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Eighth International Conference on
THIN-WALLED STRUCTURES ICTWS 2018
Lisbon, Portugal, July 24-27, 2018
STAINLESS STEEL I BEAMS WITH SLENDER WEBS SUBMITTED
TO TORSION
K. Lauwens*, D. Debruyne** and B. Rossi*
* KU Leuven, Department of Civil Engineering, Belgium
e-mails: [email protected], [email protected]
** KU Leuven, Department of Materials Engineering, Belgium
e-mail: [email protected]
Keywords: Stainless steel; Torsion; Instability.
Abstract. Design guidance for stainless steel, a material which is increasingly used in structural
applications, has significantly improved in recent years. Yet, so far, not much attention has been paid
to the behaviour of members submitted to torsion, in combination with bending or not. This paper
presents a numerical study of duplex stainless steel welded I beams submitted to pure torsion. Firstly, a
finite element model of a simply supported welded beam with a single concentrated torque applied at
mid span is described. This model is validated against reference experiments. Since the observed
behaviour of beams submitted to torsion is considerably different when their web is slender, different
cross-section geometries are modelled to study the behaviour of both slender and non-slender webs.
The analysis shows that, in beams with slender webs, local instability causes the beam to fail before the
uniform strain is reached. Buckling of the web affects the behaviour of the flanges, causing the beam to
fold rather than to rotate when submitted to torsion.
1 INTRODUCTION
The number of civil engineering applications in which stainless steel is used, for the whole
structure or only part of it, is more and more increasing; artistic elements, railway, road and
pedestrian bridges, building envelopes and storage tanks are some examples. The main reasons
for the adoption of this material are its favourable mechanical properties, good ductility and
excellent resistance against corrosion and fire. Even though the development of structural
design guidance has significantly improved in recent years [1], so far not much attention has
been paid to the behaviour of members submitted to torsion, in combination with bending or
not.
The authors could not find any references in literature concerning pure torsion tests on
stainless steel beams. Even experiments on carbon steel I beams submitted to pure torsion are
scarce and most of them date back to the 1950’s. In 1934, Johnston & Lyse [2-4] tested simply
supported and fixed-ended steel I beams by loading them with a torsional moment in the middle.
In the 1950’s, Kubo [5] carried out a study on built-up (bolted and riveted) I beams, where the
ends were fixed and the torque was applied in the middle. Chang, Knudsen & Johnston [6]
tested multiple fabricated (riveted, bolted and welded) I sections and one rolled section. Free
end conditions were developed and the load was applied at one of the ends. Farwell & Galambos
[7] performed experiments on rolled wide-flange beams in the inelastic range in 1969. Three
loading conditions i.e. a single concentrated torque at 0.3L, a single concentrated torque at 0.5L
and two concentrated torques at 0.3L and 0.7L were imposed, all three using simple supports.
In 2007, Gosowski [8] studied the effect of longitudinal stiffeners on the torsional behaviour of
simply supported rolled I sections loaded with a torque in the middle.
K. Lauwens et al.
2
None of the above references discusses local buckling problems, either because the
cross-sections were not slender or they were not tested (far enough) into the plastic range, or a
combination of both. Instabilities in cylindrical metal shells have been studied more
extensively; an overview is given in [9, Ch. 8] and the buckling behaviour of regular polygonal
tubes in uniform torsion was assessed in [10] and [11], however no references were found
discussing this phenomenon for I cross-section beams submitted to pure torsion.
2 FINITE ELEMENT MODEL
A shell finite element (FE) model was developed using ANSYS to simulate the behaviour
of a simply (fork) supported I beam with a single concentrated torque at mid span, see Figure
1. This section first describes the characteristics of the model based on the experiment of
Farwell and Galambos [7] (described in §2.4). Next, the influence of four geometrical
parameters on the numerical results are discussed. Finally, the FE models are compared to
elastic theory and to the experimental results of Farwell and Galambos [7].
Figure 1: Simply supported I beam with a torsional moment applied at mid span.
2.1 Description of the model
2.1.1 Mesh and mesh sensitivity
The FE model uses shell elements to represent the flanges and the web of the I beam since
the thickness is small compared to the other two dimensions and the plates are in a plane stress
state. Two types of structural shell elements, i.e. the 4-noded SHELL181 and the 8-noded
SHELL281, were successively considered. Both have six degrees of freedom (DOF) at each
node and are well suited for large rotation and large strain applications. The effect of transverse
shear deformation was included. For both the linear and quadratic elements, the default number
of integration points, being 3, through the thickness was used. This number was increased to a
minimum of 5 when plasticity is present. The linear SHELL181 element uses reduced
integration, to avoid suffering from shear lock, with hourglass control.
First, the optimal amount of substeps per radian was determined to ensure convergence of
the solution while minimising computational time. The optimal amount of substeps was found
to be 50 substeps per radian. Afterwards, for the same reason, a mesh refinement was performed
for both the linear and the quadratic elements. Element sizes (E) of half the flange thickness
(6 mm), the web thickness (8 mm) and the flange thickness (12 mm) were studied with aspect
K. Lauwens et al.
3
ratios of 0.5, 1 and 2. The torque-rotation curves for the linear and quadratic shell models can
be found in Figure 2.
Linear shell Quadratic shell
Asp
ect
rati
o 0
.5
Asp
ect
rati
o 1
Asp
ect
rati
o 2
Figure 2: Mesh refinement.
To further validate the shell models, these results were compared to a full solid model built
using Abaqus. In this model, 8-noded linear brick elements with reduced integration and
hourglass control were used with a mesh size of approximately 2 mm (which is a quarter of the
thickness of the web and a sixth of the thickness of the flanges). The same material model and
boundary conditions (but applied to surfaces instead of nodes) as in the shell models were used.
The torque-rotation curves for the solid model can also be found in Figure 2. The torque-rotation
curves for both the linear shell models as well as the quadratic shell models perfectly match the
solid model up to approximately 180 degrees. The linear shell simulations always prematurely
end. As for the quadratic shell models, they are able to reach their maximum torsional moment.
Nevertheless, it should be noted that the elements on the flange tips of the mid-section show
localized high strains, as a consequence of the knife effect that the stiffener has on the flanges.
This distortional effect is more significant for smaller elements and smaller aspect ratios.
Figure 3 shows a zoom of the torque-rotation curves for the quadratic shell elements with an
aspect ratio of 2. It can be noted that the element size has a minor influence on the torque-
rotation curves from 180 degrees onwards.
K. Lauwens et al.
4
Consequently, an element size which is the smallest value of (1) the web thickness or (2) the
flange thickness, in this case 8 mm, with an aspect ratio of 2 is selected as the most suitable
mesh considering both accuracy and computing time.
Figure 3: Quadratic shell – Aspect ratio: 2 (zoom).
2.1.2 Boundary conditions
Due to symmetry, only one half of the beam was modelled to save computing time. Rigid
regions were created for the displacement perpendicular to the mid cross-section’s plane (UZ)
and for the rotations parallel to the cross-section’s plane (ROTX & ROTY). The centroid of the
cross-section, which is the reference point of the rigid regions, is constrained for these three
DOFs as well as for the displacement in the direction of the weak axis. Furthermore, a rigid
region for the rotation about the longitudinal axis (ROTZ) with the centroid as reference point,
was used to model the mid-section. The torsional load was applied in this reference point. A
stiffener, with a thickness of the highest value of (1) 2 times the web thickness or (2) 2 times
the flange thickness, is added to strengthen the mid-section against local deformations. Due to
symmetry, this stiffener does not influence the torsional behaviour.
Flanges Web Cross-section
Symmetry BC - - UZ, ROTX, ROTY + ROTZ
End BC UY UX ROTZ
Figure 4: Boundary conditions: rigid regions.
To simulate the end boundary conditions, the cross-section is divided in 3 parts: the upper
flange, the web and the lower flange. For each of them, and for the full cross-section, a rigid
region is created in accordance with Figure 4. Each time, the reference point is the mid node of
the web or flange. The mid node of the cross-section is constrained for displacement in the
direction of the strong axis (UX) and for the rotation around the longitudinal axis (ROTZ). The
displacement in the direction of the weak axis (UY) is constrained for the mid node of both
flanges.
K. Lauwens et al.
5
(a) Torque-rotation diagram (b) Deformed shape at 180°
Figure 5: Boundary conditions: Rigid regions vs. Contact, for BC1.
In order to check the boundary conditions defined with rigid regions, the fork supports were
also modelled in the solid model using contact. Rigid bodies, having the shape of bars with a
diameter of 50 mm, are placed next to the beam. These bars interact with the beam in the form
of mechanical contact with isotropic friction. A low friction coefficient of 0.12 is defined.
Figure 5 (a) shows the toque-rotation curves for these FE models having a stiffener at the
support with a thickness of one time the flange thickness. Both graphs match up reasonably
well until the point where the beam has shortened too much because the rotation and sliding in
the supports increases considerably. At this point, around 180 degrees, the place of the stiffeners
does not correspond to the place of the fork supports anymore and the flanges start to buckle,
Figure 5 (b). That is why the curves starts to deviate from each other and the contact model
shows premature failure.
2.1.3 Imperfections
Imperfections, such as residual stresses and geometrical imperfections, are ignored. The
overlap between the flanges and the web, which occurs because of the discretization of the
section, is taken into account to approximate the fillet surface. The influence of the overlap is
discussed in §2.2.1.
2.1.4 Analysis
A static analysis including large-deflection effects was performed for all models. The dead
weight of the beam was neglected.
2.2 Effect of the geometry
This section analyses the effect of four geometrical parameters (Table 1) on the model: the
overlap between the flanges and the web (OL), the overhang length Lo (OH), the stiffeners at
the supports (BC) and the stiffeners under the load application.
Table 1: Geometrical parameters.
Overlap flanges-web Overhang length Stiffeners at the supports
OL0 Without overlap OH0 Without overhang BC0 Without stiffeners
OL1 Half overlap OH1 With overhang BC1 Stiffeners 1t
OL2 Full overlap BC2 Stiffeners 2t
with t = max(tw; tf)
K. Lauwens et al.
6
2.2.1 Overlap flanges-web
The model uses shell elements to represent the flanges and the web of the I beam by
discretizing the section as three sheets having each their thickness. The discretization can be
realized in three ways depending on the reference surface of the flanges (Figure 6).
OL0: Without overlap OL1: Half overlap OL2: Full overlap
Figure 6: Types of overlap.
First of all, the inner surfaces of the flanges can be used as reference surfaces and the whole
thickness is offset to the top for the top flange and to the bottom for the bottom flange, meaning
that the web height is included between the flanges (OL0). Using this model, there is no overlap
between the web and the flanges. Secondly, the middle surfaces can be used as reference
surfaces (OL1), in which case the web overlaps the flange until half of the flange thickness.
Lastly, the outer sides of the flanges can be used as reference surface and the whole thickness
is offset to the bottom for the top flange and to the top for the bottom flange, meaning that the
height of the web equals the height of the profile (OL2). Using this model, the web overlaps the
full flange thickness.
The influence of the overlap between the flanges and the web on the initial stiffness is very
limited. Furthermore, the maximum torsional moment is generally a bit higher with less overlap.
The overlap between the flanges and the web, adding extra stiffness to the beam, is taken into
account to approximate the fillet surface of a welded or rolled profile. Therefore OL1, where
the mid surfaces are used as reference surfaces and where the web overlaps half the thickness
of the flange, is chosen.
Figure 7: Influence the overhang length and of the stiffeners at the supports.
K. Lauwens et al.
7
2.2.2 Overhang length
If the beam ends exactly at the (frictionless) supports, warping can freely occur. However,
if the beam extends after the supports, the torsional moment diagram drops to zero and, along
with it, the amount of warping. But since the adjacent cross-sections are attached, the warping
cannot suddenly drop or jump and thus the warping deformation is restrained. This is why the
extra length of the beam beyond the supports, namely the overhang length Lo, influences the
torsional behaviour.
Figure 7 shows the influence of the overhang length for the models OL1 together with the
influence of the stiffeners. It is shown that the influence of the overhang length is negligible for
small rotations but becomes significant when high rotations are reached. The effect of the
overhang length is bigger when there are no stiffeners.
2.2.3 Stiffener at the supports
It stands to reason that a stiffener will prevent warping. The amount of resistance to warping
depends on its stiffness, which usually depends on the thickness. In [7], one beam, with a
torsional load at one third of the length, was tested with and without stiffeners and it was
concluded that the change in boundary conditions was not significant. However, when
comparing the FE results for a beam without stiffeners (BC0) and with stiffeners with a
thickness of, respectively, one (BC1) or two (BC2) times the highest value of (a) the web
thickness or (b) the flange thickness, the influence was found to be rather substantial (Figure
7), especially when large rotations are reached.
2.2.4 Stiffener under the load application
In the present loading case, the load is applied in the middle of the beam. Because of
symmetry, the beam is restrained from warping at this point. Apart from preventing possible
local effects, a stiffener under the load application will not influence the behaviour of the beam.
This stiffener will always be modelled with a thickness of two times the highest value of (a) the
web thickness or (b) the flange thickness to prevent local effects.
2.3 Comparison against elastic theory
This paragraph compares the model described in §2.1 to elastic theory. The elastic equation
for the angle of twist at mid span for a simply supported beam is given by Equation (1). This
equation does not take the overhang length or stiffeners into account, however the overlap
between the flanges and the web is taken into account for the calculation of the St. Venant
torsion constant It and the warping constant Iw, which results in an increase in stiffness of 0.5%.
a
L
a
L
a
L
a
L
a
L
GI
Ta
t 2sinh
2coshtanh
2sinh
4 (1)
The torsional bending constant a is given by Equation (2).
tw GIEIa (2)
The corresponding FE model - which contains no stiffeners at the supports (BC0), no
overhang length (OL0) and an overlap between the flanges and the web (OL1) - is compared to
elastic theory in Figure 8.
K. Lauwens et al.
8
Figure 8: Comparison to elastic theory.
2.4 Comparison against the Farwell and Galambos experiment [7]
This paragraph compares the model described in §2.1 to a simply supported beam with a
single concentrated torque at mid span, tested by Farwell and Galambos [7], Figure 9. The same
type of mesh (SHELL281), boundary conditions and analysis as described earlier have been
used.
(a) Picture (b) Sketch
Figure 9: Testing setup of Farwell and Galambos [1].
The dimensions of the tested beam, together with the corresponding number of elements are
given in Table 2. The overlap is taken into account to approximate the fillet surface. As in the
test, an overhang length Lo of 51 mm beyond each support was modelled. The specimen of
Farwell and Galambos [7] had a stiffener with the same thickness as the circular loading frame
(25.4 mm) at the mid-section, and stiffeners at the supports. The thickness of the latter stiffeners
was unfortunately not mentioned in the paper, thus stiffeners with a thickness of, respectively,
the flange thickness and two times the flange thickness were successively modelled as well as
no stiffener at all.
Since the measured stress-strain curve was also not available in the paper, the multilinear
material model with constitutive material parameters selected in [12] for the ASTM-36 grade
was used. Specifically, the curve was scaled to the measured yield stress and converted to true
stress-strain.
K. Lauwens et al.
9
Table 2: Dimensions of the tested specimen and number of elements in the FE model.
Dimension Symbol Value # Elements
Height h 151 mm 18
Width b 151 mm 20
Web thickness tw 8 mm -
Flange thickness tf 12 mm -
Span length L 1931 mm 120
Length L + 2Lo 2032 mm 120+2.3
The comparison of the SHELL 281 FE models with overlap (OL1), with overhang length
(OH1) and with different types of stiffeners at the supports (BC0, BC1 and BC2) as well as the
solid model where the fork supports are modelled using contact regions, are depicted in Figure
10 together with the test results of Farwell and Galambos [1].
Figure 10: Comparison to the test of Farwell and Galambos [1].
The effect of the boundary conditions is barely noticeable in the elastic region, but their
influence becomes significant at the onset of plasticity. It can be presumed from the graph that
the stiffeners most likely had a thickness equal to two times the flange thickness. Furthermore,
it should be noted that the contact boundary conditions are more suitable to represent this testing
setup: the shortening of the beam, within their supports which stay in place, does causes the
beam to prematurely fail.
3 PARAMATRIC STUDY
In this chapter, several duplex stainless steel (grade EN1.4162) beams are studied. The
stainless steel nonlinear material properties are taken into account, as described in §3.1, by the
modified Ramberg-Osgood formulation proposed by Arrayago et al. [13]. The behaviour of a
number of slender cross-sections is compared to that of a non-slender (stocky) HEM 300 profile
and their torque-rotation curves are analysed.
K. Lauwens et al.
10
3.1 Stainless steel material model
The stainless steel nonlinear material properties were accounted for by employing a
piece-wise multi-linear stress-strain curve, using the Von Mises criterion with isotropic
hardening, defined by the modified Ramberg-Osgood formulation proposed by Arrayago et al.
[13] (Equation 3) using nominal properties. This material model is a revised version of the one
proposed by Rasmussen [14], which is currently included in Annex C of EN 1993-1-4 [15].
uy
m
yu
y
u
y
yy
y
n
y
ffff
f
E
f
E
f
ffE
for 002.0
for 002.0
(3)
Where E is the Young's modulus, fy is the yield stress and fu is the ultimate stress. Nominal
values according to EN 1993-1-4 (Table 3) are used for these parameters. Ey is the tangent
modulus at the yield stress given by Equation 4, n is the strain hardening parameter (which is 8
for duplex and lean duplex), m is the second strain hardening parameter given by Equation 5
and εu the ultimate strain given by Equation 6.
Table 3: Nominal values for E, fy and fu according to EN 1993-1-4 [15].
Grade Young's modulus E Yield stress fy Ultimate stress fu
1.4162 | Duplex 200 000 N/mm² 450 N/mm² 650 N/mm²
y
y
f
En
EE
002.01
(4)
u
y
f
fm 8.21 (5)
grades ferriticfor 1
gradesduplex lean andduplex ,austeniticfor 1
u
y
u
y
u
f
f
f
f
(6)
3.2 Geometries
In this parametric study, the following geometries were studied: 10 slender cross-sections,
5 IPE and 5 HEA sections, were modelled. For each of them, 10 lengths, i.e. 500 up to
5000 mm, every 500 mm, have been selected. Additionally, 1 non-slender cross-section, a
HEM 300 beam with a length of 2000 mm, was modelled to compare the behaviour of slender
and non-slender cross-sections.
To approximate the theory (§2.3) rather than experiments, stiffeners have been placed under
the load, i.e. in the middle, but not at the supports and no overhang length was modelled. Whilst
the contact boundary conditions are more suitable to model the testing setup, rigid regions were
chosen because they better represent the theoretical case.
K. Lauwens et al.
11
Slender Non-slender / Stocky
e.g. IPE 300
300x150x07x11
L = 2000 mm
e.g. HEM 300
340x310x21x39
L = 2000 mm
Torq
ue-
rota
tion
curv
e
“Ela
stic
” beh
avio
ur
Fir
st y
ield
Spre
ad o
f pla
stic
ity i
n
the
flan
ges
Sec
ond
slo
pe
is
reac
hed
K. Lauwens et al.
12
Slender Non-slender / Stocky
e.g. IPE 300
300x150x07x11
L = 2000 mm
e.g. HEM 300
340x310x21x39
L = 2000 mm
Onse
t of
inst
abil
ity
NA
The
ult
imat
e st
ress
fu
is r
each
ed
…
…
0 77 144 217 289 361 433 506 578 650 N/mm²
Figure 11: Behaviour of a slender vs a non-slender beam: Von Mises stresses.
K. Lauwens et al.
13
3.3 Structural behaviour
Two beams, a IPE 300 and a HEM 300, with a length of 2000 mm are used to illustrate the
structural behaviour of I beams submitted to pure torsion. The IPE 300 beam illustrates the
typical response of a slender cross-section, while the HEM 300 beam illustrates the typical
response of a stocky cross-section. Figure 11 depicts the torque-rotation curves as well as the
deformed shapes, on which Von Mises stresses are displayed, for both types of behaviour at
different loading stages.
Both the slender and the stocky cross-section beams start with an “elastic” behaviour i.e. the
stage before the yield stress is reached. Since stainless steel is modelled, the elastic material
behaviour is not linear. Then yielding occurs at the flange tips of the mid-section of the beam,
at a rather low torque. The torque-rotation diagram starts to deviate from linearity. The onset
of plasticity leads to a reduction in stiffness until a second slope is reached. Afterwards, as a
result of the helical deformation, longitudinal tension takes place in the outer edges of the beam.
This phenomenon is referred to as the Wagner or helix effect and leads to an increase in the
stiffness and a subsequent ultimate torsional moment up to twice the predicted value.
In the case of stocky cross-section beams, such as the HEM 300 beam, the next stage is the
achievement of the ultimate stress and, afterwards, failure strain upon which the beam fails.
These cross-sections are able to reach their ultimate strength. In the case of slender cross-section
beams, such as the IPE 300 beam, the slope diminishes before the ultimate stress and/or the
failure strain is reached. Afterwards, the slope stays approximately horizontal for a while until
the torsional moment starts to diminish with increasing deformations. Hence, these cross-
sections reach their maximum moment prematurely due to instability. The web starts to buckle
and the flanges follow, causing the beam to fold rather than to rotate. This instability
phenomenon is clearly visible in Figure 11.
3.4 Results and analysis
Figure 12 shows the torque-rotation curves for all the modelled beams. All the IPE beams
as well as the HEA 300, HEA 400 and HEA 500 beams, fail before their ultimate moment is
reached due to instability. The HEA 100 and HEA 200 beams reach their ultimate moment.
Table 4: Geometrical slenderness of the web hw/tw and web slenderness λp.
100 200 300 400 500
hw/tw IPE 21.6 32.7 39.2 43.4 45.9
HEA 16.0 26.2 30.8 32.0 37.0
p IPE 0.54 0.82 0.98 1.08 1.14
HEA 0.40 0.65 0.77 0.80 0.92
The geometrical slenderness of the web hw/tw influences the response of the slender
cross-section beams. One might think that the limiting slenderness for shear buckling 56.2ε/η,
which comes down to 33.03 for the studied stainless steel grade, would be suitable in the case
of torsion too, but that is shown not to be appropriate (Table 4). The current limit provided by
EN 1993-1-4 [15] and [1] for shear buckling cannot be used for the studied cross-sections to
determine if instabilities influence the ultimate resistance. Presently, for the 10 studied cross-
sections, a limit of about 46.4ε/η, or 27.3 for this grade, seems to be a lot more suitable.
According to the Continuous Strength Method [1], a method initially developed to better tackle
the nonlinear response of the stress strain curve of stainless steel, a cross-section slenderness
limit of 0.68 is used to distinguish the slender cross-section from the stocky one. The same limit
for the web slenderness was presently found. The IPE 100 beam is an exception to this limit,
since its web is classified as stocky, however the section does fail due to instability.
K. Lauwens et al.
14
IPE HEA 100
200
300
400
500
Figure 12: Torque-rotation curves.
K. Lauwens et al.
15
Furthermore, the presence of non-slender flanges counteracts the effect of buckling. It is
clear from Figure 12 and Figure 13 that not only the cross-sectional dimensions, but also the
overall length influences the torsional behaviour: instabilities occur at lower torques for longer
beams, leading to a smaller ultimate resistance. None of the studied beams reach their maximum
(whether ultimate or due to instability) resisting moment, at rotations lower than 10 degrees. At
such high rotations, the Serviceability Limit States (SLS) governs.
IPE HEA
Figure 13: Ultimate torsional moment vs Length.
4 CONCLUSION
This paper presents a numerical study of duplex stainless steel welded I beams submitted to
pure torsion. First, a finite element model of a simply supported welded beam with a single
concentrated torque applied at mid span is described. The effects of four geometrical aspects
on the model are analysed. It is shown that the impact of the overhang length is negligible for
small rotations but becomes significant when high rotations are reached and is bigger when
there are no stiffeners. Further, the influence of a stiffener at the supports is found to be rather
substantial, especially when large rotations are reached, while a stiffener under the load
application does not affect the behaviour of the beam.
Next, different cross-section geometries were modelled to study the behaviour of
cross-sections with both slender and non-slender webs. Both the slender and the stocky
cross-section beams start with an “elastic” behaviour followed by yielding at the flange tips of
the mid-section of the beam, at a rather low torque. The onset of plasticity leads to a reduction
in stiffness until a second slope is reached. Stocky cross-sections are able to reach their ultimate
strength in the next stage. But in the case of slender cross-section beams, the slope diminishes
before the ultimate stress and/or the failure strain is reached, and these cross-sections reach their
maximum moment capacity prematurely due to instability.
The geometrical slenderness of the web hw/tw influences the response of the slender cross-
section beams, but it is presently shown that the current limit provided by EN 1993-1-4 [15]
and [1] for shear buckling cannot be used to determine if instabilities will take place. Finally, it
has also been demonstrated that the overall length relatively strongly influences the torsional
behaviour. Furthermore, the presence of non-slender flanges counteracts the effect of buckling,
which is herein mostly the case. The behaviour might be completely different for cross-sections
with slender flanges.
K. Lauwens et al.
16
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[14] Rasmussen K.J. R., “Full-range stress–strain curves for stainless steel alloys”, Journal of
Constructional Steel Research, 59(1), 47-61, 2003.
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