effective length of aluminium t-stub connections by parametric analysis.pdf

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Effective length of aluminium T-stub connections by parametric analysis

Gianfranco De Matteis , Muhammad Tayyab Naqash, Giuseppe Brando

Department of Engineering, University G. dAnnunzio of Chieti-Pescara, Viale Pindaro 42, 65127 Pescara, Italy

a r t i c l e i n f o

Article history:

Received 5 December 2011

Revised 9 March 2012

Accepted 26 March 2012Available online 18 May 2012

Keywords:

Aluminium T-stub

Finite Element model

Parametric analysis

Component method

Eurocode 9

Effective length

a b s t r a c t

The paper presents a parametric analysis carried out on welded aluminium T-stubs by means of Finite

Element models. The applied models are suitably calibrated on the basis of available experimental tests.

The study is carried out on a large variety of specimens with different features and different type of bolts,in order to analyse all possible failure mechanisms. Totally, 43 models are analysed and the obtained

results are carefully elaborated in order to check the reliability of the methods presently provided by

Eurocode 9. The paper represents a significant extension of the experimental and numerical analyses car-

ried out by the authors in the past, which were especially devoted to analyse the definition of effective

length for aluminium T-stubs. The obtained results allow to yield interesting outcomes that should be

incorporated in future editions of relevant codes dealing with aluminium structures.

2012 Elsevier Ltd. All rights reserved.

1. Introduction

It is well known, that some aluminium alloys exhibit special

properties, such as corrosion resistance, versatility, reversibility,

reasonable ductility and lightness, especially if compared to other

conventional materials like steel. Consequently, they highly attract

designers for their employment in building projects[1].

Nevertheless, only few studies have been undertaken in the past

for the identification of the behaviour of aluminium connections

and joints for structural purposes. This leads to state that thecurrent

Eurocode 9[2]approach on joints design is generally not complete

enough for formulating a reliable component method, contrarily

to the one already recommended by Eurocode 3[3]for steel joints,

this being based on the outcomes of several researches and specific

studies carried out in the last four decades.

The paramount role of T-stub in the component method formu-

lation for defining both strength and stiffness of joints is widely

recognised. It is a typical component of bolted joints used to modelcolumn flange in bending, end plate in bending and flange cleats in

bending, etc.

The so-called T-stub consists of two T-section elements, sym-

metrically connected to each other in their flanges by one or more

series of bolt rows, which undergo flexural deformations due to a

pulling force usually transmitted by webs transversally located at

the centre of the flanges (seeFig. 1).

The T-stub behaviour is governed by various phenomena,

namely the bolts strength and deformability, the flexural stiffness

of the flange, the geometrical properties that can entail different

yield lines on the connected plates when incipient collapse phe-

nomena involve the whole system, etc.

In the last years, many researches have been devoted to enhance

the knowledge on T-stub connections. These have been developed

by means of experimental, analytical and numerical analyses. Inter-

esting experimental tests have been provided by Girao Coelho et al.

[4], who dealt with extendedend plate connections for determining

the influence of both material grade and plate thickness. De Matteis

et al. [5,6] investigated for the first time the possibility of extending

the provision for T-stub given by Eurocode 3 also to aluminium

joints. Piluso and Rizzano[7]performed experimental analyses on

bolted steel T-stubs under cyclic loads. Moreover, theoretical mod-

els have been provided by Lemonis and Gante[8]and Stamatopou-

los and Ermopoulos[9], who investigated the influence of the T-

stub flexibility. Also, numerical analyses have been developed by

Mistakidis et al. [10], who proposed a computationally non-cum-

bersome 2-D numerical FEM model, by Giro Coelho et al. [11],who dealt with both rolled and welded T-stub models, by Efthymi-

ou[12], De Matteis et al.[13]and Xu et al.[14].

With particular regard to aluminium connections, the current

version of Eurocode 9 provides formulations based on the k-meth-

od whichhas been proposed by theauthors. Thecurrentpaper rep-

resents an extension with respect to theprevious researches, which

were based on the assumption of the same effective length for

aluminium T-stubs as provided by EC3-Part 1.8 for steel T-stub.

Hence,a parametric study implemented on thebasis of FEMnumer-

ical aluminiumT-stub modelsis provided in order to identify theef-

fects of the most important geometrical and mechanical

parameters on failure modes, yield patterns and, therefore, on the

0141-0296/$ - see front matter 2012 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.engstruct.2012.03.052

Corresponding author. Tel.: +39 0854537261; fax: +39 0854537255.

E-mail address:[email protected](G. De Matteis).

Engineering Structures 41 (2012) 548561

Contents lists available at SciVerse ScienceDirect

Engineering Structures

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / e n g s t r u c t
http://dx.doi.org/10.1016/j.engstruct.2012.03.052mailto:[email protected]://dx.doi.org/10.1016/j.engstruct.2012.03.052http://www.sciencedirect.com/science/journal/01410296http://www.elsevier.com/locate/engstructhttp://www.elsevier.com/locate/engstructhttp://www.sciencedirect.com/science/journal/01410296http://dx.doi.org/10.1016/j.engstruct.2012.03.052mailto:[email protected]://dx.doi.org/10.1016/j.engstruct.2012.03.052


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actual effective length which is able to return the T-stub ultimate

strength according to the simplified formulation presently adoptedin EC9.

2. Aluminium T-stub failure mechanisms (EC9 k-method)

T-stub connections must be designed taking into account all the

possible yielding mechanisms and failure modes. For aluminium

connections, EC9 (Annex-k) proposes thek-method for the calcula-

tion of ultimate strength of T-stub connections. This method also

accounts for strain hardening and reduced ductility of the base

material.

Four failure mechanisms are detected, namely mode1 com-

plete flange failure, mode 2a partial flange failure with the

attainment of elastic strength in bolts, mode 2b bolts failure

with the attainment of the elastic strength in flanges and mode3 which consists in the complete bolts failure (seeFig. 2).

The ultimate resistance of the T-stub failure modes 1, 2a, 2b and

3 are given in Eqs. (1)(4), respectively.

Fu;Rd;1 2Mu;1w 2Mu;1b

m 1

Fu;Rd;2a 2Mu;2 n

PB0

m n 2

Fu;Rd;2b 2M0;2 n

PBu

m n 3

Fu;Rd;3 X

Bu 4

The actual collapse load of the T-stub joint is determined from theminimum value of the resisting forces governing the failure modes.

In the above equations, Buand Boare the ultimate and conven-

tional elastic tensile strength of bolts, respectively. (Mu,1)w and

(Mu,1)bare the plastic moments of the critical flange cross sections,

located close to the T-stub web and bolt rows, respectively, when a

failure mode1 arises (Eqs.(5) and (6)).Mu,2(Eq.(7)) is the plastic

moment of the flange when the failure type is mode2. M0,2 (Eq.

(8)) is the elastic moment at 0.2% proof strength.

Mu;1w 0:25 t2

f Reff;u;1 f0;haz1

k 5

Mu;1b 0:25 t2

f Reff;u;1 fu 1

k 6

Mu;2 0:25 t2

f Reff;u;2 fu 1

k 7

M0:2 0:25 t2

f eff;u;2 f0:2 1

k 8

In Eqs. (5)(8), eff,u,1 and eff,u,2 are the flange section effective

lengths, defined according to the failure mode and the yield line

developing (circular or non-circular pattern),f0.2 and fuare the con-

ventional yield and ultimate stress, respectively of the base mate-

rial, f0,haz is the ultimate strength of the heat affected zone, tf is

the flange thickness, m is the distance of the weld seams from the

centre of bolts, n is the minimum between 1.25mand the distance

eof bolts from the flange edges (seeFig. 2).

Thek factor is defined as:

1

k

f0:2fu

1 w fu f0:2f0:2

9

where

w eu 1:5 e0:21:5 eu e0:2

10

Fig. 1. Idealization and schematization of T-stub.

Fig. 2. Failure modes of aluminium T-stubs prescribed by EC9.

G. De Matteis et al./ Engineering Structures 41 (2012) 548561 549


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eu and e0.2 being the ultimate and yielding strain respectively.

The method given by EC9 properly extends the formulation pro-

posed by Eurocode 3 for steel T-stub by using a correction factor

1/k, which allows to take into account both the different strain

hardening and the reduced ductility of aluminium materials with

respect to steel.

3. The numerical model

3.1. General

The base model used for parametrical analysis is calibrated on

the basis of available experimental tests carried out by De Matteis

and Mazzolani[6]. In particular, three welded coupons, subjected

to a monotonic pulling force up to the failure, are taken into

account. These are hereafter named as specimen Sample A, spec-

imen Sample B and specimen Sample C.

The mechanical and geometrical features of tested specimens

are listed inTable 1, whereas the stressstrain relationship of the

related materials, including also the heat affected zone closed to

the welds, is provided in Section3.4.

It is worthy to note that one material only, namely Aluminium

alloy AW-6082, is considered for the T-stub flanges, as this para-

metric analysis is not devoted to analyse the effect of material

hardening.

3.2. Geometric modelling

T-stub connections are fairly complex to be modelled; in fact,

their geometry is generally three-dimensional, material and geo-

metrical nonlinearities are strongly involved in the loading process

and different contact phenomena, due to the interaction between

flanges and bolts, are present. Hence, compromises in the model-

ling phase are usually taken into consideration so to circumvent

these difficulties.

In the case under consideration, in order to reduce the cumber-

someness of the analysis, the proposed geometry of the model (see

Fig. 3a) takes into account the T-stub symmetry. As a consequence,

a rigid body fixed in the space is put below the flange of one of the

two T-sections so to simulate the presence of the other part of the

specimen. For the same reason, only half of the bolt is modelled,

with the middle plane of the shank suitably restrained.

In order to take into consideration the reduction of the diameter

of the bolts due to the threaded part, a 20% reduced area with re-

spect to the nominal one is considered. Indeed, for the adopted

M10 bolt, the existing codes provide a reduction of almost 25%,

but in the proposed model a slightly higher resistant area of bolts

is taken into account as the threaded portion is assumed to con-

tribute to the bolt stiffness.

The T-stub model is implemented by the Code ABAQUS 6.7[15],

where 8 node linear brick elements with reduced integration andhourglass control (C3D8R) are used (see Fig. 3b) for webs and

flanges. The bolts are meshed with 4 node linear tetrahedron

(C3D4) elements (seeFig. 3b). This is due to their more complex

geometry, which requires tetrahedral elements in order to realise

a less refined mesh without jeopardising the accuracy of the model

by contact problems. Hex dominant meshing algorithm is used to

obtain meshes with a mix of hexahedral, pyramids and tetrahedral

finite elements.

3.3. Boundary conditions, loads and interactions

The T-stub web is pulled by imposing a uniform vertical dis-

placement applied to a reference point constrained by a rigid cou-

pling with the top of the web itself. On the other hand, the bottom

part of the rigid body below the T-stub flange is fixed by applying a

clamping boundary condition.

The bolt load option provided by Abaqus has been used to

simulate the preload force Fp,Cd, accordingly to the following

equation:

Fp;Cd 0:7 fub As 11

whereAsis the resisting area of the bolt andfubis the ultimate stress

of the bolt material.

This bolt load option allows to automatically adjust the length

of the bolts in order to achieve the prescribed amount of pre-

tension.

Three contact interactions are defined, namely (i) the bearing ofthe back of the T-stub section against the interface with the rigid

body, (ii) the interaction between the hole and the bolt shank

and (iii) the interaction between the bolts head and the surface

of the T-stub. The first is defined as a penalty contact characterised

by a friction coefficient of 0.3, whereas the others are taken into ac-

count as frictionless contact.

3.4. Material modelling

The material constants used for all aluminium parts areE= 70,000 N/mm2 (elastic modulus), m= 0.3 (Poisson ratio) andq= 2700 kg/m3 (material density), whereas steel bolts are mod-

elled with E= 210,000 N/mm2, m= 0.3 and q= 7600 kg/m3. The

proof strengths for all the aluminium components of the T-stubare referred to a conventional stress off0.2.

In order to interpret correctly the behaviour of the system also

for large deformation, the available material test data are properly

transformed in true stresstrue strain, as depicted inFig. 4, where

the experimental curves are also provided for all the parts of the

tested specimens.

Table 1

T-stub tested specimens used for calibration of the proposed models.

Sample ID Aluminium alloy for flange Aluminium alloy for web Bolt material Flange thickness (mm) Web thickness (mm) Bolt diameter (mm)

Sample A 6082 7020 4.8 10 12 10

Sample B 6082 7020 7075 10 12 10

Sample C 6082 7020 10.9 10 12 10

Fig. 3. T-stub (a) geometry and (b) FEM model.

550 G. De Matteis et al. / Engineering Structures 41 (2012) 548561


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3.5. Analysis implementation

The analysis of the models is carried out by using standard mul-

tiple step (two steps) analysis. In the first step, the bolt preload is

statically applied by means of the bolt load option, provided in

the ABAQUS library. In the second step, a static Riks analysis is ap-

plied up to the collapse of the whole system in order to reproduce

the loading process of the whole T-stub.

3.6. FEM sensitivity analysis

A preliminary sensitivity analysis is carried out on specimen

Sample A, in order to check the influence of both mesh size, finite

element adoptions and contact typology on the proposed model re-sponse. To this purpose, in a first stage, T-stub models with

(a) (b)

(c) (d)

(e) (f)

Fig. 4. Nominal and true stress/strain curves for (a) flange, (b) web, (c) HAZ, (d) 4.8

steel bolts, (e) 7075 aluminium bolts, and (f) 10.9 steel bolts.

Fig. 5. Sensitivity analysis for mesh size (a) 3 mm, (b) 4 mm, and (c) 5 mm.

Table 2

Mesh size of T-stub model and related number of elements and nodes.

Approximate global mesh

size (mm)

No. of

nodes

No. of elements

[C3D8R]

Normalised

CPU time

3 12,738 9700 3.1

4 8412 6344 2.7

5 4271 2976 1.0

(a) (b)

(c)

Fig. 6. Sensitivity analysis for (a) T-stub mesh, (b) bolts mesh, and (c) contacts.



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approximate global mesh size of 3 mm, 4 mm and 5 mm (see

Fig. 5ac) are analysed. The obtained numbers of elements, as well

as the corresponding CPU time consuming (normalised to mini-

mum value) are provided inTable 2.From the analysis of the obtained response, given inFig. 6a in

terms of pulling force F vs. vertical displacement D, it is possi-

ble to observe that the selected mesh sizes do not influence signif-

icantly the overall result. However, since using a global mesh size

of 4 mm requires sustainable time analysis consuming, giving pre-

cisely the same results of a 3 mm mesh side length, the former is

assumed for all the implemented models.

The same type of remarks can be made for bolts finite elements

typology and size. With respect to the options listed inTable 3, it is

possible to observe that using C3D4 elements with an average

mesh size of 3 mm gives the same results of C3D8R elements with

1 mm mesh side length, requiring half of the CPU time. For this rea-

son, the former mesh typology is adopted (seeFig. 6b).

Finally, the sensitivity of the model with respect to the four dif-ferent contacts combination listed inTable 4is investigated. All the

possible combinations need more or less the same normalised CPU

time, giving approximately the same results for small displace-

ments. Nevertheless, contacts combination 1, with penalty coef-

ficient of 0.3 for the T-stub to base and frictionless contacts for

bolt to T-stub, is assumed, as it gives less convergence problems

for larger displacements.

3.7. Numerical vs. experimental results

The reliability of the proposed models is proved by comparing

the experimental outcomes with the numerical ones. As shown

in Fig. 7a, in case of experimental specimen Sample A, a failuremode 2a is detected, whereas for specimens Sample B and

Sample C failure modes 2b and 1 are recognised, respectively.

The same failure modes are evidenced by numerical model (Fig. 8).

On the other hand, the proposed numerical results are in goodagreement with the experimental ones if compared in terms of

force vs. displacement curves (Fig. 9).

The obtained models are therefore reliable enough to allow for

carrying out a parametric study.

4. Analysis of results and discussion

4.1. General

In the following, the main results of a parametrical analysis, car-

ried out by changing both the mechanical and geometrical proper-

ties of the above calibrated models, are described. Totally, 43

different geometries are managed, with the aims of proving thereliability of the formulations currently provided by EC9.

Table 3

Mesh size for bolt model and related number of elements and nodes.

Approximate global

mesh size (mm)

Element

type

No. of

nodes

No. of

elements

Normalised

CPU time

1 C3D4 3136 13,336 8.7

2 C3D4 612 2303 6.0

3 C3D4 249 860 4.1

4 C3D4 166 525 2.2

3 C3D8R 372 248 1.01 C3D8R 5595 4664 7.1

Table 4

Different contact combinations for sensitivity analysis.

Combination T-stub to base T-stub to bolts Normalised CPU time

1 Penalty-0.3 Frictionless 1.3

2 Penalty-0.3 Rough 1.3



Fig. 7. Deformed shapes of (a) test Sample A, (b) test Sample B, and (c) test Sample

C.

Fig. 8. Deformed shapes and stress contour of (a) FEM Sample A, (b) FEM Sample B,

and (c) FEM Sample C.

(a) (b)

(c)

Fig. 9. Experimental vs. numerical results for: (a) Sample A, (b) Sample B, and (c)

Sample C.



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In all cases the nominal values suggested by EC9 for the

mechanical features of the used materials, as listed in Table 5,

are considered.

In particular, for aluminium parts the stress strain curves are

defined using a Ramberg Osgood law, as expressed in Eq. (12),

which is properly transformed in terms of true stressestrue

strains.

e rE k

rE

n12

In the above equation, e is the strain, r is the stress, E is the

Youngs modulus, k= 0.002 and n= 14 is the hardening constantwhich depends on the material under consideration.

The material ultimate strain (eu) is evaluated based on the

approximate formulation given in EC9 Annex-E as represented by

eu 0:3 0:22 f0400

when f0 < 400 N=mm2 13

Models with two bolt rows and resulting by the adoption of four

thicknesses of the flangetfof the T-stub (8 mm, 10 mm, 12 mm and

15 mm), different bolt grades (Type a = grade 4.6, Type b = alu-

minium alloy 6082 and Type c = grade 10.9) and four geometries

that consider different bolt pitches p (40 mm, 60 mm, 80 mm and120 mm) are proposed (see Table 6). In this table, the notations

Table 5

Mechanical features of the materials used in parametric analyses.

Part Material f0 (Mpa) fu (Mpa) eu (%) E (Mpa) Poissons ratio

Flange/web EN AW-6082 T6151 200 275 12 70,000 0.3

EN AW-6082 T6151 (HAZ) 125 185 12 70,000 0.3

Bolts Grade 4.6 240 400 16 210,000 0.3

EN AW-6082a 260 310 14 70,000 0.3

Grade 10.9 900 1000 7 210,000 0.3

a No temper grade designation is given in Eurocode for this material when it is used for bolts.

Table 6

Values of geometrical parameters (mm) for analysed T-stubs.

Group S. no. Label tf B b m t w p e=e1 Bolts type

1 1 40p8-a 8 140 80 40 10 40 20 11 4.6

2 40p10-a 10 142 80 40 12 40 20 11 4.6

3 40p12-a 12 144 80 40 14 40 20 11 4.6

4 60p8-a 8 160 120 40 10 60 30 11 4.6

5 60p10-a 10 162 120 40 12 60 30 11 4.6

6 60p12-a 12 164 120 40 14 60 30 11 4.6

7 80p8-a 8 180 160 40 10 80 40 11 4.6

8 80p10-a 10 182 160 40 12 80 40 11 4.6

9 80p12-a 12 184 160 40 14 80 40 11 4.6

10 120p8-a 8 220 240 40 10 120 60 11 4.611 120p10-a 10 222 240 40 12 120 60 11 4.6

12 120p12-a 12 224 240 40 14 120 60 11 4.6

2 13 40p8-c 8 140 80 40 10 40 20 11 10.9

14 40p10-c 10 142 80 40 12 40 20 11 10.9

15 40p12-c 12 144 80 40 14 40 20 11 10.9

16 40p15-c 15 147 80 40 17 40 20 11 10.9

17 60p8-c 8 160 120 40 10 60 30 11 10.9

18 60p10-c 10 162 120 40 12 60 30 11 10.9

19 60p12-c 12 164 120 40 14 60 30 11 10.9

20 60p15-c 15 167 120 40 17 60 30 11 10.9

21 80p8-c 8 180 160 40 10 80 40 11 10.9

22 80p10-c 10 182 160 40 12 80 40 11 10.9

23 80p12-c 12 184 160 40 14 80 40 11 10.9

24 80p15-c 15 187 160 40 17 80 40 11 10.9

25 120p8-c 8 220 240 40 10 120 60 11 10.9

26 120p10-c 10 222 240 40 12 120 60 11 10.9

27 120p12-c 12 224 240 40 14 120 60 11 10.9

28 120p15-c 15 227 240 40 17 120 60 11 10.9

29 150p10-c 10 252 300 40 12 150 75 11 10.9

30 150p12-c 12 254 300 40 14 150 75 11 10.9

31 150p15-c 15 257 300 40 17 150 75 11 10.9

3 32 40p8-b 8 140 80 40 10 40 20 11 AW-6082

33 40p10-b 10 142 80 40 12 40 20 11 AW-6082

34 40p12-b 12 144 80 40 14 40 20 11 AW-6082

35 60p8-b 8 160 120 40 10 60 30 11 AW-6082

36 60p10-b 10 162 120 40 12 60 30 11 AW-6082

37 60p12-b 12 164 120 40 14 60 30 11 AW-6082

38 80p8-b 8 180 160 40 10 80 40 11 AW-6082

39 80p10-b 10 182 160 40 12 80 40 11 AW-6082

40 80p12-b 12 184 160 40 14 80 40 11 AW-6082

41 120p8-b 8 220 240 40 10 120 60 11 AW-6082

42 120p10-b 10 222 240 40 12 120 60 11 AW-6082

43 120p12-b 12 224 240 40 14 120 60 11 AW-6082



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(a1)

(b1) (b2) (b3)

(a3)(a2)

Fig. 10. Ultimate resistance vs. displacement graphs related to different bolt pitch: T-stub with 4.6 steel bolts: (a1) tf= 8 mm, (a2) tf= 10 mm, (a3) tf= 12 mm; T-stub with

6082 aluminium bolts: (b1) tf= 8 mm, (b2)tf= 10 mm, (b3) tf= 12 mm.

(a) (b)

(c) (d)

Fig. 11. Ultimate resistance vs. displacement graphs: for 10.9 bolt grades with different pitches (a) tf= 8 mm, (b)tf= 10 mm, (c) tf= 12 mm, (d) tf= 15 mm.



8/14

tf,B,b,m, twand are thickness of flange, breadth of T-stub, width

of T-stub, bolt to web-face distance, thickness of web and diameter

of hole, respectively; these notations are also indicated in Fig. 12.

4.2. Numerical results

In the following numerical results are presented in term of

graphs and tables.Fig. 10shows the force vs. displacement dia-grams for all the analysed models when bolt pitch varies and when

4.6 steel bolts (graphs Type a) and aluminium alloy AW-6082

bolts (graphs Type b) are assumed. Fig. 11 shows the same

force vs. displacement graphs in the case of 10.9 grade steel bolts,

also considering a flange thickness of 15 mm.Fig. 12. Monitored points in the model for the identification of failure modes.

(a1) (a2) (a3)

(d1) (d2) (d3)

(c1) (c2) (c3)

(b1) (b2) (b3)

Fig. 13. Failure mechanism identification for 4.6 steel bolts: (a1) tf= 8 mm, p40; (a2) tf= 10 mm, p40; (a3)tf= 12 mm, p40; (b1)tf= 8 mm, p60; (b2)tf= 10 mm, p60; (b3)tf= 12 mm, p60; (c1)tf= 8 mm, p80; (c2)tf= 10 mm, p80; (c3)tf= 12 mm, p80; (d1)tf= 8 mm, p120; (d2) tf= 10 mm, p120; (d3) tf= 12 mm, p120.



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From such curves, the ultimate strength can be detected as the

smaller among the peak value of the related curve and the force

corresponding to the attainment of ultimate material deformation

in anyone of the points of the T-stub in which failure may arise. To

this purpose, points p1, p2, and p3 shown inFig. 12are mon-

itored, in order to identify the failure mechanisms of the models inthe FEM analyses.

The failure mechanisms characterising FEM models with 4.6

steel bolts can be identified by the graphs given inFig. 13. It is pos-

sible to retrieve the stresses of the parts in which failure may de-

velop vs. the global displacement of the T-stub. In all the cases, a

failure mode 2a is detectable due to the weakness of the bolts

which, nevertheless, yield only after that the flange attains theplastic moment in the HAZ.

(a1) (a2) (a3)

(b1) (b2) (b3)

(c1) (c2) (c3)

(d1) (d2) (d3)

Fig. 14. Failure mechanism identification for 6082-alloy aluminium bolts: (a1) tf= 8 mm, p40; (a2)tf= 10 mm, p40; (a3)tf= 12 mm, p40; (b1)tf= 8 mm, p60; (b2)tf= 10 mm,

p60; (b3)tf= 12 mm, p60; (c1) tf= 8 mm, p80; (c2)tf= 10 mm, p80; (c3)tf= 12 mm, p80; (d1) tf= 8 mm, p120; (d2) tf= 10 mm, p120; (d3) tf= 12 mm, p120.



10/14

Figs. 14 and 15 show the stress vs. displacement diagrams for

AW-6082 aluminium and 10.9 steel bolts, respectively. In the firstcase, a failure mode 2b is always detectable, whereas in the case

of 10.9 bolts the failure of T-stub flanges takes place, giving back a

failure mode1, as the bolts are very far by the attainment of the

elastic limit.

4.3. Comparison with Eurocode 9 results

In order to check the validity of the method proposed by Euro-

code 9, the above results obtained by FEM analyses are compared

with the ones provided by the k-method. To this purpose, the cod-

ified method is applied consideringa material safetyfactor cM= 1.0.

It should be noted that EC9 formulation gives failure mode 2a

for all cases when 4.6 steel bolts are employed. These results

are also provided by stress analyses in Fig. 13. In addition, forall the models with 6082 aluminium bolts, a failure mode 2b is

(a1) (a2) (a3) (a4)

(b1) (b2) (b3) (b4)

(c1) (c2) (c3) (c4)

(d1) (d2) (d3) (d4)

Fig. 15. Failure mechanism identification for 10.9 steel bolts: (a1) tf= 8 mm, p40; (a2) tf= 10 mm, p40; (a3) tf= 12 mm, p40; (a4) tf= 15 mm, p40; (b1) tf= 8 mm, p60; (b2)

tf= 10 mm, p60; (b3)tf= 12 mm, p60; (b4) tf= 15 mm, p60; (c1) tf= 8 mm, p80; (c2)tf= 10 mm, p80; (c3) tf= 12 mm, p80; (c4)tf= 15 mm, p80; (d1) tf= 8 mm, p120; (d2)

tf= 10 mm, p120; (d3) tf= 12 mm, p120; (d4)tf= 15 mm, p120.

Table 7

Failure modes for 12 mm and 15 mm thick flanges using 10.9 steel bolts.

Specimen tf= 12 mm Specimen tf= 15 mm

EC9 FEM EC9 FEM

40p12-c 1 1 40p15-c 1 1

60p12-c 1 1 60p15-c 2a 1

80p12-c 1 1 80p15-c 2a 1

120p12-c 2a 1 120p15-c 2b 1



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(a) (b)

(d)(c)

Fig. 16. Ultimate strength (Fu) obtained from FEM analyses and EC9 formulation for analysed cases: (a) p = 40 mm, (b) p = 60 mm, (c) p = 80 mm, and (d)p = 120 mm.

(a) (b)

(d)(c)

Fig. 17. FEM vs. EC9 results in terms of tendency lines: (a)p = 40 mm, (b) p = 60 mm, (c) p = 80 mm, and (d) p = 120 mm.



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identified (Fig. 14). This result is given also by EC9, except for

model 120p12-b, for which a failure mode 3 can be detected.

As far as the cases related to 10.9 bolts with 12 mm thick flange

are concerned (Fig. 15), a failure mode 1 is obtained from both

EC9 and FEM analysis, apart from model 120p12-c, for which a

mode 2a is obtained using EC9 formulations. On the contrary,

in the case of 15 mm thick flange, except model 40p15-c for

which mode 1 is obtained from both EC9 and FEM analysis, all

the rest of the failure mechanisms obtained from EC9 disagree with

the one obtained from FEM analysis, as shown in Table. 7.

Fig. 16 shows that EC9 formulation is in good agreement incases of low pitches (40 mm and 60 mm). On the contrary, it is evi-

dent that when high pitches (80 mm and 120 mm) are assumed,

the EC9 formulation overestimates the ultimate strength, it result-

ing therefore not conservative, especially for 12 mm and 15 mm

thick flanges.

The overestimation of the ultimate strength for high thick-

nesses is probably due to the fact that, in these cases, the expres-

sion of the effective length by EC9 is not reliable enough.

The overestimation of ultimate strength is evident by the com-

parison given inFig. 16. In addition it can be observed that FEM

analysis results provided in Fig. 17 are quite consistent in terms

of tendency lines for all the analysed thicknesses, whereas thecurves obtained from the EC9 formulation present a different rate

Table 8

Effective lengths for T-stub from FEM and EC9 using 10.9 steel bolts.

Pitch Label effEC9 (mm) effEC9 (mm) Pitch Label effFEM (mm) effFEM (mm)

(p40) 40p8-c 80 134.8 (p80) 80p8-c 160 218.7

40p10-c 80 115.1 80p10-c 160 168.8

40p12-c 80 89.2 80p12-c 160 126.5

40p15-c 80 72.0 80p16-c 160 96.0

(p60) 60p8-c 120 179.8 (p120) 120p8-c 240 275.7

60p10-c 120 147.7 120p10-c 240 201.4

60p12-c 120 118.5 120p12-c 240 153.2

60p15-c 120 83.0 120p15-c 240 109

Fig. 18. Von Mises stress contours for the T-stub flanges of models with steel 10.9 bolts: (a1) tf= 8 mm, p= 40 mm; (a2) t

f= 10 mm, p= 40 mm; (a3) t

f= 12 mm, p= 40 mm;

(b1)tf= 8 mm ,p= 60 mm; (b2) tf= 10 mm ,p= 60 mm; (b3) tf= 12 mm, p= 60 mm; (c1) tf= 8 mm,p= 80 mm; (c2) tf= 10 mm ,p= 80 mm; (c3) tf= 12 mm, p= 80 mm; (d1)

tf= 8 mm , p = 120 mm; (d2)tf= 10 mm , p = 120 mm; (d3) tf= 12 mm, p = 120 mm.



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with increased pitch of bolts, when high strength bolts are used.

Reminding that FEM 120p12-b presents a failure mode 2band FEM 120p12-c model presents a mode 1 failure mode,

whereas EC9 gives back mode 3 and mode 2a respectively, it

is apparent that the formulation given by EC9 for the effective

length must be generally recalibrated, depending on the bolts pitch

and flange thicknesses.

4.4. Effective length evaluation

The above remarks about the effective length are actually con-

firmed by the fact that, as the bolts pitch increases, the inactive

area of the flange contributing to the ultimate strength increases

as well, with a proportionally shorter yielding pattern which tends

to a circular shape. On the contrary, it can be observed that for the

models with a pitch of 40 mm the entire flange transversal sectioncontributes to the resistance of the T-stub. This is clearly shown in

Fig. 18where the stress contours for models according to the adop-

tion of 10.9 steel bolts is depicted.

Similarly, it is quite evident that as the thickness of the flange

increases the effective area of the flange contributing to the

strength reduces. This indicates that as the thicknesses of the

flange of T-stub increases, the effective length consequently should

decrease as well.

With reference to the code formulation, it has to be underlined

that for all the analysed cases, EC9 imposes a non-circular pattern

for the calculation of the effective lengths. This seems contradic-

tory to the above results, proving again that EC9 rule for selecting

the effective lengthleffis not reliable for certain geometric config-

urations and needs to be revised.InTable 8, the effective length leff computed according to the

ultimate strength obtained by both FEM analysis and EC9 formu-

lation are listed for all the models with 10.9 steel bolts. These are

plotted inFig. 19a in terms of tendency lines. In detail, the effec-

tive lengths from FEM analyses are obtained by using the numer-

ical ultimate strength and by reversing the Eurocode 9

formulation. This allows the evaluation of discrepancies present

in EC9 formulation and hence an assessment of the effective

length.

It is evident that when flange thicknesses increase, FEM-ten-

dency line and the EC9-tendency line intersect each other or tend

to intersect in one point (PI). This means that the effective lengths

given by the code are not always on the safe side as shown in

Fig. 19b. This is due to the fact that EC9 formulation does not takeinto account the variation of effective length with the thickness for

the failure modes where flange is strongly involved such as mode

1 and mode2a. The above points PIprovide a limit of applica-bility for the present codified formulation. This is evidenced in

Fig. 19b where the line joining these points is graphed.

5. Conclusions

The presented paper dealt with parametric analyses carried out

on 43 welded aluminium T-stubs models, suitably calibrated on

the basis of available experimental tests. The obtained results have

been carefully elaborated in order to check the reliability of the

methods presently provided by Eurocode 9.

The most important outcomes reached in the study may be

summarised in the following points:

The EC9 k-method is quite reliable for interpreting the T-stub

connections behaviour especially when weak bolts are

employed. The ultimate strengths according to EC9 are overestimated

when T-stubs with thick flanges and large bolt pitches are used,

especially in the case of failure mode 1, which is strongly

related to the effective length concept.

An improvement of the code for assessing the effective length

would be therefore advisable by revising the definition of

effective length formulation. In such a revision the transition

of failure pattern from non-circular to circular, which takes

place when the thickness and the pitch exceed a certain limit,

should be more carefully taken into account.

In addition, further studies could be carried out also to check

the reliability of the formulation provided by Eurocode 3 for steel

T-stub effective length.

Acknowledgements

This research is a continuation of previous studies developed

within the work for the preparation of Eurocode 9, Aluminium

Structures, coordinated by Prof. F.M. Mazzolani.

The authors also acknowledge the financial support for PhD stu-

dent Eng. Tayyab Naqash given by Reti per la Conoscenza e lOri-

entamento Tecnico-Scientifico per lo Sviluppo della Competitivit

(Re.C.O.Te.S.S.C.). Finally, the hosting of Eng. Tayyab Naqash at the

University of Naples Federico II, within the framework activitiesof Master in Design of Steel Structures, is gratefully acknowledged.

(a) (b)

Fig. 19. Effective lengths for 10.9 grade steel bolts from FEM and EC9 approach (a) tendency lines (b) limit curve for safe evaluation of effective length.



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