Behaviour of welded aluminium T-stub joints under monotonic loading

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Behaviour of welded aluminium T-stub joints under monotonic loading

G. De Matteis

a,b,*

, M. Brescia

b

, A. Formisano

b

, F.M. Mazzolani

b

a

Department of Design, Rehabilitation and Control of Architectural Structures, University of Chieti/Pescara ‘‘G. d’Annunzio”, Pescara, Italy b

Department of Structural Engineering, University of Naples ‘‘Federico II”, P.Le Tecchio 80, 80125 Naples, Italy

a r t i c l e

i n f o

Article history:

Received 14 November 2006 Accepted 29 April 2008 Available online 30 January 2009

Keywords: T-stub Aluminium alloy Heat affected zone (HAZ) FEM model

K-method Eurocode 9

a b s t r a c t

This paper deals with the behaviour of aluminium alloy T-stub joints subjected to monotonic tensile loads. In particular, a numerical model developed by means of the non linear code ABAQUS has been accurately calibrated on the basis of previous experimental test results related to 26 specimens, charac-terised by different geometry and connection type. In particular, four different geometries (by varying geometrical dimensions, plate thickness, number and location of the bolts), three aluminium alloys as base material and three types of bolts (including both aluminium and steel bolts) have been taken into consideration. Such parameters determine the modification of the connection response in terms of initial stiffness, ultimate strength and deformation capacity. The comparison with the experimental results shows that the proposed model is able to accurately reproduce the behaviour of the joint in all examined cases. Test results have been also compared with the ones derived from the application of the calculation method provided in the final version of Eurocode 9 (EN-1999-1-1), showing the reliability of the codified procedure, also in relation to a direct evaluation of the connection effective width (beff), as it is evidenced

by the developed numerical simulations.

1. Introduction

The prediction of the structural behaviour of complex systems requires the correct evaluation of the joint response in terms of strength, stiffness and dissipation capacity. For this reason, the modern structural codes provide appropriate procedures for the classification of joints aiming at preventively determining the importance of their influence on the global response of the whole system. On the other hand, the prediction of the actual joint behav-iour is quite difficult due to the large variety of connection types as well as due to the high and particular stress concentration

espe-cially deriving from contact phenomena [1], which induces to

either carry out direct laboratory tests or to realize accurate numerical models.

While few studies have been performed on bolted joints made of aluminium alloys [2,3], several laboratory experiments and numerical simulations have been already carried out for steel connections, allowing for the deﬁnition of accurate codiﬁed calculation procedures. On the basis of such considerations, a large research project dealing with aluminium joints has been recently carried out at the University of Naples ‘‘Federico II”. It was mainly

concerned with the behaviour of bolted T-stub joints, which may be regarded both as stand-alone connection and as a part of several, more complex bolted joint conﬁgurations[4].

With reference to steel T-stub joints, the EC3 Part 1.8[5] consid-ers three possible failure mechanisms, which are schematically illustrated inFig. 1, where the corresponding analytical formula-tions for the evaluation of the ultimate strength (Fu) are indicated

as well, being Muand M0the parameters representing the plastic

and the conventional elastic moments of the cross section of the T-stub ﬂange while Bu is the yielding tensile strength of bolts.

The proposed procedure is based on the equivalence between the three-dimensional behaviour of the T-stub connection and the simpliﬁed linear model of a continuous beam on four supports, with an effective width (beff), which is determined according to

speciﬁc rules provided by the code.

For aluminium T-stub joints the above collapse mechanisms can be strongly influenced by the peculiar mechanical features of the adopted material. In fact, the reduced ductility of the flange mate-rial can limit the development of failure mechanism Type 1 (devel-opment of four plastic hinges in the flange), while the pronounced strain hardening may produce both a different distribution of the bending moment on the flange and an increase of the moment capacity of plastic hinges. Finally, the limited deformation capacity of aluminium bolts could cause the premature collapse of the T-stub component in case of Type 2 collapse mechanism (plastic behaviour of bolts and development of two plastic hinges in the flange)[6].

*Corresponding author. Address: Department of Structural Engineering, Univer-sity of Naples ‘‘Federico II”, P.Le Tecchio 80, 80125 Naples, Italy. Tel.: +39 0817682444; fax: +39 081 5934792.

E-mail address:demattei@unina.it(G. De Matteis).

Contents lists available atScienceDirect

Computers and Structures

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Previous studies have already shown that for aluminium alloy T-stub joints the failure mechanism Type 2 is not so clearly deﬁned as for steel [7]. In such a case, as schematically represented in

Fig. 2, where the symbols Moand Borepresent the conventional

elastic flexural strength of the cross-section of the T-stub flange and the conventional yielding tensile strength of the bolt, respec-tively, two different collapse mechanisms can be recognised: the first one (mechanism Type 2a) is characterized by the attainment of the ultimate strain (

e

tf) in the ﬂange material; the second one

(mechanism Type 2b) is limited by the ultimate deformation (

e

tb)

obtained in the bolts. In the current paper, the analysis of the above collapse mechanisms has been carried out by means of a reﬁned numerical FEM model, which has been calibrated on the basis of the available experimental results and used in order to verify the correctness of the calculation procedure provided by EC9-Annex B[8].

2. The experimental research program

The behaviour of bolted aluminium alloy T-stub joints has been recently analysed within a wide experimental research project car-ried out at the University of Naples ‘‘Federico II”[9,10]. The tested

specimens (Fig. 3) have been obtained by using plates made of three different heat treated wrought aluminium alloys (AW 6061 – AW 6082 – AW 7020), whose mechanical characteristics are gi-ven in Fig. 4in terms of both engineering and true stress–strain curves.

The main elements of the joint (web and flange plates) have been firstly directly obtained from the base sheeting and then assembled among them by means of welded connections. The combination of flange and web elements arising from the three dif-ferent aluminium alloys allowed the definition of four basic geo-metrical configurations (by varying geogeo-metrical dimensions and number of bolts), each of them subdivided into three subgroups, obtained by varying the flange material, as shown inFig. 5. In addi-tion two different assemblage condiaddi-tions, namely coupling two T-stub specimens each other and joining a T-T-stub component with a rigid steel support, have been adopted (seeFig. 6). Then, aiming at investigating the influence of bolts on both stiffness and failure mechanism of aluminium T-stubs, two different configurations (one-bolt and two-bolt row) and three different materials (alumin-ium alloy AW 7075 and steel grades 4.8 and 10.9) have been con-sidered, in all cases adopting a diameter of 10 mm.

The obtained specimen conﬁgurations have been tested in monotonic and cyclic ways under displacement control; in partic-ular for the cyclic tests, the complete testing procedure provided

by ECCS Recommendations[11]has been applied.

A complete overview of both the main properties of tested T-stub specimens and the total number of performed tests are sum-marised inTable 1.

Type 1 Type 2a Type 2b Type 3

Q Fu u M M Q u F M Mu Bo u o M<M<M M Fu Q u Fu u B M Bo Bu Bu Bu

Fig. 2. Collapse mechanisms for aluminium T-stub joints according to EC9.

Fig. 3. The tested aluminium T-stub specimens.

Type 1

Type 2 Type 3

Q Q F_u.1 F_u.1 2 +Q Q Q F_u.2 Bu n m m n Bu F_u.3 Bu m m Bu Mu Mu Mu n m m n

m

M

F

_u_,₁

=

4

u

n

m

B

n

M

F

_u u u

+

=

2

∑

2 ,

F

u,3

=

∑

B

u

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3. The material characterization

In this section a survey of the experimental results on the mate-rials, which the analysed T-stub joints are made of (ﬂange and web elements, bolts and welds), is provided. The mechanical character-istics of the materials have been determined by tensile tests carried out on specimens directly extracted from T-stub assemblages

(Fig. 7a). Moreover, considering that T-stub specimens have been built-up by means of welded connections, the effect induced by the welding process on the mechanical properties of the material has been determined by means of detailed characterization of the heat affected zones (HAZ). The evaluation of the extension of such parts represents an important aspect to be considered in or-der to correctly account for the variation of the material strength AW 6061 0 50 100 150 200 250 300 350 400 450 500 0 2 4 6 8 10 12 14 16 18 20 (%) (N/mm2 ) engineering true stress-true strain

AW 6082 0 50 100 150 200 250 300 350 400 450 500 0 2 4 6 8 10 12 14 16 18 20 (%) (N/mm2 ) engineering true stress-true strain

AW 7020 0 50 100 150 200 250 300 350 400 0 2 4 6 8 10 12 14 16 18 20 (%) (N/mm2 ) engineering true stress-true strain

0 100 200 300 400 500 0 5 10 15 20 25 30 35 40 (%) (N/mm2 ) AW 6061 AW 6082 AW 7020

Fig. 4. Stress–strain curves for analysed aluminium alloys and related comparison.

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as a function of the distance from the weld[12]. To this purpose, tests on specimens located in different position of the T-assem-blage have been carried out (seeFig. 7a). Moreover, test specimens transversally oriented respect to the welded joint have been con-sidered as well. All the concon-sidered specimens, having the typical dog-bone conﬁguration, have been tested under uniaxial tensile loading by means of an universal tensile machine (MTS type) in or-der to determine their stress–strain relationships (Fig. 7b)[13].

Based on performed tensile tests, the main mechanical feature of the material, both in the longitudinal (Fig. 8a) and transversal (Fig. 8b) directions respect to the welding joints, have been deter-mined. For the sake of simplicity, the following test results are rep-resented in terms of average values of conventional elastic strengths (f0.1and f0.2) and of hardening ratio, the latter

character-ized by means of exponent (n) of the well known Ramberg–Osgood relationship[14].

Transversal tests have been made only for some specimens, belonging to different T-stub geometries. The obtained results are shown in Fig. 9, where the labels 1A, 2A, 3A, 1B, 2B, 3B, 1C, 2C and 3C refer to the T-stub typology (seeFig. 4) while the subse-quent digit (1 or 2) indicates the progressive identiﬁcation number for testing specimens of the same T-stub typology.

In the same figure, typical results of transversal tests are also gi-ven in terms of engineering curves, considering different T-stub configurations (in terms of base flange material) and welding typology (for T-stub type A). Similarly, typical results in terms of engineering stress–strain curves related to material tests of longi-tudinal specimens, differentiated into affected and unaffected material zones, are provided inFig. 10for every adopted alumin-ium alloys. Finally, the stress–strain curves of grade 4.8 steel and AA 7075 aluminium alloy bolts have been obtained as given inFigs. 11 and 12, where the average curves of the three specimens tested for each bolt type are depicted as well.

4. Numerical simulation of experimental tests 4.1. The FEM model

The correct numerical simulation of the response of bolted alu-minium alloy T-stub joints must taken into account the effect of different inﬂuential parameters, namely the actual stress–strain relationship of the material in the heat affected zones, the slip among the contact surfaces, the interaction between T-stub ﬂanges Fig. 6. Tensile tests on aluminium T-stubs: coupled specimens (a) and assemblage

with a rigid support (b).

Table 1

The experimental program on aluminium T-stub joints.

Geometry of specimens Flange materials Bolt classes Type of assemblage Type and number of test

Monotonic Ciclic

1 Type1A AW6061-T6 10.9 4.8 AW-7075 Rigid support 3 3

Type 1B AW 6082-T6 10.9 4.8 AW-7075 Rigid support 3 3

Type 1C AW 7020-T6 10.9 4.8 AW-7075 Rigid support 3 3

2–3 Type 2–3 A AW6061-T6 10.9 AW-7075 Rigid support 2 2

10.9 AW-7075 Coupled T-stub 2 2

Type 2–3 B AW6082-T6 10.9 AW-7075 Rigid support 2 2

Type 2–3 C AW 7020-T6 10.9 AW-7075 Rigid support 2 2

4 Type 4 AW6061-T6 10.9 4.8 AW-7075 Rigid support 3 3

5 Type 5 AW 6061-T6 4.8 AW-7075 Rigid support 2 2

Total 26 26 WEB 1 WEB 2 WEB 4 WEB 3 WEB 8 WEB 7 WEB 6 WEB 5 WEB 9 FL 1 FL 3 FL 5 FL 7 FL 4 FL 8 FL 6 FL 2

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and bolts and the possible contact interaction between the ﬂanges of coupled elements. The proposed numerical model, which has been implemented by means of the ABAQUS non linear numerical code[15]on the basis of the available experimental results, repre-sents an effective computational tool able to follow the evolution of the connection behaviour evidenced during monotonic tests. In the proposed FEM model, both the single T-stub and the rigid support have been modelled with solid hexahedral elements (type C3D8R), while tetrahedral elements have been used to represent the bolts. The basic components used for the implementation of the numerical model are schematised inFig. 13.

Based on the results of tensile tests on both longitudinal and transversal strips, the average stress–strain curves for each alu-minium alloy, taking into account the difference between heat af-fected and unafaf-fected zones, have been determined for flanges and webs. As an example,Figs. 14 and 15show the obtained average curves for web and flange elements of the T-stub type 1A1, respec-tively. It is worth noticing that despite the definition of the analyt-ical models for stress–strain relationships of materials could be based on the provisions of the current version of Eurocode 9, in or-der to achieve a better calibration of the applied FEM models, the material characteristics have been determined directly by test re-sults. Therefore, the obtained non-linear constitutive laws have been introduced in the ABAQUS model as multilinear true stress– true strain curves by using a Young modulus (E) of 70,000 N mm 2 and a Poisson ratio (

m

) equal to 0.3, in accordance with Eurocode 9.

For the model calibration, the interaction between contact sur-faces, based on the surface-to-surface contact simulation deﬁned in the ABAQUS library and appropriate preloading forces have been assigned to the bolts. The load condition has been given by impos-ing a vertical displacement to the points belongimpos-ing to the upper web surface, while the lower surface of the rigid support (or the lower web part, in case of coupled T-stubs) has been fully re-strained. The system response has been obtained by applying the modiﬁed Riks algorithm, which uses the Newton–Raphson proce-dure and belongs to the ‘‘arc-length” analysis method. Such an algorithm has been used in order to better follow the evolution of the joint response also after the attainment of the maximum strength (decreasing branch of the curve). A more detailed descrip-tion of the implemented numerical model is given in[16]. 4.2. The obtained numerical results

The implemented numerical model has been used to interpret the monotonic behaviour of several tested aluminium alloy T-stub joints. In the following, a selection of the obtained numerical re-sults is presented in details, aiming at evidencing the capability of the model to interpret correctly the behaviour of tested alumin-ium joints in relation to the different exhibited collapse mecha-nisms. In particular, for each T-stub joint, the deformations of some key points, namely the bolts (bolt), the ﬂange points corre-sponding to the bolt position (pl1) and the points belonging to Fig. 8. Testing specimens: longitudinal (a) and transversal (b) bar samples.

AW 6061-T6 0 50 100 150 200 250 300 350

1A1 1A2 2A1 3A1 3A2 3A3

N/mm 2 f_0.1 f_0.2 n AW 6082-T6 0 40 80 120 160 200 1B1 1B2 2B1 2B2 3B1 3B2 N/mm 2 f_0.1 f_0.2 n AW 7020-T6 0 40 80 120 160 200 1C1 1C2 2C1 2C2 3C1 3C2 N/mm 2 f f n 0.1 0.2 0 50 100 150 200 250 300 0 1 2 3 4 5 6 7 8 9 10 (%) (N/mm2₎ Type 1A Type 2-3A Type 1-2-3B Type 1-2-3C

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0 50 100 150 200 250 300 350 400 f f n f f n HAZ non-affected material TYPE 1B N/mm2

web (AW 7020-T6) flange (AW 6061-T6)

2 . 0 1 . 0 2 . 0 1 . 0 0 50 100 150 200 250 300 350 f f n f f n HAZ non-affected material TYPE 1C N/mm2

2 . 0 1 . 0 2 . 0 1 . 0 0 50 100 150 200 250 300 350 400 450 f f n f f n HAZ non-affected material TYPE 2A-3A N/mm2

2 . 0 1 . 0 2 . 0 1 . 0 0 50 100 150 200 250 300 350 400 f f n f f n HAZ non-affected materia l N/mm2 TYPE 2B-3B

2 . 0 1 . 0 2 . 0 1 . 0 0 50 100 150 200 250 300 350 400 f f n f f n HAZ non-affected material N/mm2 TYPE 2C-3C web (AW 6082-T6)

2 . 0 1 . 0 2 . 0 1 . 0 0 50 100 150 200 250 300 350 400 f f n f f n HAZ non-affected material N/mm2 TYPE 4-5

2 . 0 1 . 0 2 . 0 1 . 0

Fig. 10. Results of material tests on longitudinal specimens.

0 100 200 300 400 500 600 700 800 900 0.0% 2.0% 4.0% 6.0% 8.0% 10.0% (%) (N/mm2) first test second test third test average 0 100 200 300 400 500 600 700 800 0.0% 0.5% 1.0% 1.5% 2.0% 2.5% 3.0% 3.5% (%) (N/mm2) first test second test third test average

Fig. 12. Stress–strain tensile curves for grade 4.8 steel bolt (a) and AA 7075 aluminium bolt (b). AW 6082-T6 Type 2B 0 50 100 150 200 250 300 350 400 0 2 4 6 8 10 12 14 16 18 20 (%) (N/mm2 ) affected material unaffected material AW 6061-T6 Type 2A 0 50 100 150 200 250 300 350 400 0 2 4 6 8 10 12 14 16 18 20 (%) (N/mm2 ) affected material unaffected material AW 7020-T6 Type 2C 0 50 100 150 200 250 300 350 400 0 2 4 6 8 10 12 14 16 18 20 (%) (N/mm2 ) affected material unaffected material

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the web-to-ﬂange junction (pl2) have been monitored (see

Fig. 16c).

Fig. 16shows the numerical model for T-stub type 1A1, which is characterized by AW 7020 aluminium alloy web, AW alumin-ium alloy 6061 ﬂange and grade 4.8 steel bolts, together with the collapse mechanism exhibited by the tested specimen. Such a simulation, according to the experimental result, shows that the formation of plastic hinges occur at the web-to-ﬂange

con-nection, with plastic engagement of bolts and the attainment of the ultimate strain in the ﬂange, giving rise to a collapse mecha-nism type 2a. The correct numerical interpretation of the T-stub experimental behaviour is also evidenced by the comparison in terms of applied force (F)–maximum relative displacement (D) curve (Fig. 17a), as well as the strain (

e

) attained at the monitored points versus the maximum system displacement (D) (Fig. 17b), the latter emphasising the occurrence of maximum plastic

Fig. 13. Basic components of the adopted FEM model.

0 60 120 180 240 300 360 420 480 540 0 2 4 6 8 10 12 14 16 18 20 (%) (N/mm2₎ FL1 FL2 AVERAGE 0 50 100 150 200 250 300 350 400 0 2 4 6 8 10 12 14 16 18 20 ε (%) σ (N/mm2₎ FL3 FL4 FL5 FL6 FL7 FL8 AVERAGE f0.2 = 275 f0.2 = 300

Fig. 15. Stress–strain curves of heat affected (HAZ) (a) and unaffected (b) ﬂange zones (T-stub type 1A1).

pl1

pl2

bolt

_bolt

pl1

Fig. 16. T-sub type 1A1: experimental (a) and numerical (b) failure mechanism and monitored points during the analysis (c). 0 60 120 180 240 300 360 420 480 0 2 4 6 8 10 12 14 16 18 20 %) (N/mm2 ) WEB1 WEB2 AVERAGE 0 60 120 180 240 300 360 420 480 0 2 4 6 8 10 12 14 16 18 20 (%) (N/mm2₎ WEB3 WEB4 WEB5 WEB6 WEB7 WEB8 WEB9 AVERAGE f0.2 = 245 f0.2 = 290

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deformation in the T-stub ﬂange, according to the type 2a col-lapse mechanism.

Specimen type 1A2 is characterized by the use of AA7075 alu-minium alloy bolts, while AW 7020 alualu-minium alloy and AW 6061 aluminium alloy have been adopted for the web and for the

ﬂange, respectively. Tested specimen exhibited both the presence of plastic hinges at the web-to-ﬂange connection and the attain-ment of the ultimate strain in the bolts (Fig. 18a), determining a failure mechanism type 2b. The numerical model provides the same collapse mechanism evidenced during the experimental test,

pl1

pl2

bolt

_bolt

pl1

Fig. 18. T-stub type 1A2: experimental (a) and numerical (b) failure mechanism and monitored points during the analysis (c).

TYPE 1A2 0 10 20 30 40 50 60 70 80 90 0 0.5 1 1.5 2 2.5 3 (mm) F(kN) Experimental FEM 0% 1% 2% 3% 4% 5% 6% 7% (mm) (%) bolt pl1 pl2 0 0.5 1 1.5 2 2.5 3

Fig. 19. Specimen type 1A2: F–D (a) ande D (b) curves.

pl1

pl2

bolt

_bolt

pl1

Fig. 20. T-stub type 1A3: experimental (a) and numerical (b) failure mechanism and monitored points during the analysis (c). TYPE 1A1 0 10 20 30 40 50 60 70 80 90 0 1 2 3 4 5 6 7 8 9 10 11 (mm) F(kN) Experimental FEM 0% 1% 2% 3% 4% 5% 6% 7% 0 2 4 6 8 10 12 (mm) ( %) bolt pl2 pl1

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as shown inFigs. 18b and 19, where the stress state of the speci-men at the end of test and the evolution of the deformation of monitored points during the test are given. The very good agree-ment between experiagree-mental and numerical results is also apparent by examining the comparison in terms of F-Dcurves (seeFig. 19a). The T-stub type 1A3 is similar to the previous specimens, but grade 10.9 steel bolts have been applied. Plastic hinges occurring both at the web-to-ﬂange junction and the position corresponding to the bolt location (Fig. 20a) clearly show a failure mechanism type 1. The experimental–numerical comparison, in terms of deformed shape inFig. 20b, validates the proposed numerical mod-el, which is able to simulate both the mechanical response of the specimen (Fig. 21a) and the corresponding failure mode (Fig. 21b).

Figs. 22 and 23summarize the results related to the specimen type 4–1, which is characterized by ﬂange and web made of AW 6061 aluminium alloy and grade 4.8 steel bolts. The observed col-lapse mechanism, which is characterised by the attainment of the bolt failure without any plastic engagement of the ﬂange material (Fig. 22b), is representative of type 3. The good agreement between

experimental and numerical results is apparent, both in terms of deformed shape and mechanical behaviour of the specimen[17].

The results of additional numerical simulations related to many other T-stub typologies are synthetically depictedFig. 24, where the comparison with the experimental force (F)–displacement (D) curves is also illustrated. It is apparent that the proposed numerical model is able to correctly interpret the behaviour of all tested specimens in terms of resistance, stiffness and ductility, by accurately considering the effect of all evidenced inﬂuential parameters.

5. Application of the EC9 procedure

The analytical method stated in EC9[8]allows for the calcula-tion of the ultimate resistance of bolted aluminium alloy T-stub joints. In particular, starting from the deﬁnition of the effective width of the equivalent continuous beam, the plastic resistance of the effective cross-section is evaluated as a function of the ulti-mate ulti-material strength by means of a coefﬁcient (1/k), which takes

pl1

pl2

bolt

_bolt

pl1

Fig. 22. Specimen type 4-1: experimental (a) and numerical (b) failure mechanism.

TYPE 4-1 0 10 20 30 40 50 3.5 0 (mm) F(kN) Experimental FEM 0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 0 (mm) (%) pl2 bolt 4.5 4 3.5 3 2.5 2 1.5 1 0.5 3 2 2.5 1.5 1 0.5

Fig. 23. T-stub type 4-1: F–D (a) ande D (b) curves. TYPE 1A3 0 20 40 60 80 100 120 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 (mm) F(kN) Experimental FEM 0.0% 0.5% 1.0% 1.5% 2.0% 2.5% 3.0% 3.5% 4.0% 0 2 4 6 8 10 12 (mm) (%) fl HAZpl2 flpl1 \ \

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into account both the actual strain-hardening and the reduced ulti-mate deformation of the ulti-material. The calculation method – the so called ‘‘K-method”-, which is accurately described in[17], has been applied for estimating the ultimate strength of the different T-stub typologies under examination[18]. Such a method has been

ini-tially applied considering the nominal values of both ﬂange and bolts material resistance and the specimen geometry, together with the partial safety factors assumed in EC9. The obtained re-sults, which are related to specimens exhibiting collapse mecha-nisms type 1 and 2a only (those inﬂuenced by the assumption of

TYPE 1B1 0 20 40 60 80 100 120 0 1 2 3 4 5 6 7 8 9 10 (mm) F(kN) Experimental FEM TYPE 1B2 0 15 30 45 60 75 90 105 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 (mm) F(kN) Experimental FEM TYPE 1B3 0 20 40 60 80 100 120 140 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 (mm) F(kN) Experimental FEM TYPE 1C1 0 20 40 60 80 100 0 1 2 3 4 5 6 7 8 9 10 11 (mm) F(kN) Experimental FEM TYPE 1C2 0 20 40 60 80 100 0 0.25 0.5 0.75 1 1.25 1.5 (mm) F(kN) Experimental FEM TYPE 1C3 0 20 40 60 80 100 120 140 160 180 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 (mm) F(kN) Experimental FEM TYPE 2A1+2A5 0 20 40 60 80 100 120 140 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 (mm) F(kN) Experimental FEM TYPE 2A2 0 10 20 30 40 50 60 70 80 90 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 (mm) F(kN) Experimental FEM TYPE 2A3 0 20 40 60 80 100 120 140 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 (mm) F(kN) Experimental FEM TYPE 2A4+2A6 0 10 20 30 40 50 60 70 80 90 100 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 (mm) F(kN) Experimental FEM

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the effective width and the moment capacity of plastic hinges), show that the analytical method is signiﬁcantly conservative (see

Table 2).

In order to check the reliability of the codiﬁed procedure, the proposed analytical method has been subsequently applied by

con-sidering the actual values of both the geometry and the material resistance[19], without considering any partial safety factors and neglecting the reduction factors of bolt tensile strength provided by EC9 (0.9 and 0.6 for steel and aluminium bolts, respectively). In addition, as further comparison criterion, also the reduction of TYPE 2B1+2B6 0 20 40 60 80 100 120 140 160 0 0.5 1 1.5 2 2.5 3 3.5 4 (mm) F(kN) Experimental FEM TYPE 2B2 0 20 40 60 80 100 120 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 (mm) F(kN) Experimental FEM TYPE 2B3 0 30 60 90 120 150 180 0 0.5 1 1.5 2 2.5 3 3.5 (mm) F(kN) Experimental FEM TYPE 2B4+2B5 0 20 40 60 80 100 120 0 0.5 1 1.5 2 2.5 3 3.5 4 (mm) F(kN) Experimental FEM TYPE 2C1+2C6 0 20 40 60 80 100 120 140 160 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 (mm) F(kN) Experimental FEM TYPE 2C2 0 20 40 60 80 100 120 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 (mm) F(kN) Experimental FEM TYPE 2C3 0 30 60 90 120 150 180 0 0.5 1 1.5 2 2.5 3 3.5 4 (mm) F(kN) Experimental FEM TYPE 2C5+2C4 0 10 20 30 40 50 60 70 80 90 100 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 (mm) F(kN) Experimental FEM TYPE 4-2 0 10 20 30 40 50 60 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 (mm) F(kN) Experimental FEM TYPE 4-3 0 20 40 60 80 100 120 140 0 1 2 3 4 5 6 7 (mm) F(kN) Experimental FEM Fig. 24 (continued)

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internal plastic hinge length external plastic hinge length b m

Fig. 25. Inﬂuence factors for the application of the analytical method: (a) effect of the bolt head; (b) actual development of plastic lines for the evaluation of the effective width. TYPE 5-1 0 10 20 30 40 50 60 70 0 1 2 3 4 5 6 7 8 9 10 (mm) F(kN) Experimental FEM TYPE 5-2 0 10 20 30 40 50 60 0 0.25 0.5 0.75 1 1.25 1.5 (mm) F(kN) Experimental FEM Fig. 24 (continued) Table 2

Application of the EC9 method.

Test specimens Type of bolt Flange material Experimental results EC9 Results - Fu,Rd (kN)

Fu,k (kN) Mode Nominal value Effective value Effective value modiﬁed method

1A1 Steel 4.8 AW6061-T6 78 2’ 37.88 74.46 74.46

1A3 Steel 10.9 AW6061-T6 90 1 55.71 72.52 83.63

1B1 Steel 4.8 AW6082-T6 91 2’ 43.35 83.47 83.47

1B3 Steel 10.9 AW6082-T6 133 i 83.76 105.25 120.18

1C1 Steel 4.8 AW7020-T6 88 2’ 50.01 85.81 85.81

1C3 Steel 10.9 AW7020-T6 145 1 98.98 111.45 127.53

2A3 Steel 10.9 AW6061-T6 119 1 67.16 88.82 105.81

2B3 Steel 10.9 AW6082-T6 154 1 89.65 126.44 130.24

2C3 Steel 10.9 AW7020-T6 153 1 98.65 131.25 132.05

2A1 + 2A5 Steel 10.9 AW6061-T6 119 1 67.16 89.26 106.3

2B1 + 2B6 Steel 10.9 AW6082-T6 148 1 89.65 127.89 130.84 2C1 + 2C6 Steel 10.9 AW7020-T6 137 1 98.56 131.79 132.95 EC9(mm) FEM(mm) 1A3 76.8 82 1B3 80 89 1C3 82 104 2A3 81.4 86.4 2B3 80 86 2C3 82.2 87.2 2A1+2A5 81.8 86.8 2B1+2B6 81.6 86.6 2C1+2C6 81 86 1A1 80.2 93 1B1 82 91 1C1 81.4 94 T-stub type beff according to

0% 5% 10% 15% 20% 25% 30% 1A3 1B3 1C3 2A3 2B3 2C3 2A1+2A 5 2B1 +2B6 2C1 +2C 6 1A1 1B1 1C1 K-METHOD F.E.M.

(13)

the flexural effects in the flange due to the pressure applied by the bolts head (Fig. 25a), as already foreseen in the EC3 Part 1.8[5], has been considered (modified method). It is apparent how the scatter between analytical and experimental strength value is meaning-fully reduced, even if the codified method remains slightly conservative.

Finally, it is interesting to observe that in case of collapse mech-anisms type 1 and 2a the scatter can be significantly reduced by taking into account the actual T-stub effective width, the latter being strictly related to the patch of plastic lines which develops in complex way especially at the bolt location. The extension of such a zone can be evaluated by observing the results achieved through the proposed numerical model. The comparison between the codified (EC9) and the numerical (FEM) effective width values (beff) is provided inFig. 26. In the same figure, the percentage

scat-ter of the theoretical collapse loads of analysed T-stubs with re-spect to the experimental ones is plotted, considering both theoretical and numerical values of the effective width. In particu-lar, it can be noted that when considering the numerically evalu-ated effective width, the mean scatter is extremely limited (about 5%)[19].

6. Concluding remarks

A reﬁned numerical FEM model devoted to the evaluation of the monotonic response of bolted aluminium alloy T-stub connections has been proposed in this paper. The numerical model has been calibrated on the basis of several experimental tests concerning different types of aluminium t-stub joints, which were able to emphasise all the collapse modes of the analysed structural com-ponents due to the main inﬂuential factors. The comparison with test results has shown the accuracy of the proposed model, which is able to correctly reproduce the mechanical response of the joint even for large deformation levels, as well as to provide a correct interpretation of the related collapse mechanism.

The obtained results have also given a chance to provide a de-tailed comparison with the design method implemented in the present version of EC9. The ﬁndings underline the reliability of the codiﬁed procedure, which is always slightly conservative in the evaluation of the strength of aluminium T-stub joints. Finally, it has been observed that the EC9 design method could be still im-proved through a more precise evaluation of the effective width of the equivalent continuous beam schematising the structural behaviour of a T-sub joint. This seems to be an important research

ﬁeld that deserves further investigations for both steel and alumin-ium T-stubs.

References

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[8] EN 1999-1-1. Eurocode 9, design of aluminium structures – Part 1-1: general structural rules; version of February 2007.

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[11] ECCS Publication N.45. Recommended testing procedure for assessing the behaviour of structural steel elements under cyclic loads; 1986.

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[13] Recommendation Rilem Draft. Tension testing of metallic structural materials for determining stress–strain relations under monotonic and uniaxial tensile loading. Mater Struct 1990.

[14] Mazzolani FM. Aluminium alloy structures. London: E & FN SPON; 1996. [15] Hibbitt, Karlsson, Sorensen, Inc., ABAQUS/Standard, version 6.4, Patwtucket,

USA; 2004.

[16] Brescia, M. Experimental calibration of numerical models for bolted aluminium alloy T-stub joints. Graduation thesis, Supervisors: Prof. F.M. Mazzolani, Prof. G. De Matteis, Eng. A. Formisano, University of Naples ‘‘Federico II”, Engineering Faculty, June 2005 [in Italian].

[17] De Matteis G, Mandara A, Mazzolani FM. Calculation methods for aluminium T-stubs: a revision of EC3 Annex J. In: Proceedings of the 8th international conference on joints in aluminium (INALCO 2001), Fachgebiet Leichtmetallbau und Ermudung and Technische Universitat Munchen, Munich; March 2001. p. 6.2.1–12.

[18] De Matteis G, Mandara A, Mazzolani FM. Design of aluminium T-stub joints: calibration of analytical methods. In: Proceedings of the third European conference on steel structures, vol. II. Coimbra; September 2002. p. 1017–26. [19] De Matteis G, Brescia M, Formisano A, Mazzolani FM. Numerical analysis of aluminium alloy welded T-stub joints. In: Proceedings of the XX C.T.A. Italian congress. Ischia: ACS ACAI SERVIZI Srl Publisher; 2005. p. 369–76.