numerical investigation of the plastic behaviour of short welded aluminium double-t beams.pdf

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Engineering Structures 30 (2008) 20222031

www.elsevier.com/locate/engstruct

Numerical investigation of the plastic behaviour of short welded aluminiumdouble-T beams

E.K. Koltsakisa,, F.G. Preftitsi b,c

a Civil Engineering Department, Aristotle University of Thessaloniki, Greeceb Technological Educational Institution of Serres, Greece

c Technological Educational Institution of West Macedonia, Greece

Received 17 August 2006; received in revised form 2 December 2007; accepted 13 December 2007

Available online 20 February 2008

Abstract

The present work is a numerical approach to the mechanical behaviour of short aluminium beams, both extruded and welded at the webflange

junction. The studied beams were taken to be short so as to ensure that their design is dominated by shear. In order to investigate the effects of the

weld and the consequent existence of a heat-affected zone (HAZ), both welded and extruded beams of identical geometric characteristics were

studied. Three alloys, 6063-T6, 6005A-T6 and 7020-T6, were chosen because of their varying strength characteristics, as well as the different

severity of mechanical degradation that each one undergoes in the HAZ. The numerical investigation is performed in the framework of small

displacements, and the possibility of lateral buckling is excluded. All the studied cases qualify as Class-I cross sections for normal actions. The

RambergOsgood stressstrain relation is used to describe the hardening of the material. The results obtained by means of finite element models

are compared to those of classical beam theory and to the resistance checks of Eurocode 9.c

2007 Elsevier Ltd. All rights reserved.

Keywords: Aluminium structures; Heat-affected zone; Short beams

1. Introduction

Unlike steel, where the effect of welding-induced heat leaves

the properties of the surrounding material unaffected (at least

as far as common practice civil engineering applications are

concerned), the case of aluminium calls for a totally different

approach. A severe degradation of the mechanical resistance in

the vicinity of the fusion line, known as the heat-affected zone

(HAZ), appears. This adverse effect is taken quite seriously

in the draft of Eurocode 9[1], which is structured around theconcept of discriminating the cross sections into welded and

extruded types. Reduced values of proof and ultimate stress

apply for the material in the vicinity of the welds. The fact that

the presence of an HAZ strongly affects the failure mechanism

Corresponding address: Metal Structures Lab., Civil EngineeringDepartment, Aristotle University, Thessaloniki, GR-54124, Greece. Tel.: +302310 929476, +30 6946798995; fax: +30 2310 995642.

E-mail addresses: [email protected](E.K. Koltsakis),[email protected](F.G. Preftitsi).

of beams is well established in the literature; to mention but a

few, Lai and Nethercot as well as Mazzolani published results

on the effect of HAZ for beams [2,3]; Evans et al. in [4,5]

reported HAZ failures in girder webs; many other studies[6,7]

reported experimental results concerning HAZ-related failures

in connections.

The present work attempts to investigate the behaviour of

short double-T aluminium beams subjected to loading levels

that make them undergo plastic deformation. This is done bymeans of numerical simulation based on finite element (FE)

models. The present study does not include geometric non-

linearities.

The computations are performed for welded and extruded

beams of exactly the same geometry so as to assess the effect

of the presence of the HAZ on the resistance of the member.

Finally the results of the FE analysis are compared to the

behaviour predicted by simple beam theory (with material non-

linearity taken into account), as well as to the resistance checks

of Eurocode 9.

0141-0296/$ - see front matter c

2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.engstruct.2007.12.012
http://www.elsevier.com/locate/engstructmailto:[email protected]:[email protected]://dx.doi.org/10.1016/j.engstruct.2007.12.012http://dx.doi.org/10.1016/j.engstruct.2007.12.012mailto:[email protected]:[email protected]://www.elsevier.com/locate/engstruct


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E.K. Koltsakis, F.G. Preftitsi / Engineering Structures 30 (2008) 20222031 2023

Table 1

Material resistance characteristics

Alloy Thickness

(mm)

f0.2(N/mm2)

fu(N/mm2)

fHAZ0.2

(N/mm2)

fHAZu(N/mm2)

n/nHAZ

(N/mm2)

=fHAZ

0.2 /f0.2

fp/f0.2 fHAZp /f

HAZ0.2

6063-T6 t 25 160 195 65 110 24/47 0.41 0.831 0.908

6005A-T6

t 5 225 270 115 165 25/38 0.51 0.800 0.8705< t 10 215 260 24/37 0.53 0.800 0.87010< t 25 200 250 20/33 0.58 0.800 0.870

7020-T6 t 15 290 350 205 280 23/35 0.71 0.797 0.844

15< t< 40 275 350 19/27 0.75 0.797 0.844

Fig. 1. RambergOsgood stress strain relations for several aluminium alloys.

2. Modelling of the material in the current study

The present study addresses the behaviour of structural

elements; consequently, the authors decided to keep their

choice of aluminium alloys/tempers combinations among those

considered in Eurocode 9, where values for the conventional

yield stress f0.2, the ultimate stress fu, as well as their

counterparts holding inside the heat-affected zone fHAZ0.2 and

fHAZu are provided. Uniaxial stressstrain curves obtained by

means of the RambergOsgood (RO) relation

p= 0.002

f0.2

n, (1)

for the materials covered in Eurocode 9, are depicted in Fig. 1.

Here, p is the plastic strain, f0.2 the conventional yield limit

equal to the stress corresponding to 0.2% plastic strain, is

the stress and n the hardening parameter of the alloy. Three

materials (alloy/temper combinations) were selected for thepurposes of the current study as representative of the low (6063-

T6), medium (6005A-T6) and high (7020-T6) strength variety.

Details of their resistance characteristics are listed in Table 1.

The values of n appearing in (1) are those provided by the

Eurocode 9 for the thermally intact material. The values ofn

holding inside the HAZ were obtained by means of the scheme

proposed in [3].

The modelling of the plastic behaviour of aluminium has

drawn much attention in recent years. Anisotropic yield criteria

have been proposed by Hill [8] and Barlat and Lian [9], as

well as Karafillis and Boyce[10]. Also, strain-hardening rules

other than the well known RO relation, such as, for example,

the exponential hardening rule

= Y+ Q1(1 eC1p) + Q2(1 eC2p ), (2)are used in the literature (see [11,12] and the references

therein), whenever experimental data to determine the

parametersQ 1, Q 2,C1,C2and Yare available.

As data concerning the parameters of anisotropic yieldcriteria are rather difficult to find in the literature, the authors

decided to use the von Mises yield criterion along with isotropic

hardening and the RO hardening rule. The limitations of this

approach are known (see e.g. [12]) but, given the fact that the

loading path in the current study is proportional, the task faced

by the FE model is not as demanding as the sheet metal forming

simulations that seem to have spurred much of the anisotropy

related work. Moreover, simulations based on the RO hardening

model were compared against experimental data in [23] and

were found to be in a very good accord for cases very similar

to those of the present work, i.e. welded aluminium beams and

connections in bending and shear.As is obvious, whenever a continuous stressstrain relation

is used in conjunction with a yield function, there arises the

problem of determining a proportionality limit fp for the

material; the matter is discussed in some detail in Annex E of

Eurocode 9, where guidelines on the proportionality limit of the

material are given.

A consideration having to do with fp used in an FE

computation is that the choice of too small a value for the

proportionality limit results in load increments that produce an

overall structural behaviour only very slightly deviating from

linearity. Therefore, the authors decided to use a conventional

proportionality limit that was determined as the strain, where

the second derivative of the RO law exceeds 1/10 of its range.

In this way the behaviour of the material is kept elastic,

wherever the RO curve is practically linear. The hence obtained

values of fp and fHAZp are given in Table 1 as fractions of

f0.2. Subsequent points of the law are obtained in an

analogous manner, thus generating a discretized RO law (a

series ofi i pairs), where the density of the discretization

is kept proportional to the curvature. This technique was

found to accelerate the convergence of the computation. On

the downside, introducing a conventional fp naturally means

trading the true values of the initial elastic modulus of the

material with secant values ES. However, the deviation of the

initial secant moduli remains within a 0.05% margin from the


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2024 E.K. Koltsakis, F.G. Preftitsi / Engineering Structures 30 (2008) 20222031

Fig. 2. (a) RambergOsgood plastic evolution curves. (b) DiscretizedRO curve and normalized derivatives.

true value of Eel= 70000 N/mm2. The RO plastic evolutioncurves used in the analysis are depicted in Fig. 2a for both

the thermally intact and heat-affected materials.Fig. 2b depictsa part of the RO curve for the 7020-T6 material (marked

1) focusing at the elasticplastic transition zone, along with

appropriately scaled plots of its first and second derivatives

(respectively marked 2 and 3) to show the resulting density of

points.

3. On the selection of cross sections

Given the lack of a widely accepted standardization for

series of aluminium profiles, especially in Europe (concerning

the US see [13,14]), the authors had to devise some rational

way to generate profiles, whereupon to base the subsequent

numerical investigation.First, the cross section depth and flange width data of the

SteelHEA series were observed. Next, two requirements were

considered, whereupon the generation of an aluminium series

of profiles was based:

a. the cross sections had to qualify for Class-I in compression,

andb. theIy= Iflgy /Iweby ratio had to stay above a minimum value

ashp increases.

Here hp is the depth of the profile (see Fig. 3a) and Iy is

the major-axis second moment of inertia of the respective cross

section part. The first requirement is a matter of versatility for

the generated cross section series. The need for the second

requirement arises when one attempts to generate an aluminium

series that complies with the first requirement: as the second

moment of inertia of the web Iweby increases by h3p and the

flange width bf stays below 300 mm in the HEA series,

requiring the flange to be Class-I ((bf tw 2wf)/2tf hp(j)).As we seek values oftw, tffor the (j+ 1)-thAlHEAprofile,we first determine the minimum value oftw,(j+1) that will givea Class-I web. We then determine a flange thickness so that

a. Iflg

y,(j+1) Iflg

y,(j)and

b. (j+1)I y

(1)I y/,

where the parameter was taken equal to 5, a value that was

chosen by studyingI y as a function ofhp for the SteelHEA


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Table 2

Geometric characteristics fulfilling the Class-I requirement (mm)

Material Designation hp b f tw tf r

6063-T6 AlHEA180 171 180 7.9 15.3 6.

AlHEA220 210 220 9.8 19.1 6.

6005A-T6

AlHEA180 171 180 8.8 17.9 6.

AlHEA220 210 220 10.7 20.9 6.

7020-T6 AlHEA180 171 180 9.9 19.9 6.

AlHEA220 210 220 12.3 24.8 6.

profiles. The complete results of this procedure are presented

in [15].Table 2lists thetw, tfvalues obtained forAlHEA180

andAlHEA220for the three chosen materials.As can be seen in Table 2, the higher the strength of an

alloy, the thicker the web and flange turn out to be, due to the

Class-I requirement. In the present analysis, use was made of

the profile data of the 7020-T6 material, as these envelope theClass-I requirement for the other two, weaker materials.

4. Issues concerning welded aluminium profiles

Welding heat-treated aluminium alloys results in degrada-

tion of the additional strength obtained via the heat treatment

process. This adverse effect is caused by the heat released dur-ing the welding process and affects a zone around the weld,

known as the heat-affected zone (HAZ). The proof stress f0.2and the ultimate stress fuare reduced by a factorranging from

0.41 to 0.75, whereas the modulus of elasticity Eand Poissons

ratio remain unaffected.Regarding the extents of the HAZ, several approaches exist

such as, for example, the one inch rule, the rules of Eurocode

9, and the RobertsonDwight (RD) method. In the presentwork, the extent of the HAZ was computed according to the

RD method [16], which is based on the Rosenthal heat-flowequations. This approach, although somewhat complicated,

seemed more accurate as compared to the one inch or the

Eurocode 9 rules, where the extent of the HAZ is determined

rather crudely. Following this method, a heat-affected cross

section area Az that primarily depends on the cross sectionarea of the weld deposit Aw , is computed. The value of

Az is determined by means of a set of rules that take into

account factors as the base material (alloy composition), the

thermal control during the welding, the applied welding method

(MIG or TIG), the weld size, etc. The hence computed Azis subsequently distributed among the welded elements, in a

manner that the HAZ branches are of the same length SRD for

all the joined elements, as seen inFig. 3b.In the present study, MIG double torch welding and normal

thermal control were assumed. The resulting values ofSRD are

given inTable 3along with the corresponding values following

the rules of Eurocode 9. Note that the extent of the HAZ

according to the RD method is distinctively smaller than the

one proposed in Eurocode 9.We now come to the matter of the residual stresses. First we

note that residual stresses produced by the extrusion process are

generally very low (lower than 20 N/mm2), irrespective of the

heat treatment [3,17]. It is also known that the detrimental effect

Table 3

HAZ extents for a 6 mm double fillet weld (mm)

Material hp SEC9flg

SEC9web

SRD

6063T6 171 35. 30. 10.2

210 35. 35. 10.2

6005AT6 171 35 30. 10.2

210 35. 35. 10.2

7020T6 171 35. 30. 12.0

210 35. 35. 12.0

of residual stresses on the resistance of welded aluminium bars

in compression is smaller than in steel [18], and the zone of

the locked-in longitudinal tension at an aluminium weld is

generally narrower than the HAZ[16].

In addition, as Class-I sections are studied, no second-order

effects are included in our models. Buckling having been ruled

out, the other major effect of residual stresses concerns the

deflection of the beam, their presence having an amplifying

effect [19]. As the present paper attempts to point out a type

of premature failure related to the development of excessive

deformation, neglecting residual stresses constitutes the most

unfavourable conditions under which this unwanted mechanism

might arise. Due to this and the fact that no methodology for

the estimation of residual stresses is given in Eurocode 9, the

authors chose not to include them in the numerical simulations.

Last, concerning the size of the web-flange welds, the

requirements of the U.S. Aluminium Specification [20]

concerning minimum and maximum fillet weld sizes were

followed. The prescribed minimum weld sizes are those used in

the numerical models. A weld radiusaw equal to 6 mm covers

all the studied cases. The welds chosen are capable of resistingthe shear strength of the weakest of the welded parts, i.e. the

web, as 2fwaw > twf0.2, where fw is the strength of the filler

metal 5356.

5. The numerical model

The Castem [21] finite element code was used for the

numerical modelling. The mesh for the models that included

a heat-affected zone is made up of 1190 8-node, reduced

integration, thick-shell elements resulting in 3709 nodes. In

Fig. 4a the mesh used in the FE analysis is depicted. The

structure under study is essentially a cantilever beam supported

at x = L/2 and loaded at the opposite end. The lengthof all the models was taken equal to 2.5hp. Considering the

boundary conditions at the fixed end, the following restraints

were considered:

(1) uz restrained along the web (segment BE),

(2) ux restrained along the flanges (segments AC, DF),

(3) uy restrained along the flanges (AC, DF): this restraint

expresses the presence of an end plate,

(4) ux restrained along the height of the web (segment BE).

Applying all four restraints makes up the boundary

conditions type A; using only 1, 2 and 3 makes up the boundary

conditions type B. This differentiation in the type of the


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Fig. 4. (a)AlHEA220:FE mesh and loading. (b) Shell thickness field [mm].

boundary conditions has a noticeable effect on the behaviour

of the structure, especially in the plastic regime. A linear

load of density fz is applied along a length sL = 0.8hp ofthe webplate junction of the model, in order to avoid stress

localizations. The generation of the mesh was based on a set ofparameters that ensure that similar mesh densities are obtained

regardless of the profile height. One can note the refinement of

the mesh along the z-axis near the webflange junction. Two

issues relate to this refinement:

(1) first, the authors felt it would be good for the accuracy of the

computation to include the variation of the shell thickness

in the vicinity of the welds due to the weld material, and

(2) as will become evident in the section describing the results,

this area is one in which severe strain accumulation appears.

The shell thickness fields are depicted inFig. 4b, where the

increase of the thickness of the web and flange plates around thewebflange junction due to the weld deposit is clearly shown.

ObservingFig. 4b more closely, one can see that the thickness

variation takes place over two elements (web) and can therefore

be considered a meaningful alternative to the option of a 3D-

mesh. However, it must be mentioned that this procedure had

to be programmed on a Gauss-point level and is somewhat

complicated and time-consuming.

The simplest way to incorporate the HAZ into the FE model

would be to discretize two separate zones of elements: one

inside and one outside the HAZ. This approach is restrictive

as it requires a different mesh every time that the weld radius or

other qualitative parameters affecting the HAZ extent change.

In addition, exact similarity of the FE meshes was a major

concern in order to exclude differences in plastic regime

behaviour owing to this factor.

The authors chose to generate the field of distances of the

Gauss points of the FE model from the welds and to assign the

property of being inside or outside the HAZ based on the value

of this field: let d1 be the distance of an arbitrary point of the

FE model from the upper-flange/web junction and d2 be the

respective distance from the lower-flange/web junction. Then,

for a web (resp. flange) point to lie outside the HAZ, the index

function web(resp. flg)

web= min(d1, d2) (SRD

+ wf+ tf/2) (3)

flg= min(d1, d2) (SRD + wf+ tw/2) (4)will have to be positive. These distance functions are depicted

inFig. 5a. Note that the concept of the distance field allows

the easy introduction of a transient HAZ around the nominalboundary of the zone. However, although the concept of a

gradual transition from the heat-affected material to the intact

area away from the weld was easy to implement, the authors

refrained from doing so, due to the scarcity of experimental data

on transient HA zones in the literature.

6. Overview of the results

Before discussing the results of the FE computations, the

authors consider it important to propose a way of comparing

the behaviour of a shell elasticplastic model to the Eurocode 9

resistance checks. The traditional approach is to use the concept

of moment and shear resistance My,Rd, Vz,Rd and MV,Rd atcritical cross sections and rely on these to provide a measure of

whether a structural element can safely bear the imposed load

or not. However,My,RdandVz,Rdare but measures originating

from classic beam theory: as we model a structure by more

elaborate means, other measures of its response to the imposed

level of loading seem necessary. Our idea is to express the

response of our model as a function gs of the applied load:

uA= gs(PR) (5)where uA and PR respectively are displacements and loads

defined in an average sense as below:

uA=

sLuzdx

sL, PR=

sL

fz dx . (6)

Here uA is the average of the uz displacements over the

length sL of application of the load (see Fig. 4a) and PR the

resultant of the applied load. The function gs will be termed the

structural response function. The derivative Srs= gs/ PRwill be referred to as the structural response slope. Our

idea therefore is to compare the traditional concept of cross

section resistance to the results of the elastoplastic FE analysis

as expressed by means of the structural response function gs .

It is rather straightforward that the model can be considered

to approach a state of structural failure if the slope of gs


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Fig. 5. (a)AlHEA220/7020T6:the field min(d1, d2)(mm). (b) Proportionality stress field (N/mm2)forw = 6 mm, SR D= 12 mm.

(a)AlHEA180. (b)AlHEA220.

Fig. 6. Load displacement functionsgs for 6063-T6.

(a)AlHEA180. (b)AlHEA220.

Fig. 7. Load displacement functionsgs for 6005A-T6.

increases significantly with respect to its initial, elastic regime

value Selrs . In fact, Srs was used as a stopping criterion for

the calculations: the load incrementation loop was forced toexit when the ratio Srs(PR)/S

elrs exceeded the value of 10. The

structural response functions of the studied cases are plotted in

Figs. 68. Each sub-figure depicts response functions related

to a single combination of a cross section and a material, andcontains five curves:

(a) the welded beam with restrained uwebx (labelled HAZ-

BC#A),(b) the welded beam where uwebx is free to develop (labelled

HAZ-BC#B),(c) the extruded beam where no HAZ is present (labelled

NHZ),(d) a beam theory computation of the deflection (including

shear deformations and material non-linearity) for a weldedcross section (HAZs exist),

(e) a beam theory computation of the deflection (as above) of

an extruded cross section (HAZs are absent).

(a)AlHEA180.

(b)AlHEA220.

Fig. 8. Load displacement functionsgs for 7020-T6.

In addition to these curves, vertical dashed lines are drawn

showing the maximum value of PR for the welded and the

extruded cases (respectively labelled PHAZmax and PNHZ

max ) that

were computed following the checks of Eurocode 9. Let it be

noted that the Vz,Rdcheck was the critical one as our models

are rather short. The resulting numerical values of the checks

are given inTable 4.

Curves (d) and (e) were computed by means of elementary

beam theory adapted to the non-linearity of the material. The

procedure is as following:

(1) The cross section was discretized on the yz plane; the

momentcurvature (M) diagram was computed by

means of integration of stresses over the cross section. The

said stresses were obtained via the law corresponding

to each element of the cross section discretization, for a

number of extreme fibre strains; the planarity assumption

was observed.

(2) as the My(x) diagram of the cantilever is known, the

distribution of the curvature (x)is obtained via the M


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Table 4

PEC9max values: Eurocode 9 shear, moment and interaction checks (kN)

Alloy designation c/s type P(Vz,Rd) P(My,Rd) P(My+ Vz)

6005AT6-171. Welded 125. 242. 125.

Extruded 146. 283. 146.

6005AT6-210. Welded 181. 377. 181.

Extruded 207. 428. 207.

6063T6-171. Welded 89. 181. 89.

Extruded 109. 221. 109.

6063T6-210. Welded 137. 283. 137.

Extruded 166. 334. 166.

7020T6-171. Welded 179. 362. 179.

Extruded 197. 397. 197.

7020T6-210. Welded 274. 555. 274.

Extruded 300. 600. 300.

diagram and integrated twice producing the displacementuz(x)due to bending.

(3) additional displacements due to shear, obtained again for

the non-linearlaw, are superimposed.

Acceptable coincidence appears to have been obtained

between the beam theory and the shell models only for the cases

where an HAZ does not exist. The discrepancy that shows upfor the welded cases will be discussed in what follows.

A first remark regarding the behaviour of the extrudedprofiles is that altering the boundary condition type from A

to B produced very close results (curves labelled NHZ);

this is the reason why only response functions for type-Aboundary conditions are plotted to show the behaviour of the

extruded cross sections. However, the type of the web boundaryconditions seems to affect the response of the welded crosssections in a distinctive manner. A clear divergence of the

response of the welded cross sections with respect to the web-

ux constraint is rather evident in the plastic regime: the modelswhere web-ux is free develop a softening behaviour well before

their counterparts where web-ux is constrained. Referring to the

response of the extruded profiles (no HAZ), one can observethat their gs plots intersect with the respective Eurocode 9

strength limit (vertical line labelled PNHZmax ), well before any of

the softening, characterizing their final load steps, shows up.This however, is not the case for the welded cross sections,

where a significant reduction of the macroscopic stiffness

(1/Srs) of the models takes place before the PHAZ

max limit is

reached. One can see that the greater the severity of the heateffect (coefficient inTable 1), the earlier the softening of the

model appears; the effect exists but is clearly milder for the

7020 alloy (= 0.71).In order to elucidate this particular behaviour of the welded

cases, Figs. 9 and 10 depict the patterns of the web shearstrain x z at various stages of the loading process for the

AlHEA180/6005A-T6case. Fig. 9pertains to type-A bound-

ary conditions (constrained web-ux ), whereas Fig. 10 showsrespective results obtained with the type-B boundary condi-

tion (free web-ux ). The plots of the slope of the structural re-

sponse with respect to the load, are depicted in Figs. 9a, b,

10a, b. The slopes are normalized with respect to Selrs , which is

the slope ofgs at the elastic regime of the model; additionally,

the load on the horizontal axis of the Srs plots is normalized

by the Ppr

R load value. The upper index pr stands for pro-

portionality, hence the value of Ppr

R is equal to the maximum

load for which our model remains everywhere elastic.

First, let us observe the field of web-x z depicted inFig. 9d:

it corresponds to a state very close to the PEC9max load of the

extruded cross section (actually PEC9max = 146 kN, limited tothis value by the Vz,Rdcheck; seeTable 4).

The pattern of the web shear strain xz is rather expected;

in a state where the shear resistance of the cross section is

reached, the maximum xz value is evenly distributed over the

web. Note also that the x z field ofFig. 9d corresponds to thepoint marked 1 inFig. 9b, which lies well within the horizontal

part of the Srs curve: it would take a further 18% increase of

the load to reach the point marked 2 in Fig. 9b and obtain a

substantial reduction of the structural stiffness (by a factor of

Srs= 2.35; seeFig. 9f). Even at this load, which is well beyondthe Eurocode 9 resistance of the model, the corresponding strain

field shown inFig. 9f retains, to a reasonable degree, its evenly

distributed form.

Coming now to the web-xz fields of the welded beams

(Fig. 9c, e, g), we see that as the Srs curve departs from its

initial horizontal part, strain accumulates along two slit-like

regions lying in the vicinity of the weld foot, inside the HAZ(seeFig. 5b, where the HAZ is depicted). This is expected, as

the part of the web between the end of the weld foot and the

fringes of the HAZ is the weakest part of the model, and the

shear flow of the web has to pass through there to ensure the

integrity of the cross section.

The result is that the planarity assumption of the cross

sections is violated and a decoupling of the beam cross section

into three loosely connected elements (lower flange, web and

upper flange) seems to develop [22]. In the authors opinion,

this has to be the reason for the discrepancy between the gsof welded models obtained via the beam theory and those

of the shell FE models: in beam theory the cross sections


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Fig. 9. (a) Welded CS: tip compliance evolution. (b) Extruded CS: tip compliance evolution. (ch) Fields of web strains x z for various load intensity levels;

boundary conditions type: A.

are implicitly constrained to remain planar by the Bernoulli

assumption.

The formation of strain accumulation zones is more evident

for the type-B boundary conditions (unconstrained web-ux ). In

fact, as our model is now less constrained kinematically, the

increase of the structural response slope is steeper. Observingthe form ofSrsinFig. 10a against that ofFig. 9a we can see that

in the case of unconstrained web-ux (Fig. 10a), the rise ofSrstakes place over 35% of the plotted horizontal axis range ( P

prR

factor), whereas in the case of type-A boundary conditions,

this rise happens in a milder way, taking almost 60% of the

respective load range. The result obviously is less ductility for

the case of unconstrained web-ux .

One last remark concerns the development of strain

accumulation zones in the case of extruded profiles, like those

showing up inFig. 10h. One should keep in mind thatFig. 10f

and10h correspond to load levels 21% and 29% higher than

the Eurocode 9 predicted resistance. In addition, these strain

accumulation zones tend to remain confined in the vicinity of

the support.

7. Conclusions

The present work is an FE study of the behaviour of

welded aluminium beams, where shear is the critical factor.The presence of the HAZ, an unavoidable consequence of theweld, seems to have caused premature failure of the models due

to the formation of shear accumulation bands along the foot

of the web-flange welds. For alloy/heat temper combinations

with a low value (less than 0.60), the Eurocode 9 predicted

resistance in shear appears to be optimistic. The authors believe

that further research, both numerical and experimental, isneeded to shed more light on the quantitative aspects of this

unfavourable situation.Until such results become available in the literature, the

authors propose that such beams be designed in shear using the

f

HAZ

0.2 value over the whole area of their cross section.


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Fig. 10. (a) Welded CS: tip compliance evolution. (b) Extruded CS: tip compliance evolution. (ch) Fields of web strainsYx z for various load intensity levels;

boundary conditions type: B.

Acknowledgements

The authors wish to express their sincere thanks to the

Castem-Code development group as well as to Professor

K. Thomopoulos for his moral support and many helpful

comments.

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