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Method for Modelling Dynamic Response of Timber Frame Building

Bruno DUJICPh.D., Civ. Eng.Teaching AssistantUniversity of LjubljanaFaculty of Civil andGeodetic EngineeringLjubljana, Slovenia

bdujic@fgg.uni-lj.si

Roko ZARNICPh.D., Civ. Eng.Associate ProfessorUniversity of LjubljanaFaculty of Civil andGeodetic Engineering

Ljubljana, Sloveniarzarnic@fgg.uni-lj.si

Born 1971, Ph.D. from 2001,Teaching Assistant for BuildingMaterials and Experimental

Analysis of Structures,analytical and experimentalresearch in materials andseismic resistance of timber andcomposite structures.

Born 1950, Ph.D. from 1992,Professor of Building Materialsand Experimental Analysis ofStructures. Chair of Research inMaterials and Structures.Experimentally based modellingof structures, expertise in repair

and strengthening of structuresin earthquake prone areas.

Summary

The versatility of the construction systems for prefabricated houses with timber frame constructionand the interaction of components are important sources of difficulties for analytical determinationof their response to seismic excitation. The solving of the problem of reliable prediction ofstructural behaviour response to earthquake excitation can be approached by the experimentally

based development of inelastic computational model. The inelastic spring element for DRAIN-2DXwas developed at the University of Ljubljana and named as ULS element (Universal Longitudinal

Spring). Inelastic behaviour is determined by universal hysteretic rules. ULS element is capable tosimulate the behaviour of all kinds of connectors or supports, which responses are in inelasticrange. The paper describes the approach to modelling wood frame structure with DRAIN-2DX andCANNY-E programs where ULS was applied.

1. Introduction

In light-frame buildings, shear walls are typically composed of wood framing and panel sheathingattached with dowel-type fasteners, usually nails. The dowel-type mechanical connections are

performing in an inelastic manner. Consequently, the behaviour of timber frame wall panels tovarying loads is inelastic too. Deformability of shear wall reflects in elastic deformation ofsheathing material and framing members and inelastic deformation of fasteners. For modelling thedisplacement response of shear wall it is very important to develop an accurate model for the

orthotropic inelastic behaviour of fasteners in wood materials. Therefore, the three linear pinchinghysteretic model with stiffness degradation and strength deterioration for the nail connection wasmodelled. The reliability of a computational model can be assessed by its comparison toexperimental response by means of several parameters evaluated from hysteretic response.

2. Numerical model

There are a number of calculation models based on the Finite Element Method available. However,the analysis of more significant constructions by means of microelements is still time consuming. Inaddition, the simulation of the inelastic behaviour of the fasteners is in most cases not accurateenough. Therefore, the use of macroelements is more efficient when larger wood frame structuresare analysed. On the macroelement level the loaded wall with its characteristics is treated as asingle physical element. The specific behaviour characteristics of load-bearing woodframe wall isguided by the behaviour of mechanical fasteners. Therefore, the most suitable approach was todevelop a two-step model for the calculation of the entire wood structure response. Within the first

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step (cyclic analysis) each single woodframe wall is numerically analysed on the basis of the knowninelastic behaviour of fasteners. The result of analysis is a hysteretic response of the wall. Thisresponse is a source for the derivation of mechanical characteristics of inelastic spring thatsimulates the behaviour of a physical body woodframe wall. In the second step of the analysis(dynamic analysis) the entire building structure is simulated with inelastic springs replacing load-

bearing walls.

The availability of presumably appropriate software and other computational tools influenced thedevelopment of the modelling strategy. Procedure (Fig. 1) is based on two different software

packages, i.e. DRAIN-2DX [1] and CANNY-E [2]. The results of two-dimensional analysesperformed by DRAIN-2DX are used for the composition of three-dimensional structural modelsuitable for the prediction of response of analysed wood framed building. Three-dimensionalanalysis is performed by CANNY-E program.

ULS element

Exact modeltransformation

Equivalent strut

model

3D equivalent

strut modelStandard simplelinear elastic panel

glulam beams

nails and to grains

Standard beam-column elementwith plastic-hinge

wood framing segments

sheathing plate

anchors

Fig. 1 Two-step mathematical model for the dynamic analysis of timber frame structures.

The realistic prediction of structural response on earthquake excitation can be achieved by the

experimentally based development of inelastic computational model. The element, used for thesimulation of inelastic behaviour of nailed connection called ULS (Universal Longitudinal Spring)has been developed in our research team. This element is suitable both for mathematical modellingof inelastic behaviour of structural struts and structural connectors. The inelastic spring model, usedas basic element in our mathematical model, had been originally developed for the modelling ofmasonry infill of reinforced concrete frame [3] and later modified for the simulation of inelasticresponse of nailed sheathing to framing connections [4]. It applies the significantly modifiedhysteretic rules proposed by the authors of IDARC program [5] and own skeleton curve withductility and descending sections [6]. ULS was installed in DRAIN-2DX program because of itsalgorithm that applies event-to-event solution strategy. The inelastic spring element itself is alongitudinal spring with appropriate length down to infinitely short dimension. Non-elastic

behaviour is determined by universal hysteretic rules (Fig. 2). Properties of inelastic springs are

determined by actual state of behaviour and load history of the spring. The trilinear skeleton curvegoverns the inelastic spring responses, while the shapes of hysteretic loops are governed by threeadditional parameters. The trilinear envelope is defined as non-symmetric by three points separately

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in tension and in compression. The additional characteristic of the envelope is its strengthdeterioration after the deformation defined by rupture point. The independent parameters, relevantfor our case, define the degrading reversal stiffness of spring, the deterioration of stiffness due todamage propagation and pinching effect because of the slipping of connectors. The descendingstiffness of hysteretic curves is controlled by parameter . The parameter influences the dissipationof energy. Stiffness degradation in inelastic range can be correlated with the development of

damages according to Park-Angs model and is controlled by parameter . Therefore, the springstiffness depends on the quantity of the dissipated energy. Parameter enables the simulation ofslipping of mechanical ties. The slope of the descending part of the envelope determines thestrength degradation of inelastic element after overrunning of the rupture point.

descending stiffnessstiffness degradationslipping or pinching effect

Pc+

Py+

Py-

Pc-

Ko+

Ko-

+-

Ku+

Ku-

+

-

+

- -

-

+

uy+

+

uy-

displacement

hardening ductility

force

Fig. 2 ULS model with trilinear part and descending curves controlled separately in the

compression and the tension zone.

The mathematical model of building load-bearing walls represents the assemblage made ofsheathing plates connected to wooden frame by the same number and distribution of nails as in the

prototype structural element. The fenestration of walls can be taken into account with realdistribution and dimensions of openings including the sheathing beneath and above them. Thecontribution of intermediate studs was assumed to have less negligible influence on lateralresistance in comparison to its influence on boundary studs. Therefore, the mathematical modelincludes only boundary nailing. In the mathematical model each nail is represented by twolongitudinal inelastic spring elements. The first spring element simulates the behaviour of the nail

parallel to the grain of wood connection, while the second one represents the behaviour of the nailperpendicular to the grain of wood connection. The framing members of the shear walls weremodelled with linear elastic beam elements with plastic-hinges at both edges. Sheathing panelswere modelled by linear elastic panel elements. The studs at the edges of sheathing segments wereanchored with tie-downs or anchors, depending on the position of the stud, and modelled withinelastic spring elements. The deformability of supports is roughly estimated with respect to themechanical properties of wood and the behaviour of nails parallel to grain or using data obtainedwith experimental testing of anchors. The mathematical model that encompasses large openings isvery sensitive to the deformability properties of supports. Therefore, mechanical properties ofanchorage system are need for accurate analysis of building response. The second step is thedynamic analysis of the 3D model performed with the CANNY-E program. The wood framedstructure can be modelled as multi story frame-floor system with equivalent strut bracing and stiffdiaphragms representing slab and roof construction.

As mentioned above, the result of the first step of the analysis is a hysteretic response of the entirewall. This response is a source for the derivation of mechanical characteristics of inelastic spring,which simulates the behaviour of building walls. For all load bearing walls the equivalent strutmodels are used to simulate inelastic behaviour by axial deformation (Fig. 5). The response of the

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load bearing wall is defined by three parameters (story drift, force and stiffness) that aretransformed in two diagonal directions of equivalent bracing springs (Eq. 1).

cos2,1

uud ;cos22,1

F

Fd ;

2cos22,1

2,1

2,1

K

u

FK

d

d

d (1)

uF

ud

F

Fd

Fd

Figure 5. The scheme for the transformation of the calculated force displacement response ofwalls by DRAIN-2DX into equivalent strut elements in 3D model for dynamic analysis by CANNY.

3. Conclusion

Efficiency of the here-described modelling approach was demonstrated within the CUREE-CaltechWoodframe Project. The shake table tests on a full scale two-story wood framed residential buildingwere carried out in Charles Lee Powell laboratory in La Jolla, California. The authors of this paper

joined the project with blind prediction of response of the tested structure [7]. The input dataprovided for the blind prediction by the project coordinator were geometry of tested structure,material properties of wood frame elements and sheathing plates, monotonous response ofsheathing to framing mechanical connections in two perpendicular directions, cyclic response ofsheathing to framing mechanical connection in the direction parallel to the grains of framing

member and acceleration time histories applied to the tested building. Good correlation between thenumerical prediction and the test results demonstrated high efficiency of the mathematical model,although only very basic data were available [4].

4. References

[1] Prakash, V., Powell, G.H., DRAIN-2DX, DRAIN-3DX and DRAIN BUILDING: BaseProgram Design Documentation,Report no. UCB/SEMM-93/17, Berkeley, University ofCalifornia, 1993.

[2] Li K.N., Three-dimensional Nonlinear Dynamic Structural Analysis Computer ProgramPackage CANNY-E, CANNY Consultant Pte Ltd, Singapore, 1996.

[3] Zarnic, R., Inelastic model of reinforced concrete frame with masonry infill analyticalapproach, Int. Journal of Engineering Modelling, 7, 1-2, Split, Croatia, 1994, pp 47-54.

[4] Dujic B., Zarnic R., Blind prediction of seismic response of timber-frame house, Skopjeearthquake: 40 years of European Earthquake Eng.: SE 40EEE. Skopje, Macedonia 2003.

[5] Park, Y.J., Reinhorn, A.M., Kunnath, S.K., IDARC: Inelastic Damage Analysis ofReinforced Concrete Frame - Shear-Wall Structures, Technical Report NCEER-87-0008,

National Center for Earthquake Engineering Research, Buffalo, 1987.

[6] Zarnic, R., Gostic, S., Masonry Infilled Frames as an Effective Structural Sub-Assemblage,Proceedings of the International Workshop on Seismic Design Methodologies for the NextGeneration of Codes, Fajfar and Krawinkler (edit), Bled, Slovenia, 1997.

[7] Dujic, B., Zarnic, R., Numerical Model & Predictions Team Slovenia, CUREE-CaltechWoodframe Project,Proceedings of the International Benchmark Workshop, p. 15, Universityof California, San Diego, La Jolla, California, 2001.