
Assistant Professor, Department of Civil Engineering
Higher Institute of Engineering, Shorouk City, Cairo, Egypt
ABSTRACT
Two different schemes called “ties and longitudinal stiffeners” were
proposed for improving the performance of stainless steel square thin walled
tubes. An analytical study using finite element models loaded axially has been
conducted. Both geometric and material nonlinearities were considered.
Those models were verified against the results obtained from previous
researches. The analytical study compared between unstiffened, ties stiffened
and longitudinally stiffened stainless steel square thin walled tubes. The
studied parameters were square thin walled tube width-to-thickness ratio
(W/t) and the axial spacing of stiffening along the length. It was observed that
the axial load strength can be enhanced by proposed ties stiffening schemes.
Key words: Stainless Steel, Square Thin Walled Tubes, Ultimate Strength,
Finite Element Analysis, Ties, Longitudinal Stiffeners
Cite this Article: Mona M. Fawzy. Axial Behavior of Stainless Steel Square
Thin-Walled Tubes Stiffened Internally. International Journal of Civil
Engineering and Technology, 6(11), 2015, pp. 45-54.
http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=6&IType=11
1. INTRODUCTION
The excellent properties of the tubular shapes have been recognized for a long time
which led to wide use of concrete filled hollow tubes. Many researches showed that
filling hollow tubes with concrete decreased the local buckling and increased ultimate
strength. Another scheme that decreased the local buckling of tubular shapes is
stiffening the tubes internally. This procedure is preferred especially for square
hollow tube because many studies have shown that the performance of square hollow
tube is not as good as its circular counterpart regarding the local buckling of the tube.
This fact has now been widely reflected in modern design codes in which the
allowable width-to-thickness ratio (W/t) for the tubes with square cross-section is
more restricted than that for circular one. Such stiffening modifications will
consequently encourage the use of square hollow tubes in construction. Two

2. Mona M. Fawzy
http://www.iaeme.com/IJCIET/index.asp 46 editor@iaeme.com
stiffening measures have been suggested for enhancing the behaviors of those tubes.
One is to weld longitudinal stainless steel ties on the internal surface of a tube, while
the other one is to use internal longitudinal stiffeners as shown in Figs. (1) and (2)
respectively.
The author did not find any researches on stiffened stainless steel square hollow
tubes (SSSHTs), meanwhile plenty of researches were conducted on unstiffened
stainless steel hollow cross-sections or stiffened concrete filled steel hollow tubes.
Gee-Yu Liu et al. [1] experimentally studied the effectiveness of using ties internally
on the behavior of square concrete filled steel hollow columns under both axial load
and bending. It was found that the axial load strength increased because the ties
contribute in the strength. Also, the spacing instead of dimensions of the ties is the
dominant factor to the behavior. Zhong Tao et al. [2] proposed another alternative for
improving the performance of square concrete filled steel hollow columns with thin-
walled tubes. In his research, longitudinal stiffeners for the steel tubes were used. The
limit of W/t for the sub-panels and dimensions requirement for the stiffeners was
discussed experimentally. The results showed that AISC [3] and EN1993-1-4 [4]
gave a member capacity about 40% and 36% lower than the results obtained in the
tests. Compression strength of unstiffened stainless steel hollow cross-sections was
discussed by M. Ashraf et al. [5]. Sophisticated numerical models have been
developed in order to use the material stress–strain behavior to obtain the local
buckling stress for the open section stub columns. Several relevant researches were
conducted discussing the behavior of composite concrete filled hollow sections
without internal stiffeners [6-7]. That led to a new design method for stainless steel
structures which uses a common technique to determine the compressive strength for
all types of cross-sections without the need for traditional section classification.
This paper discusses stiffening measures for the SSSHTs that are manufactured of
duplex stainless steel material. Duplex stainless steel combines well the advantages of
both austenitic and carbon steel materials. The duplex grades have higher strength
than austenitic in addition to superior corrosion resistance. High nickel prices led to a
demand for lean duplexes with low nickel content, such as grade EN 1.4162 [8].
Therefore a parametric study is conducted considering W/t and the axial spacing of
stiffening either by ties or by longitudinal stiffeners.
Figure 1 Square hollow tube stiffened
with ties
Figure 2 Square hollow tube stiffened
with longitudinal stiffeners
2. FINITE ELEMENT MODEL AND VERIFICATION
2.1. General
To conduct a parametric study, the full three dimensional (3D) simulation using
ANSYS [9] software was performed. The SSSHTs, end plates and stiffeners were
simulated by using four-node quadrilateral shell element SHELL181. Membrane and
bending capabilities along with six degrees of freedom at each node: three translations

3. Axial Behavior of Stainless Steel Square Thin-Walled Tubes Stiffened Internally
http://www.iaeme.com/IJCIET/index.asp 47 editor@iaeme.com
and three rotations were observed in this shell element. The model was divided into
elements with aspect ratio one as shown in Fig. (3). Non-linear static analysis was
carried out considering both geometric i.e. an initial geometrical imperfection of
(L/1000) and material nonlinearities. The results were accurately estimated by
incremental steps until failure occurs. Solution technique was the arc length method.
Figure 3 Finite element mesh of SSSHTs
2.2. Boundary conditions and load application
Axially concentric load was applied at the surface of the upper end plate. The end
plates of the SSSHTs were restrained. One end was modelled with all three translation
degrees of freedom restrained as well as the rotational degree of freedom. The other
end was modelled with two translation degrees of freedom restrained except for the
longitudinal direction of steel beam, and also restraining the rotational degree of
freedom.
2.3. Stainless steel modelling
A minimum 0.2% proof stresses (σ0.2) of 530 MPa and an ultimate tensile strength
(σu) ranging from 700–900 MPa were the strengths of cold-formed lean duplex
stainless steel Grade EN 1.4162 [8] that was used. Von Mises material with isotropic
hardening was modeled. Stress and strain nonlinearity for stainless steel was generally
represented by the Ramberg–Osgood [10] equation as given below
ɛ =
οE
σ
+ 0.002 (
οσ
σ
) n
(1)
In Eq. (1), the nonlinearity index (n) indicated of the nonlinearity of the stress
strain behavior, with lower n values indicated a greater degree of nonlinearity.
Different grades of stainless steel had different degrees of nonlinearity. Increasing n
converged the material behavior to the elasto-plastic behavior of carbon steel (elastic-
perfectly plastic behavior for n =∞), meanwhile decreasing n values caused higher
hardening behavior.
Eq. (1) gave good agreement with experimental stress strain data up to the σ0.2
only. For this purpose, Rasmussen [10] proposed the use of an expression for the
complete stress strain curve for stainless steel alloys. Eq. (2) involved the
conventional Ramberg– Osgood parameters (n, E0, σ0.2) as well as the σu and strain
(ɛu). Good agreement between stress strain curves with tests over the full range of
strains up to the ultimate tensile strain was observed. Consequently, Eq. (2) was used
in the current investigation to generate the stress strain curve of the lean duplex
stainless steel material Grade EN 1.4162, as presented in Fig. (4).

4. Mona M. Fawzy
http://www.iaeme.com/IJCIET/index.asp 48 editor@iaeme.com
ɛ =









0.20.2
2.0u
2.0
u
0.2
2.0
0.2
n
0.2
σσfor)
-σ
-σ
(
E
-σ
σσfor)
σ
σ
(0.002
E
σ
0




 m
(2)
In the equations, E0 was the initial modulus of elasticity (e.g. 200 GPa), E0.2
represented the tangent modulus of the stress strain curve at the 0.2% proof stress and
given as
E0.2 =
n/e0.0021
E0

(3)
Where, e was the non-dimensional proof stress given as e = σ0.2/E0.
Multilinear stress strain curve was used in ANSYS. Elastic behavior represented
in the first part of the multilinear curve up to the proportional limit stress with
measured Young’s modulus E0 = 200 GPa, and Poisson’s ratio was taken as 0.3. The
proportional limit was found to be σ0.01= 300 MPa.
Figure 4 Lean duplex stainless steel stress strain curve [8]
2.4. Finite element model verification
The main aim of this section is to check the accuracy of the results obtained using the
proposed finite element model. Gardner et. al., [11] prepared several experimental
tests on square, rectangular and circular hollow tubes that were made of stainless steel
material Grade EN 1.4301. The tests showed the relationship between cross section
slenderness and cross section deformation capacity. Rectangular hollow tubes axially
loaded were tested experimentally and their ultimate loads were compared with the
ANSYS models as shown in table (1). The table showed tube cross section
dimensions, the corresponding wall thickness and tube lengths all in millimeters In
addition to that E0 and σ0.2 were included in the table. The end conditions of the tubes
were pinned. The verified results demonstrate that the used finite element model is
proper to the nonlinear analysis which gives an opportunity to use it in a wide
parametric study.

5. Axial Behavior of Stainless Steel Square Thin-Walled Tubes Stiffened Internally
http://www.iaeme.com/IJCIET/index.asp 49 editor@iaeme.com
Table 1 Test versus ANSYS
Specimen
(mm)
Thickness
(mm)
Length
(mm)
E0
(GPa)
σ0.2
(MPa)
Test
(kN)
ANSYS
(kN)
Test/ANSYS
60X40 4 180 192.8 469 492 528 1.07
120X40 3 360 197.3 419 452 482 1.07
100X50 2 300 205.9 370 182 192 1.05
100X50 3 300 200.9 455 407 363 0.89
100X50 6 300 187.2 494 1217 1171 0.96
120X80 6 360 192.3 466 1459 1427 0.98
150X100 4 450 200.3 297 660 699 1.06
Mean 1.01
Standard deviation 0.07
3. PARAMETRIC STUDY
A parametric study is conducted using the proposed finite element model, where the
first parameter is the presence of a SSSHT stiffener either ties or longitudinal internal
stiffeners. Second parameter is W/t of SSSHT and finally, the third parameter is the
axial spacing of stiffening along the length. The dimensions of stiffeners are not
included in the parameters because according to previous researches the spacing
instead of dimensions of the stiffeners is the dominant factor to the behavior.
To highlight the effect of stiffener on the behavior of the SSSHTs, each case
involving presence of stiffener is compared with another without a stiffener
(unstiffened). The width of the SSSHT is constant and equals to 400 mm, while the
thickness changes and ranges from 4 mm to 20 mm. Therefore the studied W/t ranges
from 20 to 100. All sections can be classified as class 4 according to EN 1993-1-4.
The height of the SSSHTs (L) is constant and equals to 1500 mm. Three different
axial spacing of stiffening are studied. They are expressed as factor of L i.e. L/2, L/4
and L/8. Stiffeners dimensions are shown in Figs. (1) and (2). The thickness of the
stiffeners tst is taken a minimum value of 4 mm, while the width bst is 50 mm. The
lengths of both ties and longitudinal stiffeners Lst are 140 mm. The results of the
parametric study obtained using the proposed finite element model are represented in
the form of tables and curves. The axial loads achieved using the finite element model
PFEM are normalized against the ultimate loads Pu which are obtained when ultimate
stress σu is multiplied by corresponding gross unstiffened cross section area.
4. RESULTS AND DISCUSSIONS
The results of the parametric study are shown in this section. Table (2) contains the
results of the parametric study where the effect of using either ties or longitudinal
stiffeners is demonstrated. The table demonstrates different values of W/t and their
corresponding PFEM/PU values discussing three different cases: unstiffened SSSHT
columns stiffened using ties and finally, stiffened using longitudinal stiffeners.
4.1. Deformed shape
The deformed shape of unstiffened SSSHT columns is shown in Fig. (5) where failure
occurs in the column wall. When the SSSHTs are stiffened using the different
stiffening schemes, failure occurs in column wall. The deformed shape of SSSHTs
400x20 using ties every L/4 is shown in Fig. (6), where there is increase in the

6. Mona M. Fawzy
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movement of the column wall. The deformed shape of SSSHTs 400x20 using
longitudinal stiffeners at L/4 is shown in Fig. (7), the outward movement of the
column wall is decreased by up to 3 times.
Table 2 Parametric study results
SSSHT
(mm)
Thickn
ess
(mm)
W/t Unstiffen
ed
PFEM/PU
Ties
every
L/2
Ties
every
L/4
Ties
every
L/8
Long.
stiffeners
every L/2
Long.
stiffene
rs every
L/4
Long.
stiffene
rs every
L/8
400 x 400
20 20 0.129 0.129 0.137 0.138 0.129 0.130 0.131
18 22 0.141 0.142 0.148 0.149 0.142 0.143 0.144
16 25 0.156 0.163 0.164 0.164 0.156 0.157 0.158
14 29 0.177 0.185 0.185 0.187 0.174 0.175 0.178
12 33 0.206 0.214 0.215 0.215 0.201 0.203 0.203
10 40 0.244 0.252 0.257 0.258 0.236 0.235 0.244
8 50 0.273 0.310 0.311 0.313 0.264 0.265 0.268
6 67 0.326 0.374 0.375 0.376 0.318 0.319 0.319
4 100 0.280 0.322 0.370 0.376 0.260 0.260 0.260
Figure 5 Deformed shape of unstiffened SSSHTS 400x20
Figure 6 Deformed shape of 400x20 SSSHTS stiffened using ties every L/4

7. Axial Behavior of Stainless Steel Square Thin-Walled Tubes Stiffened Internally
http://www.iaeme.com/IJCIET/index.asp 51 editor@iaeme.com
Figure 7 Deformed shape of 400x20 SSSHTS stiffened using longitudinal stiffeners
at L/4
4.2. Effect of using ties as internal stiffeners
A comparison is conducted between PFEM/PU of SSSHT columns that are unstiffened
and SSSHT columns that are stiffened with ties. It is clear that ties enhance the
behavior of SSSHTs especially for higher W/t. Fig. (8) shows different SSSHTs with
W/t from 20 to 100 when they are either unstiffened or stiffened with ties every L/2,
L/4 and L/8 and their corresponding PFEM/PU. For W/t equals to 20, stiffening SSSHTs
with ties every L/8 increases PFEM/PU more than the unstiffened case by up to 7% as
shown in Fig. (8). Meanwhile, stiffening SSSHTs every L/8 where W/t equals to 100,
improves PFEM/PU more than the unstiffened case by up to 34%. Accordingly, using ties
has better effect when W/t increases. Higher W/t means smaller SSSHT wall
thickness and when ties are used, redistribution of stresses between the ties and the
column walls occurs.
4.3. Effect of using longitudinal stiffeners as internal stiffeners
Stiffening SSSHTs with longitudinal stiffeners has no effect on the ultimate load of
SSSHTs with W/t equals to 20, 22 and 25 when they are compared with the
corresponding unstiffened cases. Unfortunately, longitudinal stiffeners decrease
ultimate load of SSSHTs with W/t that ranges 29 to 100 when compared with
unstiffened case by up to 7%. The worst case is SSSHTs with W/t equals to 100
because the longitudinal stiffeners buckled when PFEM/PU reaches 0.26 despite the
stiffening position as shown in Fig. (9). It can be concluded that the orientation of
these longitudinal stiffeners did not allow redistribution of stresses between them and
the column wall especially in SSSHTs with W/ t equals to 100.
4.4. Effect of the axial spacing of ties along the length
When the number of ties increases, PFEM/PU increases as well for all SSSHTs as shown
in Fig. (8). For SSSHTs with W/t equals to 20, the presence of ties every L/2, L/4 and
L/8 improves PFEM/PU more than unstiffened SSSHTs by 1%, 6% and 7%
respectively as shown in Fig. (10). This Fig. shows the different values of PFEM/PU for
SSSHT that corresponds to W/t equals to 20. It displays PFEM/PU for all six cases
studied in this research versus W/t. The first three cases show PFEM/PU due to stiffening
the SSSHT with ties while the other three cases show PFEM/PU due to stiffening the
SSSHT with longitudinal stiffeners. The maximum increase in PFEM/PU more than

8. Mona M. Fawzy
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unstiffened SSSHTs is by 15%, 32% and 34% for W/t equal to 100 when placing ties
every L/2, L/4 and L/8 respectively as shown in Fig. (11).
4.5. Effect of the axial spacing of longitudinal stiffeners along the length
When the number of longitudinal stiffeners increases, PFEM/PU is slightly increased for
all SSSHTs as shown in Fig. (9). For SSSHTs with W/t from 20 to 67, the presence of
longitudinal stiffeners every L/2, L/4 and L/8, improves PFEM/PU more than unstiffened
SSSHTs up to 2%. Fig. (11) shows the same values of PFEM/PU for SSSHT with W/t
equals to 100 when the SSSHT is either unstiffened or stiffened with longitudinal
stiffeners every L/2, L/4 and L/8. This shows that the orientation of these longitudinal
stiffeners did not allow redistribution of stresses between them and the column wall
so increasing their number is not effective.
Figure 8 PFEM/PU of SSSHTs with different W/t from 20 to 100 due to stiffening using
ties at L/2, L/4 and L/8
Figure 9 PFEM/PU of SSSHTs with different W/t from 20 to 100 due to stiffening using
longitudinal stiffeners at L/2, L/4 and L/8
0.10
0.15
0.20
0.25
0.30
0.35
0.40
20 22 25 29 33 40 50 67 100
PFEM/PU
W/t
Unstiffened
L/2
L/4
L/8
0.10
0.15
0.20
0.25
0.30
0.35
20 22 25 29 33 40 50 67 100
PFEM/PU
W/t
Unstiffened
Longitudinal
stiffeners every L/2
Longitudinal
stiffeners every L/4
Longitudinal
stiffeners every L/8

9. Axial Behavior of Stainless Steel Square Thin-Walled Tubes Stiffened Internally
http://www.iaeme.com/IJCIET/index.asp 53 editor@iaeme.com
Figure 10 PFEM/PU of SSSHT with W/t equals to 20 due to stiffening using either ties
or longitudinal stiffeners at L/2, L/4 and L/8
Figure 11 PFEM/PU of SSSHT with W/t equals to 100 due to stiffening using either ties
or longitudinal stiffeners at L/2, L/4 and L/8
5. CONCLUSIONS
This paper discusses axial behavior of thin walled stainless steel square hollow tubes
(SSSHTs) when using two stiffening schemes i.e. ties and longitudinal stiffeners. This
paper aims to expand the application of lean duplex stainless steel because of the
relatively low prices, higher strength than austenitic and superior corrosion resistance.
According to the results of the parametric study the following observations are
obtained: (1) The axial load strength of SSSHT columns can be enhanced by only one
of the proposed stiffening schemes, which are ties by up to 34%. (2) The ratio
between column widths to thickness (W/t) is an effective parameter as the role of
internal stiffeners increases when W/t increases. (3) The orientation of the
longitudinal stiffeners did not allow redistribution of stresses between them and the
column wall which decreases the axial strength of SSSHTs especially with W/ t
equals to 100. (4) The stiffening spacing is a dominant factor to the tie’s effectiveness.
(5) For SSSHTs with W/t equals to 20, the presence of ties every L/2, L/4 and L/8
improves the axial strength more than unstiffened SSSHTs by 1%, 6% and 7%
respectively. Finally, the author recommends discussing stiffening scheme by using
Tee sections and internal ring stiffeners.
0.10
0.11
0.11
0.12
0.12
0.13
0.13
0.14
0.14
20
PFEM/PU
W/t
Ties every L/2
Ties every L/4
Ties every L/8
Unstiffened
Longitudinal stiffeners
every L/2
Longitudinal stiffeners
every L/4
Longitudinal stiffeners
every L/8
0.10
0.15
0.20
0.25
0.30
0.35
0.40
100
PFEM/PU
W/t
Ties every L/2
Ties every L/4
Ties every L/8
Unstiffened
Longitudinal stiffeners
every L/2
Longitudinal stiffeners
every L/4
Longitudinal stiffeners
every L/8

10. Mona M. Fawzy
http://www.iaeme.com/IJCIET/index.asp 54 editor@iaeme.com
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