Journal of Constructional Steel Research 97 (2014) 24–38

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Journal of Constructional Steel Research

Response of partially-restrained bolted beam-to-column connectionsunder cyclic loads

E. Brunesi a,⁎, R. Nascimbene b,1, G.A. Rassati c,2

a ROSE Programme, UME School, IUSS Pavia, Institute for Advanced Study, Via Ferrata 1, 27100 Pavia, Italyb EUCENTRE, European Centre for Training and Research in Earthquake Engineering, Via Ferrata 1, 27100 Pavia, Italyc Dept. of Civil and Architectural Engineering, University of Cincinnati, 765 Baldwin Hall, Cincinnati, OH 45221-0071, USA

⁎ Corresponding author. Tel.: +39 0382 5169893; fax:E-mail addresses: emanuele.brunesi@eucentre.it (E. Br

roberto.nascimbene@eucentre.it (R. Nascimbene), Gian.Ra1 Tel.: +39 0382 5169827; fax: +39 0382 529131.2 Tel.: +1 513 556 3696; fax: +1 513 556 2599.

0143-974X/$ – see front matter © 2014 Elsevier Ltd. All rhttp://dx.doi.org/10.1016/j.jcsr.2014.01.014

a b s t r a c t

a r t i c l e i n f o

Article history:Received 2 July 2013Accepted 18 January 2014Available online xxxx

Keywords:Partially-restrained connectionBolted beam-to-column connectionFinite element modelsComponents slippageParametric analysisRotational stiffness

The structural response of steel moment resisting frames (MRFs) is greatly dependent on the behavior of beam-to-column joints, according to a properly detailed beam-bolts-plates-column structural chain, in light of capacitydesign principles. Amodeling procedure for bolted top-and-seat angle components and connections for potentialuse in seismic MRFs is presented herein. Although these partially-restrained (PR) connection systems have beendemonstrated to provide economic savings, they are not currently certified to be used for moment resistance inanymajor building specification jurisdiction. Examples of full-scalemoment resisting connection systems, exper-imentally tested in past programs, have been numerically analyzed, focusing on top-and-seat angle components,which were observed to control the global response of the joint in terms of failure mechanisms, limiting the dis-placement ductility capacity and dissipation energy capabilities of the whole resisting system. Refined nonlinearsolid FE models, accounting for the influence of friction, pretension of bolts, prying and relative slippage of com-ponents through highly nonlinear contact elements, have been developed to reproduce the cyclic-reversal testprotocol. Simplified approaches, based on one-dimensional inelastic force-based fiber elements, combinedwith nonlinear links, to globally represent connection elements interaction, have been developed and validatedby comparisons with experimental response.To propose an alternative and conservativemethod for quick rotational stiffness estimates of these PR bolted top-and-seat angle connections, a series of detailed parametric solid FE analyses have been performed and theeffectiveness of this analytical preliminary-design-stage tool quantified in comparison with some of the mostcommonly known analytical approaches.

© 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Steel MRFs have traditionally been used as the lateral-force resistingsystem in high seismicity areas because of their significant potential forlarge ductility under seismic loading. In the past, fully welded momentconnections have been assumed to provide the optimum combinationof strength, stiffness and ductility in special MRFs; however, the 1994Northridge and 1995 Hyogo-ken Nanbu earthquakes had revealedpoor performance of these connection systems [1,2], since numerousbrittle fractureswere observed, due to large stress/strain concentrationsin the critical joint region [3]. Indeed, traditional fully welded momentconnections had exhibited several drawbacks, mainly related to theconnection geometry, which causes large strain demands in criticalzones, and to the design approach ofmodernMRF structures, which im-plies, according to economic reasons and performance-based design

+39 0382 529131.unesi),ssati@uc.edu (G.A. Rassati).

ights reserved.

concepts [4], a concentration of the lateral resistance in a limited num-ber of connections [5]. Sensitivity to fracture of traditional welded con-nection details resulted in low rotational ductility under cyclic loadreversals, while the adoption of deeper beams to reduce drift demandgave rise to large shear demands at the connection level: in this case,to ensure the desiredweak beam–strong columnmechanism, the strainconcentration problems inherent to the connection geometry wors-ened. Therefore, increasingly wide interest in the performance of boltedconnections under seismic loading has occurred, as these solutions,characterized by promising performance in past seismic events [6], rep-resent a particularly attractive choice, applicable both to new construc-tion and to retrofitting of existing structures. In fact, bolted connectionshave thepotential to be able tomitigate some of themajor issues relatedtowelded systems, potentially providing the required stiffness, strengthand rotational capacity demanded by MRFs. With proper detailing,in many cases a high level of redundancy and a level of stiffness compa-rable to that of fully welded connections can be achieved. In addition,steel MRFs with more flexible beam-to-column connections ensuremany economical and construction advantages over rigid frames [7].Past studies [8,9] also demonstrated that the adoption of PR boltedbeam-to-column connections does not necessarily imply a larger drift

25E. Brunesi et al. / Journal of Constructional Steel Research 97 (2014) 24–38

response than that experienced inMRFs with rigid joints. Therefore, thebelief that excessive deformations will take place or that instabilityunder gravity loads and P-delta effect might occur during strong earth-quakes was refuted. In particular, in many cases, low-rise buildingscould reveal an improved structural response, according to the benefi-cial contribution of component slippage, thus showing increased energydissipation capabilities, without any added plastic deformation exploi-tation of the components, directly implying lower force demands atthe connection level.

In the light of the aforementioned observations, this paper investi-gates the response of bolted clip angle connections for potential use inlow and medium seismicity areas, where limited ductility in MRF isexpected and, consequently, stiffness rather than strength of such con-nections is crucial, particularly in the satisfaction of the building perfor-mance objectives for the immediate occupancy performance level or theserviceability limit state. Hence, detailed FE models have been devel-oped to properly capture the experimental behavior of two full-scalePR bolted top-and-seat angle connections, tested in past programs.Based on this validation, the connection response has been investigated,by varying friction coefficients, pretension of bolts, and bolt-plates gapto assess their influence both on global load-displacement curve andlocal stress/strain distributions, observed in the critical joint region;finally, 16 different PR bolted beam-to-column connections with flangeangle cleats have been designed, according to European standards [10]and their rotational stiffness has been compared to those predicted byconventional methods [10,11], in order to propose a closed-form ex-pression, depending on components and bolts geometry only.

2. Literature review

Through the years, bolted connections have been widely investigat-ed to assess their performance under cyclic-reversal pseudo-static load-ing [12–14]. Even though they may experience a slight loss of elasticstiffness due to slippage, this was gradual and stable and almost thewhole initial elastic stiffness was recovered at the end of the slip pla-teau. Also, larger rotational ductility, achieved through slippage offaying surfaces, prevented the severe local buckling induced by weldedconnections; semi-rigid bolted connectionswere observed to be robust-ly ductile and slippage was evidenced to improve the response of steelMRF subjected to earthquakes. Piluso and Rizzano [14] carried out anexperimental program devoted to assess the cyclic force-displacementresponse of 28 bolted T-stubs, subjected to both constant and variableamplitude cyclic loading histories. Stiffness and strength degradationruleswere derived as a function of the displacement amplitude requiredat any cycle and of the energy dissipated in the previous loading history,in order to propose a semi-analytical model for predicting the cyclic be-havior of bolted T-stubs starting from the knowledge of their geometri-cal and mechanical properties. Maggi et al. [13] experimentally studiedseveral full-scale specimens of bolted extended end plate connections,observing that the T-stub analogy presents limitations for the accurateprediction of the yield lines at the endplate, when combined to bolt ten-sion failures, due to the component interaction; criticalities in account-ing for prying action also emerged, since the center of rotation for theplate was not placed at the compression flange level, as conventionallyaccepted in the design process, but at the level of the first bolt in com-pression. Furthermore, Girão Coelho et al. [12] statically tested 8 ex-tended end plate moment connections, designed to trigger failure inthe end plate and/or bolts without exploitation of the full plastic mo-ment capacity of the beam; the influence of the end plate thicknessand steel grade on the observed monotonic response was highlighted.In addition, Eq. 6.27 of Eurocode 3 (EC3) [10] was proven to largelyoverestimate the initial rotational stiffness experimentally observed,as roughly doubled predictions were obtained. This quite large and un-safe mismatch was motivated by the “unbalanced” connection systemstested, characterized by some of their components designed to bemuchweaker than the remaining; however, the need of further investigations,

by assessing joint configurations, designed in accordance with commondesign practice [10], seems to be at least justified.

Although PR bolted beam-to-column connections usually presentcomplex component interaction, characterized by mechanisms such asslip, bearing, and ovalization, the feasibility of the FE models to accu-rately simulate connection response has been verified during the lasttwo decades by a number of research efforts [15–23], mainly addressedto capture behavioral changes as a consequence of geometric variations.The majority of these studies was focused on end plate connections andeven though simplification in components geometry, bolts, contact con-ditions and friction effects have been employed in many early studies[15–17], accurate prediction of experimental results is shown. In partic-ular, Bose et al. [15] characterized themoment carrying behavior of endplate joints, identifying their potential failure modes. More recent re-searches explicitly recognize bolt head-angle contact, while neglectingbolt shank–hole interaction [18] or apply a general nonlinear contactscheme to represent contact conditions between each component ofthe connection system, anyway analyzed in a monotonic fashion only[19,20]. Over the last years, significant improvements have beenachieved in simulating the interface between the end plate and the col-umn flange, as well as the pretension force in the bolts [21]; Geramiet al. [22] investigates the cyclic behavior of bolted end plate joints,while Girão Coelho [23] specifically applies ductile fracture models topredict the rotation capacity of bolted end plate joints subjected tolarge scale plasticity.

3. Nonlinear FE analyses

In light of this scenario, advanced nonlinear FE analyses, based onthe use of refined 3D solid models with highly nonlinear contact algo-rithms, accounting for friction and relative slippage of components, ap-pear to be an attractive tool in providing stiffness and strength estimatesfor a large variety of connection geometries, after reliable validationwith experimental tests. In addition, these detailed FE studies aim atcapturing the evolution of local quantities, such as principal stresses/strains, crucial in interpreting damage patterns and failure modes ofthe bolted connection under investigation, aswell as at developing sim-plified connection modeling approaches, generally based on inelasticspring elements and addressed to represent connection element inter-action in an equivalent and simplified manner, that can be easily incor-porated intomodern structural analysis programs. Hence, an exhaustivepast research program [3], carried out at the Georgia Institute of Tech-nology was selected in order to obtain a suitable experimental databaseof destructive tests.

3.1. Cases of study definition from past experimental database

As a part of the SAC Program [3], a series of 10 full-scale beam–col-umn connection tests under cyclic loads was performed and collectedin [24]; their calibration was achieved in light of an initial series of48 T-stub and 10 clip angle components tested in cyclic tension andcompression. In particular, this paper is focused on two full-scale top-and-seat angle experimental tests conducted by Schrauben [24], respec-tively named FS-01(CA-02) and FS-02(CA-04), to quantify the sensitiv-ity of the response, in terms of failure mechanism, flexural and shearstrengths, rotational stiffness, displacement ductility capacity and ener-gy dissipation capabilities with respect to the connection systemconfiguration. Specimen FS-01(CA-02) consisted of a W18 × 40(W460 × 60) beam bolted to a W14 × 145 (W360 × 216) column by a9″ × 3-1/8″ × 5/16″ (229 × 79 × 8 mm) shear tab and clip anglescut from a L8 × 6 × 1 (L203 × 152 × 25). Two 7/8″ (22 mm) diameter,3-1/4″ (83 mm) long A490 high-strength bolts with one washer wereused to fasten one leg of each clip angle to the flange of the column.The gage distance of these “tension” bolts was 2-1/2″ (63 mm). Four7/8″ (22 mm) diameter, 3″ (76 mm) long A490 high-strength boltswith two washers were used to fasten the other leg to the beam flange

26 E. Brunesi et al. / Journal of Constructional Steel Research 97 (2014) 24–38

and three 7/8″ (22mm) diameter, 2″ (51mm) long A490 high-strengthbolts with one washer were used to fasten the beam web to the sheartab. Specimen FS-02(CA-04) was similar to the previous, since thesame components were adopted, except the gage distance of the ten-sion bolts which was 4″ (102 mm), as schematized in Fig. 1. A compre-hensive discussion both of the experimental test set up and cyclicloading history, consisting of symmetric stepwise increasing deforma-tion cycles, is furnished in [20,25]. In the following discussion, the twospecimens will be identified as FS-01 and FS-02, while “CA-02” and“CA-04”, omitted for the sake of simplicity, indicate the clip angleclassification based on the component tests performed by Swansonand Leon [3].

Both specimens collapsed by a tension bolt rupture due to a combi-nation of direct bolt tension and prying forces in the clip angles. The ex-perimentally observed actuator load-tip beam displacement and topclip angle load-slip curves, obtained from the two tests, are graphedtogether in Fig. 2a and 2b respectively; the expected dependency ofthe connection behavior with respect to the connection configuration(i.e. bolts position) was confirmed. In fact, Specimen FS-01 was able tocarry a maximum actuator force of approximately 90 kN, experiencinga maximum tip displacement of about 182 mm, while Specimen FS-02reached a lower shear force at the connection level (16%) at larger max-imum tip displacement levels (18%). A similar discrepancy can be ob-served in terms of maximum resisting moment: 408 and 343 kNm forSpecimen FS-01 and FS-02, respectively. Both connections accommo-dated amaximum total rotation of about 0.040 rad, anyway undergoingdifferent maximum plastic and concentrated rotation levels of about0.023 and 0.030 rad for Specimen FS-01 and 0.028 and 0.035 rad forFS-02, evidencing a discrepancy ranging from16 and 20%. In accordancewith Schrauben [24], their definition is provided as follow:

• The total rotation was computed as the ratio between beam tip dis-placement and length;

• Theplastic rotationwas obtained from the total rotation by subtractingthe contribution of the elastic rotation, determined as the ratiobetween moment and elastic stiffness;

• The concentrated rotation was obtained by subtracting the average ofthe sum of the top left and right angle displacements and the averageof the sum of the bottom left and right angle displacements. Thisvalue, divided by the beam depth, gave the concentrated rotation.

Similar levels of dissipated energy were observed, since a differencebelow 3% can be appreciated, while the most evident discrepancy be-tween the two experimental responses is in the initial elastic stiffnessand maximum cumulated plastic rotation, 20 and 40%, respectively.Hence, even small geometric variations result in manifest differences

Fig. 1. FS-01 and FS-02 con

in the connection response, mainly due, in this case, to the increasedlever arm, which in turn implies a much more visible prying action.

3.2. Proposed modeling approach

To accurately reproduce the experimental response of the two refer-ence specimens, high-definition 3D FE models have been developed, byadopting isoparametric displacement-based (DB) solid elements tomodel all the connection components. The contact conditions are ex-plicitly recognized in the framework of a general nonlinear contactscheme, including the combined effects of slip and friction. NX Nastransolver [26] is adopted to play out the detailed FE approach proposed forparametric analyses of these PR bolted beam–column connections,using FEMAP as the pre- and post-processing software. The campaignof numerical investigations carried outmakes useof amethod for apply-ing pretension in the bolt shanks, as discussed later, allowing for thefrictional force transfer by clamping plates together with the bolts.Such a conventionalmechanism for this type of top-and-seat angle con-nections has been prepared to quantify the effect of several geometricaland material parameters on the overall force-displacement responseobserved for the two studied connection configurations, through an ex-tensive campaign of parametric analyses.

Hence, the proposed modeling philosophy, calibrated on the previ-ous experimental studies [24] of top-and-bottom seat angle connec-tions, is observed to be general, robust and applicable for accuratemodeling of a wide range of other types of PR connections, properlyaccounting for the pronounced effect of slip and friction between con-nection components. Detailed solid FEmodels of the connection compo-nents and the whole tested geometries, such as that shown in Fig. 3,were developed, properly accounting for both geometrical andmaterialnonlinearities. In fact, large displacement-large strain kinematics, withautomatic switching between the updated Lagrangian Hencky (ULH)and the updated Lagrangian Jaumann (ULJ) formulations [26], wereemployed. Considered as a smooth approximation of the Tresca criteri-on through a circular cylinder in the principal stress space, the classicalVon Mises yielding criterion with combined isotropic and kinematicstrain hardening was assumed to accurately reproduce the cyclicstress–strain relationship of the steel members, accounting for bothtranslations and expansions/contractions of the yielding surface tofaithfully represent the permanent deformations exhibited by plasticmaterials during the applied loading–unloading history. By means ofaverage resistances, the assumed true stress-strain constitutive lawswere calibrated on the results of the characterization experimentaltests, performed on connection components at the Georgia Institute ofTechnology [24]. Potential element rupture [26] was activated, thus im-plying the removal of elements and related contactor segments when a

nection characteristics.

−250 −200 −150 −100 −50 0 50 100 150 200 250

−100

−50

0

50

100

Tip Displacement [mm]

Act

uato

r Lo

ad [k

N]

FS01FS02

−6 −4 −2 0 2 4 6

−1000

−500

0

500

1000

Top Clip Angle Slip [mm]

Top

Clip

Ang

le L

oad

[kN

]

FS01FS02

ba

Fig. 2. Experimental comparison between FS-01 and FS-02: (a) actuator load-tip beam displacement and (b) top clip angle load-slip curves.

27E. Brunesi et al. / Journal of Constructional Steel Research 97 (2014) 24–38

conventionally fixed ultimate strain limit was exceeded. This approach,developed within a death element framework, results into a suddenelement cut-off; in this paper, the first strain limit exceedance was con-ventionally interpreted as a conservative check of the “near collapse”limit state for the connections investigated. As previously mentioned,the influence of friction, pretension of bolts, prying and relative slippageof connection components was captured, in a phenomenological sense,through highly nonlinear contact algorithms, based on constraint func-tion and consistent stiffness methods to account for the expected largedisplacement-large strain kinematic effects, and allowing for potentialpenetration as well. The gap between bolts and plates was directlyintroduced through the contact algorithm, while friction phenomenawere reproduced by exponentially decaying curves, to account forthe variation of the friction coefficient with respect to the slidingvelocity. Furthermore, the constraint function method was exploited

Fig. 3. Specimen FS-01: detail of the FE mesh and contact surfaces

to approximate, via frictional constraints linearization, the rigid non-differentiable stick–slip transition, resulting in a slightly smootherpassage from stick to slip and vice versa, that was expected to reduceconvergence difficulties. An implicit solution strategy [23], withan energy-normalized convergence criterion, whose limit was set to10−3, was assumed, while the adopted integration time step was up-dated by analysis restart procedure.

3.3. Parametric investigation on partial models of connection components

Since the behavior of these PR connection systems is governed bythe interaction of their subassemblies, single-lap, single- and multi-bolt joints were cut from specimen FS-01, as shown in Fig. 3, and partialFEmodels, incorporating geometric andmaterial properties of the refer-ence full-scale connection, developed. Their monotonic response was

of partial and full-scale models. Note: dimensions are in mm.

28 E. Brunesi et al. / Journal of Constructional Steel Research 97 (2014) 24–38

assessed to describe themotion of joint components and to quantify theinfluence of bolt pretension, bolt-plates gap and friction, as will be donefor the entire specimen. Sensitivity to plate thickness was investigatedby comparing the two multi-bolt joints, in order to show the differentmechanisms induced in the load pick-up by the different top-to-bottom plate thickness ratios.

A mesh of 3D continuum ten-node tetrahedrons [21] was establishedthrough a parametric mesh generator program. Sensitivity to the meshand element type was investigated and a parametric campaign of FEanalyses, according to Table 1, performed. The reference bolt preloadand bolt-plates gap were those of the entire connection tested bySchrauben [24], while the reference friction coefficient was assumed tobe 0.2, as representative of a smooth contact surface, in accordance withChung and Ip [27]. These quantities will be respectively identified by N,G and μ; the combination of these letters is used, in the following discus-sion, for model labeling.

To capture high strain/stress gradients, the typical FE mesh presentsa relatively high radial mesh density in the overlap region, near the holeand under the washer. The contact condition between the two flangeswas defined, by means of master-slave pairs, as well as those betweenplates and bolt shank/bolt head, allowing for their relative sliding inter-action, while bolt head and washer are assumed to be rigidly connectedto each other, which, as demonstrated in [28], have no significant influ-ence on the response of the whole connection system. Pin-loadedboundary conditionswere introduced, since the gripped part of the ide-alized specimen was assumed perfectly tightened and, therefore, notmodeled, while the load was imposed in two steps. In fact, to properlysimulate bolt pretension, orthotropic thermal expansion coefficients,allowing for thermal expansion/contraction only along the longitudinalaxis of the bolt, were firstly provided, while a secondphasewas adoptedtomonotonically load in shear the connection sub-system, by applying aprescribed displacement. Hence, bolts and plates are clamped together,since the temperature gradient, applied to the bolt shanks, in combina-tion with the release of the restraint on the underside of the bolt head,caused bolt contraction, which in turn caused the heads of the bolts tocome into contact with the plates, thus allowing for the traditional fric-tional force transfer. The obtained monotonic shear force-displacementcurves, according to the adopted combinations of bolt-plates gap, boltprestress and peak friction coefficient, are presented in Fig. 4(a) and(b), for the single-bolt joint analyzed.

Quite similar post-slip plateau shear force both at yielding and ulti-mate conditions were shown by each specimen (of about 255 and335 kN, respectively),whilemodel N1G3μ1, characterized by the largestbolt-plates gap, presents a difference of 10% with respect to modelN1G1μ1, considered as reference. Analogous considerations can bedrawn for what concerns the observed displacement ductility capacity.More appreciable discrepancy can be observed in terms of slip plateau(both displacement and force) and initial elastic stiffness. A consistentreduction in stiffness, due to loss of pretension in the bolt and reductionof friction contribution is clearly visible, while no influence was detect-ed with respect to the initial bolt-flanges gap. Conversely, this parame-ter was observed to mainly control the actual slippage of the idealizedspecimen, with discrepancies ranging from about 25 and 56%. Again,the level of constant force at which slippage occurred was mostlygoverned by bolt pretension and friction, since they were expected tocontrol the contact pressure distribution between bolt and plates. Anevident delay in the load pick-up was achieved for the G2 and G3 gap

Table 1Analyses parameters — partial models: bolt-plates gap, bolt prestress and static frictioncoefficient.

Gap [mm] % N [MPa] % μ [–] %

1 0.8 – 641 – 0.20 –

2 1.0 +20 513 −20 0.15 −253 1.6 +50 321 −50 0.25 +25

joints, which is slightly larger, in percentage, than the nominal gaps as-sumed. As bolts were initially centered in the hole, this delay is due tothe fact that the gap has to be taken up before the bolt makes contactwith the hole to transfer shear forces. After yielding took place, theslope of the shear force-displacement capacity curves evidentlydropped due to the development of damage in the joint, as confirmedby the observed evolution of the maximum principal strain distribu-tions, shown in Fig. 5. Herein, a section through the mid-plane of thejoint is presented to highlight the motion of their components. Thewasher, rigidly connected to the bolt head, slides relative to the under-lying flange which, in turn, loses contact with the spherically pinnedplate at one side of the single-bolt joint; in addition, the bolt-platesgap opens up on one side of the bolt, particularly at the mid-boltdepth, but closes on the other. A significant bolt bending is also evident,resulting in shear and Von Mises stress peaks placed at the location ofthe joint shear plane, since high force transfer across the bolt takesplace in this region, as confirmed by Fig. 6. The observed contact pres-sure distributions at ultimate conditions are depicted, as well the dam-age experienced by the plates, proving the reliability of the proposedmodeling approach.

To more clearly observe this behavior, maximum principal straindistributions were graphed vs. the normalized bolt depth in correspon-dence to three vertical stripes, radially located in different positions, re-ferred as edge, loaded and pinned side, respectively; the normalizedbolt depth was computed as the ratio between the coordinate overthe length of the bolt shank and whole bolt shank length. Over thelength of the bolt, peakswere observed in correspondence to the centerline at the location of the joint shear plane, while fairly anti-symmetricdistributions, with clearly lower maxima (of about 18%), were depictedat the hinged and loaded side of the bolt, as depicted in Fig. 7. An iden-tical behavior was evidenced also in terms of Von Mises stresses.Furthermore, the ultimate maximum principal strain distributions, ob-tained from the parametric analyses were compared in Fig. 8(a) and(b), presenting trends in close agreement with those previously de-scribed for the global capacity curves. In particular, since the bolt ismuch freer to move relatively to the flanges, slightly larger peaks (byapproximately 5%) show as bolt-plates gap increases and bolt preloaddecreases, according to an increased delay in the load pick-up. This isdue to the fact that the gaphas to be taken up before the boltmakes con-tact with the hole and also to a reduction in the clamping action provid-ed by prestress.

As shown in Fig. 9, quite similar behavior has been observed whenthe other multi-bolt joints, extracted from the examined connections,are considered, although a more clearly spread damage into the platesis observed in the case of the 3-bolt joint (i.e. beam-shear tab), due totheir reduced thickness in comparison to the single-bolt joint. Similarly,the 2-bolt joint (i.e. clip angle-beam), characterized by an almost dou-bled thickness ratio between the top and bottom plates, presents ananalogous mechanism with damage more evidently concentrated inthe thinnest of the two plates in correspondence of the pinned side ofthe joint, thus showing a more complex interaction between itscomponents.

3.4. Numerical results of full-scale models

To assess the accuracy of the previously proposed modeling ap-proach, the experimental behavior of the two reference specimens wasreproduced through advanced FE analyses, based on detailed solidmodels such as that shown in Fig. 3, where “single-sided” contact condi-tions, involving a “master–slave” type algorithm, are introduced be-tween the faying surfaces of column-clip angles, beam-clip angles,beam-shear tab, bolt shanks-holes and bolt heads-relative flanges.Since the only difference between the two connections was in the gagedistance of the column bolts (i.e. 2.5″ (63.5 mm) vs. 4″ (101.6 mm) forSpecimen FS-01 and FS-02, respectively), geometry and mesh wereupdated by parametric meshing tools. The bolt holes were modeled as

0 2 4 6 8 100

50

100

150

200

250

300

350

400

Displacement Dz [mm]

She

ar F

orce

Fz

[kN

]

m1N1G1µ1

m2N1G1µ1

m1N1G1µ2

m1N1G1µ3

m1N1G2µ1

m1N1G3µ1

m1N2G1µ1

m1N3G1µ1

0 1 2 3 40

50

100

150

200

Displacement Dz [mm]

She

ar F

orce

Fz

[kN

]

m1N1G1µ1

m2N1G1µ1

m1N1G1µ2

m1N1G1µ3

m1N1G2µ1

m1N1G3µ1

m1N2G1µ1

m1N3G1µ1

ba

Fig. 4. Single-bolt joint: (a) Monotonic shear force-displacement curves from parametric analyses; (b) enlarged view. Note: m stands for mesh type.

29E. Brunesi et al. / Journal of Constructional Steel Research 97 (2014) 24–38

1/16″ (1.6 mm) larger than the bolt shaft diameter and bolt pretensionset to 641 MPa, according to Schrauben [24], as outlined in Table 2.This case, namedModel N1G1, is the reference for the series of paramet-ric analyses performed to capture behavioral changes as consequence ofbolt-plates gap increment and bolt prestress reduction.

A first loading stage is used to incrementally pretension the bolts,resulting in the Von Mises stress concentrations depicted in Fig. 10(a),which allow for bolts and relative flanges being clamped together totransfer forces by friction during the imposed displacement history.Both monotonic and cyclic analyses were performed, evidencing agood agreement with experimental results in terms of failure mecha-nism, initial stiffness, displacement and rotation ductilities, shear andbending resistances, as will be discussed later. In particular, Fig. 10(b)presents an example of the numerically predicted failure mechanism,governed by a tension bolt fracture; the Von Mises stress depicted inthe fifteen bolts of the connection investigated (Specimen FS-01) re-veals prominent concentrations, up to the ultimate stress of the A490high-strength bolts, in correspondence to the top-right one. Levels ofapproximately 1100 MPa have been experienced in this tension bolt atprincipal strains close to 9.5% that may be reasonably assumed to be aconventional ultimate value. In addition, Fig. 11 more deeply describesthemonotonic evolution of the VonMises stress distributions, observedin the whole connection system studied.

The FE analyses confirmed that specimens' response is governed bya pronounced slippage in the connection which results in an evidentstiffness drop in the capacity curve until bearing is achieved betweenthe bolt shaft and the hole in the plates. The initial slip is observed at ap-proximately 1% drift, for actuator load levels of about 45 kN. Slip is reg-ular and continued throughout the load steps with loads picking up as

Fig. 5. Evolution of maxim

the bolts go into bearing in the oversized holes. Prying action in the an-gles occurs for about 3% drift, resulting in initial yielding in both beamand angles; therefore, a distinct yield line appears across the shear legof the angle, evidencing the formation of a plastic hinge. Yielding takesplace in the shear tab around the bolts and a clean fracture in one ten-sion bolt reveals the failure of the specimen. In particular, such mecha-nism is faithfully reflected by the distribution of themaximumprincipalstrains, at ultimate condition, shown in Fig. 12 for the critical regions ofthe connection system FS-01. Although designed to be more ductilethan FS-01, Specimen FS-02 evidences quite a similar tension bolt fail-ure mode with hinging in the angles, anyway allowing for more defor-mation. Again, an initial slip between clip angle shear legs and thebeam flanges occurs at about 1% drift; the uplift of the angles is ob-served, as well as “pinching” at the end of the beam similar to thatnoted in FS-01 caused yielding near the k-line in the web. Similarly,3% drift produces yielding near the k-line in the shear leg of the angle.Much more visible prying action is observed and less damage to thebeam incurred, due to the location of the tension bolts farther awayfrom the k-line of the angles, as confirmed by Fig. 13(a).

As the advanced FE solid models developed are clearly time-consuming, particularly for predicting the behavior of these PR top-and-seat angle connections against cyclic loadings, therefore makingthis representation unfeasible if the response of a whole MRF is investi-gated, a simplifiedmodeling approach is additionally proposed and cal-ibrated on the observed experimental results. Examples of simplifiedapproaches [29,30], mostly used to represent bolted joints, are availablein the literature. In particular, Ekh and Schön [29] adopted linear beamsto model both the bolts and laminates, while nonlinearity induced byphenomena such as bolt-hole clearance was captured through connector

um principal strain.

Fig. 6. (a) Maximum principal strain and (b) Von Mises stress in the flanges; (c) relative contact pressure in the bolt, at ultimate condition.

30 E. Brunesi et al. / Journal of Constructional Steel Research 97 (2014) 24–38

elements. Hence, as schematized in Fig. 13(b), simplified FE models,based on inelastic force-based fiber elements, combined with zero-length tri-linear links to represent the effects of the nonlinear contact al-gorithms in an equivalent manner, have been developed. Although care-ful calibration and validation is needed to ensure that no possible failuremodes are omitted, reasonable connection response seems to beachieved, as confirmed by the deformed shape at failure, observed inFig. 13(c). In fact, even if this FE approach is, by definition, not nearly com-plex enough to accomplish a perfect match with experimental curves,

a

0 4 8 12 16 200

0.2

0.4

0.6

0.8

1

Principal Strain [%]

Nor

mal

ized

Bol

t Dep

th [−

]

LF=0.100LF=0.150LF=0.200LF=0.250LF=0.300LF=0.350LF=0.400LF=0.420

c

Fig. 7. (a) Evolution of the maximum principal strain distributions in the bo

particularly forwhat concerns the slip plateau, since the post-slip stiffnessis captured into an equivalentmanner, it allows a quite accurate andhigh-ly efficient response prediction if the connection is studied at a globalscale, as shown in Fig. 14(a) and (b).

Conversely, the refined FE models demonstrate their potential forachieving a close agreement with experimental tests throughout theimposed loading history, properly representing relative slippage offaying surfaces, frictional force transfer, prying and pinching actions,which, in turn, result in the damage of the connection components.

0 4 8 12 16 200

0.2

0.4

0.6

0.8

1

Principal Strain [%]

Nor

mal

ized

Bol

t Dep

th [−

]

LF=0.100LF=0.150LF=0.200LF=0.250LF=0.300LF=0.350LF=0.400LF=0.420

b

0 4 8 12 16 200

0.2

0.4

0.6

0.8

1

Principal Strain [%]

Nor

mal

ized

Bol

t Dep

th [−

]

LF=0.100LF=0.150LF=0.200LF=0.250LF=0.300LF=0.350LF=0.400LF=0.420

d

lt: focus on the (b) edge, (c) loaded and (d) pinned side, respectively.

0 4 8 12 16 200

0.2

0.4

0.6

0.8

1

Principal Strain [%]

Nor

mal

ized

Bol

t Dep

th [−

]N1G1µ1N1G1µ2N1G1µ3N1G2µ1N1G3µ1N2G1µ1N3G1µ1

0 4 8 12 16 200

0.2

0.4

0.6

0.8

1

Principal Strain [%]

Nor

mal

ized

Bol

t Dep

th [−

]

N1G1µ1N1G1µ2N1G1µ3N1G2µ1N1G3µ1N2G1µ1N3G1µ1

ba

Fig. 8. Ultimate maximum principal strain from parametric analyses, collected at (a) loaded and (b) pinned side.

31E. Brunesi et al. / Journal of Constructional Steel Research 97 (2014) 24–38

Although monotonic analyses tend to slightly overestimate the experi-mentally observed capacity for medium drift levels, as during the testthe faying surfaces slipped over repeatedly, producing more plasticdeformations, a good match with the experimental trend is reached,particularly in predicting the ultimate load. A satisfying fit with experi-mental data can be evidenced if the cyclic analyses are considered. Asshown in Fig. 15(a) and (b), the capacity curve shape of these types ofclip angle connections is characterized by an increased “pinching” effect,as the larger drift cycles approach their peaks; during the cyclic reversal,the angle in tension is observed to pull out, flattening the capacity curve,while the angle on the compression beam flange reseats itself and be-gins to bear on the columnflange, resulting in an increased relative stiff-ness and additional load carrying capacity. As observed in [20], thepronounced effect of slip occurs when connections have thick seatangles.

Based on the comparison between experimental and numerical ca-pacity curves, presented in Fig. 15(a) and (b), the advanced FE approachsuggested is validated and, hence, a parametric campaign of monotonicanalyses is performed, according to Table 2. Fig. 16(a) and (b) highlightthe shear force-tip displacement curves obtained for Specimen FS-01;sensitivity of the response with respect to bolt preload and bolt-platesgap is again evidenced, particularly in terms of slip plateau. Indeed, a50% increase in bolt-flanges gap roughly implies a 30% elongation ofthe slip plateau for a constant force, while a 20% reduction of bolt pre-tension results in a 15% decrease of the force atwhich slip occurs and si-multaneously in an anticipated (17%) and longer slip plateau (9%), asshown in Fig. 16(b). In addition, increased bolt-plates gap was also

Fig. 9. Ultimate maximum principal strains in the plat

observed to slightly limit shear strength and displacement ductilitycapacity, of about 3% and 5%, respectively.

Furthermore, in Fig. 17(a), (b), (c) and (d) attention is focused onthe critical tension bolt, governing the failure mechanism; in fact,Fig. 17(a) and (b) depict the monotonic evolution of the maximumprincipal strains, observed for Specimen FS-01 and FS-02. Althoughpeaks within 2% of each other and roughly placed at the same positionover the bolt length are noted, different shapes are observed, as con-firmed by the comparison at ultimate conditions, shown in Fig. 17(d).According to the prying action, developed by the different locations ofthe tension bolt line, FS-01 presents a more uniform distribution, as op-posed to that experienced by the critical tension bolt of FS-02, charac-terized by a more evidently concentrated damage at the top of thebolt; the results are related to case N1G1. Finally, Fig. 17(c) comparesthe ultimate maximum principal strains, according to the investigatedcombinations of bolt-plates gap and bolt prestress. Hence, a preloaddecrease results in slightly larger peaks (5%) and closer to the jointshear plane, due to a reduced clamping action between bolts andflanges, while an increment in the bolt-plates gap is observed to be in-effectivewith respect to the peak location, even if it inducesmuch largermaxima (10%).

4. Rotational stiffness assessment

Theproposed FE approach, validated by a consistentmatchwith full-scale destructive experimental test results, is able to predict the ob-served tension bolt failure mechanism, faithfully reflecting the

es of the multi-bolt joints investigated (N1G1μ1).

Table 2Analyses parameters — full-scale models: bolt-plates gap and bolt prestress.

Gap [mm] % N [MPa] %

1 0.8 – 641 –

2 1.0 +20 577 −103 1.6 +50 513 −20

32 E. Brunesi et al. / Journal of Constructional Steel Research 97 (2014) 24–38

connection behavior, in accordance with the complex interactionamong the connection elements. Therefore, in light of the obtained nu-merical results, matching past experimental data, a series of FE analysesis performed, varying connection system configuration, designed forthree assumed levels of resisting moment, according to EC3 [10] provi-sions, to propose an alternative analytical method, applicable aspreliminary-design-stage tool for the evaluation of the rotational stiff-ness of these PR bolted top-and-seat angle connections. Comparisonswith Kishi and Chen [11] equation and the so-called component ap-proach, codified in EC3 [10] will be given. The series of numerical pre-dictions was used to determine a closed-form approximateexpression, by a linear fitting procedure, depending on bolt and compo-nent geometric characteristics only.

In particular, provided that the axial force in the connectedmemberdoes not exceed 5% of the design resistance of its cross-section, the rota-tional stiffness Sj of a beam-to-column joint, for a moment less than thedesign moment resistance of the joint, may be obtained, according toEq. 6.27 of EC3 [10]:

Sj ¼Ez2

uXni¼1

1ki

ð1Þ

where E is the Youngmodulus of the material used for each connectioncomponent, conventionally assumed as 210,000 MPa, z is the lever armestimated as the distance between the center of rotation of the connec-tion and the row of bolts in tension and ki are the elastic stiffness coef-ficients of each basic joint component, determined from Table 6.11 ofEC3 [10]. Finally, u is a correction factor, defined as the ratio betweenthe initial and secant stiffness, accounting for the expected/desired con-nection nonlinearity. Since in this paper attention is focused only on theinitial rotational stiffness, u is set equal to 1, according to 6.3.1(4) of EC3[10]. Therefore, the rotational stiffness of a bolted beam-to-column con-nection can be obtained, using Eq. 1, from the flexibility of its basic

Fig. 10. Von Mises stress in the bolts (a) after pretensio

components, including, in general, column web panel in shear, columnflange in bending, flange cleat in bending, bolts in tension and boltsin shear. Although only the linear branch is used for our purposes, thisprocedure, commonly known as the component method, can be easilyextended to a nonlinear moment-rotation curve, by making use ofa simplified bi- or tri-linear diagram [31]. However, since manymathematical steps with reference to several factors involved are re-quired, this method, considered as the basis of all the observationsdrawn in this study, gives rise to a quite lengthy and iterative procedure.The application of this analytical approach requires three basic steps:the preparation of a list of all the components making up the connection(beam, column, angles, bolts, etc.), the validationof the force-deformationresponse for each component in terms of initial stiffness, strength and de-formation capacity, and the final assemblage of all the components inorder to evaluate the actual connection behavior. In particular, the assem-blage of each portion, either in series or in parallel depending on how thecomponents are arranged in the connection, is crucial to reflect as closelyas possible the overall rotational stiffness of the connection. Therefore,even if approximate, a closed-form expression could appear to be moreattractive, particularly for quick estimates.

4.1. Design of the PR connections and FE simulations

Sixteen bolted beam-to-column connections with flange anglecleats are designed for three levels of beam plastic moment, Mp, toassess the relative variation of the rotational stiffness. The steel gradeadopted both for beams and columns is S450 (i.e. E = 210,000 MPa,fyk = 450 MPa and fu = 510 MPa). Six hot-rolled profiles, rangingfrom IPE 360 to IPE 600, are selected as beam sections and, hence, thedesign moment of the connection, Md, directly established for thethree cases considered:

Md ¼0:25Mp ¼ 0:25Wp f yd Case 10:50Mp ¼ 0:50Wp f yd Case 20:75Mp ¼ 0:75Wp f yd Case 3:

8<: ð2Þ

Although in high seismic zones the design approach requires beam-to-column connections to withstand the plastic moment resistanceof the beam and to push plastic hinge formation in the beam, such anapproach could be inconvenient to provide from a practical and eco-nomical point of view in low seismicity cases. Thus, even if current seis-mic codes [32] specify the design moment of a beam-to-columnconnection to be approximately taken as 1.3 times the plastic resistanceof the beam, design for low-dissipative structural behavior (DCL),

n (clamping action) and (b) at ultimate conditions.

Fig. 11. Numerical failure mechanism: Von Mises stress evolution in Specimen FS-01, for significant displacement levels (DL).

33E. Brunesi et al. / Journal of Constructional Steel Research 97 (2014) 24–38

named in Eurocode 8 (EC8) [32] as design concept (a), is allowed fornon-seismically isolated buildings in low seismicity cases only, as spec-ified in 6.1.2(4) of EC8 [32]. Therefore, the so-called design concept (a),which admits design according to EC3 [10] without any additional re-quirement, is assumed. Furthermore, in light of capacity design princi-ples, the columns are sized to resist the design moments, withoutexploiting any plastic resistance:

Mp;col≥Md withX

Mcol ¼X

Mbeam: ð3Þ

Additional check is performed to account for axial load variation,assumed to range from 1000 kN to 5000 kN, in order to satisfy the fol-lowing criterion, suggested by EC3 [10]:

NEd

NRd

� �þ MEd

MRd

� �≤1 ð4Þ

where NEd and MEd are the design actions, while NRd and MRd the inde-pendent resistances. Table 3 summarizes the HE profiles selected tomeet the provisions of the iterative design process for each caseconsidered.

Fig. 12. Specimen FS-01: ultimate maximum principal stra

In this study, bolted connections are designed as Category A of EC3[10] with bolt class 8.8 (i.e. fyb = 640 MPa and fub = 800 MPa), whichis one of the most commonly used in the construction industry; S450steel is assumed for the angles. The connectionmust be capable of trans-ferring both shear forces and bending moments between the beam andcolumn. The entire shear forces developed in the beam are resisted bydouble shear in the bolt lines at the beamweb-angle interface, since an-gles are used on both sides of the beamweb. Ultimately, the shear forceto be resisted by the bolts is expressed as the ratio between a fraction ofthe beam plastic resistance and the span, while the bending momentdeveloped in thebeammust be resisted by a pair of shear forces inducedin the bolt lines at the interface between angles and beam flanges. Sub-sequently, the shear forces, evaluated as the ratio between the designmoment and the effective beam depth, must be transferred to the col-umn through the axial load developed in the bolts at the angle-column flange interface. In addition, to prevent abrupt failures of theconnections, both shear and tensile resistance of the bolts, as well asbearing strength of bolts and angles were checked, according toTable 3.4 of EC3 [10]. Hence, plates' thickness, bolts size and spacingare determined in accordance with additional restrictions of commondesign practice, by limiting the number of bolts per row to a maximumof four and angles' thickness to that of beam flange. Finally, the resultant

ins in the top clip angle, beam and failed tension bolt.

a

cbFig. 13. Specimen FS-02: (a) numerically predicted failure mechanism; (b) simplified model of the analyzed connection and (c) deformed shape at failure.

34 E. Brunesi et al. / Journal of Constructional Steel Research 97 (2014) 24–38

bolts number and sizes are given in Table 4. In Case 3, the design processfor IPE 550 and IPE 600 was aborted as the number of bolts and theirsizeswere too high to be able to consider their application for a practicaluse, thus validating the assumed design moment scenario for such PRconnections.

−200 −150 −100 −50 0 50 100 150 200

−100

−50

0

50

100

Tip Displacement [mm]

Act

uato

r Lo

ad [k

N]

ExpSimp FEM MonSimp FEM Cyc

a

Fig. 14. Simplified FE approach: experimental vs. numerical cyclic and

Therefore, to assess the initial rotational stiffness of the 16 PR boltedconnections, designed for three levels of flexural resistance, accordingto European Standards, numerical models of the connection sub-assemblages have been developed by adopting the refined FE approach,previously described in detail. Each sub-assembly consists of a half

−250 −200 −150 −100 −50 0 50 100 150 200 250

−100

−50

0

50

100

Tip Displacement [mm]

Act

uato

r Lo

ad [k

N]

ExpSimp FEM MonSimp FEM Cyc

b

monotonic capacity curves for Specimen (a) FS01 and (b) FS02.

−200 −150 −100 −50 0 50 100 150 200

−100

−50

0

50

100

Tip Displacement [mm]

Act

uato

r Lo

ad [k

N]

ExpFEM MonFEM Cyc

−250 −200 −150 −100 −50 0 50 100 150 200 250

−100

−50

0

50

100

Tip Displacement [mm]

Act

uato

r Lo

ad [k

N]

ExpFEM MonFEM Cyc

ba

Fig. 15. Detailed FE approach: experimental vs. numerical cyclic and monotonic capacity curves for Specimen (a) FS01 and (b) FS02.

35E. Brunesi et al. / Journal of Constructional Steel Research 97 (2014) 24–38

beam, half top and bottom columns and the entire bolted beam-to-column connection system. Although attention is just focused on theinitial elastic branch of the determined capacity curves, both materialand geometric nonlinearities have been potentially accounted for, with-in a nonlinear FE analysis framework, allowing for explicit contactmodeling. The monotonically increasing displacement is applied hori-zontally at the top of the upper column to obtain force–deformation re-lationships; the base of the bottom column is assumed to be pinned,while the beamend is idealized as a roller. By considering the geometriccharacteristics of the investigated connection system, the resultantforce–deformation relationships are converted to moment-rotationcurves, thus obtaining the initial rotational stiffness as the gradient oftheir initial linear branch.

4.2. Results of FE simulations and proposed approach for rotational stiffnessevaluation

In Fig. 18, the rotational stiffness assessed by each FE analysis per-formed is plotted versus the six beam profiles used, in comparisonwith the analytical predictions by EC3 [10] and Kishi and Chen [11]methods, for the three design targets considered. Obviously, the stiff-ness increases as the beam height increases; FE results depict trendssimilar to those achieved by conventional analytical approaches. How-ever, both EC3 [10] and Kishi and Chen [11] often overestimate FE stiff-ness, mainly for deeper beams, while a reduced discrepancy can be

0 50 100 150 2000

25

50

75

100

Tip Displacement [mm]

She

ar F

orce

[kN

]

N1G1µ1N2G1µ1N3G1µ1N1G2µ1N1G3µ1

a

Fig. 16. Specimen FS-01: (a) monotonic force-displacemen

appreciated if smaller beam sizes are considered. In addition, by assum-ing EC3 [10] as reference, the initial rotational stiffness predicted bothby FE and Kishi and Chen [11] approaches is normalized with respectto the EC3 [10] one and plotted against. As shown in Fig. 19, stifferthan EC3 [10] estimates are achieved by Kishi and Chen [11], while FEsimulations always present conservative results, except for two cases(0.25Mp), characterized by slightly larger predictions of about 10%. Inparticular, the maximum and minimum normalized stiffness levels aregiven for each design moment selected:

0:71≤ Sj;FEM=Sj;EC3

� �0:25Mp

≤1:13

0:57≤ Sj;FEM=Sj;EC3

� �0:50Mp

≤0:86

0:64≤ Sj;FEM=Sj;EC3

� �0:75Mp

≤0:81:

ð5Þ

Hence, verifications against interstory drift requirements and P-delta effects can be safely carried out by scaling EC3 [10] predictionsaccording to the lowest bound assessed via FE analyses (60%). Never-theless, in themajority of the cases, over-conservative estimates are ex-pected through a lengthy procedure, as all the EC3 [10] steps have to befulfilled. In light of these observations, sensitivity analyses, in order toinvestigate the dimensional connection parameters which are mainlydominant in the rotational stiffness estimation, have been performed.Dependency on beam height, hb, is implicitly shown in Fig. 18 and

25 35 45 55 65 7530

40

50

60

Tip Displacement [mm]

She

ar F

orce

[kN

]

N1G1µ1N2G1µ1N3G1µ1N1G2µ1N1G3µ1

b

t curves from parametric analyses; (b) enlarged view.

0 4 8 12 16 200

0.2

0.4

0.6

0.8

1

Principal Strain [%]

Nor

mal

ized

Bol

t Dep

th [−

]LF=25%LF=40%LF=55%LF=65%LF=75%LF=85%LF=95%LF=100%

0 4 8 12 16 200

0.2

0.4

0.6

0.8

1

Principal Strain [%]

Nor

mal

ized

Bol

t Dep

th [−

]

LF=25%LF=40%LF=55%LF=65%LF=75%LF=85%LF=95%LF=100%

ba

0 4 8 12 16 200

0.2

0.4

0.6

0.8

1

Principal Strain [%]

Nor

mal

ized

Bol

t Dep

th [−

]

N1G1µ1N1G2µ1N1G3µ1N2G1µ1N3G1µ1

0 4 8 12 16 200

0.2

0.4

0.6

0.8

1

Principal Strain [%]

Nor

mal

ized

Bol

t Dep

th [−

]

FS01FS02

dc

Fig. 17. Critical tension bolt: evolution of maximum principal strains in Specimen (a) FS-01 and (b) FS-02; (c) comparison between ultimate distributions from parametric analyses(FS-01); (d) FS-01 vs. FS-02.

36 E. Brunesi et al. / Journal of Constructional Steel Research 97 (2014) 24–38

similar trends are observed for what concerns column flange thickness,tcf, angle thickness, ta, and bolt area divided by length, Ab/Lb. In particu-lar, the rotational stiffness increases as these quantities increase. There-fore, a series of regression analyses was carried out by using the leastsquares technique, in order to find the “best” fit of the FE resultswith re-spect to different combinations of the parameters, with differentweights. The criterion selected was the maximization of the coefficientof determination, R2, in compliance with the avoidance of proposalsbased on complex expression, composed of too artificial combinationsof parameters.

Table 3HE column profiles of the designed PR connections.

Beam section Column section

Case 1 — 0.25Mp Case 2 — 0.50Mp Case 3 — 0.75Mp

IPE 360 HE 180 B HE 220 B HE 240 BIPE 400 HE 200 B HE 220 B HE 260 BIPE 450 HE 200 B HE 240 B HE 280 BIPE 500 HE 220 B HE 260 B HE 240 MIPE 550 HE 240 B HE 280 B HE 260 MIPE 600 HE 260 B HE 240 M HE 280 M

Hence, the proposed equation, plotted in Fig. 20, is chosen to belinear with respect to the combined parameter p, defined in Eq. 6:

p ¼ Ab

Lb� tcf � ta � hb: ð6Þ

The simplified closed-form expression, depending on componentsand bolts geometry only, shows a good match with FE data, beingcharacterized by a coefficient of determination slightly larger than0.97. Thus, Eq. 7, given its range of applicability, provides quick and ap-proximate initial rotational stiffness estimates for this type of PR boltedconnections; the average of the ratio between the stiffness predicted byFE analyses and Eq. 7 is 0.99 with a standard deviation of about 13%.

Sj kNm=rad½ � ¼ 121pþ 3318

¼ 121Ab

Lb� tcf � ta � hb

� �þ 3318 where 24≤p≤240m4

ð7Þ

5. Conclusions

Procedures for predicting the behavior of PR bolted connections andcomponents, via detailed solid FE models, incorporating contactalgorithms, and simplified one-dimensional inelastic force-based fiberelements, combined with nonlinear shear links, to globally represent

Table 4Bolts number and sizes in the designed PR connections.

Case 1 — 0.25Mp

IPE 360 400 450 500 550 600No. bolts in angle leg-column flange 2 M20 2 M20 2 M22 4 M20 4 M22 4 M24No. bolts in angle leg-beam flange 4 M20 4 M20 4 M22 6 M20 6 M22 6 M24No. bolts in angle-column flange-shear 2 M20 2 M20 2 M20 2 M20 2 M22 2 M22No. bolts in angle-beam web-shear 2 M20 2 M20 2 M20 2 M20 2 M22 2 M22

Case 2 — 0.50Mp

IPE 360 400 450 500 550 600No. bolts in angle leg-column flange 4 M20 4 M22 4 M24 6 M22 6 M24 6 M27No. bolts in angle leg-beam flange 6 M20 6 M22 6 M24 8 M24 8 M27 8 M30No. bolts in angle-column flange-shear 2 M20 2 M20 2 M20 2 M24 2 M24 2 M27No. bolts in angle-beam web-shear 2 M20 2 M20 2 M20 2 M24 2 M24 2 M27

Case 3 — 0.75Mp

IPE 360 400 450 500 550 600No. bolts in angle leg-column flange 4 M24 4 M26 6 M24 6 M27 – –

No. bolts in angle leg-beam flange 6 M24 6 M26 8 M27 8 M30 – –

No. bolts in angle-column flange-shear 2 M20 2 M22 2 M24 2 M24 – –

No. bolts in angle-beam web-shear 2 M20 2 M22 2 M24 2 M24 – –

Fig. 18. Predicted rotational stiffness according to FEM, EC3 [10], Kishi & Chen [11].

37E. Brunesi et al. / Journal of Constructional Steel Research 97 (2014) 24–38

the interacting connection elements, were developed and verified by arobust agreement with experimental response, governed by slippageand pinching. Sensitivity to bolt-plates gap, bolt preload and friction

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5x 104

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Sj,EC3

[kNm/rad]

Sj,i /

Sj,E

C3

[−]

Kishi&Chen − 0.25MpFEM − 0.25MpKishi&Chen − 0.50MpFEM − 0.50MpKishi&Chen − 0.75MpFEM − 0.75MpEC3 prediction

Fig. 19. FEM and Kishi & Chen [11] vs. EC3 [10].

was established, in terms of both global and local quantities, and the val-idated numerical approach was used to assess the rotational stiffness ofPR bolted beam-to-column connections, with top-and-seat angles and

0 50 100 150 200 2500

0.5

1

1.5

2

2.5

3

3.5 x 104

Ab/L

b*t

cf*t

a*h

b [m4]

Sj [

kNm

/rad

]

0.25Mp0.50Mp0.75MpProposed

Fig. 20. Proposed approximation for rotational stiffness estimates and relative scatter.

38 E. Brunesi et al. / Journal of Constructional Steel Research 97 (2014) 24–38

double flange angle cleats, designed, according to European standards,for three levels of plastic flexural capacity. Linear fitting techniqueshave been exploited to propose an alternative and conservativeclosed-form equation, observed to provide a satisfying match with FEresults, for quick rotational stiffness estimates of such type of connec-tion systems, faithfully reflecting behavioral changes as a consequenceof geometrical variations and proving its potential as a time savingpre-design tool.

References

[1] Tremblay R, Timler P, Bruneau M, Filiatrault A. Performance of steel structures dur-ing the January 17, 1994 Northridge earthquake. Can J Civ Eng 1995;22:338–60.

[2] Tremblay R. Seismic design of steel buildings: lessons from the 1995 Hyogo-kenNanbu earthquake. Can J Civil Eng 1995;23:727–56.

[3] Swanson JA, Leon RT. Bolted steel connections: tests on T-stub components. J StructEng — ASCE 2000;126:50–6.

[4] Wijesundara KK, Nascimbene R, Sullivan T. Equivalent viscous damping for steelconcentrically braced frame structures. Bull Earthquake Eng 2011;9:1535–58.

[5] Nascimbene R, Rassati GA, Wijesundara KK. Numerical simulation of gusset-plateconnections with rectangular hollow section shape brace under quasi-static cyclicloading. J Constr Steel Res 2011;70:177–89.

[6] Roeder CW, Knechtel B, Thomas E, Vaneaton A, Leon RT, Preece FR. Seismic behaviorof older steel structures. J Struct Eng — ASCE 1996;122:365–73.

[7] Weynand K, Jaspart JP, Steenhuis M. Economy studies of steel building frames withsemi-rigid joints. J Constr Steel Res 1998;46:1–3.

[8] Nader MN, Astaneh-Asl A. Dynamic behavior of flexible, semi-rigid and rigid steelframes. J Constr Steel Res 1991;18:179–92.

[9] Nader MN, Astaneh-Asl A. Shaking table tests of rigid, semi-rigid and flexible steelframes. J Struct Eng — ASCE 1996;122:589–96.

[10] Eurocode 3. Design of steel structures — Part 1–8: design of joints, EN 1993-1-8.Belgium: Brussels; 2005.

[11] Kishi N, ChenWF. Moment rotation relations of semi-rigid connectionswith angles. JStruct Eng — ASCE 1990;116:1813–34.

[12] Girão Coelho AM, Bijlaard FSK, Silva LS. Experimental assessment of the ductility ofextended end plate connections. Eng Struct 2004;26:1185–206.

[13] Maggi YI, Gonçalves RM, Leon RT, Ribeiro LFL. Parametric analysis of steel bolted endplate connections usingfinite elementmodeling. J Constr Steel Res 2005;61:689–708.

[14] Piluso V, Rizzano G. Experimental analysis andmodelling of bolted T-stubs under cy-clic loads. J Constr Steel Res 2008;64:655–69.

[15] Bose B, Sarkar S, Bahrami M. Extended end plate connections: comparison betweenthree-dimensional nonlinear finite element analysis and full-scale destructive tests.Struct Eng Rev 1996;3:111–9.

[16] Bursi OS, Jaspart JP. Calibration of a finite element model for isolated bolted end-plate steel connections. J Constr Steel Res 1997;44:225–62.

[17] Sherbourne AN, Bahaari MR. Finite element prediction of end plate bolted connec-tion behavior. I: parametric study. J Struct Eng — ASCE 1997;123:157–64.

[18] Yang JG, Murray TM, Plaut RH. Three dimensional finite element analysis of doubleangle connections under tension and shear. J Constr Steel Res 2000;54:227–44.

[19] Swanson JA, Kokan DS, Leon RT. Advanced finite element modeling of bolted T-stubconnection components. J Constr Steel Res 2002;58:1015–31.

[20] Citipitioglu AM, Haj-Ali RM, White DW. Refined 3D finite element modelling of par-tially restrained connections including slip. J Constr Steel Res 2002;58:995–1013.

[21] Shi G, Shi Y,Wang Y, BradfordMA. Numerical simulation of steel pretensionedboltedend-plate connections of different types and details. Eng Struct 2008;30:2677–86.

[22] Gerami M, Saberi H, Saberi V, Daryan AS. Cyclic behaviour of bolted connectionswith different arrangement of bolts. J Constr Steel Res 2011;67:690–705.

[23] Girão Coelho AM. Rotation capacity of partial strength steel joints with three-dimensional finite element approach. Comput Struct 2013;116:88–97.

[24] Schrauben CS. Behavior of full-scale bolted beam-to-column T-stub and clip angleconnections under cyclic loading. [MS thesis] Georgia Institute of Technology;1999.

[25] Brunesi E, Nascimbene R, Rassat GA. Evaluation of the response of partiallyrestrained bolted beam-to-column connection subjected to cyclic pseudo-staticloads. tructures Congress 2013: Bridging Your Passion with Your Profession -Proceedings of the 2013 Structures Congress 2013:2310–21.

[26] Nastran NX. Advanced Nonlinear Theory and Modeling Guide, Siemens; 2012.[27] Chung KF, Ip KH. Finite element modeling of bolted connections between cold-

formed steel strips and hot rolled steel plates under static shear loading. Eng Struct2000;22:1271–84.

[28] Bursi OS, Jaspart JP. Benchmarks for finite element modeling of bolted steel connec-tions. J Constr Steel Res 1997;43:17–42.

[29] Ekh J, Schön J. Finite element modeling and optimization of load transfer in multi-fastener joints using structural elements. Compos Struct 2008;82:245–56.

[30] Eriksson I, Backlund J, Moller P. Design of multiple-row bolted composite jointsunder general in-plane loading. Compos Eng 1995;5:1051–68.

[31] Rassati GA, Leon RT, Noè S. Component modeling of partially restrained compositejoints under cyclic and dynamic loading. J Struct Eng — ASCE 2004;130:343–51.

[32] Eurocode 8. Design of structures for earthquake resistance — Part 1: general rules,seismic actions and rules for buildings, EN 1998-1-1. Belgium: Brussels; 2005.