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Mechanical behaviour of bolt-channel joining technology for aluminium structures
Construction and Building Materials 73 (2014) 76–88
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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Mechanical behaviour of bolt-channel joining technology for aluminium structures Luigi Fiorino, Vincenzo Macillo, Federico Massimo Mazzolani ⇑ Department of Structures for Engineering and Architecture, University of Naples ‘‘Federico II’’, Naples, Italy
h i g h l i g h t s The extrusion process allows to conceive more rational connections: special joints. Bolt-channel joints consist in an extruded track where the bolt can be located. These joints are very competitive with respect to the traditional joining systems. Experimental tests aimed at investigating joint behaviour has been carried out. On the basis of experimental results, FEM models have been developed and calibrated.
a r t i c l e
i n f o
Article history: Received 24 February 2014 Received in revised form 15 September 2014 Accepted 25 September 2014
Keywords: Aluminium Bolt-channel Experimental tests Joining technologies Numerical modelling
a b s t r a c t The wide choice of cross-sectional shapes obtainable by extrusion process provides the possibility to individuate new joining solutions for aluminium profiles. The achievable joining technologies are very competitive with respect to conventional solutions, because of the possibility of rapid execution, optimization of parent material, treatments and machining reduction. For these reasons, the aluminium industry is very interested to enhance the knowledge about the structural behaviour of these joint systems. Bolt channel joints are one of the possible technologies that entail the advantage of the extrusion shapes for joining aluminium elements. The system consists of a track or channel section profile where a bolt head, nuts or plates with threaded holes can be located. Bolt-channel joints are commonly used in building applications and in transportation structures. Nevertheless, very little literature is available for this system and no specifications are provided by aluminium structural codes. In order to evaluate the structural behaviour of bolt-channel joints, an experimental campaign has been carried out at University ‘‘Federico II’’ of Naples. Two different cross-sections corresponding to different bolt diameters have been selected and three different load directions have been considered. The obtained experimental results have been used for the calibration of non-linear numerical models. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction The profiles for aluminium structures are usually obtained by means of extrusion process that, as well-known, allows many possibilities of cross-sectional shapes. In particular, extruded shapes can be customized according to the different possible uses by incorporating essential design features, such as stiffener, rib, bulbs, slots and tracks. These features can be exploited to conceive, in a more rational way, connection technologies to join together
⇑ Corresponding author at: Department of Structures for Engineering and Architecture, University of Naples ‘‘Federico II’’, University of Naples ‘‘Federico II’’, p.le Tecchio, 80 – 80125 Naples Italy. Tel.: +39 081 7682443; fax: +39 081 419215. E-mail addresses: lfi[email protected] (L. Fiorino), [email protected] (V. Macillo), [email protected] (F.M. Mazzolani). http://dx.doi.org/10.1016/j.conbuildmat.2014.09.086 0950-0618/Ó 2014 Elsevier Ltd. All rights reserved.
aluminium profiles. The achievable joining methods are various and they may or may not involve the use of fasteners. These systems are generally known as ‘‘special joints’’ or ‘‘non-conventional joints’’ for aluminium extrusions. Typical special joints consist in tracks and slots obtained in the extruded shapes, in which mechanical fasteners, such as bolts and screws, can be located. The high competitiveness of these joining technologies is related to the ease and rapidity of assembly, machining reduction, optimization and saving of the parent material with a consequent cost reduction. These joint typologies are commonly used in many structural applications not only in building and civil engineering, but also in transportation industry. Typical applications in buildings are door and windows frames, photovoltaic support systems, staircases, shelves and industrial furniture. The possibility to use these joints in structural applications, even if under moderate loads,
L. Fiorino et al. / Construction and Building Materials 73 (2014) 76–88
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Fig. 1. Bolt-channel joint [4].
Fig. 2. T-slotted profile system [5].
Fig. 3. The ‘‘Loblolly House’’ [6].
requires their design calculation and verification. Nevertheless very little information for the design of special joints is provided by aluminium structural codes and few researches are available on this topic. Therefore, now-a-day the design assisted by tests procedure represents the only way to evaluate the joint strength.
As an attempt to overcome this lack of information, a research about the mechanical behaviour of special joints [1] was undertaken at University of Naples ‘‘Federico II’’ with the financial support of METRA S.p.A. In order to define the main issues related to the joint geometry, the influence of load type and the joint
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L. Fiorino et al. / Construction and Building Materials 73 (2014) 76–88
Fig. 4. The ‘‘Cellophane House’’ [7].
structural response, an extended study on screw ports [2] and boltchannel [3] joints has been carried out by means of experimental tests and numerical modelling. The present paper shows the activity carried out on bolt-channel joints. 2. Bolt-channel joints
g z
C/ 2
2.1. Joint description and applications The Bolt-Channel (BC) joint system consists in an extruded section with a track, where the head or nut of bolt is located for connecting the profile to the other joint components (Fig. 1). This joining technique allows to set the bolts anywhere along the profile length without any machining, with the possibility of ease relocation by moving the bolt head along the track [4]. In the case of joints with more bolts disposed at a given distance, a plate with threaded holes can be introduced in the track defining the bolt position. In general, plates with threaded holes can be located into the channel and used as nuts. As an alternative solution, special bolt or nuts can be used. For instance, T-bolts has the advantage to be installed directly in the given position without the need to slide it from the end of the profile, or rhombus nuts that, after turning, result self-locked inside the channel. A typical use of BC joints is the T-slot profile system, which consists in a semi-hollow extruded profile having, at each side, one or more slots for special bolt heads or nuts. These profiles can be joined together all along their length by introducing simple elements, such as angle and gusset plates (Fig. 2). The result is a versatile modular system, which can be used in any type of frame structure, such as industrial furniture, shelves, windows frames and support structures for solar panel plants [5]. T-slot system has been used in two fascinating, creative and innovative buildings designed by the architecture firm KieranTimberlake: the ‘‘Loblolly House’’ [6] and the ‘‘Cellophane House’’ [7]. The first building (Fig. 3) is a single family dwelling positioned in a dense grove of loblolly pines, from which the house takes the name. The ‘‘Loblolly’’ house has two storeys and it is raised from the ground by means of wooden piles. It is composed by two different blocks connected by a glazed bridge. The ‘‘Cellophane House’’ (Fig. 4) is a five storeys building, which was located in New York City for a threemonth exhibition and the onsite erection needed only sixteen days.
x
b tlat
w
y
w g
Top flanges
tsup Webs
tlat
h
Bottom flange tinf
Fig. 5. Assumed symbols for bolt-channel joints.
Both buildings are completely off-site fabricated, eco-sustainable and the main structure is obtained by using only aluminium T-slot profiles. The great advantage of these two innovative buildings lies on the full reversibility of the adopted connections, that allow to disassembly and reuse the structure in very easy and fast way. 2.2. State-of-the-art Although there are various possibilities of structural applications obtainable with BC joints, there is very little information Table 1 Range of validity of bolt-channel joint. Bolt diameter
Sapa – CNR/DT 208 w (mm)
h (mm)
g (mm)
w (mm)
Hydro h (mm)
g (mm)
M4 M5 M6 M8 M10 M12 M14 M16
7.3 ± 0.15 8.3 ± 0.15 10.3 ± 0.20 13.4 ± 0.20 16.5 ± 0.20 18.5 ± 0.20 21.7 ± 0.20 24.7 ± 0.20
4.0 5.5 6.0 8.0 9.5 12.5 14.0 16.0
4.4 5.4 6.4 8.5 10.7 12.7 15.0 17.0
7.4 8.4 10.5 13.5 17.5 19.5 22.6 24.6
4.0 4.5 5.0 7.0 8.5 9.5 10.5 11.5
4.5 5.5 6.5 8.5 11.0 13.0 15.0 17.0
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L. Fiorino et al. / Construction and Building Materials 73 (2014) 76–88 Table 3 Aluminium alloys tests results.
M10 Specimen
Material
E (MPa)
f0.2 (MPa)
fu (MPa)
eu (%)
np
AW 6005A-T6
63963
235
279
10
23
M18 Specimen
Fig. 6. Bolt-Channel specimens.
Fig. 7. Steel plate nut dimensions.
PO
SL Fig. 9. Set-up and instrumentation for SL tests.
SH Table 4 Experimental results of SL tests. Series label
Fig. 8. Test load directions.
BC-SL-10 BC-SL-18A BC-SL-18B
about their mechanical behaviour and design rules. In literature, a study on this topic was conducted by Hellgren [8], who performed 247 tests on joints. The experimentation focused on the configuration in which the bolt head is place in the aluminium channel. The used aluminium profiles, with a channel suitable for M8 bolts, were made of AW 6063-T6 alloy. The influence of bolt head shape was investigated by considering stainless steel metric bolts with hexagonal head and special designed T-bolt. The joints were tested under three different load directions: a force parallel along the channel, a shear transversal force and a pull-out action. In addition, the influence of web channel thickness (1.0, 2.0 and 3.0 mm) in Table 2 Test program for BC joints. Series label
Load Bolt direction diameter (mm)
Tightening torque (Nm)
Preloading force (kN)
n. test
BC-SL-10 BC-SL-18A BC-SL-18B BC-SH-10 BC-SH-18 BC-PO-10 BC-PO-18
Slip Slip Slip Shear Shear Pull-out Pull-out
40 93 60 40 100 – –
20 26 17 28
6 4 4 3 3 3 3 26
M10 M18 M18 M10 M18 M10 M18
Total n. of tests:
Fslip
k (kN/mm)
Average (kN)
Standard deviation (kN)
C.o.V.
4.77 7.02 6.88
0.94 0.97 1.67
0.20 0.14 0.24
31.9 37.3 34.5
pull-out tests was investigated. As final results, on the basis of the experimental findings, empirical design formulae for ultimate strength prediction was proposed. Main design codes for aluminium structures, such as Eurocode 9 [9], do not provide any information for these joints. In particular, for joining methods not covered by the standard, it is specified that their use is permitted only if appropriate experimental tests are carried out (design assisted by tests). A recent document providing some design formulations for BC joints is the Italian Recommendations for Aluminium Structures (CNR-DT 208/2011) [10], in which some innovative features are introduced, such as special joints design. Design formulations for special joints together with information as suggested dimensions for aluminium parts are also provided in the Design Manual published by Sapa [4]. This document deals with different joining possibilities, including BC joints.
2.3. Available formulations for strength prediction Presently, few design formulations are available for the prediction of the BC joints strength. These formulations are generally derived from experimental results and their validity is strictly related to the investigated geometries. For this reason, standards
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Fig. 10. Deformed configuration after SL tests.
and design manuals always provides the design formulations together with their range of validity. In particular, design formulations are only available for the joint configuration with the bolt head in the channel. The Design Manual by Sapa provides the bolt track dimensions (Fig. 5) representing the range of validity of the proposed design formulations. This range of validity, adopted also by CNR-DT208, is reported in Table 1 together with the one proposed by Hydro [11]. The joint strength for force acting in parallel direction to the channel, which produces the slipping of bolts or plate inside the channel, can be calculated, according to Sapa [4] and Hellgren [8], through the following equation:
F x;Rd ¼ 200
Fig. 12. Material removal in SL test specimens.
F y;Rd ¼
F y;Rd ¼
Mv
nl F cM2 p;Cd
ð2Þ
where n is the number of friction interfaces, l is the friction coefficient and Fp,Cd is the bolt preloading force. The strength of BC joint subjected to transversal shear force can be calculated by the following formulations provided by Hellgren and CNR DT-208, respectively:
16
16
F [kN]
12
12
8
8
1:2btlat f u
Fslip,av =4.77 kN
16
F [kN]
#
12
4
*
2
4
6
(a) BC-SL-10
8
10
Fslip,av =6.88 kN
4
d [mm] 0
0
F [kN]
8
d [mm] 0
ð4Þ
cM3
Fslip,av =7.02 kN 4
ð3Þ
where fu is the ultimate strength of the aluminium channel, tinf is the thickness of lower flange of the channel, tlat is the webs thickness of the channel, b is the contact length between the web of the channel and the bolt head (Fig. 5), cM2 and cM3 are the partial safety factor assumed equal to 1.25 and 1.50, respectively. It has to be noticed that the two formulations have a very similar structure, both depend on the contact length of bolt inside the channel, but Hellgren formulation considers that failure occurs on lower flange (tinf), while according to CNR DT-208 it does in the web (tlat). For this loading direction, Sapa suggests to evaluate the strength as 70% of the values determined for a traditional bolted joint subjected to shear. Formulations for the pull-out strength of BC joint are provided by Hellgren and Sapa, respectively, as follows:
where Mv is the bolt torque in Nm and cM2 is the partial safety factor assumed equal to 1.25. On the other hand, CNR-DT 208 [10] recommends to evaluate this strength as well as a common bolted slip resistant joint by applying a partial safety factor cM3 equal to 1.50, as follows:
F x;Rd ¼
pffiffiffi 2f u tinf b 1:2cM2
ð1Þ
cM2
(b) BC-SL-18A-04 (curve # in Fig. 11b)
(a) BC-SL-18A-02 (curve * in Fig. 11b)
d [mm] 0
0
2
4
6
8
10
(b) BC-SL-18A Fig. 11. Experimental curves of SL tests.
0
2
4
6
(c) BC-SL-18B
8
10
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L. Fiorino et al. / Construction and Building Materials 73 (2014) 76–88
Fig. 13. Set-up and instrumentation for SH tests.
Table 5 Experimental results of SH tests. Series label
BC-SH-10 BC-SH-18
Fmax Average (kN)
Standard deviation (kN)
C.o.V.
20.8 49.3
0.60 1.83
0.03 0.04
k (kN/mm)
Failure mode
20.4 8.32
BF W
BF: Failure occurred in channel bottom flange. W: Failure occurred in channel web.
Crack development
Fig. 14. Failure mechanism in BC-SH-10 series.
Fig. 15. Failure mechanism in BC-SH-18 series.
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L. Fiorino et al. / Construction and Building Materials 73 (2014) 76–88
60
60
F [kN]
50
50
40
40
F [kN]
Fmax,av =49.3 kN
30
30
Fmax,av =20.8 kN
20
20 10
10
d [mm]
d [mm] 0
0 0
10
20
30
0
10
20
30
(b) BC-SH-18
(a) BC-SH-10 Fig. 16. Experimental curves of SL tests.
where tsup is the thickness of upper flanges of the channel, C is the bolt head perimeter in contact with upper flanges of the channel, g is the width of channel opening (Fig. 5). Both formulations consider as possible failure mode the shearing of channel web by the bolt head. Both formulations are adopted by CNR-DT 208/2011, by assuming the partial safety factor cM3 and suggesting the use of Eq. (6) because it provides more conservative strength values. 3. Experimental tests 3.1. Test program
Fig. 17. Deformed configuration of SH tests.
f t sup C F z;Rd ¼ puffiffiffi 3cM2
F z;Rd ¼ 1:2
gtsup f u
cM2
ð5Þ
ð6Þ
The experimental program is aimed at investigating the structural response of BC joint systems. The main objective is to define the influence of the extruded channel geometry, the bolt diameter and the direction of loads. The tested BC joints are made by locating a steel plate with a threaded hole located in the aluminium channel. Practically, the holed plates are named plate nuts because they behave as a bolt nut. No information, tests results and design rules are, presently, available for this joint configuration. Two extruded AW 6005A-T6 aluminium channels (Fig. 6), suitable for M10 and M18 bolt diameters, have been selected as a part of commercial profiles to obtain the BC specimens. The bolts used were 8.8 steel grade, while plate nuts are made of S355 steel. The dimensions of plate nuts are depicted in Fig. 7. In order to take into account the possible loading conditions that can occur in the different applications of BC joints, three different load directions are considered (Fig. 8). The first load direction (SL tests) consists in a force parallel to the track that
Fig. 18. Set-up and instrumentation for PO tests.
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L. Fiorino et al. / Construction and Building Materials 73 (2014) 76–88 Table 6 Experimental results of PO tests. Series label
BC-PO-10 BC-PO-18
Fmax Average (kN)
Standard devation (kN)
C.o.V.
33.3 42.8
0.33 2.93
0.01 0.07
k (kN/mm)
Failure mode
21.1 25.5
PO TF
PO: Pull-out of threaded bar. TF: Failure occurred in channel top flange.
Table 7 Comparison between predicted and experimental slip strength for BC joints. Series
Exp. (kN)
BC-SL-10 BC-SL-18A BC-SL-18A
4.77 7.02 6.88
Hellgren/Sapa (1)
CNR-DT 208 (2)
Pred. (kN)
Pred./exp.
Pred. (kN)
Pred./exp.
8.00 12.0 18.6
1.68 1.74 2.65
6.00 5.00 7.75
1.26 0.73 1.10
evaluate the effects of bolt preload, two values of tightening torques are used for M18 specimens. The second load direction (SH tests) is a transversal force perpendicular to the channel axis, which brings the plate nut in contact with the channel web. The third load direction (PO tests) consists in a tension force that tends to pullout the plate nut from the aluminium channel. All the tests are performed by using the universal test machine MTS 810 in displacement control with a loading rate of 0.02 mm/s and the data are recorded with a frequency of 10 Hz. The whole test program, including 26 tests (14 for SL tests, 6 for SH tests and 6 for PO tests), is summarised in Table 2, where the different parameters under investigation are given for each specimen series. The series label defines the specimen typology. Namely, the first group of characters (BC) means bolt-channel, the second group represents the loading direction (SL: slip, PO: pull-out and SH: shear), the third group of digits indentifies the bolt diameter (10 or 18 mm) and the final character (A or B) distinguishes the equal specimens with different tightening torque.
Fig. 19. Failure mechanism in BC-PO-10 series.
3.2. Material tests In order to characterize the mechanical properties of the materials, tensile tests are performed according to ISO 6892-1 [12]. In particular, two tests on 4 mm thick specimens made of AW 6005A-T6 alloy are performed. Test results are summarised in Table 3, where the average values of Young’s modulus (E), 0.2% proof stress (f0.2), ultimate strength (fu), ultimate strain (eu) and the exponent of the Ramberg–Osgood law (np) are shown. The obtained average value of the Young’s modulus is 63,966 MPa; the 0.2% proof stress and the ultimate strength are on the average equal to 235 and 279 MPa, respectively. 3.3. Slip tests
Fig. 20. Failure mechanism in BC-PO-18 series.
induces a slipping of bolt and plate nut along the aluminium channel. Three SL series are tested, one for M10 specimens and two for M18 specimens; in order to
50
The specimens for SL tests consist of 75 mm and 100 mm long aluminium channels for M10 and M18 configurations, respectively. Inside the channel, the plate nut is located at a depth of 5 mm with respect to the top edge. The M10 specimens are tightened with a torque of 40 Nm, which corresponds to 60% of the maximum preloading force (20 kN). In the case of M18 specimens, two different torque values, 60 and 93 Nm, are considered. These values correspond to 25% (26 kN) and 15% (17 kN) of maximum preloading, respectively. The used torque values are assumed to limit the excessive deformation of the aluminium parts induced by tightening operation in the small thickness elements of the aluminium channel.
50
F [kN]
40
F [kN]
Fmax,av =42.8 kN
40
Fmax,av =33.3 kN
30
30
20
20 10
10
d [mm]
d [mm] 0
0 0
3
6
9
(a) BC-PO-10
12
15
0
3
6
9
(b) BC-PO-18
Fig. 21. Experimental curves of SL tests.
12
15
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Table 8 Comparison between predicted and experimental shear strength for BC joints. Series
Exp. (kN)
BC-SH-10 BC-SH-18
20.8 49.3
Hellgren (3)
CNR-DT 208 (4)
Pred. (kN)
Pred./exp.
Pred. (kN)
Pred./exp.
Pred. (kN)
Pred./exp.
46.0 78.9
2.21 1.60
69.0 78.9
3.32 1.60
19.5 35.2
0.94 0.71
Table 9 Comparison between predicted and experimental pull-out strength for BC joints. Series
Exp. (kN)
BC-PO-10 BC-PO-18
33.3 42.8
Sapa
Hellgren (5)
Bc: Ux=Uy=0 Applied uniform displacement
Sapa (6)
Pred. (kN)
Pred./exp.
Pred. (kN)
Pred./exp.
66.0 85.1
1.98 1.99
18.4 26.8
0.55 0.63
Symmetry Plane (Ux=URy=URz=0)
Ux=Uy=0
Bolt Preload: 15 KN
Ux=Uy=Uz=0
Bc: Ux=Uy=Uz=0 The specimen is placed on a steel plate at the bottom and the compression load to the plate nut is applied by means of a steel flat plate clamped in the top wedge grip of the testing machine. The displacement of the plate nut is measured by means of a linear variable differential transducer (LVDT) (Fig. 9). The results of slip joint tests are summarised in Table 4, where the values of the average, the standard deviation and the coefficient of variation of slip strength (Fslip) together with the average stiffness (k) are given. The slip strength of the joint is assumed as the first peak or the plateau of the experimental curve depending on its shape, while the joint stiffness (k) is the slope of the first significant linear portion on the experimental curve. The observed failure mechanism is always due to large slipping of bolt inside the aluminium channel, as shown in Fig. 10. Fig. 11 shows the experimental results in terms of load vs. displacement (F–d) curves. By comparing the results of the BC-SL-10 specimens with the BC-SL-18B ones, which are characterized by similar values of preloading force, it can be observed an increase of strength of about 44% with the variation of bolt diameter from 10 to 18 mm. For M18 specimens (BC-SL-18A and B), the variation of 55% of tightening torque implies a very small increase (2%) in terms of average strength. Then, in the examined cases, the level of torque does not significantly influence the joint response. In addition, it has to be noticed that the results are quite scattered with coefficient of variation ranging from 14% to 24%. These findings can be explained by the joint sensitivity to the assembly imperfections. These imperfections consist in a non perfectly axis alignment between the channel and the plate nuts because of the tightening, which tends to rotate the plate nut entailing unforeseen contacts inside the channel influencing the response. In addition, the tightening operation can cause local permanent deformations of top flanges of the aluminium channel due to the squashing of bolt washer and/or of the plate nuts. These deformations imply a marked material removal during the test sliding, that evidently influences the joint slip strength, as shown in Fig. 12. In fact, it can be observed that the specimen in BC-SL-18A-02 (Fig. 12a), which does not present evident material removal, exhibited a lower slip strength (curve * in Fig. 11b) with respect to the specimen BC-SL-18A-04 (curve # in Fig. 11b), that shows a marked removal of material on both internal and external face of channel top flanges (Fig. 12b) 3.4. Shear tests The test specimens and set-up for SH tests of bolt-channel are designed with the aim to reproduce the transversal load transfer and to avoid unwanted or non significant mechanisms. The specimens consist in aluminium channels with length of 250 mm and 400 mm for M10 and M18 configurations, respectively. The connection under investigation (tested connection) is located in the middle of the aluminium channel and the shear load is applied by using a holed plate clamped the top wedge grip. The aluminium channel ends are connected to a U-shaped steel plate, clamped to the bottom wedge grip of the testing machine. The connections at the ends of the channel are designed to be oversized with respect to the tested ones. All the set-up plates are made of S355 steel grade and their thickness is defined in order to avoid the bearing failure. The bolts are tightened with a torque of 40 and 100 Nm for M10 and M18 specimens, respectively. The displacements of the tested connection are measured by means of a LVDT placed on bolt head and two additional LVDTs are disposed at the channel ends to measure the displacement of the oversized connections (Fig. 13).
y z
x
Fig. 22. Model geometry and boundary conditions for the SH model.
Table 5 summarises the results of SH tests on BC joints. In this table, for each specimen series the parameters defining the structural behaviour together with the observed failure mechanism are provided. In particular, the values of the average, the standard deviation and the coefficient of variation of strength (Fmax) and the average value of stiffness (k) are given. The strength is assumed as peak load of the experimental curve, while the stiffness has been evaluated as the slope of the first significant linear portion on the experimental curve. The failure mechanism of the BC-SH-10 series consists in a crack development in the aluminium channel at the bottom flange close to the corner with the web (Fig. 14). The specimens present also an evident deformation of top flange and web on the loaded side, while the bolts and the plate nut do not appear significantly deformed. In the case of the BC-SH-18 series a crack develops from the top flange on the loaded side to all the web depth and along the intersection between the web and the bottom flange, as shown in Fig. 15. Also in this case no evident deformations in bolt and plate nut occur. Fig. 16 shows the experimental results in terms of load vs. displacement (F–d) curves. The experimental curves exhibit a sudden slope change in the load range from 5 to 10 kN for BC-SH-10 specimens and in the range between 10 and 15 kN for BC-SH-18 ones. This can be ascribed to the sliding due to the clearance between the plate nut and the aluminium channel as well as between the hole of the set-up plate and the bolt. It can be also observed that the two investigated configurations show a great variation in terms of deformation capacity. In terms of strength, an increase of 137% from BC-SH-10 to BC-SH-18 is observed. On the contrary, BC-SH-10 specimens resulted 2.5 times stiffer than BC-SH-18 ones. This result, consisting in a stiffer response of the joint with the smaller bolt, can seem counterintuitive, but it is justified by the poor rational geometry of the BC-10 cross-section, which has stiffer webs with respect to the BC-18 one (Fig. 6). In addition, the strength values for both series are very little scattered with coefficient of variation lower than 4%. The low scattered values demonstrate that, for the investigated cases, the shear strength of bolt-channel joint is not affected by assembly imperfections. The low sensitivity to imperfections is also confirmed by the symmetrical global response up to the failure (Fig. 17).
3.5. Pull-out tests The specimens for PO tests are 200 mm long aluminium channels for both M10 and M18 configuration. The test set-up consists of a T-shaped element, made of S355 steel grade, which is clamped to the bottom wedge grip of the testing machine. The aluminium specimen is fixed to the steel element by means of 4 M10 bolts of 12.9 grade, placed inside the channel. The tested connection is located in the middle of the aluminium channel and it consists in a plate nut tightened with a 180 mm long threaded bar. The other end of the bar is installed in a 20 mm thick plate pulled by means of a steel holder clamped in top wedge grip of the testing
Table 10 Assumed steel material properties. Material
True yield stress (MPa)
True ultimate stress (MPa)
True ultimate plastic strain
Model parts
8.8 Grade S355
642 356
896 622
0.11 0.22
Bolts Plate nut, set-up system
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L. Fiorino et al. / Construction and Building Materials 73 (2014) 76–88
60
Bc: Ux=Uy=0 kz=900 kN/mm
F [kN]
50 40
y z
x
30 20
Symmetry Plane (Ux=URy=URz=0)
Coarse Intermediate Fine
10
d [mm]
Applied uniform displacement
0 0
10
20
30
Fig. 23. Model geometry and boundary conditions for PO model. Fig. 26. Mesh sensitivity analysis results for SH model.
Perfect
Imp. 0.25 mm
Imp. 0.50 mm
Imp. 1.00 mm
Fig. 24. Imperfection calibration models.
machine. The displacements are measured through a LVDT placed between the holder and the T-shaped element (Fig. 18). In Table 6, the values of the average, the standard deviation and the coefficient of variation of strength (Fmax) and the average value of stiffness (k), together with the observed failure mechanisms are provided for each specimen series. The strength is assumed as peak load of the experimental curve, while the stiffness has been evaluated as the slope of the first significant linear portion on the experimental curve. For all the BC-PO-10 specimens, the observed failure corresponds to the pullout of threaded bar from the plate nut with shearing of both nut and bar threads. In correspondence to the failure, the plate nut results strongly deformed and a crack develops along one of the top flanges of the aluminium channel (Fig. 19). The observed failure mechanism of BC-PO-18 series consists in a crack occurred at the one of top flanges, which tends to propagate along the web. In this case threaded bar and plate nut do not present significant deformations (Fig. 20). It has to be noticed that the response of both series is strongly non symmetrical and it is probably due to assembly imperfection. In fact, the plate nut tends to rotate in the channel because of tightening operation and, due to the clearance, it is not
Coarse (2.5-5.0 mm)
Coarse (3.0-6.0 mm)
perfectly centred in the channel. This could explain the development of cracks on only one side of the channel. The experimental results in terms of load vs. displacement (F–d) curves are shown in Fig. 21. It can be observed that the BC-PO-10 series shows a slightly higher deformation capacity with respect to BC-PO-18. The response BC-PO-18 is, in average, 29% and 21% greater than BC-PO-10 in terms of strength and stiffness, respectively. Despite the fact that the joint response is, markedly non symmetrical, for both series, the strength values for both series are little scattered with coefficient of variation lower than 7%. As a consequence, it would seem that the influence of assembly imperfections is evident in joint deformed configuration, but it does not affect the coefficient of variation of the strength.
3.6. Experimental vs. predicted strength The strength values of obtained by experimental tests on BC joints are compared to those estimated through the available prediction formulations, illustrated in Section 2.3. In order to correctly compare the experimental values with the theoretically predicted ones, the formulations are applied by considering the aluminium strength obtained by tests (Section 3.2) and by assuming the safety factors equal to 1. The values obtained by the formulation proposed by Hellgren and Sapa and the one of CNR-DT 208 are compared with the experimental results in Table 7. In case of the CNR-DT 208 formulation the bolt preloading force has been evaluated calculating as follows:
F p;Cd ¼ 0:2M v d
ð7Þ
where Mv is the applied tightening torque and d is the bolt diameter.
Intermediate (2.0-4.0 mm)
Intermediate (2.0-4.0 mm)
Fine (1.0-2.0 mm)
Fine (1.0-2.0 mm)
Fig. 25. Assumed mesh sizes for SH and PO model in sensitivity analysis.
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L. Fiorino et al. / Construction and Building Materials 73 (2014) 76–88
60
60
F [kN]
F [kN]
50
50
40
40
30
30
Coarse Intermediate Fine
20 10
20 10
d [mm]
d [mm]
0
0 0
2
4
6
8
0
2
4
6
8
Experimental Numerical perfect model Numerical - imp. 0.25 mm Numerical - imp 0.50 mm Numerical - imp. 1.00 mm
Fig. 27. Mesh sensitivity analysis results for PO model.
60
F [kN]
Fig. 30. Experimental vs numerical response curves for PO model.
50 40 30 20 Numerical Experimental
10
d [mm]
0 0
10
20
30
Fig. 28. Experimental vs. numerical response curves for SH model.
Table 11 Comparison between numerical and experimental results for SH model.
Numerical Experimental Num/Exp
Fmax (kN)
k (kN/mm)
49.7 49.3 +1%
7.51 8.32 10%
It has to be noticed that the formulation proposed by Hellgren, in the examined cases, strongly overestimates the strength with differences ranging from 68% to 165%. On the other hand, CNR-DT 208 provides a better estimation of the joint strength with differences ranging from 10% to 27%. As far as shear strength is concerned, the results obtained by applying the formulation provided by Hellgren and CNR-DT 208 together the Sapa’s indications are summarised in Table 8. The results show that both Hellgren and CNR-DT 208 formulations give higher values than experimental ones with errors in the range from 60% to 232%. Sapa’s indications to evaluate the strength as 70% of the one evaluated for a common bolted joint is, for the examined case, quite conservative with differences ranging from 6% to 29%. Table 9 shows the prediction of bolt-channel pull-out strength according to the formulation suggested by Hellgren and Sapa. The comparison of predicted values with experimental ones shows that the strength obtained with Hellgren formulation is about 2 times the experimental values. Contrary, Sapa formulation strongly underestimates the strength with scatters of up to 45%. As general remark, the available formulations are calibrated on the basis of experimental tests carried out on a joint configuration different to this tested in this work. This difference could explain the great divergence between predicted and experimental values. In addition, the formulations that well approximate the experimental results are the Eq. (2) given in CNR-DT 208 for slip strength and the Sapa’s indication for shear strength. Both formulations are not calibrated on tests results, but they are based on design rules for traditional bolted joints.
4. Numerical modelling 4.1. Model assumptions
Fig. 29. Deformed configuration at failure for SH model.
Two models representative of BC joint under transversal shear (SH model) and pull-out force (PO model) have been calibrated, on the basis of experimental results. Both models are implemented by means of the ABAQUS 6.10 non linear software [13]. The main parts of the models are the aluminium channel, the bolt and the plate nut. In particular, the bolt, the washer and plate nuts are modelled as only one part, because the observed experimental behaviour does not exhibit any mutual deformation of these components. All the parts are schematized as three dimensional solid deformable parts and the geometrical non-linearity is taken into account. In addition, only one half of the actual geometry is modelled by exploiting the model symmetry with respect to middle plane of the whole system. The aluminium alloy (AW 6005A-T6) used for both specimens is modelled by means of the Ramberg–Osgood law [14], based on the experimental results and transformed in true stress-true strain format. In order to correctly catch the material behaviour for large deformation, the exponent of Ramberg–Osgood law (n = 23) is evaluated considering as reference points the 0.2% proof strength (f0 = 235 MPa) and the ultimate strength (fu = 279 MPa). The other material constants are: E = 63900 MPa (Young’s modulus) and
L. Fiorino et al. / Construction and Building Materials 73 (2014) 76–88
Perfect
Imp. 0.25 mm
Imp. 0.50 mm
Imp. 1.00 mm
Fig. 31. Deformed configurations for the assumed imperfection values.
Table 12 Comparison between numerical and experimental results for PO model.
Experimental Perfect Imp. 0.25 mm Imp. 0.50 mm Imp. 1.00 mm
Fmax (kN)
Fmax Num/exp
k (kN/mm)
k Num/exp
42.8 50.5 50.5 46.3 42.9
+18% +18% +8% +0.2%
28.6 33.2 32.8 32.1 31.5
+15% +15% +12% +10%
m = 0.30 (Poisson’s ratio). The part representing bolt and plate nuts is mechanically characterized by two different materials, corresponding to 8.8 and S355 steel grade, respectively. Both materials are modelled by a bilinear elastic-strain hardening law with E = 200,000 MPa and m = 0.30. The other properties that define the material behaviour are assumed as the nominal values and their true stress and true strain values are shown in Table 10. The material of the set-up system is S355 steel. The SH model reproduces the experimental tests of BC-SH-18 series, where beside the aluminium channel and the bolt with plate nuts, also the set-up plate is implemented (Fig. 22). The geometrical symmetry is defined by restraining middle plane against the translation along x-axis (Ux = 0) and the rotation about y- and z-axis (URy = URz = 0). In order to schematize the oversized connections at the channel ends, the internal surface of the aluminium channel top flanges is restrained against the translation. All the interactions are defined by the normal ‘‘hard-contact’’ behaviour and the tangential ‘‘penalty-contact’’ with friction coefficient of 0.3. The bolt tightening is simulated by ‘‘bolt load’’ ABAQUS option, in which the imposed load is of 15 kN, which corresponds to the tightening torque assumed in the experimental phase. The shearing load consists in a uniform displacement along y-axis applied to the top surface of set-up plate. The PO model is calibrated on the basis of the BC-PO-18 tests. In addition to the specimen parts (aluminium channel, bolt and plate nut), a rigid discrete planar ‘‘shell’’ element is introduced in order to reproduce the support plane of the set-up where the aluminium
87
channel is laid on (Fig. 23). The symmetry condition is defined by restraining this middle plane against the translation along x-axis (Ux = 0) and the rotation about y- and z-axis (URy = URz = 0). The interaction between the aluminium channel and the rigid shell is modelled by the ‘‘hard-contact’’ behaviour, while the set-up bolted connection is schematized by restraining x and y translations and a spring with stiffness of 900 kN/mm is introduced in z direction, in order to take into account the axial deformability of bolts. All the interactions are taken into account in a tangential ‘‘penalty-contact’’, with a friction coefficient of 0.3 and a normal ‘‘hard-contact’’ behaviour. The loading condition consists in applying a uniform displacement up to 6 mm along z-axis to the end of bolt shank. In order to model the non symmetric response observed in experimental tests, the presence of imperfections is taken into account and calibrated. The imperfections are introduced by locating the plate nuts in not centred position with respect of aluminium channel, as shown in Fig. 24. Therefore, in addition to the perfectly symmetric model, simply named ‘‘perfect’’, three models corresponding to imperfection amplitudes of 0.25, 0.50 and 1.00 mm are analysed. Both SH and PO models are meshed by means of an 8-node linear brick with reduced integration and hourglass control (C3D8R), which is generally used in case of problems related to material plasticity and contact interactions. The mesh size is defined by two limit values: the minimum in contact zones between the bolts and the aluminium channel and the maximum in the peripheral zones. All the analyses are performed by means of the Newton– Raphson incremental method. The optimal mesh size is defined by means of a sensitivity analysis, where three different mesh configurations are considered: coarse, intermediate and fine (Fig. 25). In both cases the intermediate mesh is adopted, because it allows to contain computational analysis time with a good results accuracy (Figs. 26 and 27). 4.2. Experimental vs. numerical results – SH model The comparison between experimental and numerical results in terms of response curve is shown in Fig. 28. The numerical curve describes the experimental results with acceptable approximation and the slipping plateau of the curve is slightly higher than those experimentally obtained. Another difference lies on the marked irregularity in experimental curve, probably depending on local phenomena. Table 11 shows the comparison between numerical and experimental results in terms of joint strength (Fmax) and stiffness (k). In particular, the model catches the joint strength in very good agreement with experimental results with an error of 1%; while the initial stiffness is underestimated of 10%. The reliability
Fig. 32. Deformed configuration at failure for PO model.
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L. Fiorino et al. / Construction and Building Materials 73 (2014) 76–88
of the proposed model is proved also by the good agreement between the numerical deformed configuration at failure and the experimentally observed one, as it shown in Fig. 29. 4.3. Experimental vs. numerical results – PO model The comparison between the results of the numerical models corresponding to different imperfection amplitudes and the experimental ones is shown in Fig. 30, in terms of load vs displacement (F–d) curves. The numerical curves for the different imperfection values show a good approximation with the experimental range. The 0.25 mm imperfect model shows a response practically identical to those provided by perfect models. This is confirmed also in terms of deformed configuration and of stress distribution, which is substantially symmetric; while 0.50 mm and 1.00 mm imperfect models clearly identify non symmetric deformed configurations (Fig. 31). Table 12 shows the comparison between numerical and experimental results in terms of joint strength and stiffness. Also in this case, the influence of 0.25 mm imperfection is so low that the strength and the stiffness values are equal to those obtained with the perfect model. It has to be noticed that the difference between numerical and experimental results decreases as for as the imperfection amplitude increases. In fact, by comparing the numerical results with the experimental ones, the perfect model overestimates both strength and stiffness with differences of 18% and 15%, respectively. These differences strongly decrease for 1.00 mm imperfect models with values of 0.2% and 10% for strength and stiffness, respectively. Therefore, the 1.00 mm imperfect model seems to match the experimental results with the best approximation. This is also confirmed by the very good correspondence between the deformed configuration of such model and the experimental one, as it is shown in Fig. 32. 5. Conclusions The identification of structural response of bolt-channel joints by means of experimental tests and the calibration of the numerical models has been successfully done. The joints are tested under three different loading directions: slip (SL), shear (SH) and pull-out (PO). The SL tests show high scattered results in terms of strength (14–24%) probably due to influence of the assembly imperfections. This issue does not affect the SH tests response, whose deformed configuration is globally symmetric and presents very low scattered values in terms of strength (3–4%). In the case of PO tests, although the strength values are little scattered (1–7%), the exhibited deformed configuration is always strongly non symmetric, probably due to assembly imperfections. Finite element models for interpreting the SH and PO tests are calibrated. The SH model provides a good strength and stiffness prediction, being the differences with experimental data of 1% and 10%, respectively. The deformed configuration obtained by the SH model matches very accurately the one experimentally exhibited. In order to match
the non symmetric response observed in PO tests, the PO model is calibrated taking into account the influence of imperfections. The model with imperfection amplitude of 1 mm matches with best approximation the experimental results (+0.2% and +10% for strength and stiffness). Therefore, the experimental results show the important rule of the imperfections on the joint response as well as the shape and the proportions of the channel cross-section that may strongly influence both the strength and the failure mechanism. Also for this reason, the comparison of experimental and predicted strength values shows that the available codified formulations, calibrated on tests on other different joint configuration, are not reliable for the investigated systems. Hence, numerical models able to take into account the influence of different channel geometries and the possible source of imperfection are necessary to the full understanding of the behaviour of the boltchannel joints. In this context, the proposed models can represent a useful design tool of general validity for this kind of joints. Acknowledgments The Authors gratefully acknowledge the METRA Company (Rodengo Saiano, Italy), which sponsored this research activity within the Doctoral School in Constructional Engineering of the University of Naples ‘‘Federico II’’. References [1] Macillo V., Special Joint Systems for Aluminium Structures: Experimental Tests and Numerical Models, PhD Dissertation, University of Naples ‘‘Federico II’’, 2013. [2] Fiorino L, Macillo V, Mazzolani FM. Screwed joint for aluminium extrusions: experimental and numerical investigation. In: 12th INALCO conference, Montreal 21–22 October, 2013. [3] Macillo V, Fiorino L, Mazzolani FM. Structural behavior of aluminium boltchannel joint: calibration of numerical models on testing results, In: 12th INALCO conference, Montreal 21–22 October, 2013. [4] Sapa, Design Manual, Sapa Profiler AB, Stockholm, 2009. [5] Bosh Rexroth Corporation, Aluminum Structural Framing System – Version 7.0, 2011. [6] Kieran S, Timberlake J, Loblolly House – Elements of a New Architecture, Princeton Architectural Press, 2008. [7] Kieran S, Timberlake J. Cellophane House – Kieran Timberlake. Archit Design 2009;79:58–61. [8] Hellgren M, Strength of Bolt-Channel and Screw-Joints in Aluminium Extrusions, KTH Royal Institute of Technology, Licentiate Thesis, Stockholm, 1996. [9] CEN, EN 1999-1-1 – Eurocode 9 – Design of aluminium structures – Part 1–1: General structural rules, European Committee for Standardization, Bruxelles, 2007. [10] CNR-DT 208/2011, Istruzioni per la progettazione, l’esecuzione ed il controllo di strutture di alluminio, Consiglio Nazionale delle Ricerche, Roma, 2011. [11] Hydro, Extrusion Design Manual – A world of opportunities, Hydro Aluminum North America, Linthicum MD, 2009. [12] ISO 6892-1, Metallic materials – Tensile Testing – Part 1: Method of test at room temperature, International Organization for Standardization, Genève, 2009. [13] Simulia, Abaqus Analysis User’s manual, version 6.10, Dassault Systemes Simulia Corporation, 2010. [14] Mazzolani FM. Aluminium alloy structures. 2nd ed. London: E & FN SPON; 1995.
Contents lists available at ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Mechanical behaviour of bolt-channel joining technology for aluminium structures Luigi Fiorino, Vincenzo Macillo, Federico Massimo Mazzolani ⇑ Department of Structures for Engineering and Architecture, University of Naples ‘‘Federico II’’, Naples, Italy
h i g h l i g h t s The extrusion process allows to conceive more rational connections: special joints. Bolt-channel joints consist in an extruded track where the bolt can be located. These joints are very competitive with respect to the traditional joining systems. Experimental tests aimed at investigating joint behaviour has been carried out. On the basis of experimental results, FEM models have been developed and calibrated.
a r t i c l e
i n f o
Article history: Received 24 February 2014 Received in revised form 15 September 2014 Accepted 25 September 2014
Keywords: Aluminium Bolt-channel Experimental tests Joining technologies Numerical modelling
a b s t r a c t The wide choice of cross-sectional shapes obtainable by extrusion process provides the possibility to individuate new joining solutions for aluminium profiles. The achievable joining technologies are very competitive with respect to conventional solutions, because of the possibility of rapid execution, optimization of parent material, treatments and machining reduction. For these reasons, the aluminium industry is very interested to enhance the knowledge about the structural behaviour of these joint systems. Bolt channel joints are one of the possible technologies that entail the advantage of the extrusion shapes for joining aluminium elements. The system consists of a track or channel section profile where a bolt head, nuts or plates with threaded holes can be located. Bolt-channel joints are commonly used in building applications and in transportation structures. Nevertheless, very little literature is available for this system and no specifications are provided by aluminium structural codes. In order to evaluate the structural behaviour of bolt-channel joints, an experimental campaign has been carried out at University ‘‘Federico II’’ of Naples. Two different cross-sections corresponding to different bolt diameters have been selected and three different load directions have been considered. The obtained experimental results have been used for the calibration of non-linear numerical models. Ó 2014 Elsevier Ltd. All rights reserved.
1. Introduction The profiles for aluminium structures are usually obtained by means of extrusion process that, as well-known, allows many possibilities of cross-sectional shapes. In particular, extruded shapes can be customized according to the different possible uses by incorporating essential design features, such as stiffener, rib, bulbs, slots and tracks. These features can be exploited to conceive, in a more rational way, connection technologies to join together
⇑ Corresponding author at: Department of Structures for Engineering and Architecture, University of Naples ‘‘Federico II’’, University of Naples ‘‘Federico II’’, p.le Tecchio, 80 – 80125 Naples Italy. Tel.: +39 081 7682443; fax: +39 081 419215. E-mail addresses: lfi[email protected] (L. Fiorino), [email protected] (V. Macillo), [email protected] (F.M. Mazzolani). http://dx.doi.org/10.1016/j.conbuildmat.2014.09.086 0950-0618/Ó 2014 Elsevier Ltd. All rights reserved.
aluminium profiles. The achievable joining methods are various and they may or may not involve the use of fasteners. These systems are generally known as ‘‘special joints’’ or ‘‘non-conventional joints’’ for aluminium extrusions. Typical special joints consist in tracks and slots obtained in the extruded shapes, in which mechanical fasteners, such as bolts and screws, can be located. The high competitiveness of these joining technologies is related to the ease and rapidity of assembly, machining reduction, optimization and saving of the parent material with a consequent cost reduction. These joint typologies are commonly used in many structural applications not only in building and civil engineering, but also in transportation industry. Typical applications in buildings are door and windows frames, photovoltaic support systems, staircases, shelves and industrial furniture. The possibility to use these joints in structural applications, even if under moderate loads,
L. Fiorino et al. / Construction and Building Materials 73 (2014) 76–88
77
Fig. 1. Bolt-channel joint [4].
Fig. 2. T-slotted profile system [5].
Fig. 3. The ‘‘Loblolly House’’ [6].
requires their design calculation and verification. Nevertheless very little information for the design of special joints is provided by aluminium structural codes and few researches are available on this topic. Therefore, now-a-day the design assisted by tests procedure represents the only way to evaluate the joint strength.
As an attempt to overcome this lack of information, a research about the mechanical behaviour of special joints [1] was undertaken at University of Naples ‘‘Federico II’’ with the financial support of METRA S.p.A. In order to define the main issues related to the joint geometry, the influence of load type and the joint
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L. Fiorino et al. / Construction and Building Materials 73 (2014) 76–88
Fig. 4. The ‘‘Cellophane House’’ [7].
structural response, an extended study on screw ports [2] and boltchannel [3] joints has been carried out by means of experimental tests and numerical modelling. The present paper shows the activity carried out on bolt-channel joints. 2. Bolt-channel joints
g z
C/ 2
2.1. Joint description and applications The Bolt-Channel (BC) joint system consists in an extruded section with a track, where the head or nut of bolt is located for connecting the profile to the other joint components (Fig. 1). This joining technique allows to set the bolts anywhere along the profile length without any machining, with the possibility of ease relocation by moving the bolt head along the track [4]. In the case of joints with more bolts disposed at a given distance, a plate with threaded holes can be introduced in the track defining the bolt position. In general, plates with threaded holes can be located into the channel and used as nuts. As an alternative solution, special bolt or nuts can be used. For instance, T-bolts has the advantage to be installed directly in the given position without the need to slide it from the end of the profile, or rhombus nuts that, after turning, result self-locked inside the channel. A typical use of BC joints is the T-slot profile system, which consists in a semi-hollow extruded profile having, at each side, one or more slots for special bolt heads or nuts. These profiles can be joined together all along their length by introducing simple elements, such as angle and gusset plates (Fig. 2). The result is a versatile modular system, which can be used in any type of frame structure, such as industrial furniture, shelves, windows frames and support structures for solar panel plants [5]. T-slot system has been used in two fascinating, creative and innovative buildings designed by the architecture firm KieranTimberlake: the ‘‘Loblolly House’’ [6] and the ‘‘Cellophane House’’ [7]. The first building (Fig. 3) is a single family dwelling positioned in a dense grove of loblolly pines, from which the house takes the name. The ‘‘Loblolly’’ house has two storeys and it is raised from the ground by means of wooden piles. It is composed by two different blocks connected by a glazed bridge. The ‘‘Cellophane House’’ (Fig. 4) is a five storeys building, which was located in New York City for a threemonth exhibition and the onsite erection needed only sixteen days.
x
b tlat
w
y
w g
Top flanges
tsup Webs
tlat
h
Bottom flange tinf
Fig. 5. Assumed symbols for bolt-channel joints.
Both buildings are completely off-site fabricated, eco-sustainable and the main structure is obtained by using only aluminium T-slot profiles. The great advantage of these two innovative buildings lies on the full reversibility of the adopted connections, that allow to disassembly and reuse the structure in very easy and fast way. 2.2. State-of-the-art Although there are various possibilities of structural applications obtainable with BC joints, there is very little information Table 1 Range of validity of bolt-channel joint. Bolt diameter
Sapa – CNR/DT 208 w (mm)
h (mm)
g (mm)
w (mm)
Hydro h (mm)
g (mm)
M4 M5 M6 M8 M10 M12 M14 M16
7.3 ± 0.15 8.3 ± 0.15 10.3 ± 0.20 13.4 ± 0.20 16.5 ± 0.20 18.5 ± 0.20 21.7 ± 0.20 24.7 ± 0.20
4.0 5.5 6.0 8.0 9.5 12.5 14.0 16.0
4.4 5.4 6.4 8.5 10.7 12.7 15.0 17.0
7.4 8.4 10.5 13.5 17.5 19.5 22.6 24.6
4.0 4.5 5.0 7.0 8.5 9.5 10.5 11.5
4.5 5.5 6.5 8.5 11.0 13.0 15.0 17.0
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L. Fiorino et al. / Construction and Building Materials 73 (2014) 76–88 Table 3 Aluminium alloys tests results.
M10 Specimen
Material
E (MPa)
f0.2 (MPa)
fu (MPa)
eu (%)
np
AW 6005A-T6
63963
235
279
10
23
M18 Specimen
Fig. 6. Bolt-Channel specimens.
Fig. 7. Steel plate nut dimensions.
PO
SL Fig. 9. Set-up and instrumentation for SL tests.
SH Table 4 Experimental results of SL tests. Series label
Fig. 8. Test load directions.
BC-SL-10 BC-SL-18A BC-SL-18B
about their mechanical behaviour and design rules. In literature, a study on this topic was conducted by Hellgren [8], who performed 247 tests on joints. The experimentation focused on the configuration in which the bolt head is place in the aluminium channel. The used aluminium profiles, with a channel suitable for M8 bolts, were made of AW 6063-T6 alloy. The influence of bolt head shape was investigated by considering stainless steel metric bolts with hexagonal head and special designed T-bolt. The joints were tested under three different load directions: a force parallel along the channel, a shear transversal force and a pull-out action. In addition, the influence of web channel thickness (1.0, 2.0 and 3.0 mm) in Table 2 Test program for BC joints. Series label
Load Bolt direction diameter (mm)
Tightening torque (Nm)
Preloading force (kN)
n. test
BC-SL-10 BC-SL-18A BC-SL-18B BC-SH-10 BC-SH-18 BC-PO-10 BC-PO-18
Slip Slip Slip Shear Shear Pull-out Pull-out
40 93 60 40 100 – –
20 26 17 28
6 4 4 3 3 3 3 26
M10 M18 M18 M10 M18 M10 M18
Total n. of tests:
Fslip
k (kN/mm)
Average (kN)
Standard deviation (kN)
C.o.V.
4.77 7.02 6.88
0.94 0.97 1.67
0.20 0.14 0.24
31.9 37.3 34.5
pull-out tests was investigated. As final results, on the basis of the experimental findings, empirical design formulae for ultimate strength prediction was proposed. Main design codes for aluminium structures, such as Eurocode 9 [9], do not provide any information for these joints. In particular, for joining methods not covered by the standard, it is specified that their use is permitted only if appropriate experimental tests are carried out (design assisted by tests). A recent document providing some design formulations for BC joints is the Italian Recommendations for Aluminium Structures (CNR-DT 208/2011) [10], in which some innovative features are introduced, such as special joints design. Design formulations for special joints together with information as suggested dimensions for aluminium parts are also provided in the Design Manual published by Sapa [4]. This document deals with different joining possibilities, including BC joints.
2.3. Available formulations for strength prediction Presently, few design formulations are available for the prediction of the BC joints strength. These formulations are generally derived from experimental results and their validity is strictly related to the investigated geometries. For this reason, standards
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L. Fiorino et al. / Construction and Building Materials 73 (2014) 76–88
Fig. 10. Deformed configuration after SL tests.
and design manuals always provides the design formulations together with their range of validity. In particular, design formulations are only available for the joint configuration with the bolt head in the channel. The Design Manual by Sapa provides the bolt track dimensions (Fig. 5) representing the range of validity of the proposed design formulations. This range of validity, adopted also by CNR-DT208, is reported in Table 1 together with the one proposed by Hydro [11]. The joint strength for force acting in parallel direction to the channel, which produces the slipping of bolts or plate inside the channel, can be calculated, according to Sapa [4] and Hellgren [8], through the following equation:
F x;Rd ¼ 200
Fig. 12. Material removal in SL test specimens.
F y;Rd ¼
F y;Rd ¼
Mv
nl F cM2 p;Cd
ð2Þ
where n is the number of friction interfaces, l is the friction coefficient and Fp,Cd is the bolt preloading force. The strength of BC joint subjected to transversal shear force can be calculated by the following formulations provided by Hellgren and CNR DT-208, respectively:
16
16
F [kN]
12
12
8
8
1:2btlat f u
Fslip,av =4.77 kN
16
F [kN]
#
12
4
*
2
4
6
(a) BC-SL-10
8
10
Fslip,av =6.88 kN
4
d [mm] 0
0
F [kN]
8
d [mm] 0
ð4Þ
cM3
Fslip,av =7.02 kN 4
ð3Þ
where fu is the ultimate strength of the aluminium channel, tinf is the thickness of lower flange of the channel, tlat is the webs thickness of the channel, b is the contact length between the web of the channel and the bolt head (Fig. 5), cM2 and cM3 are the partial safety factor assumed equal to 1.25 and 1.50, respectively. It has to be noticed that the two formulations have a very similar structure, both depend on the contact length of bolt inside the channel, but Hellgren formulation considers that failure occurs on lower flange (tinf), while according to CNR DT-208 it does in the web (tlat). For this loading direction, Sapa suggests to evaluate the strength as 70% of the values determined for a traditional bolted joint subjected to shear. Formulations for the pull-out strength of BC joint are provided by Hellgren and Sapa, respectively, as follows:
where Mv is the bolt torque in Nm and cM2 is the partial safety factor assumed equal to 1.25. On the other hand, CNR-DT 208 [10] recommends to evaluate this strength as well as a common bolted slip resistant joint by applying a partial safety factor cM3 equal to 1.50, as follows:
F x;Rd ¼
pffiffiffi 2f u tinf b 1:2cM2
ð1Þ
cM2
(b) BC-SL-18A-04 (curve # in Fig. 11b)
(a) BC-SL-18A-02 (curve * in Fig. 11b)
d [mm] 0
0
2
4
6
8
10
(b) BC-SL-18A Fig. 11. Experimental curves of SL tests.
0
2
4
6
(c) BC-SL-18B
8
10
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L. Fiorino et al. / Construction and Building Materials 73 (2014) 76–88
Fig. 13. Set-up and instrumentation for SH tests.
Table 5 Experimental results of SH tests. Series label
BC-SH-10 BC-SH-18
Fmax Average (kN)
Standard deviation (kN)
C.o.V.
20.8 49.3
0.60 1.83
0.03 0.04
k (kN/mm)
Failure mode
20.4 8.32
BF W
BF: Failure occurred in channel bottom flange. W: Failure occurred in channel web.
Crack development
Fig. 14. Failure mechanism in BC-SH-10 series.
Fig. 15. Failure mechanism in BC-SH-18 series.
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L. Fiorino et al. / Construction and Building Materials 73 (2014) 76–88
60
60
F [kN]
50
50
40
40
F [kN]
Fmax,av =49.3 kN
30
30
Fmax,av =20.8 kN
20
20 10
10
d [mm]
d [mm] 0
0 0
10
20
30
0
10
20
30
(b) BC-SH-18
(a) BC-SH-10 Fig. 16. Experimental curves of SL tests.
where tsup is the thickness of upper flanges of the channel, C is the bolt head perimeter in contact with upper flanges of the channel, g is the width of channel opening (Fig. 5). Both formulations consider as possible failure mode the shearing of channel web by the bolt head. Both formulations are adopted by CNR-DT 208/2011, by assuming the partial safety factor cM3 and suggesting the use of Eq. (6) because it provides more conservative strength values. 3. Experimental tests 3.1. Test program
Fig. 17. Deformed configuration of SH tests.
f t sup C F z;Rd ¼ puffiffiffi 3cM2
F z;Rd ¼ 1:2
gtsup f u
cM2
ð5Þ
ð6Þ
The experimental program is aimed at investigating the structural response of BC joint systems. The main objective is to define the influence of the extruded channel geometry, the bolt diameter and the direction of loads. The tested BC joints are made by locating a steel plate with a threaded hole located in the aluminium channel. Practically, the holed plates are named plate nuts because they behave as a bolt nut. No information, tests results and design rules are, presently, available for this joint configuration. Two extruded AW 6005A-T6 aluminium channels (Fig. 6), suitable for M10 and M18 bolt diameters, have been selected as a part of commercial profiles to obtain the BC specimens. The bolts used were 8.8 steel grade, while plate nuts are made of S355 steel. The dimensions of plate nuts are depicted in Fig. 7. In order to take into account the possible loading conditions that can occur in the different applications of BC joints, three different load directions are considered (Fig. 8). The first load direction (SL tests) consists in a force parallel to the track that
Fig. 18. Set-up and instrumentation for PO tests.
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L. Fiorino et al. / Construction and Building Materials 73 (2014) 76–88 Table 6 Experimental results of PO tests. Series label
BC-PO-10 BC-PO-18
Fmax Average (kN)
Standard devation (kN)
C.o.V.
33.3 42.8
0.33 2.93
0.01 0.07
k (kN/mm)
Failure mode
21.1 25.5
PO TF
PO: Pull-out of threaded bar. TF: Failure occurred in channel top flange.
Table 7 Comparison between predicted and experimental slip strength for BC joints. Series
Exp. (kN)
BC-SL-10 BC-SL-18A BC-SL-18A
4.77 7.02 6.88
Hellgren/Sapa (1)
CNR-DT 208 (2)
Pred. (kN)
Pred./exp.
Pred. (kN)
Pred./exp.
8.00 12.0 18.6
1.68 1.74 2.65
6.00 5.00 7.75
1.26 0.73 1.10
evaluate the effects of bolt preload, two values of tightening torques are used for M18 specimens. The second load direction (SH tests) is a transversal force perpendicular to the channel axis, which brings the plate nut in contact with the channel web. The third load direction (PO tests) consists in a tension force that tends to pullout the plate nut from the aluminium channel. All the tests are performed by using the universal test machine MTS 810 in displacement control with a loading rate of 0.02 mm/s and the data are recorded with a frequency of 10 Hz. The whole test program, including 26 tests (14 for SL tests, 6 for SH tests and 6 for PO tests), is summarised in Table 2, where the different parameters under investigation are given for each specimen series. The series label defines the specimen typology. Namely, the first group of characters (BC) means bolt-channel, the second group represents the loading direction (SL: slip, PO: pull-out and SH: shear), the third group of digits indentifies the bolt diameter (10 or 18 mm) and the final character (A or B) distinguishes the equal specimens with different tightening torque.
Fig. 19. Failure mechanism in BC-PO-10 series.
3.2. Material tests In order to characterize the mechanical properties of the materials, tensile tests are performed according to ISO 6892-1 [12]. In particular, two tests on 4 mm thick specimens made of AW 6005A-T6 alloy are performed. Test results are summarised in Table 3, where the average values of Young’s modulus (E), 0.2% proof stress (f0.2), ultimate strength (fu), ultimate strain (eu) and the exponent of the Ramberg–Osgood law (np) are shown. The obtained average value of the Young’s modulus is 63,966 MPa; the 0.2% proof stress and the ultimate strength are on the average equal to 235 and 279 MPa, respectively. 3.3. Slip tests
Fig. 20. Failure mechanism in BC-PO-18 series.
induces a slipping of bolt and plate nut along the aluminium channel. Three SL series are tested, one for M10 specimens and two for M18 specimens; in order to
50
The specimens for SL tests consist of 75 mm and 100 mm long aluminium channels for M10 and M18 configurations, respectively. Inside the channel, the plate nut is located at a depth of 5 mm with respect to the top edge. The M10 specimens are tightened with a torque of 40 Nm, which corresponds to 60% of the maximum preloading force (20 kN). In the case of M18 specimens, two different torque values, 60 and 93 Nm, are considered. These values correspond to 25% (26 kN) and 15% (17 kN) of maximum preloading, respectively. The used torque values are assumed to limit the excessive deformation of the aluminium parts induced by tightening operation in the small thickness elements of the aluminium channel.
50
F [kN]
40
F [kN]
Fmax,av =42.8 kN
40
Fmax,av =33.3 kN
30
30
20
20 10
10
d [mm]
d [mm] 0
0 0
3
6
9
(a) BC-PO-10
12
15
0
3
6
9
(b) BC-PO-18
Fig. 21. Experimental curves of SL tests.
12
15
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Table 8 Comparison between predicted and experimental shear strength for BC joints. Series
Exp. (kN)
BC-SH-10 BC-SH-18
20.8 49.3
Hellgren (3)
CNR-DT 208 (4)
Pred. (kN)
Pred./exp.
Pred. (kN)
Pred./exp.
Pred. (kN)
Pred./exp.
46.0 78.9
2.21 1.60
69.0 78.9
3.32 1.60
19.5 35.2
0.94 0.71
Table 9 Comparison between predicted and experimental pull-out strength for BC joints. Series
Exp. (kN)
BC-PO-10 BC-PO-18
33.3 42.8
Sapa
Hellgren (5)
Bc: Ux=Uy=0 Applied uniform displacement
Sapa (6)
Pred. (kN)
Pred./exp.
Pred. (kN)
Pred./exp.
66.0 85.1
1.98 1.99
18.4 26.8
0.55 0.63
Symmetry Plane (Ux=URy=URz=0)
Ux=Uy=0
Bolt Preload: 15 KN
Ux=Uy=Uz=0
Bc: Ux=Uy=Uz=0 The specimen is placed on a steel plate at the bottom and the compression load to the plate nut is applied by means of a steel flat plate clamped in the top wedge grip of the testing machine. The displacement of the plate nut is measured by means of a linear variable differential transducer (LVDT) (Fig. 9). The results of slip joint tests are summarised in Table 4, where the values of the average, the standard deviation and the coefficient of variation of slip strength (Fslip) together with the average stiffness (k) are given. The slip strength of the joint is assumed as the first peak or the plateau of the experimental curve depending on its shape, while the joint stiffness (k) is the slope of the first significant linear portion on the experimental curve. The observed failure mechanism is always due to large slipping of bolt inside the aluminium channel, as shown in Fig. 10. Fig. 11 shows the experimental results in terms of load vs. displacement (F–d) curves. By comparing the results of the BC-SL-10 specimens with the BC-SL-18B ones, which are characterized by similar values of preloading force, it can be observed an increase of strength of about 44% with the variation of bolt diameter from 10 to 18 mm. For M18 specimens (BC-SL-18A and B), the variation of 55% of tightening torque implies a very small increase (2%) in terms of average strength. Then, in the examined cases, the level of torque does not significantly influence the joint response. In addition, it has to be noticed that the results are quite scattered with coefficient of variation ranging from 14% to 24%. These findings can be explained by the joint sensitivity to the assembly imperfections. These imperfections consist in a non perfectly axis alignment between the channel and the plate nuts because of the tightening, which tends to rotate the plate nut entailing unforeseen contacts inside the channel influencing the response. In addition, the tightening operation can cause local permanent deformations of top flanges of the aluminium channel due to the squashing of bolt washer and/or of the plate nuts. These deformations imply a marked material removal during the test sliding, that evidently influences the joint slip strength, as shown in Fig. 12. In fact, it can be observed that the specimen in BC-SL-18A-02 (Fig. 12a), which does not present evident material removal, exhibited a lower slip strength (curve * in Fig. 11b) with respect to the specimen BC-SL-18A-04 (curve # in Fig. 11b), that shows a marked removal of material on both internal and external face of channel top flanges (Fig. 12b) 3.4. Shear tests The test specimens and set-up for SH tests of bolt-channel are designed with the aim to reproduce the transversal load transfer and to avoid unwanted or non significant mechanisms. The specimens consist in aluminium channels with length of 250 mm and 400 mm for M10 and M18 configurations, respectively. The connection under investigation (tested connection) is located in the middle of the aluminium channel and the shear load is applied by using a holed plate clamped the top wedge grip. The aluminium channel ends are connected to a U-shaped steel plate, clamped to the bottom wedge grip of the testing machine. The connections at the ends of the channel are designed to be oversized with respect to the tested ones. All the set-up plates are made of S355 steel grade and their thickness is defined in order to avoid the bearing failure. The bolts are tightened with a torque of 40 and 100 Nm for M10 and M18 specimens, respectively. The displacements of the tested connection are measured by means of a LVDT placed on bolt head and two additional LVDTs are disposed at the channel ends to measure the displacement of the oversized connections (Fig. 13).
y z
x
Fig. 22. Model geometry and boundary conditions for the SH model.
Table 5 summarises the results of SH tests on BC joints. In this table, for each specimen series the parameters defining the structural behaviour together with the observed failure mechanism are provided. In particular, the values of the average, the standard deviation and the coefficient of variation of strength (Fmax) and the average value of stiffness (k) are given. The strength is assumed as peak load of the experimental curve, while the stiffness has been evaluated as the slope of the first significant linear portion on the experimental curve. The failure mechanism of the BC-SH-10 series consists in a crack development in the aluminium channel at the bottom flange close to the corner with the web (Fig. 14). The specimens present also an evident deformation of top flange and web on the loaded side, while the bolts and the plate nut do not appear significantly deformed. In the case of the BC-SH-18 series a crack develops from the top flange on the loaded side to all the web depth and along the intersection between the web and the bottom flange, as shown in Fig. 15. Also in this case no evident deformations in bolt and plate nut occur. Fig. 16 shows the experimental results in terms of load vs. displacement (F–d) curves. The experimental curves exhibit a sudden slope change in the load range from 5 to 10 kN for BC-SH-10 specimens and in the range between 10 and 15 kN for BC-SH-18 ones. This can be ascribed to the sliding due to the clearance between the plate nut and the aluminium channel as well as between the hole of the set-up plate and the bolt. It can be also observed that the two investigated configurations show a great variation in terms of deformation capacity. In terms of strength, an increase of 137% from BC-SH-10 to BC-SH-18 is observed. On the contrary, BC-SH-10 specimens resulted 2.5 times stiffer than BC-SH-18 ones. This result, consisting in a stiffer response of the joint with the smaller bolt, can seem counterintuitive, but it is justified by the poor rational geometry of the BC-10 cross-section, which has stiffer webs with respect to the BC-18 one (Fig. 6). In addition, the strength values for both series are very little scattered with coefficient of variation lower than 4%. The low scattered values demonstrate that, for the investigated cases, the shear strength of bolt-channel joint is not affected by assembly imperfections. The low sensitivity to imperfections is also confirmed by the symmetrical global response up to the failure (Fig. 17).
3.5. Pull-out tests The specimens for PO tests are 200 mm long aluminium channels for both M10 and M18 configuration. The test set-up consists of a T-shaped element, made of S355 steel grade, which is clamped to the bottom wedge grip of the testing machine. The aluminium specimen is fixed to the steel element by means of 4 M10 bolts of 12.9 grade, placed inside the channel. The tested connection is located in the middle of the aluminium channel and it consists in a plate nut tightened with a 180 mm long threaded bar. The other end of the bar is installed in a 20 mm thick plate pulled by means of a steel holder clamped in top wedge grip of the testing
Table 10 Assumed steel material properties. Material
True yield stress (MPa)
True ultimate stress (MPa)
True ultimate plastic strain
Model parts
8.8 Grade S355
642 356
896 622
0.11 0.22
Bolts Plate nut, set-up system
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60
Bc: Ux=Uy=0 kz=900 kN/mm
F [kN]
50 40
y z
x
30 20
Symmetry Plane (Ux=URy=URz=0)
Coarse Intermediate Fine
10
d [mm]
Applied uniform displacement
0 0
10
20
30
Fig. 23. Model geometry and boundary conditions for PO model. Fig. 26. Mesh sensitivity analysis results for SH model.
Perfect
Imp. 0.25 mm
Imp. 0.50 mm
Imp. 1.00 mm
Fig. 24. Imperfection calibration models.
machine. The displacements are measured through a LVDT placed between the holder and the T-shaped element (Fig. 18). In Table 6, the values of the average, the standard deviation and the coefficient of variation of strength (Fmax) and the average value of stiffness (k), together with the observed failure mechanisms are provided for each specimen series. The strength is assumed as peak load of the experimental curve, while the stiffness has been evaluated as the slope of the first significant linear portion on the experimental curve. For all the BC-PO-10 specimens, the observed failure corresponds to the pullout of threaded bar from the plate nut with shearing of both nut and bar threads. In correspondence to the failure, the plate nut results strongly deformed and a crack develops along one of the top flanges of the aluminium channel (Fig. 19). The observed failure mechanism of BC-PO-18 series consists in a crack occurred at the one of top flanges, which tends to propagate along the web. In this case threaded bar and plate nut do not present significant deformations (Fig. 20). It has to be noticed that the response of both series is strongly non symmetrical and it is probably due to assembly imperfection. In fact, the plate nut tends to rotate in the channel because of tightening operation and, due to the clearance, it is not
Coarse (2.5-5.0 mm)
Coarse (3.0-6.0 mm)
perfectly centred in the channel. This could explain the development of cracks on only one side of the channel. The experimental results in terms of load vs. displacement (F–d) curves are shown in Fig. 21. It can be observed that the BC-PO-10 series shows a slightly higher deformation capacity with respect to BC-PO-18. The response BC-PO-18 is, in average, 29% and 21% greater than BC-PO-10 in terms of strength and stiffness, respectively. Despite the fact that the joint response is, markedly non symmetrical, for both series, the strength values for both series are little scattered with coefficient of variation lower than 7%. As a consequence, it would seem that the influence of assembly imperfections is evident in joint deformed configuration, but it does not affect the coefficient of variation of the strength.
3.6. Experimental vs. predicted strength The strength values of obtained by experimental tests on BC joints are compared to those estimated through the available prediction formulations, illustrated in Section 2.3. In order to correctly compare the experimental values with the theoretically predicted ones, the formulations are applied by considering the aluminium strength obtained by tests (Section 3.2) and by assuming the safety factors equal to 1. The values obtained by the formulation proposed by Hellgren and Sapa and the one of CNR-DT 208 are compared with the experimental results in Table 7. In case of the CNR-DT 208 formulation the bolt preloading force has been evaluated calculating as follows:
F p;Cd ¼ 0:2M v d
ð7Þ
where Mv is the applied tightening torque and d is the bolt diameter.
Intermediate (2.0-4.0 mm)
Intermediate (2.0-4.0 mm)
Fine (1.0-2.0 mm)
Fine (1.0-2.0 mm)
Fig. 25. Assumed mesh sizes for SH and PO model in sensitivity analysis.
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60
60
F [kN]
F [kN]
50
50
40
40
30
30
Coarse Intermediate Fine
20 10
20 10
d [mm]
d [mm]
0
0 0
2
4
6
8
0
2
4
6
8
Experimental Numerical perfect model Numerical - imp. 0.25 mm Numerical - imp 0.50 mm Numerical - imp. 1.00 mm
Fig. 27. Mesh sensitivity analysis results for PO model.
60
F [kN]
Fig. 30. Experimental vs numerical response curves for PO model.
50 40 30 20 Numerical Experimental
10
d [mm]
0 0
10
20
30
Fig. 28. Experimental vs. numerical response curves for SH model.
Table 11 Comparison between numerical and experimental results for SH model.
Numerical Experimental Num/Exp
Fmax (kN)
k (kN/mm)
49.7 49.3 +1%
7.51 8.32 10%
It has to be noticed that the formulation proposed by Hellgren, in the examined cases, strongly overestimates the strength with differences ranging from 68% to 165%. On the other hand, CNR-DT 208 provides a better estimation of the joint strength with differences ranging from 10% to 27%. As far as shear strength is concerned, the results obtained by applying the formulation provided by Hellgren and CNR-DT 208 together the Sapa’s indications are summarised in Table 8. The results show that both Hellgren and CNR-DT 208 formulations give higher values than experimental ones with errors in the range from 60% to 232%. Sapa’s indications to evaluate the strength as 70% of the one evaluated for a common bolted joint is, for the examined case, quite conservative with differences ranging from 6% to 29%. Table 9 shows the prediction of bolt-channel pull-out strength according to the formulation suggested by Hellgren and Sapa. The comparison of predicted values with experimental ones shows that the strength obtained with Hellgren formulation is about 2 times the experimental values. Contrary, Sapa formulation strongly underestimates the strength with scatters of up to 45%. As general remark, the available formulations are calibrated on the basis of experimental tests carried out on a joint configuration different to this tested in this work. This difference could explain the great divergence between predicted and experimental values. In addition, the formulations that well approximate the experimental results are the Eq. (2) given in CNR-DT 208 for slip strength and the Sapa’s indication for shear strength. Both formulations are not calibrated on tests results, but they are based on design rules for traditional bolted joints.
4. Numerical modelling 4.1. Model assumptions
Fig. 29. Deformed configuration at failure for SH model.
Two models representative of BC joint under transversal shear (SH model) and pull-out force (PO model) have been calibrated, on the basis of experimental results. Both models are implemented by means of the ABAQUS 6.10 non linear software [13]. The main parts of the models are the aluminium channel, the bolt and the plate nut. In particular, the bolt, the washer and plate nuts are modelled as only one part, because the observed experimental behaviour does not exhibit any mutual deformation of these components. All the parts are schematized as three dimensional solid deformable parts and the geometrical non-linearity is taken into account. In addition, only one half of the actual geometry is modelled by exploiting the model symmetry with respect to middle plane of the whole system. The aluminium alloy (AW 6005A-T6) used for both specimens is modelled by means of the Ramberg–Osgood law [14], based on the experimental results and transformed in true stress-true strain format. In order to correctly catch the material behaviour for large deformation, the exponent of Ramberg–Osgood law (n = 23) is evaluated considering as reference points the 0.2% proof strength (f0 = 235 MPa) and the ultimate strength (fu = 279 MPa). The other material constants are: E = 63900 MPa (Young’s modulus) and
L. Fiorino et al. / Construction and Building Materials 73 (2014) 76–88
Perfect
Imp. 0.25 mm
Imp. 0.50 mm
Imp. 1.00 mm
Fig. 31. Deformed configurations for the assumed imperfection values.
Table 12 Comparison between numerical and experimental results for PO model.
Experimental Perfect Imp. 0.25 mm Imp. 0.50 mm Imp. 1.00 mm
Fmax (kN)
Fmax Num/exp
k (kN/mm)
k Num/exp
42.8 50.5 50.5 46.3 42.9
+18% +18% +8% +0.2%
28.6 33.2 32.8 32.1 31.5
+15% +15% +12% +10%
m = 0.30 (Poisson’s ratio). The part representing bolt and plate nuts is mechanically characterized by two different materials, corresponding to 8.8 and S355 steel grade, respectively. Both materials are modelled by a bilinear elastic-strain hardening law with E = 200,000 MPa and m = 0.30. The other properties that define the material behaviour are assumed as the nominal values and their true stress and true strain values are shown in Table 10. The material of the set-up system is S355 steel. The SH model reproduces the experimental tests of BC-SH-18 series, where beside the aluminium channel and the bolt with plate nuts, also the set-up plate is implemented (Fig. 22). The geometrical symmetry is defined by restraining middle plane against the translation along x-axis (Ux = 0) and the rotation about y- and z-axis (URy = URz = 0). In order to schematize the oversized connections at the channel ends, the internal surface of the aluminium channel top flanges is restrained against the translation. All the interactions are defined by the normal ‘‘hard-contact’’ behaviour and the tangential ‘‘penalty-contact’’ with friction coefficient of 0.3. The bolt tightening is simulated by ‘‘bolt load’’ ABAQUS option, in which the imposed load is of 15 kN, which corresponds to the tightening torque assumed in the experimental phase. The shearing load consists in a uniform displacement along y-axis applied to the top surface of set-up plate. The PO model is calibrated on the basis of the BC-PO-18 tests. In addition to the specimen parts (aluminium channel, bolt and plate nut), a rigid discrete planar ‘‘shell’’ element is introduced in order to reproduce the support plane of the set-up where the aluminium
87
channel is laid on (Fig. 23). The symmetry condition is defined by restraining this middle plane against the translation along x-axis (Ux = 0) and the rotation about y- and z-axis (URy = URz = 0). The interaction between the aluminium channel and the rigid shell is modelled by the ‘‘hard-contact’’ behaviour, while the set-up bolted connection is schematized by restraining x and y translations and a spring with stiffness of 900 kN/mm is introduced in z direction, in order to take into account the axial deformability of bolts. All the interactions are taken into account in a tangential ‘‘penalty-contact’’, with a friction coefficient of 0.3 and a normal ‘‘hard-contact’’ behaviour. The loading condition consists in applying a uniform displacement up to 6 mm along z-axis to the end of bolt shank. In order to model the non symmetric response observed in experimental tests, the presence of imperfections is taken into account and calibrated. The imperfections are introduced by locating the plate nuts in not centred position with respect of aluminium channel, as shown in Fig. 24. Therefore, in addition to the perfectly symmetric model, simply named ‘‘perfect’’, three models corresponding to imperfection amplitudes of 0.25, 0.50 and 1.00 mm are analysed. Both SH and PO models are meshed by means of an 8-node linear brick with reduced integration and hourglass control (C3D8R), which is generally used in case of problems related to material plasticity and contact interactions. The mesh size is defined by two limit values: the minimum in contact zones between the bolts and the aluminium channel and the maximum in the peripheral zones. All the analyses are performed by means of the Newton– Raphson incremental method. The optimal mesh size is defined by means of a sensitivity analysis, where three different mesh configurations are considered: coarse, intermediate and fine (Fig. 25). In both cases the intermediate mesh is adopted, because it allows to contain computational analysis time with a good results accuracy (Figs. 26 and 27). 4.2. Experimental vs. numerical results – SH model The comparison between experimental and numerical results in terms of response curve is shown in Fig. 28. The numerical curve describes the experimental results with acceptable approximation and the slipping plateau of the curve is slightly higher than those experimentally obtained. Another difference lies on the marked irregularity in experimental curve, probably depending on local phenomena. Table 11 shows the comparison between numerical and experimental results in terms of joint strength (Fmax) and stiffness (k). In particular, the model catches the joint strength in very good agreement with experimental results with an error of 1%; while the initial stiffness is underestimated of 10%. The reliability
Fig. 32. Deformed configuration at failure for PO model.
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of the proposed model is proved also by the good agreement between the numerical deformed configuration at failure and the experimentally observed one, as it shown in Fig. 29. 4.3. Experimental vs. numerical results – PO model The comparison between the results of the numerical models corresponding to different imperfection amplitudes and the experimental ones is shown in Fig. 30, in terms of load vs displacement (F–d) curves. The numerical curves for the different imperfection values show a good approximation with the experimental range. The 0.25 mm imperfect model shows a response practically identical to those provided by perfect models. This is confirmed also in terms of deformed configuration and of stress distribution, which is substantially symmetric; while 0.50 mm and 1.00 mm imperfect models clearly identify non symmetric deformed configurations (Fig. 31). Table 12 shows the comparison between numerical and experimental results in terms of joint strength and stiffness. Also in this case, the influence of 0.25 mm imperfection is so low that the strength and the stiffness values are equal to those obtained with the perfect model. It has to be noticed that the difference between numerical and experimental results decreases as for as the imperfection amplitude increases. In fact, by comparing the numerical results with the experimental ones, the perfect model overestimates both strength and stiffness with differences of 18% and 15%, respectively. These differences strongly decrease for 1.00 mm imperfect models with values of 0.2% and 10% for strength and stiffness, respectively. Therefore, the 1.00 mm imperfect model seems to match the experimental results with the best approximation. This is also confirmed by the very good correspondence between the deformed configuration of such model and the experimental one, as it is shown in Fig. 32. 5. Conclusions The identification of structural response of bolt-channel joints by means of experimental tests and the calibration of the numerical models has been successfully done. The joints are tested under three different loading directions: slip (SL), shear (SH) and pull-out (PO). The SL tests show high scattered results in terms of strength (14–24%) probably due to influence of the assembly imperfections. This issue does not affect the SH tests response, whose deformed configuration is globally symmetric and presents very low scattered values in terms of strength (3–4%). In the case of PO tests, although the strength values are little scattered (1–7%), the exhibited deformed configuration is always strongly non symmetric, probably due to assembly imperfections. Finite element models for interpreting the SH and PO tests are calibrated. The SH model provides a good strength and stiffness prediction, being the differences with experimental data of 1% and 10%, respectively. The deformed configuration obtained by the SH model matches very accurately the one experimentally exhibited. In order to match
the non symmetric response observed in PO tests, the PO model is calibrated taking into account the influence of imperfections. The model with imperfection amplitude of 1 mm matches with best approximation the experimental results (+0.2% and +10% for strength and stiffness). Therefore, the experimental results show the important rule of the imperfections on the joint response as well as the shape and the proportions of the channel cross-section that may strongly influence both the strength and the failure mechanism. Also for this reason, the comparison of experimental and predicted strength values shows that the available codified formulations, calibrated on tests on other different joint configuration, are not reliable for the investigated systems. Hence, numerical models able to take into account the influence of different channel geometries and the possible source of imperfection are necessary to the full understanding of the behaviour of the boltchannel joints. In this context, the proposed models can represent a useful design tool of general validity for this kind of joints. Acknowledgments The Authors gratefully acknowledge the METRA Company (Rodengo Saiano, Italy), which sponsored this research activity within the Doctoral School in Constructional Engineering of the University of Naples ‘‘Federico II’’. References [1] Macillo V., Special Joint Systems for Aluminium Structures: Experimental Tests and Numerical Models, PhD Dissertation, University of Naples ‘‘Federico II’’, 2013. [2] Fiorino L, Macillo V, Mazzolani FM. Screwed joint for aluminium extrusions: experimental and numerical investigation. In: 12th INALCO conference, Montreal 21–22 October, 2013. [3] Macillo V, Fiorino L, Mazzolani FM. Structural behavior of aluminium boltchannel joint: calibration of numerical models on testing results, In: 12th INALCO conference, Montreal 21–22 October, 2013. [4] Sapa, Design Manual, Sapa Profiler AB, Stockholm, 2009. [5] Bosh Rexroth Corporation, Aluminum Structural Framing System – Version 7.0, 2011. [6] Kieran S, Timberlake J, Loblolly House – Elements of a New Architecture, Princeton Architectural Press, 2008. [7] Kieran S, Timberlake J. Cellophane House – Kieran Timberlake. Archit Design 2009;79:58–61. [8] Hellgren M, Strength of Bolt-Channel and Screw-Joints in Aluminium Extrusions, KTH Royal Institute of Technology, Licentiate Thesis, Stockholm, 1996. [9] CEN, EN 1999-1-1 – Eurocode 9 – Design of aluminium structures – Part 1–1: General structural rules, European Committee for Standardization, Bruxelles, 2007. [10] CNR-DT 208/2011, Istruzioni per la progettazione, l’esecuzione ed il controllo di strutture di alluminio, Consiglio Nazionale delle Ricerche, Roma, 2011. [11] Hydro, Extrusion Design Manual – A world of opportunities, Hydro Aluminum North America, Linthicum MD, 2009. [12] ISO 6892-1, Metallic materials – Tensile Testing – Part 1: Method of test at room temperature, International Organization for Standardization, Genève, 2009. [13] Simulia, Abaqus Analysis User’s manual, version 6.10, Dassault Systemes Simulia Corporation, 2010. [14] Mazzolani FM. Aluminium alloy structures. 2nd ed. London: E & FN SPON; 1995.