Experimental investigation on shear behaviour of riveted connections in steel structures

Engineering Structures 33 (2011) 516–531

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Experimental investigation on shear behaviour of riveted connections in steel structures M. D’Aniello a , F. Portioli a , L. Fiorino b , R. Landolfo a,∗ a

Department of Constructions and Mathematical Methods in Architecture, University of Naples ‘‘Federico II’’, Via Forno Vecchio 36, 80134 Naples, Italy

b

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

article

info

Article history: Received 3 June 2010 Received in revised form 8 October 2010 Accepted 2 November 2010 Available online 27 November 2010 Keywords: Riveted connections Historic metal structures Lap-shear tests

abstract The results of an experimental study based on lap-shear tests on riveted connections are presented in this paper. Experimental specimens were manufactured with materials and techniques used in aged metal structures and different dimensions and configurations were considered. The results of the experimental investigation allowed the influence of various parameters on the response of the connections to be assessed, such as load eccentricity, variation in net area, plate width and number of rivets. The experimental results and predicted shear strengths were compared in order to evaluate the reliability of the provisions of EN 1993:1-8. On the basis of the results obtained, modifications are proposed to the design equations given by EN 1993:1-8 for the rivet shear strength and the ultimate resistance of the net cross-section. © 2010 Elsevier Ltd. All rights reserved.

1. Introduction Hot-driven rivets were extensively used in iron and steel structures in the past. Nowadays, these constructions represent an important part of the architectural and cultural heritage that needs to be preserved. Historic metal structures include several typologies, such as large span roofing of urban passages, gasholders and railway structures. Railway structures represent a considerable part of construction heritage in many European countries. In Italy, the railway network includes approximately 3500 steel bridges and 14 000 lattice roof structures. The main part of these constructions were built in the period 1910–1960 and were assembled by riveting, although high-strength bolts started to be used in the 1930s [1]. Riveted connections are still used to build new structures and to repair damaged connections in existing railway constructions (see Fig. 1). In particular, driven rivets are commonly used to replace damaged or missing fasteners because high strength bolts do not allow a good fit with the original elements unless the holes are reamed in situ. The majority of historic steel structures are still in service and are exposed to loads that are larger than was expected. The reliability of these structures is also affected by deterioration and the poor quality of the materials that were used. A recent research project [2] has shown that aged steels do not usually fulfil the

∗

Corresponding author. Tel.: +39 081 7682447; fax: +39 081 2538052. E-mail addresses: [email protected] (M. D’Aniello), [email protected] (F. Portioli), [email protected] (L. Fiorino), [email protected] (R. Landolfo). 0141-0296/$ – see front matter © 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.engstruct.2010.11.010

requirements of EN 10025 [3] for standardized materials. Thus, there is an urgent need to check the compliance of historic steel structures with current standards and to assess their residual lifetime. The evaluation of shear strength in riveted connections is a key issue in the assessment of existing steel structures. Many studies have investigated the behaviour of riveted connections [4–11]. However, considering the sensitivity of the connection response to the manufacturing process [6,7,9], it is necessary to extend the results that have been obtained to different materials, geometries and configurations. Moreover, the compliance of existing results with the predicted response according to modern codes should be checked. Despite the different manufacturing processes, the strength of riveted and bolted lap shear splices are treated in a similar manner in EN 1993:1-8 [12], with the exception of slip-resistance. Indeed, EN 1993:1-8 does not allow riveted connections to be regarded as a slip-resistant type. Rather, they are regarded as a bearing type, owing to the variability and low average value of clamping force. The capacity of hot-driven connections is affected by several factors, such as loading conditions, geometric and mechanical parameters and manufacturing procedures. The installation of hot-driven rivets involves many variables, including the driving and finishing temperature, driving time and pressure. Indeed, after the rivets have been heated to a high temperature, the manufacturing procedure requires that the plain end of the fastener be forged into a head by means of a pneumatic hammer. Then, when the hot rivet cools, it shrinks and pulls the parts tightly together. Thus, a residual clamping force and a pre-stressing in the rivet, with a partial slip resistance of the

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a

517

b

Fig. 1. Replacement of a riveted connection of an aged Italian existing railway bridge still in service (for courtesy of RFI, 2008).

joint are obtained. Due to several parameters influencing the pre-stress state (such as the grip length, rivet diameter, material and fabrication methodology), a reliable calculation method to determine the pre-stress state of the rivet is not available [13]. An early study [5] showed that the residual shrinkage of fasteners may essentially depend on the material’s properties and the driving temperature. Tests showed that mild steel rivets may exhibit an axial shrinkage of 0.6%–1.0%, while rivets made of alloy steel (having an average of 3% of Nickel) have smaller axial contraction of 0.3%–0.5%. In general, the clamping force is not as great as that developed by high strength bolts, and cannot be relied upon. The bandwidth of the rivet pre-stress is in the range 20–220 N/mm2 , with an average value of about 100 N/mm2 [13]. With regard to the influence of the driving on the strength of rivets and plates, the results of tests [9–11] showed that the driving process could increase the tensile strength of rivets by up to about 20% with respect to undriven rivets. A considerable reduction in elongation capacity was observed with the increase in strength, thus resulting in brittle behaviour. Tests performed by Hechtman [6] on rivets hot-driven at different temperatures showed that the strength increases with the temperature. This effect could be recognized up to a threshold of 900 °C. No appreciable variation was found by varying the temperature within the range 900–1200 °C. This phenomenon is related to the modification-induced in the steel grain microstructure, which typically occurs in the steel after thermomechanical treatments [14–16]. The technique used to perforate the plates may also affect the connection strength and fatigue life of riveted structures. In old metal structures, holes were obtained by techniques such as: drilling, punching, sub-drilling and reaming, punching and reaming. Their effects on shear connections are important when splices fail in tension on the net section. Indeed, early tests [9,17,18] showed that splices made of plates with drilled holes exhibited a large deformation with high necking, while in the case of punched holes the failure occurred in a brittle manner without evident necking. To analyze the influence of different parameters on the shear capacity of typical lap shear connections representative of historic structural typologies (e.g. roofing structures, low-rise buildings and bridges), in terms of structural verification according to the modern codes, a wide experimental investigation was carried out within the framework of the PROHITECH project [19].

obtained from the RFI warehouse in Naples, where they had been stored since the 1950s. Owing to their age, both plates and rivets showed a slight patina of corrosion. Hence, as a first step both plates and rivet were sandblasted. After this superficial treatment, according to RFI requirements [20,21], holes in the plates were obtained by drilling and reaming. The specimens were assembled with hot-driven rivets. The main phases of the riveting procedure are illustrated in Fig. 2. Before their installation rivets were heated up to approximately 900 °C. This temperature was deemed to have been reached when the rivets in the forge took on the so-called ‘‘cherry-red’’ colour (see Fig. 2(a)). After heating, the rivet was inserted in the matching hole of the plates to be joined and a new head was then formed on the protruding end of the shank with a pneumatic hammer (see Fig. 2(b)–(d)). When forming the head, the diameter of the rivet increased, thus filling the entire hole, which was generally 1 mm greater than the diameter of the undriven rivet. After this process no clearance was observed between the shank and the joined plates. During the riveting process the enclosed plates were drawn together with installation bolts and by the riveting equipment.

2. Manufacturing of riveted connections

3.3. Testing programme on riveted connections and investigated parameters

To investigate the experimental behaviour of riveted connections, different specimens were manufactured by specialists working for the Italian railway network agency (RFI). The riveted specimens were assembled using aged plates and rivets that were

3. Experimental programme 3.1. General The objective of the testing programme was to analyze the influence of different parameters on the shear response of riveted connections. The specimen dimensions and details were selected by the Steel Structure Division of RFI, which is based in Naples, in order to be representative of connections typically used for its lattice roofing and bridges. The experimental programme was organized into two parts: tests on materials and tests on steel riveted joints. 3.2. Programme of material tests Tests on materials were planned in order to fully characterize both the mechanical and the chemical properties of the steel plates and rivets constituting the connections being examined. The experiments included tensile coupon tests, Brinnel hardness (BH) tests, chemical analysis and Charpy-V notch (CVN) tests.

The experimental programme on riveted specimens was planned in order to analyze the influence of the following parameters on the connection response:

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a

b

c

d

Fig. 2. The riveting process: the rivet heating (a); the pneumatic hammer (b); the head rivet forging with pneumatic hammer (c,d).

Fig. 3. Riveted specimens: investigated typologies.

1. Load eccentricity: both symmetrical and unsymmetrical specimens were considered in order to analyze the effects of secondary bending moments induced by load eccentricity on joint deformation and shear strength. 2. Net area: different values of the normalized net area An /Ag were considered in order to induce the yielding at the gross cross-section before the failure by fracture at the net cross-section. In general, this requirement is satisfied if the ratio An fu /Ag fy (An fu being the ultimate strength of the net section and Ag fy the yield strength of the gross section) is larger than 1. Based on the specified average yield and tensile strengths for the investigated type of steel, the normalized net area An /Ag has to be equal to or greater than 0.67 in order to achieve yielding of the gross section before failure of the net section occurs. In the examined cases the normalized net area An /Ag varies in the range 0.68–0.79, which corresponds to a ratio of An fu /Ag fy in the range 1.02–1.17. 3. Plate width: different values of the ratios w/d were considered, where w is the width of plates and d is the nominal diameter of the rivet, namely 3.16, 3.18, 4.38 and 4.74. The values were assigned in order to evaluate the influence of the width on the failure in tension of the plates, which becomes remarkable when the ratio (w/d) is lesser than 8, according to the literature [7,9]. 4. Joint length: the length of the joint is a function of the number of rivets, the rivet spacing p and the distance from the centre of the end rivet hole to the adjacent edge (e1 ) in the direction of shear load. In this study specimens made of one, two and four rivets were tested. Four different p/d ratios (4.09, 6.32, 8.75

and 9.21) were tested. These ratios satisfy the geometric limits of EN 1993:1-8 [12] with the exception of specimens U19-10-2_60 and U19-10-4_60, in which p/d = 9.21 while the corresponding Eurocode limit is 7.37 (being the maximum allowable spacing equal to 14 times the plate’s thickness). In addition, in our experimental series three different e1 /d ratios (1.59, 2.19 and 2.37) were analyzed. 5. Rivet clamping force: the effects of the rivet clamping force on the slip resistance were analyzed. A total of 64 lap shear tests were performed, as summarized in the programme matrix reported in Table 1. The geometries of the investigated connections are shown in Fig. 3. Specimens were labelled as C –D–TH–N, where: C is the splice configuration (i.e. S: Symmetrical joint; U: Unsymmetrical joint); D is the rivet diameter (16, 19 or 22 mm); TH is the steel plate thickness (10 or 12 mm); N is the number of rivets per specimen. Three nominally identical specimens have been built up for every type of riveted connection. This was done because similar riveted connections can show a different capacity response and they can be affected by the manual riveting [10]. In two cases (U19-10-2 and U19-10-4) RFI asked us to investigate the influence of two different values of the distance from the edge to the centre of the rivet in the transverse direction. Hence, the same tag has been adopted twice for specimens having two different widths.

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Table 1 Riveted specimens: test programme matrix. Specimen tag

Symmetric Unsymmetric Rivet diameter (mm)

Thickness plate (mm)

Width plate (mm)

Distance from edge (mm)

Rivet pitch (mm)

Rivet no.

Test no.

16 16 19 19 19 19 22 22 22 22

10 10 10 10 12 12 10 10 12 12

70 70 90 90 90 90 70 70 70 70

35 35 45 45 45 45 35 35 35 35

– – – – – – – – – –

1 1 1 1 1 1 1 1 1 1

3 (A–B–C) 3 (A–B–C) 3 (A–B–C) 3 (A–B–C) 3 (A–B–C) 3 (A–B–C) 3 (A–B–C) 2 (A–B) 2 (A–B) 3 (A–B–C)

16 16 19 19

10 10 10 10

70 70 90 90

35 35 45 45

140 140 120 120

2 4 2 2

3 (A–B–C) 3 (A–B–C) 3 (A–B–C) 3 (A–B–C)

19

10

60

30

175

4

3 (A–B–C)

19 19

10 10

90 90

45 45

120 120

4 4

3 (A–B–C) 3 (A–B–C)

19

10

60

30

175

4

3 (A–B–C)

22 22 22 22

12 12 12 12

70 70 70 70

35 35 35 35

90 90 90 90

2 2 4 4

3 (A–B–C) 3 (A–B–C) 3 (A–B–C) 3 (A–B–C)

Single rivet S-16-10-1 U-16-10-1 S-19-10-1 U-19-10-1 S-19-12-1 U-19-12-1 S-22-10-1 U-22-10-1 S-22-12-1 U-22-12-1 Rivets in row U-16-10-2 U-16-10-4 S-19-10-2 U-19-10-2 (width 90 mm) U-19-10-2 (width 60 mm) S-19-10-4 U-19-10-4 (width 90 mm) U-19-10-4 (width 60 mm) S-22-12-2 U-22-12-2 S-22-12-4 U-22-12-4

Total tests 64

a

b

Fig. 4. Coupon sampled from a plate of riveted specimen under testing (a); rivet coupon under testing (b).

3.4. Set-up of material and riveted connection tests Tests on materials included tensile, CVN, BH tests and chemical analysis. All the material coupons for tensile strength characterization were tested by means of a universal electro-mechanical MTS 500 testing machine. The strains were measured using both strain gages and a linear deformometer (see Fig. 4(a) and (b)). With reference to rivet coupons, in order to perform the uniaxial tensile test the shanks of three rivets per selected diameter were milled as shown in Fig. 5, arranging them like a dog-bone. Both

ends of the rivet were screw-threads and two cylindrical threaded sleeves were used to fix the specimens into the test machine. An impact tester (Zwick 5113) was used for CVN tests of plates and rivets. A universal hardness test machine (ELBO TH-3000-OB) was used for BH measurements. Finally, a glow discharge atomic emission spectrometer (LECO model GDS850A) was employed to identify the chemical composition of both plates and rivets. The experimental setup used for riveted connections is shown in Fig. 6(a). In particular, lap shear tests were carried out with a universal electro-mechanical Zwick/Roell testing machine (see Fig. 6(b)). The specimens were loaded in tension under

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Fig. 5. Dog-bone rivet shank.

a

b

c

d

Fig. 6. Test setup (a); the testing machine (b); the layout of LVDTs (c, d).

displacement control until failure, i.e. after the load decreased. The maximum load reached and the types of failure mode were observed for each test. The relative in-plane displacement of tested specimens was measured by means of a pair of LVDT (Linear Variable Differential Transformer) characterized by a displacement range of ±150 mm and positioned 30 mm from both ends of the regions where plate discontinuities occur in all specimens (Fig. 6(c) and (d)). The displacement rate was fixed at 0.1 mm/s and an acquisition frequency of 10 Hz was assumed. 4. Experimental results 4.1. Tests on materials Fig. 7. The stress–strain response of plates of riveted specimens.

4.1.1. Tensile tests Five specimens were sampled from plates. The stress–strain curves of the plates is shown in Fig. 7. The average yield stress of steel plate was 291 MPa (Standard Deviation ‘‘SD’’ = 5.63 MPa and Coefficient of Variation ‘‘CV’’ = 0.02), while the average ultimate stress was 433 MPa (SD = 5.48 MPa, CV = 0.01) and there was an average ultimate strain (corresponding to necking) of about 28%

(SD = 1%, CV = 0.04). This material was identified as a modern steel S 275. It was not possible to set a specific trend per rivet diameter in terms of yield and ultimate strength (see Fig. 8). Indeed, there was considerable variability in the basic material properties of the rivets. This may be assignable to the lack of adequate quality

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4.1.4. Chemical analysis The results of the chemical analyses are summarized in Tables 3 and 4. They show that the materials of plates and rivets are characterized by high sulphur (about twice the maximum value of the quantity commonly present in modern steel EN 10025 [3]), but different carbon contents. In particular, the plates have a low carbon percentage (0.08%), while the rivets have a high percentage (0.39%). Moreover, the comparison in terms of equivalent carbon percentage (Ceq ) with results given in [23–25] confirms that two types of aged steel were considered, with no precise equivalence to modern mild steel, except for the tensile strength characteristics. Nevertheless, the high sulphur content has a negative effect on both corrosion resistance and metal toughness. This aspect is emphasized for rivets, where the high carbon content implies low ductility, and difficulty in machining.

Fig. 8. The stress–strain response of rivet specimens.

control in the industrial processes of that period. However, the average value of yield stress was 315 MPa (SD = 26.03 MPa, CV = 0.08), the average ultimate stress was about 412 MPa (SD = 17.85 MPa, CV = 0.04), while the average ultimate strain (corresponding to necking) was 16% (SD = 6%, CV = 0.36). These data appear to be more consistent with steel produced by a Martin–Siemens process [22].

4.2. Tests on riveted connections 4.2.1. Monitored mechanical parameters The parameters used to describe the experimental behaviour that have been monitored during each of the tests are illustrated in Fig. 9, where: – s = (sLVDT1 + sLVDT2 )/2: average displacement (sLVDTi is the displacement recorded by the ith LVDT); – Fu : strength, which is the maximum recorded average load; – su : slip corresponding to Fu ; – Fe : conventional elastic strength. The yield force is conventionally measured on an idealized bi-linear response curve obtained from the experimental one by assuming that the areas under the actual curve and its bi-linear idealization, which has the same initial stiffness and the same peak point of the actual curve, are equal; – se : slip corresponding to Fe ; – Ke = Fe /se : elastic stiffness; – smax : displacement corresponding to a load equal to 0.80Fu on the post-peak branch of response curve; – µ = smax /se : maximum ductility.

4.1.2. Impact strength tests Four specimens sampled from plates having a cross-section of 10 × 10 mm and a V notch were tested at ambient temperature, i.e. at 20 °C. The results are summarized in Table 2. It should be noted that the average Charpy-V-Notch (CVN) fracture toughness is equal to 15 J, which is lower than the reference value of 27 J at 0 °C or +20 °C as suggested in EN 10025 [3] for modern steel. These results are in accordance with the literature [22] that provides similar CVN values and highlights that this type of aged steel is more brittle than modern ones. 4.1.3. Hardness tests In order to have more detailed information on the materials used in the riveted specimens, BH tests on plates and rivet shanks were carried out. The results are summarized in Table 2 showing an average value of BH = 121 for plates and 137 for rivets. These results are consistent with the strength evaluated by tensile tests.

4.2.2. Failure modes Three basic types of failure mode were observed: (I) rivet shear failure; (II) bearing at rivet holes of thinner plates; (III) failure in tension on the net section of the steel plate.

Table 2 Material characterization: BH measurements and CVN fracture toughness. Brinell hardness measurements

Charpy-V-Notch fracture toughness

BH (500 kgf load, 10 mm ball)

Average BH

SD

CV

CVN (+20 °C) (J)

Average CVN (+20 °C) (J)

SD (J)

CV

Plate 1 Plate 2 Plate 3 Plate 4

119 121 123 120

121

1.71

0.01

23 36 38 25

31

7.59

0.25

Rivet 1 Rivet 2 Rivet 3 Rivet 4 Rivet 5

146 139 115 140 144

137

12.52

0.09

–

–

–

–

Table 3 Chemical composition of the plates.

Plate 1 Plate 2 Plate 3 Plate 4 Average value SD CV

C (%)

Si (%)

Mn (%)

P (%)

S (%)

Cu (%)

Cr (%)

Ni (%)

V (%)

Mo (%)

N (%)

Ceq (%)

0.07 0.08 0.09 0.08 0.08 0.01 0.10

0.15 0.18 0.19 0.17 0.17 0.02 0.10

0.54 0.5 0.56 0.54 0.54 0.03 0.05

0.014 0.012 0.017 0.01 0.01 0.00 0.23

0.059 0.061 0.061 0.048 0.06 0.01 0.11

0.41 0.37 0.38 0.3 0.37 0.05 0.13

0.06 0.06 0.11 0.06 0.07 0.03 0.34

0.12 0.11 0.12 0.1 0.11 0.01 0.09

0.004 0.004 0.004 0.003 0.00 0.00 0.13

0.02 0.02 0.02 0.02 0.02 0.00 0.00

0.0104 0.0099 0.0091 0.0092 0.0097 0.0006 0.0636

0.212 0.212 0.243 0.213 0.220 0.015 0.070

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Table 4 Chemical composition of the rivets.

Rivet 1 Rivet 2 Rivet 3 Rivet 4 Rivet 5 Average value SD CV

C (%)

Si (%)

Mn (%)

P (%)

S (%)

Cu (%)

Cr (%)

Ni (%)

V (%)

Mo (%)

N (%)

Ceq (%)

0.41 0.39 0.35 0.40 0.42 0.39 0.03 0.07

0.02 0.03 0.03 0.02 0.02 0.02 0.00 0.10

0.22 0.20 0.23 0.22 0.21 0.22 0.01 0.05

0.04 0.06 0.05 0.04 0.04 0.05 0.01 0.18

0.07 0.08 0.07 0.07 0.07 0.07 0.00 0.06

0.06 0.08 0.08 0.07 0.07 0.07 0.01 0.14

0.09 0.08 0.15 0.07 0.08 0.09 0.03 0.34

0.24 0.19 0.21 0.22 0.24 0.22 0.02 0.10

0.00 0.00 0.00 0.00 0.00 / / /

0.00 0.00 0.00 0.00 0.00 / / /

0.0146 0.0197 0.0239 0.0149 0.0151 0.0176 0.0041 0.2316

0.485 0.457 0.438 0.470 0.491 0.47 0.02 0.05

Fig. 9. Monitored mechanical parameters.

Obviously, in many cases, a joint exhibited a combination of failure mechanisms. Mixed failure modes, combining types I and III, occurred in unsymmetrical specimens In contrast, a single failure mode due either to rivet shear (I) or to the bearing of thinner plates (II) occurred for the symmetrical specimens. Fig. 10 shows the main types of failure mechanism and the relevant force–displacement response curves obtained by the tests. Tables 5 and 6 summarize the mechanical parameters monitored during each test for specimens made of a single rivet and with rivets in a row, respectively. 5. Interpretation of experimental results On the basis of the results obtained, the effects of selected parameters on the response of the connections are analyzed below. 5.1. Effect of load eccentricity Tests highlighted that the shear behaviour is strictly dependant on the geometry of the joint and the loading conditions. In the case of unsymmetrical specimens the load eccentricity induced a secondary bending moment, showing significant out-of-plane displacements, which tend to lift off one plate from the adjacent one at each connection. Tests showed that the effects of bending are mainly confined to the regions where plate discontinuities occur. As the joint length increases so bending will become less pronounced and the influence on the behaviour of the connection should decrease. These effects are similarly to those related to bolted connections with similar configurations [26]. The influence of bending was most pronounced in specimens with only a single rivet in the direction of the applied shear load (e.g. specimen U16-10-1 shown in Fig. 10(a)). In such a connection the rivet was not only subjected to single shear, but a secondary tensile component, which transmits the flexural action, may also be present. Furthermore, the plate material next to the splice was subjected to high bending stresses due to the load eccentricity. Hence, the bending slightly decreased the ultimate strength of the short connections. The shear strength of longer unsymmetrical

joints was less affected by the secondary bending. Indeed, in connections with a maximum of two rivets in line (U22-12-2 shown in Fig. 10(b)) rivet failure occurred. This suggests that almost complete equalization of the load had probably occurred before rivet failure. Failure in this case appeared as a simultaneous shearing of all the rivets. In the case of symmetrical specimens the applied load was perfectly centred and no flexural deformation occurred. It was experimentally observed that the differential elongations are greater at the ends of the joint (see Fig. 10(e)). In particular, it was recognized that the main plate yielded while the lap plates were still elastic. This is due to the low level of the applied load with respect to their plastic strength, which was confirmed by the absence of Lüder lines on the plates’ surfaces. It follows that the applied load is concentrated at the end rivets. In longer specimens, the plates were not sufficiently stiff and resistant to allow equal shear distribution among the rivets. Failure in the net section occurred with large plastic elongation of the end holes. 5.2. Effect of variation in An /Ag ratio All specimens which failed in tension on the net section exhibited ultimate tensile strengths of perforated plates higher than those found in the uniaxial coupon tests. This effect has also been found by other researchers [7,9,11,27] and it is known as the ‘‘net efficiency’’. This phenomenon may be attributed to the fact that the presence of the hole also gives rise to transverse stresses generating a sort of multiple-stress effect [7], emphasized by the presence of clamping force in the rivets, which avoid free lateral contractions in their vicinity. In the cases we examined, an average increase of tensile strength equal to 13% was measured (SD = 33.10 MPa, CV = 0.07), although the maximum calculated value was considerably larger and was 23% for specimens U1222-4 and S12-22-4 (corresponding to an ultimate tensile stress of about 530 MPa). The larger increase in tensile stress was recognized for specimens having the smaller An /Ag ratios, which means the smaller gauge width where the stress concentration and the pre-stressing induced by the clamped rivet head were higher. As the gauge width increased, which corresponds to the larger An /Ag ratio, this effect was less evident. 5.3. Effect of plate width Plate width is another parameter which influences the net efficiency. This can be easily observed for specimen U19-10-4, which failed in tension in the net area, where two different plate widths were investigated for the same geometric parameters. Indeed, increasing the plate width increased the ultimate strength of the connection. In general, it was recognized that the ultimate tensile strength of specimens failed in tension on the net section increased with an average scatter of 10%, varying the plate width from the minimum to the maximum w/d ratio. In some cases, reducing the plate width modified the failure mechanism. This is clearly evident for specimen U19-10-2, where two different plate widths (i.e. 90 and 60 mm) were examined,

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(a) Rivet shear failure (U16-10-1).

(b) Plastic bending and tearing of the steel plate in net section (U22-12-2).

(c) Rivet shear failure and yield in bearing of inner plate (S16-10-1).

(d) Yield in bearing of inner plate and material upset in front of the rivet (S19-10-1).

(e) Net cross-section failure (S22-12-4). Fig. 10. Main types of failure mechanism and relevant response curve.

all other geometric parameters being equal. In this case reducing the plate width modified the joint collapse mechanism from rivet shear to net section failure. It is interesting to note that EN1993:1-8 takes into account the influence of the plate width on single row riveted connections by

means of e2 /d ratios, where e2 is the distance from the centre of a hole to the adjacent edge in the transverse direction of the applied load. The e2 /d ratios corresponding to the examined specimens are 1.08, 1.09, 1.69 and 1.87. It should be noted that in the first two cases, which correspond to the smaller values of normalized net

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Table 5 Single rivet specimens: parameters characterizing the mechanical response. Single rivet

µ = su /se

Specimen A B C

Fp 146.08 147.99 131.43

su 5.51 6.26 3.90

smax 7.00 7.59 5.34

Fe 107.01 109.22 90.06

se 0.39 0.43 0.35

ke 274.38 253.56 257.87

Average SD CV A B C

141.83 1.35 0.01 80.02 83.95 76.71

5.22 0.53 0.10 2.50 3.83 3.06

6.64 0.42 0.06 3.39 4.36 3.91

102.10 1.57 0.02 66.94 64.41 62.30

0.39 0.03 0.07 0.41 0.42 0.45

261.94 14.73 0.06 163.27 153.36 138.44

13.28 0.29 0.02 6.10 9.12 6.80

Average SD CV A B C

80.23 46.97 0.59 180.45 232.35 207.12

3.13 1.74 0.56 5.80 12.08 10.10

3.89 2.14 0.55 11.17 14.80 11.40

64.55 37.48 0.58 136.01 141.70 130.02

0.43 0.21 0.49 0.46 0.46 0.53

151.69 87.43 0.58 295.67 311.43 247.66

7.34 4.48 0.61 12.61 26.55 19.23

Average SD CV A B C

206.64 109.20 0.53 86.99 108.93 108.52

9.33 5.20 0.56 3.04 2.85 5.12

12.46 6.91 0.55 3.85 3.68 6.04

135.91 70.84 0.52 47.36 95.34 64.00

0.48 0.13 0.27 0.43 0.46 0.47

284.92 154.12 0.54 110.14 207.26 137.63

19.46 11.47 0.59 7.07 6.18 11.00

Average SD CV A B C

101.48 51.65 0.51 225.16 207.17 217.19

3.67 1.90 0.52 6.54 6.93 6.43

4.52 2.60 0.57 7.86 7.95 7.14

68.90 40.40 0.59 126.70 125.35 149.00

0.45 0.15 0.34 0.31 0.50 0.60

151.68 87.81 0.58 415.41 250.70 270.91

8.08 4.47 0.55 21.43 13.86 11.68

Average SD CV A B C

216.51 111.96 0.52 100.63 145.28 106.84

6.63 3.24 0.49 3.65 5.55 3.81

7.65 3.74 0.49 4.15 6.57 4.72

133.68 63.06 0.47 60.07 87.37 73.36

0.29 0.14 0.49 0.41 0.61 0.80

1125.07 183.31 0.16 148.32 143.23 91.70

50.70 9.40 0.19 9.00 9.10 4.76

Average SD CV A B C

117.58 62.34 0.53 173.59 184.57 190.89

4.34 2.09 0.48 8.00 4.93 6.77

5.15 2.50 0.49 10.77 10.94 10.62

73.60 36.93 0.50 133.35 138.70 136.01

0.61 0.20 0.33 0.30 0.42 0.46

127.75 81.04 0.63 444.50 330.24 298.92

7.62 4.49 0.59 26.67 11.73 14.87

Average SD CV A B

183.02 89.01 0.49 143.13 146.43

6.57 3.31 0.50 9.33 10.32

10.78 5.47 0.51 10.14 11.09

136.02 69.38 0.51 79.34 76.02

0.39 0.09 0.23 0.78 0.67

357.89 208.04 0.58 102.37 113.46

17.76 11.50 0.65 12.03 15.40

U-22-10-1

Average SD CV A B

144.78 2.33 0.02 236.18 238.23

9.83 0.70 0.07 4.32 6.02

10.62 0.67 0.06 6.11 10.05

77.68 2.35 0.03 156.72 153.36

0.73 0.08 0.11 0.48 0.56

107.92 7.84 0.07 329.94 273.86

13.72 2.38 0.17 9.08 10.74

S-22-12-1

Average SD CV A B C

237.21 1.45 0.01 143.39 128.74 148.61

5.17 1.20 0.23 3.83 5.47 3.93

8.08 2.79 0.34 4.46 6.38 4.73

155.04 2.38 0.02 94.67 84.70 137.36

0.52 0.06 0.11 0.48 0.49 0.93

301.90 39.65 0.13 197.23 172.86 147.70

9.91 1.17 0.12 7.97 11.16 4.23

Average SD CV

140.25 78.37 0.56

4.41 2.40 0.54

5.19 2.56 0.49

105.58 51.26 0.49

0.63 0.23 0.37

172.60 97.22 0.56

7.79 5.33 0.68

S-16-10-1

U-16-10-1

S-19-10-1

U-19-10-1

S-19-12-1

U-19-12-1

S-22-10-1

U-22-12-1

areas, the limiting edge distance e2 is less than the limiting value (that is e2 ≤ 1.2do ) prescribed by EN 1993:1-8 [12]. However, even in these cases, there is a large additional reserve of strength with respect to the strength calculated according to the EN 1993:1-8 formula. 5.4. Effect of joint length Tests showed that joint length is an important parameter that influences the ultimate strength of the joint, especially for single lap shear connections. Although the present study did not

14.13 14.53 11.17

explicitly aim to investigate the influence of pitch on shear capacity and specific parametric tests were not performed, tests showed that the examined range of spacing did not appreciably influence the shear strength. In terms of the influence of e1 /d ratios on the joint response, it was recognized that although in the examined specimens this ratio was larger than the EN 1992:1-8 limit (which is 1.2), when the specimen failed in pure bearing the end distance was insufficient and the rivet split out through the end of the plate, as occurred in S19-10-1 (shown in Fig. 10), S22-10-1 and S22-12-1.

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525

Table 6 Specimens with rivets in row: parameters characterizing the mechanical response. Rivets in row

U-16-10-2

U-16-10-4

S-19-10-2

U-19-10-2 (width 90 mm)

U-19-10-2 (width 60 mm)

S-19-10-4

U-19-10-4 (width 90 mm)

U-19-10-4 (width 60 mm)

S-22-12-2

U-22-12-2

S-22-12-4

U-22-12-4

Specimen A B C

Fp 141.87 162.23 161.37

su 2.78 3.84 2.88

smax 3.97 4.61 3.69

Fe 98.68 105.36 110.68

se 0.48 0.56 0.53

ke 207.75 189.84 210.82

µ = su /se

Average SD CV A B C

155.16 14.40 0.09 236.56 241.13 242.85

3.17 0.75 0.24 18.97 23.51 23.41

4.09 0.45 0.11 22.40 27.30 26.60

104.91 4.72 0.05 166.69 168.69 170.68

0.52 0.06 0.11 0.99 1.01 0.96

202.80 12.66 0.06 169.23 167.02 178.72

6.08 0.76 0.12 19.25 23.27 24.51

Average SD CV A B C

240.18 133.85 0.56 336.63 346.02 332.60

21.96 12.12 0.55 14.24 16.27 10.46

25.43 14.33 0.56 16.80 18.75 13.45

168.69 95.46 0.57 236.69 240.71 230.69

0.99 0.53 0.54 0.84 0.60 0.63

171.66 93.54 0.54 281.77 404.55 366.17

22.34 12.13 0.54 16.95 27.34 16.60

Average SD CV A B C

338.42 167.40 0.49 201.55 196.22 232.35

13.66 7.04 0.52 4.35 4.36 5.22

16.33 8.23 0.50 5.29 5.17 6.40

236.03 116.72 0.49 128.68 126.69 126.70

0.69 0.15 0.21 0.62 0.66 0.64

350.83 182.16 0.52 207.55 193.42 197.97

20.30 11.12 0.55 7.01 6.66 8.16

Average SD CV A B C

210.04 95.14 0.45 190.09 184.23 188.92

4.64 2.68 0.58 13.12 13.30 13.83

5.62 3.19 0.57 17.38 17.51 18.29

127.36 61.99 0.49 128.68 123.36 121.34

0.64 0.27 0.42 0.53 0.52 1.10

199.65 97.48 0.49 245.10 237.23 110.81

7.28 4.36 0.60 24.99 25.59 12.63

Average SD CV A B C

187.75 89.30 0.48 354.63 353.27 352.96

13.42 6.74 0.50 10.69 11.02 9.69

17.73 9.05 0.51 14.30 13.85 12.45

124.46 60.25 0.48 254.04 251.45 256.67

0.72 0.12 0.17 0.74 0.62 0.64

197.71 117.85 0.60 345.63 405.56 404.20

21.07 13.26 0.63 14.54 17.77 15.26

Average SD CV A B C

353.62 182.09 0.51 356.61 355.52 355.12

10.47 4.89 0.47 23.12 22.04 25.28

13.53 6.40 0.47 26.15 25.10 28.40

254.05 130.69 0.51 250.01 243.38 246.67

0.67 0.31 0.47 1.29 1.30 1.06

385.13 190.40 0.49 193.81 187.94 232.71

15.86 7.52 0.47 17.92 17.02 23.84

Average SD CV A B C

355.75 169.89 0.48 184.37 178.42 183.07

23.48 11.64 0.50 14.53 11.84 10.98

26.55 13.04 0.49 18.45 17.00 14.65

246.69 117.32 0.48 122.69 121.34 130.70

1.22 0.53 0.43 0.82 0.76 0.72

204.82 95.14 0.46 149.62 160.72 182.80

19.59 8.30 0.42 17.71 15.68 15.36

Average SD CV A B C

181.95 88.74 0.49 278.89 298.35 296.89

12.45 6.23 0.50 2.75 6.71 7.68

16.70 8.16 0.49 4.56 8.39 9.44

124.91 60.03 0.48 257.38 212.70 210.02

0.77 0.19 0.24 0.32 0.50 0.55

164.38 73.19 0.45 804.31 425.40 385.36

16.25 7.86 0.48 8.58 13.42 14.08

Average SD CV A B C

291.38 145.63 0.50 279.05 255.24 280.77

5.71 2.95 0.52 10.46 8.88 11.60

7.46 3.71 0.50 11.63 10.13 13.49

226.70 122.08 0.54 170.02 184.03 170.72

0.46 0.14 0.30 1.6 1.63 1.64

538.36 369.03 0.69 106.26 112.90 104.10

12.03 5.34 0.44 6.54 5.45 7.07

Average SD CV A B C

271.69 127.12 0.47 308.94 298.54 303.50

10.31 4.73 0.46 9.76 9.76 7.24

11.75 5.27 0.45 12.17 12.00 8.95

174.92 83.42 0.48 249.26 250.06 247.68

1.62 0.81 0.50 0.75 0.85 0.66

107.75 156.56 1.45 334.46 293.58 373.88

6.35 2.72 0.43 13.10 11.46 10.93

Average SD CV A B C

303.66 147.93 0.49 308.94 303.59 303.66

8.92 4.49 0.50 15.67 13.16 15.23

11.04 5.68 0.51 18.60 15.40 17.90

249.00 124.61 0.50 201.34 200.68 202.69

0.75 0.16 0.21 0.85 1.07 0.88

333.97 150.66 0.45 236.87 188.43 230.33

11.83 6.29 0.53 18.43 12.36 17.30

Average SD CV

305.40 146.89 0.48

14.69 7.14 0.49

17.30 8.40 0.49

201.57 94.64 0.47

0.93 0.46 0.49

218.54 102.06 0.47

16.03 7.72 0.48

5.84 6.91 5.49

526

M. D’Aniello et al. / Engineering Structures 33 (2011) 516–531

Fig. 11. Rivet number vs. ultimate strength (unsymmetric specimens).

Fig. 13. Symmetric vs. unsymmetric specimen shear capacity.

5.5. Effect of clamping forces

Fig. 12. Rivet number vs. ultimate strength (symmetric specimens).

Figs. 11 and 12 show in which terms the shear strength (here expressed as the ratio of strength Fu,i of the specimen having ‘‘i’’ rivets over the strength Fu,1 of the specimen having a single rivet) of the examined joint configuration varies with respect to the number of rivets and the An /Ag ratio. For both unsymmetrical and symmetrical specimens the strength does not increase linearly as the number of rivet increases. Rather, as the number of rivets increased, a decrease in the average strength occurred at a decreasing rate. This is due to the fact that, owing to the particular geometry of the specimens being analyzed, failure modes different from rivet shearing occurred. Indeed, for longer joints the redistribution of rivet force did not occur and onset of yielding in the gross section of the plate occurred. Consequently, for the configuration being tested, having a large number of rivets does not imply a high shear stress in the rivet. However, longer joints having the larger An /Ag ratio showed a lesser decrease in average shear strength when compared with the shear strength of a single rivet. Short lap joints (having up to two rivets) were hardly affected, while this was not true for symmetrical specimens. Fig. 13 shows the shear capacity of symmetrical specimens (Fsym ) related to the strength of unsymmetrical specimens (Funsym ) expressed as a function of the number of rivets and the An /Ag ratio. The latter parameter seems to be the most influential. Indeed, for a low An /Ag ratio even if lap joints have the rivets loaded in one shear plane, their capacity does not differ appreciably for symmetrical joints, which have the rivets loaded in double shear. This occurs because the inner plate of the symmetrical specimen is the weaker one and it is not strong enough to allow shear distribution among the rivets. Thus having a double number of shear planes is irrelevant in terms of the actual strength of the connection. Conversely, for the larger value of An /Ag doubling the number of shear planes implies a benefit for the shear capacity, even if failure modes other than rivet shearing may limit this effect. It should be noted that these charts were provided to RFI inspectors as a quick and easy tool with which to assess the shear capacity of the connections of RFI lattice structures. Therefore, they cannot be extended to connections having different geometries.

Although the rivet clamping forces were not measured directly, the analysis of results allowed the evaluation of the effects of variability of clamping forces on slip resistance. A gradual slip occurred as load was applied (e.g. specimens U16-10-1, U22-12-2, S 16-10-1 shown in Fig. 10(a)–(c), respectively), while in other cases the response curve exhibited a sudden slip (e.g. specimens S19-10-1 and S22-12-4 shown in Fig. 10(d) and (e), respectively). Due to the fact that the faying surfaces were not specifically treated, this different slip behaviour may be attributed to the variability of the clamping forces in the rivets, which implies different and unknown levels of pre-stressing of the surfaces of the plates in contact and an unreliable threshold for slip-resistance. Different slip behaviour has also been recognized for specimens of the same type. This may explain the variability of the measured initial stiffness (as reported in Tables 5 and 6) that is related to the degree of pre-stressing of the rivets. However, the slips were so small that they are not expected to have a significant effect on real structures. These results confirmed that the investigated connections can be considered as a bearing-type [12]. The possible initial slip should not affect the shape of the force–displacement curve to an appreciable extent. 6. Theoretical vs. experimental strength To evaluate the reliability of Eurocode formulas in predicting the strength of riveted connection, a comparison of the theoretical and experimental results was undertaken. The strength of the lap shear connections calculated in accordance with EN 1993 1-8 2005 is the minimum of the following formulas: (i) tensile strength of the critical net section (EN 1993:1-1 clause 6.2.3(2b)), Nu,Rd =

0.9Anet fu

γM2

(1)

where fu is the specified ultimate tensile strength of the plate; Anet is the net area of the plate subjected to tension; (ii) shear strength of the rivets (EN 1993:1-8 clause 3.6.1(1)), Fv,Rd =

0.6fur Ao

γM2

(2)

where fur is the ultimate tensile strength of the rivet; Ao is the area of the hole; (iii) bearing strength of the thinner plate (EN 1993:1-8 clause 3.6.1(1)). Fb,Rd =

k1 αb fu dt

γM2

(3)

M. D’Aniello et al. / Engineering Structures 33 (2011) 516–531

527

Table 7 Specimens with rivets in row: parameters characterizing the mechanical response. Failure mechanism (EN 1993 1-8) (kN)

F ∗ calculated strength (proposed formulas) (kN)

Failure mechanism (proposed formulas)

Fu /FEC 3

Fu /F ∗

99.31

V

148.97

V

1.43

0.95

49.66 140.05 70.02 140.05

V V V V

74.49 243.38 105.04 210.07

V B V V

1.62 1.48 1.45 1.55

1.08 0.85 0.97 1.03

70.02 126.20 93.88 151.44 93.88 99.31 187.46 280.10 140.05

V B V B V V V V V

105.04 189.30 140.82 227.16 140.82 148.97 259.61 341.34 210.07

V B V B V V T T V

1.68 1.45 1.54 1.57 1.49 1.56 1.28 1.21 1.50

1.12 0.97 1.03 1.04 1.00 1.04 0.93 0.99 1.00

T

140.05

V

197.11

T

1.34

0.95

353.62 355.75

T T

307.21 275.01

T V

341.34 341.34

T T

1.15 1.29

1.04 1.04

181.96

T

177.40

T

197.11

T

1.03

0.92

291.37 271.69 303.66 305.40

T V T T

249.23 187.77 249.23 249.23

T V T T

276.92 281.65 276.92 276.92

T V T T Average SD CV

1.17 1.45 1.22 1.23 1.40 0.17 0.12

1.05 0.96 1.10 1.10 1.01 0.07 0.07

Fu average strength (kN)

Failure mechanism (test)

S-16-10-1

141.83

U-16-10-1 S-19-10-1 U-19-10-1 S-19-12-1

80.22 206.64 101.48 216.51

U-19-12-1 S-22-10-1 U-22-10-1 S-22-12-1 U-22-12-1 U-16-10-2 U-16-10-4 S-19-10-2 U-19-10-2 (width 90 mm) U-19-10-2 (width 60 mm) S-19-10-4 U-19-10-4 (width 90 mm) U-19-10-4 (width 60 mm) S-22-12-2 U-22-12-2 S-22-12-4 U-22-12-4

117.58 183.02 144.78 237.21 140.25 155.16 240.18 338.41 210.04

V +B (secondary) V B V V +B (secondary) V B V B V V T T V

187.74

FEC 3 calculated strength (EN 1993 1-8) (kN)

Legend V = rivet shear failure B = plate bearing T = failure in tension in the net section.

where αb is the smallest of (αd , fub /fu or 1.0). In addition, in the direction of load transfer: e1 p αd = 3d —for end rivets; αd = 3d1 − 41 —for inner bolts. While, o o in the perpendicular to that of load transfer:  direction    kp1 = e2 min 2.8 d − 1.7 ; 2.5 —for edge rivets; k1 = min 1.4 d2 −

reduced by multiplying it by the reduction factor βLf , (EN 1993:1-8 3.8(1)), given by:

1.7 ; 2.5 —for inner rivets. d is the nominal diameter of the rivet; t is the thickness of the thinner plate; do is the hole diameter of a rivet; e1 is the end distance from the centre of a rivet hole to the adjacent end of any part, measured in the direction of load transfer; e2 is the edge distance from the centre of a hole to the adjacent edge of any part, measured at right angles to the direction of load transfer; p1 is the spacing between the centres of rivets in a line in the direction of load transfer; p2 is the spacing measured perpendicular to the load transfer direction between adjacent lines of rivets.

In order to compare the experimental results to that obtained by EN 1993:1-8 formulas, the latter have been calculated assuming the average experimental strengths of materials and that the partial safety factors γM2 are equal to unity. In Table 7 the test results are compared with the strengths and the expected failure modes predicted by the design equations of EN 1993 1-8 and those obtained by the proposed prediction equations. Fig. 14 shows the ratio between the average experimental strength (Fu ) and that calculated in accordance with EN 1993:1-8 (FEC 3 ). As can be observed, in four cases the failure mechanisms predicted by EN 1993 1-8 differ from those shown by the tests. In particular, net section failure occurred instead of rivet shear failure. The reason may be found in the large increase in ultimate shear strength induced by hot-driven process, as previously illustrated. Moreover, the calculated resistances are not in accordance with the measured values. In particular, the Eurocode prediction formulas provide conservative results, the average value of Fu /FEC 3 for all specimens is 1.40 (SD = 17%, CV = 0.12). In the plot, the letter that corresponds to the appropriate failure mechanism indicates these cases. The reasons for the large over-strength which was measured experimentally differed for the observed failure modes.



o

o

In particular, the design resistance of the rivets in a row has been taken as the sum of the design bearing resistances Fb,Rd of the individual rivets provided that the design shear resistance Fv,Rd of each individual rivet is greater than or equal to the design bearing resistance Fb,Rd . Otherwise the design resistance of a group of rivets has been taken as the number of rivets multiplied by the smallest design resistance of any of the individual rivets. Moreover, since the assumption that each rivet carries an equal share of the load becomes less and less accurate as joint length increases, in accordance with EN 1993:1-8 in all cases where the distance Lj between the centres of the end rivets in a joint, measured in the direction of force transfer, is more than 15 d, the design shear resistance Fv,Rd of all the rivets calculated according to Eq. (2) was

βLf = 1 −

Lf − 15d 200d

.

(4)

• An average Fu /FEC 3 ratio equal to 1.53 was obtained for specimens whose rivets failed in shear. This implies that the monotonic shear strength of this type of connection may be

528

M. D’Aniello et al. / Engineering Structures 33 (2011) 516–531

Fig. 14. Comparison of experimental results and predicted strength according to EC3. ∗ the abbreviation V indicates that the rivet shear failure was experimentally observed instead of the mechanism predicted by EN 1993:1-8 formulas. ∗∗ the dashed line indicates the average ratio.

noticeably higher than that calculated according to EN 1993:18. Although the driving process improves the ultimate tensile strength of the rivet by up to 20%, the experimental values of the shear capacities are still larger than the value calculated with the EN 1993:1-8 formula. In particular, the average overstrength ratio reduced by the hot-driven strengthening may be assumed to be 1.53/1.20 = 1.28, with 1.20 being the factor for the effect of the hot-driven process. This implies that the ultimate rivet shear stress fur ,v = 0.6fur calculated according to Eq. (2) is underestimated. An analysis of the results for different driving procedures and specimen configurations [7,8] showed that the rivets’ shear strength to tensile strength ratio (fur ,v /fur ) may vary within the range 0.67–0.83, with an average value of 0.75. If in the examined cases fur ,v is calculated as follows: fur ,v =

Fu 1.2 · nr ns Ao

(5)

where nr is the number of rivets and ns is the number of shear planes, then fur ,v /fur varies in the range (0.71 ÷ 0.84) with an average value of 0.76 (SD = 0.04, CV = 0.05), which confirms the values given in [7,8]. Thus, it is more appropriate to calculate the rivets’ shear strength as follows:

Ω1 · Ω2 · fur · Ao γM2

Fig. 15. Comparison of experimental and predicted strength calculated with proposed equations. ∗ the dashed line indicates the average ratio.

As can be observed in Fig. 15, the values of the strength

(F ∗ ) calculated with the proposed formulas are nearer to the experimental strengths (Fu ) than those given by EN 1993:1-8. Indeed, as it can be observed in Table 7, the average value of the Fu /F ∗ ratio for all specimens is slightly larger than 1.00 (Average value = 1.01) with scatters less than those obtained using Eurocode formulas (SD = 7%, CV = 0.07). Moreover, all the predicted failure mechanisms correspond to those obtained experimentally. 7. Statistical evaluation A statistical analysis was performed in order to verify the proposed strength functions and to determine also the appropriate value of partial factor γM ensuring that the adequate reliability index is met. Since some aspects influencing the bearing mechanism should be further investigated, only the proposed new expressions for rivet shear strength and for failure in tension on the net section have been statistically checked. The guidance for such type of analysis is given in EN 1990, Annex D [28], where the partial factor γM is defined as the ratio between the characteristic and the design value. The procedure for the assessment of a characteristic and design value is based on the following assumptions:

(6)

• the resistance is a function of a number of independent

where: – Ω1 takes into account the effect of the hot-driven process, which can be assumed to be equal to 1.20 for rivets driven in analogous manner to those examined; – Ω2 is the rivets’ shear strength to tensile strength ratio, which can be assumed to be equal to 0.75 in accordance to [4,7,8]. • The average over-strength Fu /FEC 3 ratio is equal to 1.50 if the specimen failed in bearing. A possible cause generating this large over-strength may be found in the rivets’ clamping force [4]. This implies that the shear load is partially transmitted by frictional resistance on the faying surfaces. However, because the friction resistance is related to the clamping force in the rivet, the actual influence of this effect is uncertain and further investigation is needed. • Specimens failing in tension on the net section exhibited an average Fu /FEC 3 ratio equal to 1.21. This occurs because of the net efficiency effect illustrated in Section 5.2. In the light of this result it seems that Eq. (1) may be improved by assuming no reduction factor:

• a sufficient number of tests is available; • all relevant geometrical and material properties are measured; • there is no correlation (statistical dependence) between the

Fv,Rd =

Nu,Rd =

Anet fu

γM2

.

(7)

variables Xi ;

variables in the resistance function;

• all variables follow either a normal or a log-normal distribution. The procedure is organized in the following steps: 1. development of the design model; 2. comparison of experimental and theoretical values; 3. estimation of the mean value of correction factor; 4. estimation of the coefficient of variation of the errors; 5. determination of the coefficients of variation of the basic variables; 6. determination of the characteristic value of the resistance. In particular, the first step of the analysis consists in the development of the theoretical resistance model of the experimental results. In this study the proposed resistance models are given by Eq. (6) for rivet shearing and Eq. (7) for net section failure. The examined theoretical resistances rt are assumed as functions of a number of independent variables X as the following: rt = grt (X ).

(8)

For the evaluation of these functions, the measured values of the mechanical characteristics and geometry are used.

M. D’Aniello et al. / Engineering Structures 33 (2011) 516–531

529

∆i = ln(δi )

a

¯ = ∆ s2∆ =

n 1−

n i =1 1

(12)

∆i

(13)

n − ¯ )2 (∆i − ∆

(14)

n − 1 i=1

where n is the number of tests. Finally: Vδ =

Fig. 16. Experimental strength vs. resistance model: rivet shear failure (a); net section failure (b).

The second step is the comparison of experimental and theoretical values. The experimental resistances are expressed by the vector re1 for specimens failed in rivet shear and re2 for those in net section. In Fig. 16(a) and (b) test results re1,i and re2,i are plotted versus the theoretical resistance rt1,i and rt2,i , respectively. If the resistance function was exact and complete, all points (rti , rei ) would lie on the bisector of the first quadrant. In the examined case, the points (rti , rei ) show little dispersion which may be attributed to the scatter in material properties and errors in geometry. The third step is the estimate of the mean value correction factor b, which is calculated using the least squares method. rei rti

i

b= ∑

rti2

.

(9)

i

The next step is the estimate of the coefficient of variation of the errors. The estimated error δi of each experimental result is determined from:

δi =

exp(s2∆ ) − 1.

(15)

The further step is to determine the coefficients of variation VXi of the basic variables. Indeed, to include the uncertainty of the steel grade and the fabrication of elements, the standard deviation is increased by the coefficients of variation VXi which are determined on the basis of prior knowledge. The coefficients of variations of steel constituting the plates and rivets is obtained from performed material tests. The variations of the independent geometric variables VXi were assigned according to [29]. In particular, the following variations were used:

b

∑



rei brti

.

(10)

The mean values of theoretical resistances rm are calculated by the mean values of basic variables X m : rm = brt (X m )δ = bgrt (X m )δ.

(11)

The mean values of the geometry are adopted as nominal values for the calculation of the rivets and net cross-sections. The mean values of material properties are equal to the measured ones. The material properties are equal for all specimens because all specimens were extracted from the same steel plate. On the basis of the estimated error δi , the estimator of variation coefficients for scatter Vd is determined by:

Vfu,plate = 0.075 variation coefficient for tensile strength of plates; Vfu,rivets = 0.079 variation coefficient for tensile strength of rivets; Vd0 = 0.005 variation coefficient for hole diameter; Vd = 0.005 variation coefficient for rivet diameter; Vt = 0.05 variation coefficient for plate thickness; Vw = 0.005 variation coefficient for width; Ve1 = 0.005 variation coefficient for end distance; Ve2 = 0.005 variation coefficient for edge distance. For small values Vd2 and VXi2 it is possible to determine Vr in the simplified way shown in the following: Vr2 = Vδ2 + Vrt2 ,

being Vrt2 =

j −

VXi2

i =1

(where j is the number of different variations).

(16)

For the calculation of the characteristic and the design resistances, the following standard deviations and coefficients are obtained from: Qrt = σln(rt ) =



Qδ = σln(δ) =



Qr = σln(r ) =



αrt =

Qrt

αδ =

Qδ

ln(Vrt2 + 1)

ln(Vδ2 + 1)

(18)

ln(Vr2 + 1)

(19)

Q Q

(17)

.

(20) (21)

The characteristic value for a limited number of tests is given by the following expression: rk = bgrt (X m ) exp(−k∞ αrt Qrt − kn αd Qd − 0.5Q 2 )

= bg rt (X m )Rk

(22)

where the appropriate values of fractile factors kn , kd,n , k∞ and kd,∞ are provided by EN 1990. Similarly, the design value for a limited number of tests is obtained as: rd = bg rt (X m ) exp(−kd,∞ αrt Qrt − kd,n αd Qd − 0.5Q 2 )

= bg rt (X m )Rd .

(23)

530

M. D’Aniello et al. / Engineering Structures 33 (2011) 516–531

Table 8 Results of statistic analysis. Resistance model

Failure type

N results

b

Vd

γM ,req

rt1 = Ω1 · Ω2 · fur · A rt2 = Anet fu

Rivet shear Net section failure

29 27

1.0119 1.0187

0.0908 0.0927

1.1261 1.1166

The estimate for the partial factor γM is defined as the ratio between the characteristic and the design value.

γM =

rk rd

=

exp(−k∞ αrt Qrt − kn αδ Qδ − 0.5Q 2 ) exp(−kd,∞ αrt Qrt − kd,n αδ Qδ − 0.5Q 2 )

=

Rk Rd

.

(24)

The results of the statistical analysis are presented in Table 8. The difference in the value of the partial factor γM for the two proposed verification formulas is negligible. Both proposed resistance models are characterized by a correction factor b close to 1 and a relatively small scatter (see Table 8 and Fig. 16). Therefore, they appropriately describe the rivets’ shear strength (resistance model 1) and the ultimate load at the net section (resistance model 2). The required partial factor for the proposed rivet shear resistance (Eq. (6)) is γM ,req = 1.1261. The scatter for this function is very low with V = 0.0908 and with correction factor b = 1.0119. Also the proposed formula for resistance of net section (Eq. (7)) is suitable. Indeed, the required partial factor γM ,req is equal to 1.1166, with V = 0.0927 and with correction factor b = 1.0187. Therefore both calculation formula describe the phenomena very well. According to EN1993, the partial factor to be assigned to the resistance models to form the design resistance is γM2 (with the recommended value equal to 1.25), since the resistance models are related to fracture mechanisms. It is clear that the proposed resistance models meet the reliability requirements of EN 1990, since the partial factor γM2 = 1.25 is greater than the value of γM ,req in both cases. Therefore, the design resistance can be formulated with partial factor γM2 , which provide some extra safety for parameters that were not included in our analysis, such as the effects of manufacturing tolerances that may be larger than assumed in [29]. 8. Conclusions This paper describes the results of a large experimental investigation carried out within the framework of the European project PROHITECH [18], with the aim of investigating the behaviour of riveted connections loaded in shear typically adopted in aged metal structures still in service in Italy in order to verify their strength according to EN 1993:1-8 [12]. Since the majority of riveted structures in Italy are railway constructions (both lattice roofs and bridges), the present study was undertaken in cooperation with Italian railway agency (RFI), which was interested in developing verification tools for those riveted splices in aged steel structures which are still in service. To achieve these objectives an experimental campaign has been carried out on riveted specimens made of aged steel, manufactured with the techniques in use in Italian railway practice. Specimen geometry was detailed as required by RFI. Both mechanical and chemical tests were carried out to characterize the steel constituting plates and rivets. Tests showed good mechanical and chemical properties (strength, chemical composition) on average but a large statistical dispersion of the data for the rivets was recognized. The results and observations from the lap shear tests were discussed and the main response characteristics were examined in the light of the existing literature. The experimental results highlighted that a considerable amount of out-of-plane deformation occurred in unsymmetrical

joints. It is clear that the effects of bending were mainly confined to the regions where plate discontinuities occurred. Obviously, as the joint length increased, bending was less pronounced, and its influence on the behaviour of the connection decreased. The influence of bending was most pronounced in the splice with only a single fastener in the direction of the applied load. In such a joint the fastener was not only subjected to single shear, but a secondary tensile component may also be present. Furthermore, the plate’s material in the direct vicinity of the splice was subjected to high bending stresses due to the eccentricity of the load. Hence, the bending tended to slightly decrease the ultimate strength of short connections. The shear strength of longer unsymmetrical joints seemed to be less affected by the effects of bending. Comparing the experimental strengths and the failure modes to those predicted by applying the formulas given in EN 1993:1-8 [12] it was recognized that the approach given in the code is conservative in all examined cases. However, the scatter between experimental and calculated strength seems excessively precautionary. In order to improve the theoretical prediction of shear strength of rivets, two further parameters should be taken into account: (1) the increase of ultimate tensile strength of rivets due to the hot-driven process; (2) the actual rivets’ shear strength to tensile strength ratio. The experimental over-strength in the bearing failure mode may be due to the contribution made by friction resistance between the faying surfaces constituting the splices. Owing to the uncertainties about the clamping in the rivets this effect needs further investigation. Specimens failing in tension on the net section exhibited an average strength 20% larger than that calculated according to EN 1993:1-8. This result should be ascribed to the net efficiency effect. In some cases the failure mechanisms predicted by EN 1993:1-8 differ from those exhibited by tests. This was due to the large increase in ultimate shear strength induced by the hot-driven process, which is not taken into account by EN 1993:1-8. Indeed, current EN 1993:1-8 methods for predicting the shear strength of riveted connections do not explicitly account for this factor. On the basis of the obtained experimental results, some modifications to EN 1993:1-8 prediction formulas are proposed. The provided equations are formulated considering the influence of the hot-driven process and of the net efficiency effect. The proposed formulas are closer to the experimental strengths than those given by EN 1993:1-8, in terms of both the ultimate strengths and the failure mechanisms. However, some aspects such as the effect of the friction resistance on the bearing mechanism and the presence of more rows of rivets in the connection need to be investigated in more exhaustive manner. The proposed calculation formula for rivet shear failure and for failure in tension on the net section were statistically evaluated according to EN 1990, Annex D. The analysis showed that the prescribed reliability is achieved by the recommended value of partial factor γM2 = 1.25. Due to the fact that no distinction is made in EN 1993 between riveted and bolted connections, new design equations are proposed to verify both the rivets’ shear and net area resistance, preserving the same simplicity of Eurocode verification procedure and providing more reliable control on the behaviour of riveted connections.

M. D’Aniello et al. / Engineering Structures 33 (2011) 516–531

Acknowledgements The authors gratefully acknowledge support from the PROHITECH project on ‘Earthquake protection of historical buildings by reversible mixed technologies’ within the Sixth Framework Programme FP6 of EU, and from the National Research Project PRIN prot. 2005087058_004, titled ‘‘Vulnerability and reversible consolidation techniques for historical metal structures’’. They also wish to thank Eng. Antonio D’Aniello, director of the Department of Naples at RFI for his courtesy, cooperation and assistance throughout this research and for having provided material and skilled workmanship for the manufacturing of riveted specimens. Finally, authors would like to thank Arch. Carla Ceraldi for her support given during the experimental activities at the Laboratory of Testing materials at the Dept. of Constructions and Mathematical Methods in Architecture of the University of Naples ‘‘Federico II’’.

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