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Engineering Structures 33 (2011) 3043–3053

Contents lists available at SciVerse ScienceDirect

Engineering Structures

journal homepage: www.elsevier.com/locate/engstruct

Elastic and ductile design of multi-storey crosslam massive wooden buildingsunder seismic actionsM. Fragiacomo a,∗, B. Dujic b, I. Sustersic b

a Department of Architecture, Design and Urban Planning, University of Sassari, Palazzo del Pou Salit, Piazza Duomo 6, 07041 Alghero, Italyb CBD d.o.o. - Contemporary Building Design Company, Lopata 19g, 3000 Celje, Slovenia

a r t i c l e i n f o

Article history:Available online 29 June 2011

Keywords:Cyclic testsCross-laminated panelsDuctilityEarthquake designMulti-storey buildingsPush-over analysisSeismic performanceTimberWood

a b s t r a c t

The paper discusses the seismic design of multi-storey buildings made from cross-laminated timberpanels (‘crosslam’). The use of seismic analysis methods such as the modal response spectrum and thenon-linear static (push-over) analysis is discussed at length, including issues such as the modelling ofcrosslamwalls and connections, the evaluation of the connection stiffness, and the schematization of floorpanels. Itwas found that it is crucial to account for the flexibility of the connections (hold-downs and anglebrackets) between upper and lower walls, since otherwise the vibration periods of the building would beunderestimated. The basics of capacity design to ensure the attainment of ductilemechanisms in crosslamtimber structures under seismic actions are presented. The ductile failure mechanism is characterized byplasticization of connectors (hold-downs, angle brackets and screws) between adjacent wall panels andbetween panels and foundations. The crosslam panels and the connections between adjacent floor panelsmust be designed for the overstrength of the connectors to ensure that they remain elastic during theearthquake and the ductile failure mechanism is attained. Based on the results of preliminary quasi-staticcyclic tests, a value of 1.3 was found for the overstrength factors of hold-downs and angle brackets. A casestudymulti-storey crosslammassive wooden building was then analysed using the non-linear push-overanalysis as implemented in the N2 method recommended by the Eurocode 8. The building was modelledusing shell elements and non-linear links to schematize the hold-downs and angle brackets. The buildingductility, calculated from the bilinear curve equivalent to the actual non-linear push-over curve, was theninvestigated. Such a quantity, defined as the ratio of the displacement at the near collapse state and themaximum elastic displacement of the top floor, was found to rise from 1.7 to 2.5 when ductile instead ofbrittle hold-downs and angle brackets are used. Furthermore, themaximumpeak ground acceleration thebuilding can resist raised from 0.2g to 0.4g , demonstrating the importance of using ductile connectors inseismic design.

© 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Different methods can be used for the design of seismic-resistant buildings. The most basic approach would be to evaluatethe forces induced on a building by an earthquake with a highreturn period and design the structure in elastic phase. Sincestatistically the chance of a high intensity earthquake occurringduring the lifetime of a building (in most cases 50 years) isnot particularly high (about 10%), the elastic design leads tosignificant overdesign of the building elements. For this reasonthe elastic approach is generally used only in low to moderateseismicity regions. The alternative design approach is based on theprinciples of ductile design. A ductile structure is able to dissipateenergy during the seismic event by undergoing through plastic

∗ Corresponding author. Tel.: +39 079 9720418; fax: +39 079 9720420.E-mail addresses: [email protected] (M. Fragiacomo), [email protected]

(B. Dujic), [email protected] (I. Sustersic).

0141-0296/$ – see front matter© 2011 Elsevier Ltd. All rights reserved.doi:10.1016/j.engstruct.2011.05.020

deformation. One of the advantages is the possibility to survivehigh intensity earthquakes as long as the displacement demand inthe ductile parts of the structure does not exceed the displacementcapacity. The ductility also allows more economical structures tobe built as the design seismic actions can be reduced dependingupon the ductility ratio [1]. Such an approach is generally followedfor building design in medium to high seismicity regions.

Current codes of practice [2] suggest two different approachesfor design of ductile structures in earthquake-prone regions.The first approach, well known and widely used, is referredto as the Force-Based Design (FBD) method since it mainlyfocuses on designing the strength of the structure [1]. Theobjective is the evaluation of the behaviour factor q, which isemployed to transform the elastic response spectrum into a designspectrum. In this way a non-linear structure can be designedusing a linear-elastic static or dynamic (modal response spectrum)analysis under seismic action, with the structural ductility onlyimplicitly considered when evaluating the behaviour factor q.

3044 M. Fragiacomo et al. / Engineering Structures 33 (2011) 3043–3053

Fig. 1. Failure modes for steel–timber (left) and timber–timber (right) connections, notations according to EC5-1-1 [15].

The second approach, which explicitly refers to the structuralductility in addition to the strength, is based on a Non-linear StaticAnalysis (NSA) procedure [1]. The purpose of this approach is theevaluation of the actual structural response mainly in terms ofductility demand and, hence, ultimate displacement induced inthe structure by the earthquake ground motion [3]. A numberof different methods have been proposed, including a modifiedversion of the N2 method [4], which has been adopted by thenew Italian regulation [5] and by the Eurocode 8 (EC8) [2] and isdiscussed more in detail in the following sections.

An important issue in seismic design is the identificationof suitable, ductile failure mechanisms. Capacity-based designmust then be used [6] to ensure that brittle failure mechanismswill not occur. For multi-storey timber buildings with lightframeconstruction, the most ductile failure mechanism is shear inthe nailed/screwed connections between the sheathing and theframe [7]. All other failure mechanisms are fairly brittle and,therefore, should be avoided by designing the correspondingmembers (hold-downs, bolts, timber studs, timber plates, plywoodsheathing) for the overstrength of the nailed/screwed connection.

New structural systems for multi-storey timber buildingshave recently been proposed in Europe and in Australasia.Unlike lightframe construction, these innovative systems canalso comply with the new philosophy of the Damage AvoidanceDesign, according to which a building should not only survivean earthquake at ultimate limit state, but be easily repairableand useable in a short time so as to reduce the disruption andthe associated cost to a minimum [8]. In Australasia, hybridsystems made of laminated veneer lumber (LVL) walls and framesprestressed with unbonded tendons used together with energydissipaters were developed [9,10]. In such systems the prestressedtendons keep the timber elements connected together and ensurethat after an earthquake event, due to the restoring force, thestructure returns to its initial position with little, if not, residualdeformation. The energy dissipaters ensure proper dissipationwith reduction in displacement demand to the structure. InJapan,multi-storey buildings constructed fromprefabricatedwallsand slabs made of cross-laminated timber (‘crosslam’) producedin Europe were subjected to full-scale shaking table tests.The buildings survived high intensity earthquakes with limitedstructural damage [11,12]. Furthermore, it was found that suchsystems, with a proper choice of connection details and panelsizes, can dissipate a significant amount of energy, mostly inthe connections between wall panels, and between panels andfoundation, leading to the possibility of carrying out static andmodal response spectrum analysis assuming a behaviour factorq = 3 [13].

Despite the extensive use of the crosslam technology, there arefew provisions for the seismic design of this system in currentcodes of practice such as the Eurocode 8 [2]. In addition to the lackof any value for the overstrength factor, there is no suggestion onthe choice of the ductile failure mechanism, nor indication on theway the NSA can be carried out according for example to the N2method. This paper provides some answers to the aforementionedqueries, namely it proposes somevalues of the overstrength factorsfor typical connections used in crosslam construction based on theresults of experimental cyclic tests, and presents the use of the

NSA in the design of a simple crosslam building. Further importantissues such as the numerical modelling of crosslam panels andconnections, the influence of the connection ductility on the globalductility of the building, and the seismic performance of the wholebuilding are critically discussed in the paper.

2. Choice of an appropriate ductile failure mechanism formulti-storey crosslam buildings

2.1. Provisions for a ductile connection between crosslam panels

Crosslam panels are solid slabs made from layers of timberboards with the adjacent layers glued at a right angle. Advantagesover glued-laminated elements include improved stability in bothdirections, which is of particular importance for 2D elements,and the possibility to use medium to low quality timber. Thistechnique was developed in Europe about 15 years ago and isnowadays extensively used. Crosslam buildings are erected byconnecting crosslam walls and slabs together using angular metalbracket connectors, usually nailed or screwed to the timber, andself-tapping screws. The connections between adjacent panels areusually realizedusing 8mmdiameter screwsplaced at a distance of300 mm centre to centre [14], where the penetration of the screwin the second wall is usually equal or longer than the penetrationin the first wall. The foundation–panel and upper–lower panelconnections are made from nailed or screwed angular metalbrackets, and in some cases also by hold-down connectors, nailedand bolted to the timber and reinforced concrete foundation at thefirst storey. The wall-to-floor panel connections are often made of8 mm diameter screws placed at a distance of 300 mm centre tocentre.

Different failure mechanisms can occur in a crosslam building,and only few of them are ductile. Failure of the wall panel due toin-plane loading (shear, bending and axial force) is mostly brittleand should be avoided by designing the panel for the overstrengthof the ductile elements (the connectors). The connectors betweenadjacent panels and between panels and foundation, however,may behave ductile or brittle under shear deformation dependingon whether plasticization of the steel fastener (screws and nails)is attained or not. Therefore, according to the notation of theEurocode 5 Part 1-1 [15], see Fig. 1(left), failuremode ‘b’ is regardedas ductile (one plastic hinge formation), whilstmode ‘a’ that occurswith shorter and/or thicker fasteners and has no plastic hingeformation in the steel fastener is regarded as brittle. The mostdesirable failure mechanism would be mechanism ‘e’, where twoplastic hinges are formed in the fastener. However, this wouldonly be possible if thicker steel plates were used, which does notapply to typical brackets andhold-downs. For screwed connectionsbetween adjacent panels, mode ‘f’ is themost ductile and thereforethe most desirable. Modes ‘d’ and ‘e’ are also ductile though onlyone plastic hinge is formed (Fig. 1(right)).

2.2. Definition of the overstrength factor

An important issue in seismic design is the identification ofsuitable, ductile failure mechanisms. Capacity-based design mustthen be used [6] to ensure that brittle failure mechanisms will

M. Fragiacomo et al. / Engineering Structures 33 (2011) 3043–3053 3045

Fig. 2. Backbone curves of a crosslam wall–bracket (BMF105) connection tested under cyclic loading of tension (left) and shear (right) according to EN 12512 [26] for 40and 60 mm long nails with 4 mm diameter. Solid/dashed lines refer to the response during the first/third cycle, respectively.

not occur. This is achieved by designing the structural elementswhich may fail in a brittle manner under an increased seismicdemand E ′

d given by

E ′

d = γRd · γod · Ed (1)where Ed is the seismic demand on the structural elementcalculated using the design spectrum as reduced to allow for theductile behaviour of the structure, γod is the overdesign factor,given by

γod =FdEd

(2)

where Fd is the design strength capacity of the ductile structuralelement, and γRd is the overstrength factor, given by

γRd =F0.95Fd

(3)

where F0.95 is the 95th percentile of the actual peak strengthcapacity of the ductile structural element [16]. Whilst theoverdesign factor depends on the rounding carried out in the actualdesign, the overstrength factor depends on the type of materialand structural detail. The Eurocode 8 [2] provides the values of theoverstrength factors for steel and reinforced concrete structures,which are in the range 1–1.3, however there is no provision fortimber structures. Some indications can be found in the NewZealand timber standard [17], where a value of 2 is suggested forthe overstrength factor.

2.3. Evaluation of the overstrength factors for timber–timber connec-tions

This section discusses the results of experimental cyclic testsperformed on timber to timber connections made of angularbrackets and screws. The connection behaviour governs theseismic response of timber buildings and therefore plays a majorrole in a seismic analysis. Due to the lack of information instandards and codes of practice, reference to only experimentaltests has been made in this section.

In earthquake design of crosslam buildings, a suggestion isgiven to design the nailed and screwed connections for the ductilefailure modes discussed above. Fig. 2 shows the results of cyclictests carried out by Dujic and Zarnic [18] on cross-laminated wallconnections with metal bracket loaded in tension (left) and shear(right). Ten 4 mm diameter nails were used to connect the anglebracket to the crosslam panel, which had three layers of timberboards with 30, 34 and 30 mm thickness. The connection with60 mm long nails was designed so as to ensure failure mode ‘b’is achieved. The ductile behaviour can be clearly appreciated — anaverage ductility ratio µ of about 8 for tension and 6.5 for shearis obtained. In this evaluation, the yield point was computed byfollowing the so-called Yasumura andKawai procedure [19],whichwill be discussed in more detail in an ensuing section. Converselythe use of the 40 mm long nails leads to a rather brittle behaviour,with failure occurring in the bottom rowof nails (see Fig. 3) for plug

Fig. 3. Plug shear failure in the bottom rowof nails of the bracket–panel connectionloaded in tension.

shear. This plug shear failure was a consequence of the nails notpenetrating deep enough in the middle layer of the wall. Hence arecommendation is given to use nails or screws at least 60mm longto achieve a ductile failure mechanism and avoid the brittle shearplug failure. For the same specimens, the overstrength factorswerecomputed using Eq. (3).

The design strength capacity Fd was calculated by dividing thecharacteristic experimental strength F0.05 by the strength partialfactor γM , assumed to be equal to one according to the Eurocode8 [2] for dissipative timber structures. The 5th percentile F0.05 wasestimated by assuming a student’s t-distribution on the basis ofthe maximum experimental shear and uplift strength Fmax amongthe three specimens tested. The same procedure was used forthe calculation of the 95th percentile, F0.95. Since several differenttypes of connections were tested, the number of specimens persetup was rather small but so was the scatter of results and alsothe standard deviation σ . The overstrength factors from shear testsare 1.3 for 60 mm and 2.2 for 40 mm nails (see Table 1). Theresults from uplift give an overstrength factor γRd of about 1.9 for40 mm nails and 1.2 for 60 mm nails, the latter value being basedon the results of only two specimens (see Table 1). Although toofew specimens were tested to derive a final value, the results ofthis preliminary investigation provide a first approximation for theoverstrength factor to be used for the design of the componentswith brittle failure.

An experimental investigation performed by the same au-thors [18] on screwed connections between perpendicular panelsinvolved 5 specimenswithΦ8 screws 160mm longwith an 80mmlong threaded part that were cyclically tested under shear loading.Fig. 4 shows that the screw exhibited a ductile behaviour since ei-ther ductile mechanism ‘d’ or ‘e’ according to Fig. 1 had formed.If calculating the failure modes according to the Johansen equa-tions and using the method proposed by Blass and Uibel [20] toaccount for the layered structure of the crosslam panels, mode ‘f’failure should occur. The difference among the predicted strengthsfor modes ‘d’, ‘e’ and ‘f’ is, however, very small. The over-strength factor calculated according to Eq. (3) using a student’s

3046 M. Fragiacomo et al. / Engineering Structures 33 (2011) 3043–3053

Table 1Experimental results for BMF 105 angular brackets with ten 4 mm diameter nails 40 and 60 mm long and Wuerth Assy II 8 × 160/80 self-tapping screws.

Number ofspecimens tested

Mean value ofpeak force (Fmax)

Standard deviationσ of peak force

5th percentileF0.05

95th percentileF0.95

Overstrength factorγRd (Eq. (1))

BMF 105 angular brackets Shear 3 13.5 1.73 8.4 18.5 2.12with ten 40 mm nails Uplift 3 14.8 1.51 10.4 19.3 1.85BMF 105 angular brackets Shear 3 15.0 0.59 13.3 16.8 1.26with ten 60 mm nails Uplift 2 23.1 0.31 21.2 25.0 1.18Wuerth Assy II 8 × 160/80 Shear 5 4.7 0.52 3.6 5.8 1.63self-tapping screws

Fig. 4. Typical failure of Wuerth Assy II 8× 160/80 self-tapping screws due to lowcycle fatigue (top left) and cyclic response of a specimen with 1 screw loaded inshear, including backbone curves of the first 3 cycles.

t-distribution on the basis of the maximum strength Fmax amongthe five specimens tested is γRd = 1.6 (see Table 1), which is rec-ommended for the overstrength factor of screwed connections be-tween perpendicular crosslam panels.

2.4. Additional considerations on the failure mechanism of multi-storey crosslam buildings under seismic actions

Additional issues are whether the plasticization should beallowed also at the upper storeys and within the floor diaphragm.Since the damage observed in shaking table tests of full-scalemulti-storey crosslam buildings was little [11], unlike lightframeconstruction it is suggested that plasticization should be allowedin the walls at all of the storeys. However, since the plasticizationof the floor diaphragmmay lead to a number of problems includingtorsional rotation of the building, influence of higher modes ofvibrations, and significant increase in structural damage, it issuggested that the connections between adjacent floor panels areconsidered as non-ductile and designed for the overstrength ofthe bracket and wall-to-wall connections. A typical connectionbetween adjacent floor panels is obtained with 50 mm overlapof panels (step joint) where each panel is cut in the middle of itsdepth (Fig. 5a). Φ6 screws are inserted usually perpendicularly ata distance of 300 mm centre to centre. Another option is the useof a plywood strip overlapping on the two panels (Fig. 5b) [11,21],which leads to increased ductility but also to reduced stiffness. A

desirable connection, with high in-plane strength and stiffness, isdisplayed in Fig. 5c, where screws take most of the load in thefavourable axial (tensile) direction. If gluing is applied or screwsare drilled at 45° angle also parallel to the panel length, a very stiffjoint could be achieved for in-plane axial and shear forces.

The current version of the Eurocode 8 Part 1 [2] does notprovide any value for the overstrength factors, although itrequires the use of capacity design and, in particular, that theoverstrength requirement applies especially to: (i) anchor ties andany connection tomassive sub-elements; (ii) connections betweenhorizontal diaphragms and lateral load resisting vertical elements.It should be pointed out that the last provision is questionable forcrosslam construction since the connections between inter-storeyplates and walls are ductile and practically without any possibilityof a brittle failure. However, to ensure the ductile mechanism, theuse of crosslam elements (walls and plates) with a thickness ofat least 90 mm is recommended, together with a screw lengthadjusted to the thickness of the floor plate so that either failuremechanism ‘d’ or ‘e’ (according to Fig. 1) can form. There is also apossibility of amore ductilemechanism ‘f’ and the formation of twoplastic hinges with even greater energy dissipation. Future studiesshould investigate the possibility to achieve this very ductile failuremechanism (also for angular brackets), which could enable designswith even higher behaviour factors q. Regarding the design of thepanels for the overstrength of the connections, this is of particularimportance when the panel is weakened by an opening. In thiscase, the failure may occur for stress concentration due to bendingmoment around the corners of a large opening (frame effect). Forexample, in an experimental study carried out by Dujic et al. [22],strength and stiffness were observed to depend upon the openingfactor defined by Yasumura [23] for lightframe walls:

r =1

1 +αβ

=H

∑Li

H∑

Li +∑

Ai. (4)

Variables in Eq. (4) and Fig. 6 are the panel area ratio (r), theheight of the wall element (H), the length of the wall element (L),the length of full height wall segments (

∑Li), the summation of

opening areas of the wall segment (∑

Ai), the ratio of openingsin the wall element (α =

∑Ai/HL), and the ratio of full wall

segments (β =∑

Li/L).Based on the results of recent investigations, Dujic et al. [22]

suggested that for panel area ratios greater than r = 0.4, theopenings do not affect the strength and stiffness of the timberpanels, and mostly brittle failures cannot occur in crosslam panelsbefore the ductile mechanism of the steel brackets activates.

Fig. 5. Different types of connections between adjacent floor panels.

M. Fragiacomo et al. / Engineering Structures 33 (2011) 3043–3053 3047

Table 2Blass and Fellmoser coefficients for in-plane loaded crosslam panels [24] and effective strength and stiffness for a homogenized panel (0/90 subscripts denoteparallel/perpendicular to the grain orientation of the outer layer of the panel).

k3 = 1 −

1 −

E90E0

·

am−2−am−4+···±a1am

k4 =E90E0

+

1 −

E90E0

·

am−2−am−4+···±a1am

a1 thickness of the middle layer,am panel total thickness,E0 modulus of elasticity parallel to grainE90 modulus of elasticity perpendicular to grain

Eff. strength fm,0,ef = k3fm,0 fm,90,ef = k4fm,0 ft,0,ef = k3ft,0 ft,90,ef = k4ft,0 fc,0,ef = k3fc,0 fc,90,ef = k4fc,0

Eff. stiffness Em,0,ef = k3E0 Em,90,ef = k4E0 Et,0,ef = k3E0 Et,90,ef = k4E0 Ec,0,ef = k3E0 Ec,90,ef = k4E0

The aforementioned limit value of r is generally acceptable forbuildings with gravity load in seismic condition not exceeding15 kN/m and if the walls are held down using BMF105 bracketconnections at a distance of about 50 cm centre to centre.

3. Seismic modelling of crosslam timber buildings

Crosslam structures are currently not explicitly mentionedeither in Eurocode 8 [2] or in Eurocode 5 [15]. Due to the lack ofcomprehensive design guidelines, some issues that need specialconsideration when modelling crosslam buildings under seismicactions are discussed in the ensuing sections.

3.1. Modelling of timber panels

The complex panel layout can bemodelled using an orthotropic,homogenized orthotropic or homogenized isotropic material,depending on the possibilities offered by the FEM software. Blassand Fellmoser [24] proposed the Homogenised, Orthotropic planestress Blass reduced cross Section (HOBS) method, which is basedon the reduction of a multilayer to a single layer section using thecoefficients k3 and k4 provided in Table 2 to modify the stiffnessesand strengths. By assuming a plane stress state, only twomoduli ofelasticity (E0 and E90), one shear modulus (G12) and one Poisson’scoefficient (ν12) need to be defined. The thickness of the panelsremains the same as does the shear modulus. If the adjacentboards of individual layers are not glued along their thickness,a 10% reduction in the shear modulus is suggested. In spite ofits simplicity, recent investigations demonstrated that this modelprovides results accurate enough for seismic design.

3.2. Modelling of floor diaphragms

When performing time-history analyses of crosslam buildings,some authors [11,12] have assumed the hypothesis of rigid floordiaphragms. It should be pointed out that this assumption isnot fully true. If such a simplification is made, it is advisable toprescribe gluing of adjacent floor panels or using stiffer connectionwith screws running at 45° angle (see Fig. 4c) so as to achieve astiff floor diaphragm. Appropriate overstrength factors should beapplied in the design of the floor panels and their connection. Themodelling of the floor diaphragm is an issue that deserves furtherinvestigation through non-linear dynamic analyses to evaluate thein-plane flexibility of a floor and its influence on the buildingbehaviour.

Fig. 6. Definition of panel area ratio.

3.3. Evaluation of the connection stiffness

This is a fundamental issue in any type of seismic analysis.The modal response spectrum analysis depends on the structurevibration period and therefore on its stiffness. The connectionsbetween crosslam panels play a crucial role and therefore mustbe modelled accurately. Care has to be taken when modellingangular brackets and hold-downs loaded in tension with finiteelement links. Their stiffness must be very high in compressiondue to the contact, and equal to the connection stiffness intension. Unfortunately such non-linear behaviour cannot bedirectly modelled in linear static and dynamic (modal responsespectrum) analyses. Neglecting connections between crosslampanels, namely modelling walls with rigid connections as inconcrete construction leads to large errors as itwill be shown in thecase study presented in the following section. Some guidance onhow to evaluate the correct connection stiffness will also be given.

4. Case study: elastic seismic analysis of amulti-storey crosslambuilding

4.1. Geometrical properties of the case study building and types ofmodelling

A four-storey crosslambuilding (Fig. 7)wasmodelled accordingto the recommendations given in the previous sections. Thebuilding has 140 mm thick 5-layer crosslam walls along itsperimeter. Inside the building there are only two posts and a beamthat support three adjacent 140 mm thick crosslam slabs runningfromwall ‘A’ to wall ‘C’. Wall ‘A’ is made from two separate panels,which are connected only with a beam element pinned onto thewalls. The wall panels are connected at the bottom and at the top

3048 M. Fragiacomo et al. / Engineering Structures 33 (2011) 3043–3053

11.2 m

6.5 m8.5 m

Fig. 7. 3D view, plan and wall elevations of the crosslam building analysed (dimensions in mm).

with BMF105 brackets (with ten 60mm long, 4 mm diameter nailsper bracket), which are placed at 50 cm spacing so as to resist thebase shear force calculated according to the lateral force methodof analysis. The building wasmodelled in SAP 2000 [25] using shellelements (10 × 10 cmmesh) in accordance with the HOBS model.The floor diaphragms were modelled as rigid. The connectionsamong adjacent panels were schematized in different ways: (i)with rigid links (full 3D model with rigid connections), (ii) withlinear-elastic springs for the top and bottom connections of walls,and without any connection between perpendicular walls at thesame level (pseudo-3D model), and (iii) with linear-elastic springsfor the top and bottom connections of walls, as well as connectionsbetween perpendicular walls at the same level (full 3Dmodel withelastic connections).

4.2. Calculation of the connection stiffness

An important issue is how to model the stiffness of thescrewed and bracket connections. In this paper, it is suggestedthat stiffness, strength and ductility of the steel brackets andscrewed connections are determined according to the Yasumuraand Kawai procedure [19] (see Fig. 8), sometimes also referred toas the modified CEN procedure or the 10-40-90 procedure. Such aprocedure was proposed for the evaluation of wood framed shearwalls, which is similar to the one suggested by EN 12512 [26]. Thecalculation of the ultimate strength is based on the equivalence ofthe deformation energy, but the calculation of the elastic stiffnessis slightly different from EN 12512. The yielding load is determinedby assessing the intersection of two lines. The first line is drawnthrough the points on the loading curve corresponding to 10% and

Fig. 8. Yasumura and Kawai procedure [19] for the evaluation of strength, stiffnessand ductility of a timber shear wall.

40% of the peak load Fmax. Unlike the EN 12512 procedure, thesecond line is drawn through the points corresponding to 40% and90% of Fmax. The line is thenmoved so that it becomes tangent to theactual loading curve. The intersection of this and the former linegives the yield load and the corresponding displacement. The ratiobetween the yield load and its corresponding displacement gives

M. Fragiacomo et al. / Engineering Structures 33 (2011) 3043–3053 3049

Fig. 9. Four-storey crosslam building — Comparison among different models (i, ii and iii) in terms of vibration periods (T1, T2 and T3), base shear along x (Rx) and y (Ry),and top floor displacement along x (Ux) and y (Uy).

the elastic stiffness Ky. The ultimate displacement correspondsto 80% of Fmax on the decreasing part of the loading curve. Theultimate strength Fu is calculated so that the equivalence of thedeformation energies is achieved by assuming an elasto-plasticload–displacement curve, the area under which is marked grey inFig. 8.

When determining the elastic stiffness of brackets for a use inthe 3D modal response spectrum analysis, the values of the stiff-ness Ky for shear and tension were calculated as described above.Each wall was then non-linearly modelled using gap elements(namely non-linear elements almost rigid in compression withnull tensile stiffness) and elastic links for brackets to simulate theexact boundary conditions of contact in compression and elasticbehaviour in tension and shear. The wall models were then recal-ibrated so that only the elastic links and no gap elements wereused, and the target displacements for the non-linear and linearcases were the same under the same horizontal load. With the lat-ter model, a modal response spectrum analysis was carried out. Itmust be noted that the analysis was simplified as neither the in-fluence of vertical load on the rotational stiffness of walls nor thefriction in shear were considered. Both of these simplifications re-sult in a lower stiffness, longer vibration periods and, therefore, inpotentially lower design seismic actions.

It should also be noted that the elastic stiffness of thebracket evaluated according to the Yasumura and Kawai procedureshould not be reduced when performing a modal responsespectrum analysis. Experimental tests have shown [18] that theaccumulating damage during cyclic loading does not reduce theconnection stiffness in crosslam wall setups, even if it does reducethe peak load. This behaviour can be clearly observed in Fig. 2— theload curves of the first and the third load cycle are almost identicalfor both 40 and 60 mm long nails in the initial part of the diagramwhere the stiffness is defined, although the peak load differs by15%–20%.

Furthermore, even the secant stiffness of the connectioncalculated as the ratio between the peak strength and thecorresponding displacement does not markedly reduce during thecyclic test. Experimental results on full-scale buildings [11] haveshown that after a seismic event only a limited amount of damageoccurred, meaning that the main vibration period of the buildingcould not have changed significantly. Since in most cases of multi-storey buildings longer vibration periods result in lower seismicforces, it is proposed to conservatively refer to the initial stiffnessof the connection. Even though this assumption may lead to non-conservative estimation of the displacements, this is less criticalthan a reduced force estimation.

4.3. Modal response spectrum analysis

The following data was used for the modal response spectrumanalysis of the building according to Eurocode 8: type 1 elastic

Table 3Mass and mass radius of gyration for each floor.

Mass (kg) Mass gyration radius (kg m2)

4th storey 19405 1851563rd storey 31489 3004612nd storey 31489 3004611st storey 31489 300461

response spectra and a rock foundation (type A soil according toEN 1998-1, corresponding to S = 1.0, TB = 0.15 s, TC = 0.40 s,TD = 2.00 s), behaviour factor q = 2.0 and lower bound factorfor the design spectrum β = 0.20. Ground acceleration wasassumed to be 0.25g , with a building importance factor γI =

1.0. The permanent load of the floor and roof was 3.5 kN/m2

and 2.0 kN/m2, respectively. The permanent load for floors wouldsuite a situation with medium thickness crosslam plates and afloating concrete floor atop, and includes allowance for partitions.The imposed load on the floor and roof was 2.5 kN/m2 and2.0 kN/m2, respectively, the former being themean value betweenthe imposed load for residential and office building, and the lattercorresponding to the snow load on amoderately high altitude or toimposed load for residential buildings. The self-weight of the outerwalls was 1.2 kN/m2. The building was assumed to be category ofuse ‘‘A’’ (areas for domestic and residential activities) according toEN 1991-1-1 [27], so the value ofψ2i for quasi-permanent loadwas0.3 and the factor φ was 0.5 for all floors except for the roof whereit was 1.0 assuming the roof is accessible. The mass was modelledas lumped in the centroids of the floors.Mass and radius of gyrationof floor mass in plan are summarized in Table 3.

4.4. Results of the linear analysis

Fig. 9 compares vibration periods, base shears and top floorlateral displacements of the building for the three different typesof models. The stiffness of the building is very high for model ‘i’,where all connections are assumed as rigid. This results in higherbase shears and is conservative. However if the building was lowerand hence even stiffer, the same hypothesis of rigid connectionscould yield to non-conservative results due to vibration periodsbeing in the range of increasing spectrum outside the plateauregion. On the other hand, the top displacements are only 20%of those obtained using models ‘ii’ and ‘iii’ where the connectorsare schematized as flexible. Although this significant differencedoes not compromise the general stability of the buildings (unlesssecond order effects have a remarkable impact), it can leadto underrated damage estimation. From Fig. 9 it can also beobserved that the difference between considering and ignoringvertical connections betweenperpendicularwalls at the same level(models ‘iii’ and ‘ii’, respectively) is less than 4% when long wall

3050 M. Fragiacomo et al. / Engineering Structures 33 (2011) 3043–3053

Fig. 10. Calibration of the non-linear FEM link on the backbone curve of the 3rd cycle of the experimental results for BMF105 brackets with ten 4mm diameter, 60 mm longnails subjected to axial (left) and shear force (right).

segments are used as in the case under study. This result may bedifferent when shorter wall panels are used as in the buildingsdeveloped in the SOFIE research project [11–13]. It should benoted, however, that the vibration period values for models ‘ii’and ‘iii’ are unexpectedly high — on the basis of a qualitativecomparison with the first vibration period of the 3-storey SOFIEbuilding, one would expect values of up to 0.4 s. It is believedthat the main reason for such a difference is that the influence offriction at the panel–panel and panel–foundation was neglected inthe numerical modelling. Friction affects the stiffness and strengthbut not ductility, however it is difficult to take it into account andfurther investigations will be necessary.

5. Case study: non-linear static analysis of a multi-storeycrosslam building

5.1. Numerical modelling

For a non-linear static analysis of the case study building, a 3Dshell model with non-linear springs was used in SAP2000 [25].Shear, tension and compression properties were assigned to eachlink element and their mechanical properties were calibrated onthe experimental curves of BMF105 brackets with ten 4 mmdiameter, 40 or 60 mm long nails (see Fig. 2). The backbone curvesof the 3rd cycle test were used so as to account for the effectsof cumulative damage of a seismic (cyclic) load. The curves werecalibrated on the specimens with the lowest capacity (see Fig. 10).The comparison in terms of push-over curves (base shear vs. topfloor horizontal displacement) using different nail lengths (40 mmand 60 mm, corresponding to brittle and ductile behaviour of themetal bracket, see Fig. 2) is presented in Fig. 11 for the case studybuilding. In this figure, the assumption of lateral forces appliedfrom right (wall ‘B’) to left (wall ‘D’) distributed along the buildingheight according to the first mode shape was made. In the 3D FEmodel, onlywalls ‘A’ and ‘C’ were considered, whereaswalls ‘B’ and‘D’ were neglected as were torsion effects (i.e. degrees of freedomwere limited to plane deformation). Furthermore, to investigatethe effect of the bracket ductility on the whole building ductility,also a bracketwith the same stiffness and peak strength as the BMFwith 60 mm long nails, but with twice the ductility was analysed.

5.2. The N2 method and its limitations

The N2 method [4] was used to carry out the NSA and identifythe performance point of the building. The aim of the methodis the evaluation of the seismic displacement, which is linked tothe damage control of the structure and needs to be kept belowsome reference values. The N2 method considers a performancepoint defined in terms of both strength and displacement, where

Fig. 11. Comparison among different push-over curves for the case studybuilding usingmetal bracket connectionswith different ductility, and elasto-plasticapproximation according to Yasumura and Kawai procedure [19].

the structural capacity is compared with the demand in termsof seismic ground motion. The base shear force and the topdisplacement of a Multi-Degree-of-Freedom (MDOF) system arefirst computed by means of a non-linear Push-Over Analysis (POA)and then converted respectively to the spectral acceleration anddisplacement of an equivalent Single-Degree-Of-Freedom (SDOF)system. The demand of the seismic ground motion is representedthrough the response spectrum in terms of pseudo-accelerationand displacement. Such an inelastic spectrum depends uponthe cyclic behaviour of the SDOF system and the characteristicsof the ground motion (peak ground acceleration and shape),and can be obtained from the elastic spectrum using suitablereduction factors. Such a method was found to provide the bestapproximation among various NSA methods for SDOF systemswith different hysteretic models and for MDOF systems [28]. Themethod as it is currently presented in Eurocode 8, however, ismostly suitable for reinforced concrete and steel structures, due tosome limitations on specific hysteretic behaviour incorporated inthe formulae for the reduction factor (R), which is needed to derivethe inelastic from the elastic spectrum. Current formulae do notinclude the case of systemswith a pinching hysteretic behaviour orlarger stiffness degradation, which are typical for crosslam panels(see Fig. 12). The so-called ‘‘flag’’ shape hysteresis loops is due torocking of the crosslam panels, friction with the foundation, andthe influence of the vertical load in combination with the hold-down capacity which increases the elastic stiffness of the wall.If there is no vertical load, the intermediate linear part of thehysteresis loop disappears and a loop with only pinching is left. Anextensive parametric study on SDOF systems with this hystereticbehaviour is needed to derive new formulae for the reduction

M. Fragiacomo et al. / Engineering Structures 33 (2011) 3043–3053 3051

Fig. 12. Typical crosslam wall hysteresis loops under cyclic lateral loading when15 kN/m of vertical load is applied.

Fig. 13. Inelastic spectrum and capacity curves of the SDOF system equivalentto the multi-storey crosslam building for three different types of metal bracketconnectors. The square points denote the maximum allowable displacements andthe circles the target displacements. Vibration periods of the SDOF systems are alsomarked.

factor Rwhich could be then incorporated into the N2method. Theanalysis is rather complex due to the influence of the vertical loadwhich should be considered in the formulae.

Therefore it must be noted that the results derived in thisstudy could be non-conservative, because hysteresis loops with

pinching dissipate less energy than bilinear plastic loops withthe same ductility. However, it should be also pointed out thatfor all analysed bracket setups, the SDOF systems equivalent tothe multi-storey building have vibration periods longer than Tcwhich is usually the value from where the reduction factor (R)and ductility factor (µ) are considered to be the same, regardlessthe type of hysteresis loop. The results of these analyses shouldtherefore be considered as a preliminary study aimed to investigatethe effect of different input strengths and ductility characteristicsof the brackets on the strength and ductility of the building asa whole. The limit displacement in the Near Collapse (NC) limitstate is defined by the attainment of 80% of the peak force onthe descending base shear-top floor displacement curve when thefailure mechanism is ductile. The ultimate force is derived froman elasto-plastic equivalent curve derived in accordance with theYasumura and Kawai procedure [19] (see Fig. 11). Such a curveis then used to derive the capacity curve of the SDOF systemequivalent to the case study building (see Fig. 13) and used in theN2method to derive the performance point as an intersectionwiththe inelastic spectrum (demand curve). In the case with 40 mmnails, due to the brittle failure, there is no decline in force, and thetarget displacement is set as the displacement at the failure point. Itshould be pointed out that the original procedure of theN2methodfor the determination of the equivalent elasto-plastic diagramleads to too low vibration period values, too high ductility factorsand, hence, too high allowable ground accelerationswhen theNearCollapse point is identified by 80% of the peak strength and bythe corresponding displacement (see Fig. 14(left)). Similarly, alsothe use of the peak strength and the corresponding displacementlead to unrealistic results characterized by too low ductility ratios(Fig. 14(right)). Therefore it is recommended that the Yasumuraand Kawai procedure as suggested in this paper is used to evaluatethe equivalent elasto-plastic diagram.

5.3. Results of the non-linear analysis

The results of the N2 method are displayed in Fig. 13 andsummarized in Table 4 for the different types of metal bracketconnections in terms of ductility ratios, seismic demand, seismiccapacity and peak ground acceleration (for type A ground) ofthe whole case study building. The significant role played by theductility of the connection can be clearly recognized: using aductile (µ = 8) metal bracket connection with 60 mm long nails,it is possible to raise the building ductility from 1.7 to 2.5, increase

Fig. 14. Comparison amongdifferent push-over curves for the building response and elasto-plastic approximations according to theN2methodwithmaximumdisplacementat 0.8 Fmax (left) and at F max (right).

3052 M. Fragiacomo et al. / Engineering Structures 33 (2011) 3043–3053

Table 4Ductility ratios (calculated as the ratios between maximum and elastic displacements), seismic demand and capacity of the case study building in terms of maximumacceleration depending upon the metal bracket connection ductility.

Bracket upliftductility

Bracket shearductility

Buildingductility

Targetdisplacement (mm)

Maximumdisplacement (mm)

Max. ground acceleration (g)

double bracket ductility 16 13 3.67 54 101 0.64BMF 105 bracket with 10

8 6.5 2.46 56 67 0.4160 mm long, 4 mmdiameter nailsBMF 105 bracket with 10

0 6.4 1.69 66 42 0.2240 mm long, 4 mmdiameter nails

the max peak ground acceleration the building can resist from0.22g to 0.41g , and the maximum failure displacement from 42to 67 mm.

In performance-based design, different limit states are defined,such as ‘damage limitation’ (DL), ‘significant damage’ (SD), ‘nearcollapse’ (NC) and ‘total collapse’ (TC). For timber construction,the performance indicator usually assumed is either the inter-storey drift, or the top floor horizontal displacement. Differentvalues are suggested by design codes, however an inter-storeydrift of about 3% of the wall height is commonly set as a limit.In this paper the proposal is to define the NC limit state at theattainment of 80% of the peak strength on the descending part ofthe push-over curve, as recommended in the Yasumura and Kawaiprocedure. Amore exact procedure would be to define a limit statefor each wall and consider the NC limit state of the whole buildingto be attained when the first wall reaches its NC state. The SDstate could be defined at 75% of the ultimate displacement du atNC state as suggested for other structural types (e.g. reinforcedconcrete structures or masonry walls); however this limit state isquestionable as crosslam buildings exhibit small residual damageat the end of a seismic event [11–13]. The DL state could be set atthe elastic inter-storey (or wall) displacement in accordance withthe Yasumura and Kawai procedure or, in a less conservative way,at the displacementwhere the ultimate force (Fu) is reached for thefirst time (in the elasto-plastic approximation this is the yieldingpoint).

6. Summary and conclusions

This paper deals with the seismic analysis of multi-storeycrosslam buildings. Such systems are made from massive timberpanels connected to each other and to the foundations using metalbrackets and nails (or screws), and self-tapping screws. Duringan earthquake, energy is dissipated in all the connections as wellas in friction between timber panels, although it is suggestedthat the beneficial contribution of the latter is conservativelyneglected until further investigations are performed. Capacitydesign principles are provided in the paper, where the ductilefailure mechanism is characterized by plasticization of metalbracket connections throughout the height of the building, andbrittle failures of the crosslam panels are avoided by designing thecorresponding members for the overstrength of the connections.Floor panels and their connections between adjacent panelsare also designed for the overstrength of the connections. Theoverstrength factors for BMF105 steel brackets, for which there iscurrently no information provided in the Eurocode 8, were derivedbased on some experimental results and a value of 1.3 is proposedfor shear and uplift based on some preliminary tests. Simple detailrules on the nail lengthwhich should not be shorter than 60mm toavoid brittle failure of connectionswere provided. An overstrengthratio of 1.6 was derived for self-tapping screws holding togetheradjacent perpendicular walls, although the contribution of suchconnections to the building stiffness was proved to be minimal ina 3D elastic modal response spectrum analysis of a multi-storey

building when long wall segments are used. The same analysisalso revealed the importance of modelling the flexibility of theconnections between the upper and lower panels, which is oftenneglected by designers and would lead to underestimation of thebuilding vibration periods.

The paper also discusses the possibility of using a non-linearpush-over analysis for seismic design as implemented in the N2procedure recommended by the Eurocode 8. The N2 method witha modified bilinearisation procedure was used for the calculationof the maximum ground acceleration a building can withstand.The influence of the connection ductility on the global buildingductility and seismic performance was analysed. The use of ductilehold-downs with 60mm long nails was found to raise the buildingductility from of 1.7 to 2.5 and the maximum peak groundacceleration the building can resist from 0.2g to 0.4g comparedto the case when a brittle hold-down is used, demonstrating theimportance of using ductile connectors.

However, due to limited experimental data available, furtherinvestigations are needed to confirm the conclusions on some ofthe issues highlighted in this paper. Cyclic tests of metal bracketand hold-down connectors should be carried out on at least 7–10specimens per configuration to derive more accurate values ofthe overstrength factors. Also non-linear time-history analyses (inaddition to less time consuming non-linear static analyses) shouldbe carried out on crosslam buildings where the actual hystereticbehaviour of the connections is modelled in a rigorous way toinvestigate the influence of the connection ductility on the globalbuilding ductility and seismic resistance.

Acknowledgements

The facilitating network provided by the COST Action E55 ‘Mod-elling of the performance of timber structures’ (http://www.cost-e55.ethz.ch/) is gratefully acknowledged. The research supportprovided to the second and third authors by the EU through the Eu-ropean Social Fund ‘Investing in your future’ is also acknowledged.

References

[1] Chopra AK. Dynamics of structures—theory and applications to earthquakeengineering. Upper Saddle River: NJ: Prentice Hall; 1995.

[2] European Committee for Standardization (CEN). Eurocode 8—design ofstructures for earthquake resistance, part 1: General rules, seismic actions andrules for buildings. 2004.

[3] Priestley MJN. Performance based seismic design. 12th European Conferenceon Earthquake Engineering. CD. 2000.

[4] Fajfar P. A nonlinear analysis method for performance-based seismic design.Earthq Spectra 2000;16:573–92.

[5] Italian Ministry for the Infrastructures. New technical regulation for construc-tion. Decree of the Ministry for the Infrastructures, Ministry of Interior, andDepartment of the Civil Defence. 2008.

[6] Pauley T, Priestley MJN. Seismic design of reinforced concrete and masonrybuildings. Wiley Ed.; 1992.

[7] Beattie G. Multistorey timber buildings manual, Carter Holt Harvey (Ed.),Origin, James Hardie and GIB, 2001.

M. Fragiacomo et al. / Engineering Structures 33 (2011) 3043–3053 3053

[8] Mander JB, Cheng CT. Seismic resistance of bridge piers based on damageavoidance design. Report NCEER-97-0014. 1997.

[9] Smith T, Fragiacomo M, Pampanin S, Buchanan A. Construction time and costestimates for post-tensionedmulti-storey timber buildings. Proc Inst Civil EngConstruction Mater 2009;162:141–9. Timber Structures (special issue).

[10] Buchanan A, Deam B, Fragiacomo M, Pampanin S, Palermo A. Multi-storeyprestressed timber buildings in New Zealand. IABSE Struct Eng Internat 2008;18:166–73. Tall Timber Buildings (special ed.).

[11] Ceccotti A. New technologies for construction of medium-rise buildings inseismic regions: the XLAM case. IABSE Struct Eng Internat 2008;18:156–65.Tall Timber Buildings (special ed.).

[12] Dujic B, Strus K, Zarnic R, Ceccotti A. Prediction of dynamic response af a7-storey massive XLam wooden building tested on a shaking table. WorldConference on Timber Engineering WCTE 2010. Riva del Garda, Italy, June20–24, 2010, CD.

[13] Ceccotti A, Follesa M, Lauriola MP, Sandhaas C, Minowa C, Kawai N. et al.Which seismic behaviour factor for multi-storey buildings made of cross-laminated wooden panels? Meeting 39 of the Working Commission W18-Timber Structures, CIB. Florence, Italy, 2006, paper CIB-W18/39-15-4.

[14] YatesM, LinegarM, Dujic B. Design of an 8 storey residential tower fromKLH—Cross laminated solid timber panels.World Conference on Timber EngineeringWCTE 2008. Miyazaki, Japan, June 2–5, 2008.

[15] European committee for standardization (CEN). Eurocode 5 – design of timberstructures – part 1-1: general rules and rules for buildings. 2004.

[16] Jorissen A, Fragiacomo M. General notes on ductility in timber structures. EngStruct, (submitted for publication). This special issue.

[17] New Zealand StandardTM . Timber structures standard, NZS3603:1993. Pub-lished by Standards New Zealand, Private Bag 2439, Wellington 6020, NewZealand.

[18] Dujic B, Zarnic R. Report on evaluation of racking strength of KLH system.University of Ljubljana, Faculty of civil and geodetical engineering, Slovenia,2005.

[19] Yasumura M, Kawai N. Evaluation of wood framed shear walls subjected tolateral load. Meeting 30 of the Working Commission W18-Timber Structures,CIB. Vancouver, Canada, 1997, paper CIB-W18/30-15-4.

[20] Blass HJ, Uibel T. Tragfähigkeit von stiftförmingen Verbindungsmitteln inBrettsperrholz. Lehrstuhl für Ingenieurholzbau und Baukonstruktionen 2007,Universitätsverlag Karlsruhe.

[21] Sandhaas C, Boukes J, Kuilen JWG, Ceccotti A. Analysis of X-lam panel-to-panel connections under monotonic and cyclic loading. Meeting 42 of theWorking Commission W18-Timber Structures, CIB. Dübendorf, Switzerland,2009, paper CIB-W18/42-12-2.

[22] Dujic B, Klobcar S, Zarnic R. Influence of openings on shear capacity of woodenwalls. Research report, 2005, University of Ljubljana and CBD ContemporaryBuilding Design Ltd., Slovenia.

[23] YasumuraM. Racking resistance ofwooden framewallswith various openings.Joint meeting 39 of the Working Commission W18-Timber Structures, CIB –IUFRO-S5.02. Florence, Italy. 1986.

[24] Blass HJ, Fellmoser P. Design of solid wood panels with cross layers. 8thWorldConference on Timber Engineering WCTE 2004. Lahti, Finland, June 14–17,2004, p. 543–8.

[25] Computers & structures inc. SAP2000—integrated finite element analysis anddesign of structures. Computers & structures inc.: Berkeley, CA, 2000.

[26] European Committee for Standardization (CEN). EN 12512 – Timber structures– Test methods – Cyclic testing of joints made with mechanical fasteners.Brussels, Belgium, 2001.

[27] European Committee for Standardization (CEN). Eurocode 1: actions onstructures – part 1-1: general actions – densities, self-weight, imposed loadsfor buildings. 2002.

[28] FragiacomoM, Amadio C, Rajgelj S. Evaluation of the structural response underseismic actions using non-linear static methods. Earthq Eng Struct Dyn 2006;35(12):1511–31.

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