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: kathleen.lauwens@kuleuven.be, barbara.rossi@kuleuven.be

** KU Leuven, Department of Materials Engineering, Belgium

e-mail: dimitri.debruyne@kuleuven.be

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.

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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.

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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.

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(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)

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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.

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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.

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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.

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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.

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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.

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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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