Experimental investigation on shear behaviour of riveted connections in steel structures

Engineering Structures 33 (2011) 516–531

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Engineering Structures

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Experimental investigation on shear behaviour of riveted connections insteel structuresM. 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, Italyb Department of Structural Engineering, University of Naples ‘‘Federico II’’, P.le Tecchio 80, 80125 Naples, Italy

a r t i c l e i n f o

Article history:Received 3 June 2010Received in revised form8 October 2010Accepted 2 November 2010Available online 27 November 2010

Keywords:Riveted connectionsHistoric metal structuresLap-shear tests

a b s t r a c t

The results of an experimental study based on lap-shear tests on riveted connections are presentedin this paper. Experimental specimens were manufactured with materials and techniques used inaged metal structures and different dimensions and configurations were considered. The results ofthe experimental investigation allowed the influence of various parameters on the response of theconnections to be assessed, such as load eccentricity, variation in net area, plate width and numberof rivets. The experimental results and predicted shear strengths were compared in order to evaluatethe reliability of the provisions of EN 1993:1-8. On the basis of the results obtained, modifications areproposed to the design equations given by EN 1993:1-8 for the rivet shear strength and the ultimateresistance of the net cross-section.

© 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Hot-driven rivets were extensively used in iron and steelstructures in the past. Nowadays, these constructions represent animportant part of the architectural and cultural heritage that needsto be preserved.

Historic metal structures include several typologies, such aslarge span roofing of urban passages, gasholders and railwaystructures.

Railway structures represent a considerable part of construc-tion heritage inmany European countries. In Italy, the railway net-work includes approximately 3500 steel bridges and 14000 latticeroof structures. The main part of these constructions were built inthe period 1910–1960 and were assembled by riveting, althoughhigh-strength bolts started to be used in the 1930s [1].

Riveted connections are still used to build new structures and torepair damaged connections in existing railway constructions (seeFig. 1). In particular, driven rivets are commonly used to replacedamaged or missing fasteners because high strength bolts do notallow a good fit with the original elements unless the holes arereamed in situ.

The majority of historic steel structures are still in serviceand are exposed to loads that are larger than was expected. Thereliability of these structures is also affected by deterioration andthe poor quality of the materials that were used. A recent researchproject [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 steelstructures with current standards and to assess their residual life-time.

The evaluation of shear strength in riveted connections is a keyissue in the assessment of existing steel structures. Many studieshave investigated the behaviour of riveted connections [4–11].However, considering the sensitivity of the connection responseto the manufacturing process [6,7,9], it is necessary to extend theresults that have been obtained to different materials, geometriesand configurations.

Moreover, the compliance of existing results with the predictedresponse according to modern codes should be checked. Despitethe different manufacturing processes, the strength of riveted andbolted lap shear splices are treated in a similar manner in EN1993:1-8 [12], with the exception of slip-resistance. Indeed, EN1993:1-8 does not allow riveted connections to be regarded as aslip-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 severalfactors, such as loading conditions, geometric and mechanicalparameters and manufacturing procedures.

The installation of hot-driven rivets involves many variables,including the driving and finishing temperature, driving time andpressure. Indeed, after the rivets have been heated to a hightemperature, the manufacturing procedure requires that the plainend of the fastener be forged into a head by means of a pneumatichammer. Then, when the hot rivet cools, it shrinks and pullsthe parts tightly together. Thus, a residual clamping force anda pre-stressing in the rivet, with a partial slip resistance of the

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a 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 thepre-stress state (such as the grip length, rivet diameter, materialand fabrication methodology), a reliable calculation method todetermine the pre-stress state of the rivet is not available [13]. Anearly study [5] showed that the residual shrinkage of fastenersmayessentially depend on the material’s properties and the drivingtemperature. Tests showed that mild steel rivets may exhibit anaxial shrinkage of 0.6%–1.0%, while rivets made of alloy steel(having an average of 3% of Nickel) have smaller axial contractionof 0.3%–0.5%. In general, the clamping force is not as great as thatdeveloped by high strength bolts, and cannot be relied upon. Thebandwidth 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 strengthof rivets and plates, the results of tests [9–11] showed that thedriving process could increase the tensile strength of rivets byup to about 20% with respect to undriven rivets. A considerablereduction in elongation capacity was observed with the increasein strength, thus resulting in brittle behaviour. Tests performedby Hechtman [6] on rivets hot-driven at different temperaturesshowed that the strength increases with the temperature. Thiseffect could be recognized up to a threshold of 900 °C. Noappreciable variation was found by varying the temperaturewithin the range 900–1200 °C. This phenomenon is relatedto the modification-induced in the steel grain microstructure,which typically occurs in the steel after thermomechanicaltreatments [14–16].

The technique used to perforate the plates may also affectthe connection strength and fatigue life of riveted structures. Inold metal structures, holes were obtained by techniques suchas: drilling, punching, sub-drilling and reaming, punching andreaming. Their effects on shear connections are important whensplices fail in tension on the net section. Indeed, early tests[9,17,18] showed that splices made of plates with drilled holesexhibited a large deformation with high necking, while in the caseof punched holes the failure occurred in a brittle manner withoutevident necking.

To analyze the influence of different parameters on the shearcapacity of typical lap shear connections representative of historicstructural typologies (e.g. roofing structures, low-rise buildingsand bridges), in terms of structural verification according to themodern codes, a wide experimental investigation was carried outwithin the framework of the PROHITECH project [19].

2. Manufacturing of riveted connections

To investigate the experimental behaviour of riveted con-nections, different specimens were manufactured by specialistsworking for the Italian railway network agency (RFI). The rivetedspecimens were assembled using aged plates and rivets that were

obtained from the RFI warehouse in Naples, where they had beenstored since the 1950s. Owing to their age, both plates and rivetsshowed a slight patina of corrosion. Hence, as a first step bothplates and rivet were sandblasted. After this superficial treatment,according to RFI requirements [20,21], holes in the plates wereobtained by drilling and reaming.

The specimens were assembled with hot-driven rivets. Themain phases of the riveting procedure are illustrated in Fig. 2.Before their installation rivets were heated up to approximately900 °C. This temperature was deemed to have been reached whenthe rivets in the forge took on the so-called ‘‘cherry-red’’ colour(see Fig. 2(a)). After heating, the rivet was inserted in thematchinghole of the plates to be joined and a new head was then formedon the protruding end of the shank with a pneumatic hammer (seeFig. 2(b)–(d)). When forming the head, the diameter of the rivetincreased, thus filling the entire hole, which was generally 1 mmgreater than the diameter of the undriven rivet. After this processno clearance was observed between the shank and the joinedplates. During the riveting process the enclosed plates were drawntogether with installation bolts and by the riveting equipment.

3. Experimental programme

3.1. General

The objective of the testing programme was to analyze theinfluence of different parameters on the shear response of rivetedconnections.

The specimen dimensions and detailswere selected by the SteelStructure Division of RFI, which is based in Naples, in order to berepresentative of connections typically used for its lattice roofingand 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 characterizeboth the mechanical and the chemical properties of the steelplates and rivets constituting the connections being examined. Theexperiments included tensile coupon tests, Brinnel hardness (BH)tests, chemical analysis and Charpy-V notch (CVN) tests.

3.3. Testing programme on riveted connections and investigatedparameters

The experimental programme on riveted specimens wasplanned in order to analyze the influence of the followingparameters 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 speci-mens were considered in order to analyze the effects of secondarybending moments induced by load eccentricity on joint deforma-tion and shear strength.2. Net area: different values of the normalized net area An/Ag wereconsidered in order to induce the yielding at the gross cross-sectionbefore the failure by fracture at the net cross-section. In general,this requirement is satisfied if the ratio Anfu/Ag fy (Anfu being theultimate strength of the net section and Ag fy the yield strength ofthe gross section) is larger than 1. Based on the specified averageyield and tensile strengths for the investigated type of steel, thenormalized net area An/Ag has to be equal to or greater than 0.67in order to achieve yielding of the gross section before failure of thenet section occurs. In the examined cases the normalized net areaAn/Ag varies in the range 0.68–0.79, which corresponds to a ratioof Anfu/Ag fy in the range 1.02–1.17.3. Plate width: different values of the ratios w/d were considered,wherew is the width of plates and d is the nominal diameter of therivet, namely 3.16, 3.18, 4.38 and 4.74. The values were assigned inorder to evaluate the influence of thewidth on the failure in tensionof the plates, which becomes remarkable when the ratio (w/d) islesser than 8, according to the literature [7,9].4. Joint length: the length of the joint is a function of the numberof rivets, the rivet spacing p and the distance from the centreof the end rivet hole to the adjacent edge (e1) in the directionof shear load. In this study specimens made of one, two andfour 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 ofEN 1993:1-8 [12] with the exception of specimens U19-10-2_60and U19-10-4_60, in which p/d = 9.21 while the correspondingEurocode limit is 7.37 (being the maximum allowable spacingequal to 14 times the plate’s thickness). In addition, in ourexperimental 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 theslip resistance were analyzed.

A total of 64 lap shear tests were performed, as summarizedin the programme matrix reported in Table 1. The geometries ofthe investigated connections are shown in Fig. 3. Specimens werelabelled 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 forevery type of riveted connection. This was done because similarriveted connections can show a different capacity response andthey can be affected by the manual riveting [10]. In two cases(U19-10-2 and U19-10-4) RFI asked us to investigate the influenceof twodifferent values of the distance from the edge to the centre ofthe rivet in the transverse direction. Hence, the same tag has beenadopted twice for specimens having two different widths.

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Table 1Riveted specimens: test programme matrix.

Specimen tag Symmetric Unsymmetric Rivet diameter(mm)

Thickness plate(mm)

Width plate(mm)

Distance from edge(mm)

Rivet pitch(mm)

Rivetno.

Test no.

Single rivet

S-16-10-1 16 10 70 35 – 1 3 (A–B–C)U-16-10-1 16 10 70 35 – 1 3 (A–B–C)S-19-10-1 19 10 90 45 – 1 3 (A–B–C)U-19-10-1 19 10 90 45 – 1 3 (A–B–C)S-19-12-1 19 12 90 45 – 1 3 (A–B–C)U-19-12-1 19 12 90 45 – 1 3 (A–B–C)S-22-10-1 22 10 70 35 – 1 3 (A–B–C)U-22-10-1 22 10 70 35 – 1 2 (A–B)S-22-12-1 22 12 70 35 – 1 2 (A–B)U-22-12-1 22 12 70 35 – 1 3 (A–B–C)

Rivets in row

U-16-10-2 16 10 70 35 140 2 3 (A–B–C)U-16-10-4 16 10 70 35 140 4 3 (A–B–C)S-19-10-2 19 10 90 45 120 2 3 (A–B–C)U-19-10-2 (width90 mm)

19 10 90 45 120 2 3 (A–B–C)

U-19-10-2 (width60 mm)

19 10 60 30 175 4 3 (A–B–C)

S-19-10-4 19 10 90 45 120 4 3 (A–B–C)U-19-10-4 (width90 mm)

19 10 90 45 120 4 3 (A–B–C)

U-19-10-4 (width60 mm)

19 10 60 30 175 4 3 (A–B–C)

S-22-12-2 22 12 70 35 90 2 3 (A–B–C)U-22-12-2 22 12 70 35 90 2 3 (A–B–C)S-22-12-4 22 12 70 35 90 4 3 (A–B–C)U-22-12-4 22 12 70 35 90 4 3 (A–B–C)

Total tests64

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 chemicalanalysis.

All the material coupons for tensile strength characterizationwere tested by means of a universal electro-mechanical MTS 500testing machine. The strains were measured using both straingages and a linear deformometer (see Fig. 4(a) and (b)).

With reference to rivet coupons, in order to perform theuniaxialtensile test the shanks of three rivets per selected diameter weremilled as shown in Fig. 5, arranging them like a dog-bone. Both

ends of the rivet were screw-threads and two cylindrical threadedsleeves were used to fix the specimens into the test machine.

An impact tester (Zwick 5113) was used for CVN tests of platesand rivets. A universal hardness test machine (ELBO TH-3000-OB)was used for BH measurements. Finally, a glow discharge atomicemission spectrometer (LECO model GDS850A) was employed toidentify the chemical composition of both plates and rivets.

The experimental setup used for riveted connections is shownin Fig. 6(a). In particular, lap shear tests were carried outwith a universal electro-mechanical Zwick/Roell testing machine(see Fig. 6(b)). The specimens were loaded in tension under

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

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 wereobserved for each test. The relative in-plane displacement of testedspecimens was measured by means of a pair of LVDT (LinearVariable Differential Transformer) characterized by a displacementrange of ±150 mm and positioned 30 mm from both ends of theregionswhere plate discontinuities occur in all specimens (Fig. 6(c)and (d)). The displacement rate was fixed at 0.1 mm/s and anacquisition frequency of 10 Hz was assumed.

4. Experimental results

4.1. Tests on materials

4.1.1. Tensile testsFive specimens were sampled from plates. The stress–strain

curves of the plates is shown in Fig. 7. The average yield stress ofsteel plate was 291MPa (Standard Deviation ‘‘SD’’ = 5.63 MPa andCoefficient of Variation ‘‘CV’’ = 0.02), while the average ultimatestress was 433 MPa (SD = 5.48 MPa, CV = 0.01) and there was anaverage ultimate strain (corresponding to necking) of about 28%

Fig. 7. The stress–strain response of plates of riveted specimens.

(SD = 1%, CV = 0.04). This material was identified as a modernsteel S 275.

It was not possible to set a specific trend per rivet diameterin terms of yield and ultimate strength (see Fig. 8). Indeed, therewas considerable variability in the basic material properties ofthe rivets. This may be assignable to the lack of adequate quality

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

control in the industrial processes of that period. However, theaverage 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). Thesedata appear to be more consistent with steel produced by aMartin–Siemens process [22].

4.1.2. Impact strength testsFour specimens sampled from plates having a cross-section of

10×10mm and a V notchwere tested at ambient temperature, i.e.at 20 °C. The results are summarized in Table 2. It should be notedthat the average Charpy-V-Notch (CVN) fracture toughness is equalto 15 J, which is lower than the reference value of 27 J at 0 °C or+20 °C as suggested in EN10025 [3] formodern steel. These resultsare in accordancewith the literature [22] that provides similar CVNvalues and highlights that this type of aged steel is more brittlethan modern ones.

4.1.3. Hardness testsIn order to have more detailed information on the materials

used in the riveted specimens, BH tests on plates and rivet shankswere carried out. The results are summarized in Table 2 showingan average value of BH = 121 for plates and 137 for rivets. Theseresults are consistent with the strength evaluated by tensile tests.

4.1.4. Chemical analysisThe results of the chemical analyses are summarized in Tables 3

and 4. They show that the materials of plates and rivets arecharacterized by high sulphur (about twice the maximum valueof the quantity commonly present in modern steel EN 10025 [3]),but different carbon contents. In particular, the plates have a lowcarbon percentage (0.08%), while the rivets have a high percentage(0.39%). Moreover, the comparison in terms of equivalent carbonpercentage (Ceq) with results given in [23–25] confirms that twotypes of aged steel were considered, with no precise equivalence tomodern mild steel, except for the tensile strength characteristics.Nevertheless, the high sulphur content has a negative effect onboth corrosion resistance and metal toughness. This aspect isemphasized for rivets, where the high carbon content implies lowductility, and difficulty in machining.

4.2. Tests on riveted connections

4.2.1. Monitored mechanical parametersThe parameters used to describe the experimental behaviour

that have been monitored during each of the tests are illustratedin 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 convention-

allymeasured on an idealized bi-linear response curve obtainedfrom the experimental one by assuming that the areas under theactual curve and its bi-linear idealization, which has the sameinitial stiffness and the same peak point of the actual curve, areequal;

– 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.

4.2.2. Failure modesThree 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 2Material characterization: BH measurements and CVN fracture toughness.

Brinell hardness measurements Charpy-V-Notch fracture toughnessBH (500 kgf load, 10 mm ball) Average BH SD CV CVN (+20 °C) (J) Average CVN (+20 °C) (J) SD (J) CV

Plate 1 119

121 1.71 0.01

23

31 7.59 0.25Plate 2 121 36Plate 3 123 38Plate 4 120 25

Rivet 1 146

137 12.52 0.09 – – – –Rivet 2 139Rivet 3 115Rivet 4 140Rivet 5 144

Table 3Chemical composition of the plates.

C (%) Si (%) Mn (%) P (%) S (%) Cu (%) Cr (%) Ni (%) V (%) Mo (%) N (%) Ceq (%)

Plate 1 0.07 0.15 0.54 0.014 0.059 0.41 0.06 0.12 0.004 0.02 0.0104 0.212Plate 2 0.08 0.18 0.5 0.012 0.061 0.37 0.06 0.11 0.004 0.02 0.0099 0.212Plate 3 0.09 0.19 0.56 0.017 0.061 0.38 0.11 0.12 0.004 0.02 0.0091 0.243Plate 4 0.08 0.17 0.54 0.01 0.048 0.3 0.06 0.1 0.003 0.02 0.0092 0.213Average value 0.08 0.17 0.54 0.01 0.06 0.37 0.07 0.11 0.00 0.02 0.0097 0.220SD 0.01 0.02 0.03 0.00 0.01 0.05 0.03 0.01 0.00 0.00 0.0006 0.015CV 0.10 0.10 0.05 0.23 0.11 0.13 0.34 0.09 0.13 0.00 0.0636 0.070

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Table 4Chemical composition of the rivets.

C (%) Si (%) Mn (%) P (%) S (%) Cu (%) Cr (%) Ni (%) V (%) Mo (%) N (%) Ceq (%)

Rivet 1 0.41 0.02 0.22 0.04 0.07 0.06 0.09 0.24 0.00 0.00 0.0146 0.485Rivet 2 0.39 0.03 0.20 0.06 0.08 0.08 0.08 0.19 0.00 0.00 0.0197 0.457Rivet 3 0.35 0.03 0.23 0.05 0.07 0.08 0.15 0.21 0.00 0.00 0.0239 0.438Rivet 4 0.40 0.02 0.22 0.04 0.07 0.07 0.07 0.22 0.00 0.00 0.0149 0.470Rivet 5 0.42 0.02 0.21 0.04 0.07 0.07 0.08 0.24 0.00 0.00 0.0151 0.491Average value 0.39 0.02 0.22 0.05 0.07 0.07 0.09 0.22 / / 0.0176 0.47SD 0.03 0.00 0.01 0.01 0.00 0.01 0.03 0.02 / / 0.0041 0.02CV 0.07 0.10 0.05 0.18 0.06 0.14 0.34 0.10 / / 0.2316 0.05

Fig. 9. Monitored mechanical parameters.

Obviously, in many cases, a joint exhibited a combination offailure mechanisms. Mixed failure modes, combining types I andIII, occurred in unsymmetrical specimens In contrast, a singlefailure mode due either to rivet shear (I) or to the bearing ofthinner plates (II) occurred for the symmetrical specimens. Fig. 10shows the main types of failure mechanism and the relevantforce–displacement response curves obtained by the tests. Tables 5and 6 summarize the mechanical parameters monitored duringeach test for specimens made of a single rivet and with rivets ina row, respectively.

5. Interpretation of experimental results

On the basis of the results obtained, the effects of selectedparameters on the response of the connections are analyzedbelow.

5.1. Effect of load eccentricity

Tests highlighted that the shear behaviour is strictly dependanton the geometry of the joint and the loading conditions. In thecase of unsymmetrical specimens the load eccentricity induceda secondary bending moment, showing significant out-of-planedisplacements, which tend to lift off one plate from the adjacentone at each connection. Tests showed that the effects of bendingare mainly confined to the regions where plate discontinuitiesoccur. As the joint length increases so bending will become lesspronounced and the influence on the behaviour of the connectionshould decrease. These effects are similarly to those related tobolted connections with similar configurations [26]. The influenceof bending was most pronounced in specimens with only a singlerivet in the direction of the applied shear load (e.g. specimenU16-10-1 shown in Fig. 10(a)). In such a connection the rivetwas not only subjected to single shear, but a secondary tensilecomponent, which transmits the flexural action, may also bepresent. Furthermore, the plate material next to the splice wassubjected to high bending stresses due to the load eccentricity.Hence, the bending slightly decreased the ultimate strength of theshort connections. The shear strength of longer unsymmetrical

joints was less affected by the secondary bending. Indeed, inconnections with a maximum of two rivets in line (U22-12-2shown in Fig. 10(b)) rivet failure occurred. This suggests thatalmost complete equalization of the load had probably occurredbefore rivet failure. Failure in this case appeared as a simultaneousshearing of all the rivets.

In the case of symmetrical specimens the applied load wasperfectly centred and no flexural deformation occurred. It wasexperimentally observed that the differential elongations aregreater at the ends of the joint (see Fig. 10(e)). In particular, itwas recognized that the main plate yielded while the lap plateswere still elastic. This is due to the low level of the applied loadwith respect to their plastic strength, which was confirmed by theabsence of Lüder lines on the plates’ surfaces. It follows that theapplied load is concentrated at the end rivets. In longer specimens,the plates were not sufficiently stiff and resistant to allow equalshear distribution among the rivets. Failure in the net sectionoccurred 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 sectionexhibited ultimate tensile strengths of perforated plates higherthan those found in the uniaxial coupon tests. This effect has alsobeen found by other researchers [7,9,11,27] and it is known asthe ‘‘net efficiency’’. This phenomenon may be attributed to thefact that the presence of the hole also gives rise to transversestresses generating a sort of multiple-stress effect [7], emphasizedby the presence of clamping force in the rivets, which avoid freelateral contractions in their vicinity. In the cases we examined, anaverage increase of tensile strength equal to 13% was measured(SD = 33.10 MPa, CV = 0.07), although the maximum calculatedvalue was considerably larger and was 23% for specimens U12-22-4 and S12-22-4 (corresponding to an ultimate tensile stressof about 530 MPa). The larger increase in tensile stress wasrecognized for specimens having the smaller An/Ag ratios, whichmeans the smaller gaugewidthwhere the stress concentration andthe pre-stressing induced by the clamped rivet head were higher.As the gauge width increased, which corresponds to the largerAn/Ag ratio, this effect was less evident.

5.3. Effect of plate width

Plate width is another parameter which influences the netefficiency. This can be easily observed for specimen U19-10-4,which failed in tension in the net area, where two different platewidths were investigated for the same geometric parameters.Indeed, increasing the plate width increased the ultimate strengthof the connection. In general, it was recognized that the ultimatetensile strength of specimens failed in tension on the net sectionincreased with an average scatter of 10%, varying the plate widthfrom the minimum to the maximum w/d ratio.

In some cases, reducing the plate width modified the failuremechanism. This is clearly evident for specimen U19-10-2, wheretwo different plate widths (i.e. 90 and 60 mm) were examined,

M. D’Aniello et al. / Engineering Structures 33 (2011) 516–531 523

(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 reducingthe plate width modified the joint collapse mechanism from rivetshear to net section failure.

It is interesting to note that EN1993:1-8 takes into account theinfluence of the plate width on single row riveted connections by

means of e2/d ratios, where e2 is the distance from the centre of ahole to the adjacent edge in the transverse direction of the appliedload. The e2/d ratios corresponding to the examined specimens are1.08, 1.09, 1.69 and 1.87. It should be noted that in the first twocases, which correspond to the smaller values of normalized net

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Table 5Single rivet specimens: parameters characterizing the mechanical response.Single rivet Specimen Fp su smax Fe se ke µ = su/se

S-16-10-1

A 146.08 5.51 7.00 107.01 0.39 274.38 14.13B 147.99 6.26 7.59 109.22 0.43 253.56 14.53C 131.43 3.90 5.34 90.06 0.35 257.87 11.17Average 141.83 5.22 6.64 102.10 0.39 261.94 13.28SD 1.35 0.53 0.42 1.57 0.03 14.73 0.29CV 0.01 0.10 0.06 0.02 0.07 0.06 0.02

U-16-10-1

A 80.02 2.50 3.39 66.94 0.41 163.27 6.10B 83.95 3.83 4.36 64.41 0.42 153.36 9.12C 76.71 3.06 3.91 62.30 0.45 138.44 6.80Average 80.23 3.13 3.89 64.55 0.43 151.69 7.34SD 46.97 1.74 2.14 37.48 0.21 87.43 4.48CV 0.59 0.56 0.55 0.58 0.49 0.58 0.61

S-19-10-1

A 180.45 5.80 11.17 136.01 0.46 295.67 12.61B 232.35 12.08 14.80 141.70 0.46 311.43 26.55C 207.12 10.10 11.40 130.02 0.53 247.66 19.23Average 206.64 9.33 12.46 135.91 0.48 284.92 19.46SD 109.20 5.20 6.91 70.84 0.13 154.12 11.47CV 0.53 0.56 0.55 0.52 0.27 0.54 0.59

U-19-10-1

A 86.99 3.04 3.85 47.36 0.43 110.14 7.07B 108.93 2.85 3.68 95.34 0.46 207.26 6.18C 108.52 5.12 6.04 64.00 0.47 137.63 11.00Average 101.48 3.67 4.52 68.90 0.45 151.68 8.08SD 51.65 1.90 2.60 40.40 0.15 87.81 4.47CV 0.51 0.52 0.57 0.59 0.34 0.58 0.55

S-19-12-1

A 225.16 6.54 7.86 126.70 0.31 415.41 21.43B 207.17 6.93 7.95 125.35 0.50 250.70 13.86C 217.19 6.43 7.14 149.00 0.60 270.91 11.68Average 216.51 6.63 7.65 133.68 0.29 1125.07 50.70SD 111.96 3.24 3.74 63.06 0.14 183.31 9.40CV 0.52 0.49 0.49 0.47 0.49 0.16 0.19

U-19-12-1

A 100.63 3.65 4.15 60.07 0.41 148.32 9.00B 145.28 5.55 6.57 87.37 0.61 143.23 9.10C 106.84 3.81 4.72 73.36 0.80 91.70 4.76Average 117.58 4.34 5.15 73.60 0.61 127.75 7.62SD 62.34 2.09 2.50 36.93 0.20 81.04 4.49CV 0.53 0.48 0.49 0.50 0.33 0.63 0.59

S-22-10-1

A 173.59 8.00 10.77 133.35 0.30 444.50 26.67B 184.57 4.93 10.94 138.70 0.42 330.24 11.73C 190.89 6.77 10.62 136.01 0.46 298.92 14.87Average 183.02 6.57 10.78 136.02 0.39 357.89 17.76SD 89.01 3.31 5.47 69.38 0.09 208.04 11.50CV 0.49 0.50 0.51 0.51 0.23 0.58 0.65

U-22-10-1

A 143.13 9.33 10.14 79.34 0.78 102.37 12.03B 146.43 10.32 11.09 76.02 0.67 113.46 15.40Average 144.78 9.83 10.62 77.68 0.73 107.92 13.72SD 2.33 0.70 0.67 2.35 0.08 7.84 2.38CV 0.02 0.07 0.06 0.03 0.11 0.07 0.17

S-22-12-1

A 236.18 4.32 6.11 156.72 0.48 329.94 9.08B 238.23 6.02 10.05 153.36 0.56 273.86 10.74Average 237.21 5.17 8.08 155.04 0.52 301.90 9.91SD 1.45 1.20 2.79 2.38 0.06 39.65 1.17CV 0.01 0.23 0.34 0.02 0.11 0.13 0.12

U-22-12-1

A 143.39 3.83 4.46 94.67 0.48 197.23 7.97B 128.74 5.47 6.38 84.70 0.49 172.86 11.16C 148.61 3.93 4.73 137.36 0.93 147.70 4.23Average 140.25 4.41 5.19 105.58 0.63 172.60 7.79SD 78.37 2.40 2.56 51.26 0.23 97.22 5.33CV 0.56 0.54 0.49 0.49 0.37 0.56 0.68

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, evenin these cases, there is a large additional reserve of strength withrespect to the strength calculated according to the EN 1993:1-8formula.

5.4. Effect of joint length

Tests showed that joint length is an important parameterthat influences the ultimate strength of the joint, especially forsingle lap shear connections. Although the present study did not

explicitly aim to investigate the influence of pitch on shear capacityand specific parametric tests were not performed, tests showedthat the examined range of spacing did not appreciably influencethe shear strength.

In terms of the influence of e1/d ratios on the joint response,it was recognized that although in the examined specimens thisratiowas larger than the EN1992:1-8 limit (which is 1.2), when thespecimen failed in pure bearing the end distance was insufficientand the rivet split out through the end of the plate, as occurred inS19-10-1 (shown in Fig. 10), S22-10-1 and S22-12-1.

M. D’Aniello et al. / Engineering Structures 33 (2011) 516–531 525

Table 6Specimens with rivets in row: parameters characterizing the mechanical response.Rivets in row Specimen Fp su smax Fe se ke µ = su/se

U-16-10-2

A 141.87 2.78 3.97 98.68 0.48 207.75 5.84B 162.23 3.84 4.61 105.36 0.56 189.84 6.91C 161.37 2.88 3.69 110.68 0.53 210.82 5.49Average 155.16 3.17 4.09 104.91 0.52 202.80 6.08SD 14.40 0.75 0.45 4.72 0.06 12.66 0.76CV 0.09 0.24 0.11 0.05 0.11 0.06 0.12

U-16-10-4

A 236.56 18.97 22.40 166.69 0.99 169.23 19.25B 241.13 23.51 27.30 168.69 1.01 167.02 23.27C 242.85 23.41 26.60 170.68 0.96 178.72 24.51Average 240.18 21.96 25.43 168.69 0.99 171.66 22.34SD 133.85 12.12 14.33 95.46 0.53 93.54 12.13CV 0.56 0.55 0.56 0.57 0.54 0.54 0.54

S-19-10-2

A 336.63 14.24 16.80 236.69 0.84 281.77 16.95B 346.02 16.27 18.75 240.71 0.60 404.55 27.34C 332.60 10.46 13.45 230.69 0.63 366.17 16.60Average 338.42 13.66 16.33 236.03 0.69 350.83 20.30SD 167.40 7.04 8.23 116.72 0.15 182.16 11.12CV 0.49 0.52 0.50 0.49 0.21 0.52 0.55

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

A 201.55 4.35 5.29 128.68 0.62 207.55 7.01B 196.22 4.36 5.17 126.69 0.66 193.42 6.66C 232.35 5.22 6.40 126.70 0.64 197.97 8.16Average 210.04 4.64 5.62 127.36 0.64 199.65 7.28SD 95.14 2.68 3.19 61.99 0.27 97.48 4.36CV 0.45 0.58 0.57 0.49 0.42 0.49 0.60

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

A 190.09 13.12 17.38 128.68 0.53 245.10 24.99B 184.23 13.30 17.51 123.36 0.52 237.23 25.59C 188.92 13.83 18.29 121.34 1.10 110.81 12.63Average 187.75 13.42 17.73 124.46 0.72 197.71 21.07SD 89.30 6.74 9.05 60.25 0.12 117.85 13.26CV 0.48 0.50 0.51 0.48 0.17 0.60 0.63

S-19-10-4

A 354.63 10.69 14.30 254.04 0.74 345.63 14.54B 353.27 11.02 13.85 251.45 0.62 405.56 17.77C 352.96 9.69 12.45 256.67 0.64 404.20 15.26Average 353.62 10.47 13.53 254.05 0.67 385.13 15.86SD 182.09 4.89 6.40 130.69 0.31 190.40 7.52CV 0.51 0.47 0.47 0.51 0.47 0.49 0.47

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

A 356.61 23.12 26.15 250.01 1.29 193.81 17.92B 355.52 22.04 25.10 243.38 1.30 187.94 17.02C 355.12 25.28 28.40 246.67 1.06 232.71 23.84Average 355.75 23.48 26.55 246.69 1.22 204.82 19.59SD 169.89 11.64 13.04 117.32 0.53 95.14 8.30CV 0.48 0.50 0.49 0.48 0.43 0.46 0.42

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

A 184.37 14.53 18.45 122.69 0.82 149.62 17.71B 178.42 11.84 17.00 121.34 0.76 160.72 15.68C 183.07 10.98 14.65 130.70 0.72 182.80 15.36Average 181.95 12.45 16.70 124.91 0.77 164.38 16.25SD 88.74 6.23 8.16 60.03 0.19 73.19 7.86CV 0.49 0.50 0.49 0.48 0.24 0.45 0.48

S-22-12-2

A 278.89 2.75 4.56 257.38 0.32 804.31 8.58B 298.35 6.71 8.39 212.70 0.50 425.40 13.42C 296.89 7.68 9.44 210.02 0.55 385.36 14.08Average 291.38 5.71 7.46 226.70 0.46 538.36 12.03SD 145.63 2.95 3.71 122.08 0.14 369.03 5.34CV 0.50 0.52 0.50 0.54 0.30 0.69 0.44

U-22-12-2

A 279.05 10.46 11.63 170.02 1.6 106.26 6.54B 255.24 8.88 10.13 184.03 1.63 112.90 5.45C 280.77 11.60 13.49 170.72 1.64 104.10 7.07Average 271.69 10.31 11.75 174.92 1.62 107.75 6.35SD 127.12 4.73 5.27 83.42 0.81 156.56 2.72CV 0.47 0.46 0.45 0.48 0.50 1.45 0.43

S-22-12-4

A 308.94 9.76 12.17 249.26 0.75 334.46 13.10B 298.54 9.76 12.00 250.06 0.85 293.58 11.46C 303.50 7.24 8.95 247.68 0.66 373.88 10.93Average 303.66 8.92 11.04 249.00 0.75 333.97 11.83SD 147.93 4.49 5.68 124.61 0.16 150.66 6.29CV 0.49 0.50 0.51 0.50 0.21 0.45 0.53

U-22-12-4

A 308.94 15.67 18.60 201.34 0.85 236.87 18.43B 303.59 13.16 15.40 200.68 1.07 188.43 12.36C 303.66 15.23 17.90 202.69 0.88 230.33 17.30Average 305.40 14.69 17.30 201.57 0.93 218.54 16.03SD 146.89 7.14 8.40 94.64 0.46 102.06 7.72CV 0.48 0.49 0.49 0.47 0.49 0.47 0.48

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

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

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 specimenhaving ‘‘i’’ rivets over the strength Fu,1 of the specimen havinga single rivet) of the examined joint configuration varies withrespect to the number of rivets and the An/Ag ratio. For bothunsymmetrical and symmetrical specimens the strength does notincrease linearly as the number of rivet increases. Rather, as thenumber of rivets increased, a decrease in the average strengthoccurred at a decreasing rate. This is due to the fact that, owing tothe particular geometry of the specimens being analyzed, failuremodes different from rivet shearing occurred. Indeed, for longerjoints the redistribution of rivet force did not occur and onset ofyielding in the gross section of the plate occurred. Consequently,for the configuration being tested, having a large number of rivetsdoes not imply a high shear stress in the rivet. However, longerjoints having the larger An/Ag ratio showed a lesser decrease inaverage shear strength when compared with the shear strength ofa single rivet. Short lap joints (having up to two rivets) were hardlyaffected, 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/Agratio. The latter parameter seems to be themost influential. Indeed,for a low An/Ag ratio even if lap joints have the rivets loadedin one shear plane, their capacity does not differ appreciably forsymmetrical joints, which have the rivets loaded in double shear.This occurs because the inner plate of the symmetrical specimenis the weaker one and it is not strong enough to allow sheardistribution among the rivets. Thus having a double number ofshear planes is irrelevant in terms of the actual strength of theconnection. Conversely, for the larger value of An/Ag doubling thenumber of shear planes implies a benefit for the shear capacity,even if failuremodes other than rivet shearingmay limit this effect.

It should be noted that these charts were provided to RFIinspectors as a quick and easy tool with which to assess the shearcapacity of the connections of RFI lattice structures. Therefore, theycannot be extended to connections having different geometries.

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

5.5. Effect of clamping forces

Although the rivet clamping forces were not measured directly,the analysis of results allowed the evaluation of the effects ofvariability of clamping forces on slip resistance. A gradual slipoccurred 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 othercases the response curve exhibited a sudden slip (e.g. specimensS19-10-1 and S22-12-4 shown in Fig. 10(d) and (e), respectively).Due to the fact that the faying surfaces were not specificallytreated, this different slip behaviour may be attributed to thevariability of the clamping forces in the rivets, which impliesdifferent and unknown levels of pre-stressing of the surfaces ofthe plates in contact and anunreliable threshold for slip-resistance.Different slip behaviour has also been recognized for specimens ofthe same type. This may explain the variability of the measuredinitial stiffness (as reported in Tables 5 and 6) that is related to thedegree of pre-stressing of the rivets. However, the slips were sosmall that they are not expected to have a significant effect on realstructures.

These results confirmed that the investigated connections canbe considered as a bearing-type [12]. The possible initial slipshould not affect the shape of the force–displacement curve to anappreciable extent.

6. Theoretical vs. experimental strength

To evaluate the reliability of Eurocode formulas in predictingthe strength of riveted connection, a comparison of the theoreticaland experimental results was undertaken.

The strength of the lap shear connections calculated inaccordancewith EN19931-8 2005 is theminimumof the followingformulas:

(i) tensile strength of the critical net section (EN 1993:1-1 clause6.2.3(2b)),

Nu,Rd =0.9Anetfu

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 =0.6furAo

γM2(2)

where fur is the ultimate tensile strength of the rivet; Ao is thearea of the hole;

(iii) bearing strength of the thinner plate (EN 1993:1-8 clause3.6.1(1)).

Fb,Rd =k1αbfudt

γM2(3)

M. D’Aniello et al. / Engineering Structures 33 (2011) 516–531 527

Table 7Specimens with rivets in row: parameters characterizing the mechanical response.

Fu averagestrength (kN)

Failuremechanism(test)

FEC3 calculatedstrength (EN1993 1-8) (kN)

Failuremechanism(EN 1993 1-8)(kN)

F∗ calculatedstrength(proposedformulas) (kN)

Failuremechanism(proposedformulas)

Fu/FEC3 Fu/F∗

S-16-10-1 141.83 V + B(secondary)

99.31 V 148.97 V 1.43 0.95

U-16-10-1 80.22 V 49.66 V 74.49 V 1.62 1.08S-19-10-1 206.64 B 140.05 V 243.38 B 1.48 0.85U-19-10-1 101.48 V 70.02 V 105.04 V 1.45 0.97S-19-12-1 216.51 V + B

(secondary)140.05 V 210.07 V 1.55 1.03

U-19-12-1 117.58 V 70.02 V 105.04 V 1.68 1.12S-22-10-1 183.02 B 126.20 B 189.30 B 1.45 0.97U-22-10-1 144.78 V 93.88 V 140.82 V 1.54 1.03S-22-12-1 237.21 B 151.44 B 227.16 B 1.57 1.04U-22-12-1 140.25 V 93.88 V 140.82 V 1.49 1.00U-16-10-2 155.16 V 99.31 V 148.97 V 1.56 1.04U-16-10-4 240.18 T 187.46 V 259.61 T 1.28 0.93S-19-10-2 338.41 T 280.10 V 341.34 T 1.21 0.99U-19-10-2 (width90 mm)

210.04 V 140.05 V 210.07 V 1.50 1.00

U-19-10-2 (width60 mm)

187.74 T 140.05 V 197.11 T 1.34 0.95

S-19-10-4 353.62 T 307.21 T 341.34 T 1.15 1.04U-19-10-4 (width90 mm)

355.75 T 275.01 V 341.34 T 1.29 1.04

U-19-10-4 (width60 mm)

181.96 T 177.40 T 197.11 T 1.03 0.92

S-22-12-2 291.37 T 249.23 T 276.92 T 1.17 1.05U-22-12-2 271.69 V 187.77 V 281.65 V 1.45 0.96S-22-12-4 303.66 T 249.23 T 276.92 T 1.22 1.10U-22-12-4 305.40 T 249.23 T 276.92 T 1.23 1.10

Average 1.40 1.01SD 0.17 0.07CV 0.12 0.07

LegendV = rivet shear failureB = plate bearingT = failure in tension in the net section.

where αb is the smallest of (αd, fub/fu or 1.0). In addition, in thedirection of load transfer:αd =

e13do

—for end rivets; αd =p13do

−14—for inner bolts.While,

in the direction perpendicular to that of load transfer: k1 =

min2.8 e2

do− 1.7

; 2.5

—for edge rivets; k1 = min

1.4 p2

do−

1.7; 2.5

—for inner rivets.

d is the nominal diameter of the rivet; t is the thickness of thethinner plate; do is the hole diameter of a rivet; e1 is the enddistance from the centre of a rivet hole to the adjacent endof any part, measured in the direction of load transfer; e2 isthe edge distance from the centre of a hole to the adjacentedge of any part, measured at right angles to the directionof load transfer; p1 is the spacing between the centres ofrivets in a line in the direction of load transfer; p2 is thespacingmeasured perpendicular to the load transfer directionbetween adjacent lines of rivets.

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

reduced bymultiplying it by the reduction factor βLf , (EN 1993:1-83.8(1)), given by:

βLf = 1 −Lf − 15d200d

. (4)

In order to compare the experimental results to that obtained byEN 1993:1-8 formulas, the latter have been calculated assumingthe average experimental strengths of materials and that thepartial safety factors γM2 are equal to unity.

In Table 7 the test results are compared with the strengths andthe expected failuremodes predicted by the design equations of EN1993 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 (FEC3).

As can be observed, in four cases the failure mechanismspredicted by EN 1993 1-8 differ from those shown by the tests. Inparticular, net section failure occurred instead of rivet shear failure.The reason may be found in the large increase in ultimate shearstrength induced by hot-driven process, as previously illustrated.Moreover, the calculated resistances are not in accordancewith themeasured values. In particular, the Eurocode prediction formulasprovide conservative results, the average value of Fu/FEC3 for allspecimens is 1.40 (SD= 17%, CV= 0.12). In the plot, the letter thatcorresponds to the appropriate failure mechanism indicates thesecases. The reasons for the large over-strengthwhichwasmeasuredexperimentally differed for the observed failure modes.

• An average Fu/FEC3 ratio equal to 1.53 was obtained forspecimens whose rivets failed in shear. This implies that themonotonic 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 toEC3. ∗ the abbreviation V indicates that the rivet shear failure was experimentallyobserved instead of the mechanism predicted by EN 1993:1-8 formulas. ∗∗ thedashed line indicates the average ratio.

noticeably higher than that calculated according to EN 1993:1-8. Although the driving process improves the ultimate tensilestrength of the rivet by up to 20%, the experimental values ofthe shear capacities are still larger than the value calculatedwith the EN 1993:1-8 formula. In particular, the average over-strength ratio reduced by the hot-driven strengthening may beassumed to be 1.53/1.20 = 1.28, with 1.20 being the factorfor the effect of the hot-driven process. This implies that theultimate rivet shear stress fur,v = 0.6fur calculated according toEq. (2) is underestimated. An analysis of the results for differentdriving procedures and specimen configurations [7,8] showedthat the rivets’ shear strength to tensile strength ratio (fur,v/fur )may vary within the range 0.67–0.83, with an average value of0.75. If in the examined cases fur,v is calculated as follows:

fur,v =Fu

1.2 · nrnsAo(5)

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

Fv,Rd =Ω1 · Ω2 · fur · Ao

γM2(6)

where:– Ω1 takes into account the effect of the hot-driven process,

which can be assumed to be equal to 1.20 for rivets drivenin analogous manner to those examined;

– Ω2 is the rivets’ shear strength to tensile strength ratio,whichcan be assumed to be equal to 0.75 in accordance to [4,7,8].

• The average over-strength Fu/FEC3 ratio is equal to 1.50 ifthe specimen failed in bearing. A possible cause generatingthis large over-strength may be found in the rivets’ clampingforce [4]. This implies that the shear load is partially transmittedby frictional resistance on the faying surfaces. However,because the friction resistance is related to the clamping forcein the rivet, the actual influence of this effect is uncertain andfurther investigation is needed.

• Specimens failing in tension on the net section exhibited anaverage Fu/FEC3 ratio equal to 1.21. This occurs because of thenet efficiency effect illustrated in Section 5.2. In the light of thisresult it seems that Eq. (1) may be improved by assuming noreduction factor:

Nu,Rd =AnetfuγM2

. (7)

Fig. 15. Comparison of experimental and predicted strength calculated withproposed 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 theexperimental strengths (Fu) than those given by EN 1993:1-8.Indeed, as it can be observed in Table 7, the average value ofthe Fu/F∗ ratio for all specimens is slightly larger than 1.00(Average value = 1.01) with scatters less than those obtainedusing Eurocode formulas (SD = 7%, CV = 0.07). Moreover, allthe predicted failure mechanisms correspond to those obtainedexperimentally.

7. Statistical evaluation

A statistical analysis was performed in order to verify the pro-posed strength functions and to determine also the appropriatevalue of partial factor γM ensuring that the adequate reliability in-dex is met. Since some aspects influencing the bearing mechanismshould be further investigated, only the proposed new expressionsfor rivet shear strength and for failure in tension on the net sectionhave 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 ratiobetween the characteristic and the design value.

The procedure for the assessment of a characteristic and designvalue is based on the following assumptions:

• the resistance is a function of a number of independentvariables Xi;

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

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. devel-opment of the design model; 2. comparison of experimental andtheoretical values; 3. estimation of the mean value of correctionfactor; 4. estimation of the coefficient of variation of the errors;5. determination of the coefficients of variation of the basic vari-ables; 6. determination of the characteristic value of the resistance.

In particular, the first step of the analysis consists in the de-velopment of the theoretical resistance model of the experimentalresults. In this study the proposed resistance models are given byEq. (6) for rivet shearing and Eq. (7) for net section failure.

The examined theoretical resistances rt are assumed asfunctions of a number of independent variables X as the following:

rt = grt(X). (8)

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

M. D’Aniello et al. / Engineering Structures 33 (2011) 516–531 529

a

b

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

The second step is the comparison of experimental andtheoretical values. The experimental resistances are expressed bythe vector re1 for specimens failed in rivet shear and re2 for thosein net section. In Fig. 16(a) and (b) test results re1,i and re2,i areplotted 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 theexamined case, the points (rti, rei) show little dispersionwhichmaybe attributed to the scatter in material properties and errors ingeometry.

The third step is the estimate of the mean value correctionfactor b, which is calculated using the least squares method.

b =

∑ireirti∑

ir2ti

. (9)

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

δi =reibrti

. (10)

The mean values of theoretical resistances rm are calculated bythe mean values of basic variables Xm:

rm = brt(Xm)δ = bgrt(Xm)δ. (11)

The mean values of the geometry are adopted as nominal valuesfor the calculation of the rivets and net cross-sections. The meanvalues of material properties are equal to the measured ones.The material properties are equal for all specimens because allspecimens were extracted from the same steel plate.

On the basis of the estimated error δi, the estimator of variationcoefficients for scatter Vd is determined by:

∆i = ln(δi) (12)

∆ =1n

n−i=1

∆i (13)

s2∆ =1

n − 1

n−i=1

(∆i − ∆)2 (14)

where n is the number of tests.Finally:

Vδ =

exp(s2∆) − 1. (15)

The further step is to determine the coefficients of variation VXi ofthe basic variables. Indeed, to include the uncertainty of the steelgrade and the fabrication of elements, the standard deviation isincreased by the coefficients of variation VXi which are determinedon the basis of prior knowledge. The coefficients of variations ofsteel constituting the plates and rivets is obtained from performedmaterial tests. The variations of the independent geometricvariables VXi were assigned according to [29]. In particular, thefollowing variations were used:

Vfu,plate = 0.075 variation coefficient for tensile strength ofplates;Vfu,rivets = 0.079 variation coefficient for tensile strength ofrivets;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 V 2d and V 2

Xi it is possible to determine Vr in thesimplified way shown in the following:

V 2r = V 2

δ + V 2rt , being V 2

rt =

j−i=1

V 2Xi

(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 obtainedfrom:

Qrt = σln(rt) =

ln(V 2

rt + 1) (17)

Qδ = σln(δ) =

ln(V 2

δ + 1) (18)

Qr = σln(r) =

ln(V 2

r + 1) (19)

αrt =Qrt

Q(20)

αδ =Qδ

Q. (21)

The characteristic value for a limited number of tests is given bythe following expression:

rk = bgrt(Xm) exp(−k∞αrtQrt − knαdQd − 0.5Q 2)

= bg rt(Xm)Rk (22)

where the appropriate values of fractile factors kn, kd,n, k∞ andkd,∞ are provided by EN 1990.

Similarly, the design value for a limited number of tests isobtained as:

rd = bg rt(Xm) exp(−kd,∞αrtQrt − kd,nαdQd − 0.5Q 2)

= bg rt(Xm)Rd. (23)

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

Table 8Results of statistic analysis.

Resistance model Failure type N results b Vd γM,req

rt1 = Ω1 · Ω2 · fur · A Rivet shear 29 1.0119 0.0908 1.1261rt2 = Anetfu Net section failure 27 1.0187 0.0927 1.1166

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

γM =rkrd

=exp(−k∞αrtQrt − knαδQδ − 0.5Q 2)

exp(−kd,∞αrtQrt − kd,nαδQδ − 0.5Q 2)=

Rk

Rd. (24)

The results of the statistical analysis are presented in Table 8. Thedifference in the value of the partial factor γM for the two proposedverification formulas is negligible.

Both proposed resistance models are characterized by acorrection factor b close to 1 and a relatively small scatter (seeTable 8 and Fig. 16). Therefore, they appropriately describe therivets’ shear strength (resistance model 1) and the ultimate loadat the net section (resistance model 2). The required partial factorfor the proposed rivet shear resistance (Eq. (6)) is γM,req = 1.1261.The scatter for this function is very low with V = 0.0908 andwith correction factor b = 1.0119. Also the proposed formula forresistance of net section (Eq. (7)) is suitable. Indeed, the requiredpartial factor γM,req is equal to 1.1166, with V = 0.0927 and withcorrection factor b = 1.0187. Therefore both calculation formuladescribe the phenomena very well.

According to EN1993, the partial factor to be assigned to theresistance models to form the design resistance is γM2 (with therecommended value equal to 1.25), since the resistancemodels arerelated to fracture mechanisms.

It is clear that the proposed resistance models meet thereliability 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 parametersthat were not included in our analysis, such as the effects ofmanufacturing tolerances that may be larger than assumed in [29].

8. Conclusions

This paper describes the results of a large experimentalinvestigation carried out within the framework of the Europeanproject PROHITECH [18], with the aim of investigating thebehaviour of riveted connections loaded in shear typically adoptedin aged metal structures still in service in Italy in order to verifytheir strength according to EN 1993:1-8 [12]. Since the majority ofriveted structures in Italy are railway constructions (both latticeroofs and bridges), the present study was undertaken in co-operation with Italian railway agency (RFI), which was interestedin developing verification tools for those riveted splices in agedsteel structures which are still in service.

To achieve these objectives an experimental campaign has beencarried out on riveted specimensmade of aged steel,manufacturedwith the techniques in use in Italian railway practice. Specimengeometry was detailed as required by RFI.

Both mechanical and chemical tests were carried out tocharacterize the steel constituting plates and rivets. Tests showedgood mechanical and chemical properties (strength, chemicalcomposition) on average but a large statistical dispersion of thedata for the rivets was recognized.

The results and observations from the lap shear tests werediscussed and themain response characteristics were examined inthe light of the existing literature.

The experimental results highlighted that a considerableamount of out-of-plane deformation occurred in unsymmetrical

joints. It is clear that the effects of bending were mainly confinedto the regions where plate discontinuities occurred. Obviously,as the joint length increased, bending was less pronounced, andits influence on the behaviour of the connection decreased. Theinfluence of bending was most pronounced in the splice with onlya single fastener in the direction of the applied load. In such a jointthe fastenerwas not only subjected to single shear, but a secondarytensile component may also be present. Furthermore, the plate’smaterial in the direct vicinity of the splice was subjected to highbending stresses due to the eccentricity of the load. Hence, thebending tended to slightly decrease the ultimate strength of shortconnections. The shear strength of longer unsymmetrical jointsseemed to be less affected by the effects of bending.

Comparing the experimental strengths and the failure modesto those predicted by applying the formulas given in EN 1993:1-8[12] it was recognized that the approach given in the codeis conservative in all examined cases. However, the scatterbetween experimental and calculated strength seems excessivelyprecautionary.

In order to improve the theoretical prediction of shear strengthof rivets, two further parameters should be taken into account:(1) the increase of ultimate tensile strength of rivets due to thehot-driven process; (2) the actual rivets’ shear strength to tensilestrength ratio.

The experimental over-strength in the bearing failure modemay be due to the contribution made by friction resistancebetween the faying surfaces constituting the splices. Owing to theuncertainties about the clamping in the rivets this effect needsfurther investigation.

Specimens failing in tension on the net section exhibited anaverage strength 20% larger than that calculated according to EN1993:1-8. This result should be ascribed to the net efficiency effect.

In some cases the failuremechanisms predicted by EN 1993:1-8differ from those exhibited by tests. This was due to the largeincrease in ultimate shear strength induced by the hot-drivenprocess, which is not taken into account by EN 1993:1-8. Indeed,current EN 1993:1-8 methods for predicting the shear strength ofriveted connections do not explicitly account for this factor.

On the basis of the obtained experimental results, somemodifications to EN 1993:1-8 prediction formulas are proposed.The provided equations are formulated considering the influenceof the hot-driven process and of the net efficiency effect. Theproposed formulas are closer to the experimental strengths thanthose given by EN1993:1-8, in terms of both the ultimate strengthsand the failure mechanisms. However, some aspects such as theeffect of the friction resistance on the bearing mechanism andthe presence of more rows of rivets in the connection need to beinvestigated in more exhaustive manner.

The proposed calculation formula for rivet shear failure and forfailure in tension on the net section were statistically evaluatedaccording to EN 1990, Annex D. The analysis showed that theprescribed reliability is achieved by the recommended value ofpartial factor γM2 = 1.25.

Due to the fact that no distinction is made in EN 1993between riveted and bolted connections, new design equations areproposed to verify both the rivets’ shear and net area resistance,preserving the same simplicity of Eurocode verification procedureand providing more reliable control on the behaviour of rivetedconnections.

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

Acknowledgements

The authors gratefully acknowledge support from the PRO-HITECH project on ‘Earthquake protection of historical buildingsby reversiblemixed technologies’ within the Sixth Framework Pro-gramme FP6 of EU, and from the National Research Project PRINprot. 2005087058_004, titled ‘‘Vulnerability and reversible consol-idation techniques for historical metal structures’’.

They also wish to thank Eng. Antonio D’Aniello, director ofthe Department of Naples at RFI for his courtesy, cooperationand assistance throughout this research and for having providedmaterial and skilledworkmanship for themanufacturing of rivetedspecimens.

Finally, authors would like to thank Arch. Carla Ceraldi for hersupport given during the experimental activities at the Laboratoryof Testingmaterials at theDept. of Constructions andMathematicalMethods in Architecture of the University of Naples ‘‘Federico II’’.

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