Assessment and comparison of experimental and numerical model studies of cross-laminated timber mechanical connections under cyclic loading

Construction and Building Materials 77 (2015) 197–212

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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat

Assessment and comparison of experimental and numerical model studies of cross-laminated timber mechanical connections under cyclic loading J. Schneider a,⇑, Y. Shen b, S.F. Stiemer c,1, S. Tesfamariam a,2 a b c

School of Engineering, The University of British Columbia, Okanagan Campus, 3333 University Way, Kelowna, BC V1V 1V7, Canada China Electronics engineering Design institute, Beijing 100142, People’s Republic of China Dept. of Civil Engineering, The University of British Columbia, Vancouver Campus, 6250 Applied Science Lane, Vancouver, BC V6T 1Z4, Canada

h i g h l i g h t s  Cross-laminated timber connections were tested and modeled with finite element model.  Test and model results were analyzed with two assessment methods to evaluate the model.  The equivalent energy elastic–plastic model showed good correlation of test and model.  The cumulative energy method is more precise to evaluate hysteretic models.

a r t i c l e

i n f o

Article history: Received 17 June 2014 Received in revised form 2 December 2014 Accepted 17 December 2014

Keywords: Cross-laminated timber Connections SAWS model Seismic performance Damage index Damage prediction Damage assessment

a b s t r a c t Earthquake engineering is a major consideration for structures along the west coast of North America. The current building code of Canada is based on design criteria, which are defined by stresses and member forces calculated from prescribed levels of applied lateral shear force. Traditional wood-frame buildings are known to perform well in earthquakes. However, with the development of new engineered wood products, such as CLT (cross-laminated timber) and more consideration to build higher than the existing six stories limit in wood-frame structures, highlights the need to use innovative hybrid techniques for buildings. Hybrid buildings with steel frame structures incorporated with CLT infill walls offer one possible solution to residential and commercial multi-level buildings to overcome the height limitation. In order to make such a structure applicable for an earthquake prone area, it is important to understand the structural performance of the connection between steel and CLT elements. In this research, six connection combinations have been tested and modeled in a finite element program. The load–displacement test results are assessed with two evaluation methods. The first method follows the American Society of Testing Method, where ductility ratio, elastic shear stiffness, and the EEEP-curve (equivalent energy elastic–plastic curve) are generated and assessed. The second method follows an energy-based accumulation principle, where the test results are used to calculate a damage index at each time step. Both methods are used to compare test and model results and assess the accuracy of the model as well as addressing the capability of each assessment method. Depending on the purpose of the model one or the other assessment method might be suitable. For an analysis of the overall ductility or elastic shear stiffness, applying the method provided by ASTM will give relatively accurate results to assess a hysteretic load–displacement model such as the SAWS model in this research. The assessment with a damage accumulation method is a great tool to capture more details of the hysteretic load–displacement curve. Energy dissipation is valuable indicator besides ductility and elastic shear stiffness to evaluate the model. Ó 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. E-mail addresses: [email protected] (J. Schneider), shenyinlan@hotmail. com (Y. Shen), [email protected] (S.F. Stiemer), [email protected] (S. Tesfamariam). 1 Tel.: +1 (604) 600 1924. 2 Tel.: +1 (250) 807 8185. http://dx.doi.org/10.1016/j.conbuildmat.2014.12.029 0950-0618/Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction Earthquakes resistant engineering is a major consideration for structures along the west coast of North America. Especially higher buildings need to be properly designed, in order to provide serviceability or life safety in a seismic event. Generally, wood-frame

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buildings are known to perform well in earthquakes [24]; however, there are limitations under code that prevent the use of wood framing in all desired building designs. For instance, the provincial building code of British Columbia (BC) limits multi-story wood frame buildings to a maximum height of six stories [3]. The current code is based on design criteria, which are defined by stresses and member forces calculated from prescribed levels of applied lateral shear force [15]. Innovative hybrid techniques, where steel frame structures are incorporated with cross-laminated timber (CLT) infill walls, offer one possible solution to residential and commercial multi-level buildings to overcome the six-storey height limitation [7,28]. Seismic demand and seismic capacity of a structure are important factors for the design procedure. Timber-frame structures are relatively lightweight structures that obtain their great seismic performance through ductile connections between studs and sheathing, which provide sufficient ductility to the shearwall system through a variety of load paths [24]. CLT shearwall panels, however, are relatively rigid bodies with no studs or sheathing; therefore, different methods and connections must provide ductility and energy dissipation. CLT wall-to-floor connections are designed using L-shaped steel brackets, which are nailed or screwed to the CLT wall panel on one side, and bolted to the floor on the other side of the bracket. To apply such bracket connections within a CLT-based hybrid structure (Fig. 1), comprehensive understanding of their structural performance under reversed cyclic loading is required (e.g. [9,26]). Performance-based design is a methodology, where structural design criteria have to achieve a certain level of performance [15]. Damage, displacement, or drift, which are easily measurable, can be related to such performance objectives. However, to measure and evaluate damage is more complex undertaking. Damage is influenced by accumulation of structural damage, variation of failure modes of the structural components, and number of cycles before failure occurs [30]. One possible way to assess and evaluate is the introduction of damage indices (e.g. [25]). Beyond calculating the maximum capacity prior to failure of a connection, it is also important to characterize and understand the path to failure (e.g. what is damage? How can damage be quantified? Are there intermediate damage stages before collapse? How does a

load–displacement curve of a cyclic loading protocol relate to damage progression over time?). Over the years many different damage assessment attempts have been made (Table 1). Damage indices are categorized into global and local damage indices. Global damage indices describe the overall damage state of a structure, whereas local damage indices describe the damage which occurs in an individual member or joint between adjacent members. Damage can be measured in relation to curvature, rotation, energy or displacement. For most damage principles, a damage index D is calculated. The goal of damage indices is to provide a means of quantifying numerically the damage under earthquake loadings [30]. The damage index has to be calibrated and should range between zero and one. Zero represents no damage, where one is considered collapsed or destroyed. In previous research, the damage index was computed at one point after the entire loading procedure was completed (e.g. [19]) Schneider et al. [25] investigated six connection types and developed a damage scale for Kraetzig’s energy-based damage index (Table 1). The proposed preliminary damage scale distinguished five damage limit states: None, Minor, Moderate, Severe and Collapse (Table 2). The proposed prediction scale applying Kraetzig’s damage accumulation model is necessarily limited to the connections tested; however, it provides a preliminary approach for pre-

Table 1 Categories of damage principles. Damage principle

Description

References

Non-cumulative indices Deformation-based cumulative indices Energy-based cumulative indices Combined cumulative indices

The model neglects the effect of repeating cycles that occur in earthquakes Models connect damage directly to the displacement or rotation of an element or structure Models consider the energy absorption in a system or element under cyclic loadings

[30]

Combined models consider displacement and energy absorption in one index

[22,30,21]

Fig. 1. Proposed timber-steel hybrid structure.

[29,30]

[16,18,30]

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J. Schneider et al. / Construction and Building Materials 77 (2015) 197–212 Table 2 Relationship between damage index and observed damage of connection test. Degree of damage

Damage description

Kraetzig’s damage index

None Minor Moderate

No visible damage observed Minor pull-out of fasteners (20% of fastener length); light plastic deformation of bracket; minor repairs are required Visual permanent deflections of bracket; shear failure of up to 2 fasteners; extensive pull-out of fasteners (50% of fastener length); can be fixed and reactivated as a connection More than 80% of the fasteners failed (shear and pull-out failure); severe crack in bracket; separation of bracket from CLT panel; requires replacement of bracket in different position at CLT wall to be serviceable again; severe wood crushing in outer layer of CLT Total or partial collapse of connection (90% or more fasteners failed)

D < 0.20 0.20 6 D < 0.35 0.35 6 D < 0.65

Severe

Collapse

0.65 6 D < 0.80

D > 0.80

Table 3 List of previous research on modelling wood connections. Author

Model

Comment

Polensek and Laursen [23]

Development of a tri-linear curve to describe the backbone curve of nailed plywood-to-wood connection Development of a hysteretic constitutive law based on exponential curves

Pinchinga was considered in the model

Dolan [8]

Ceccotti and Vignoli [4] Foliente [10]

Chui et al. [6]

Foschi [13]

Development of a general model based on mechanical interaction between the connector and the surrounding wood medium

He et al. [17]

Modification of the model of Foschi [13] in a three dimension timber light-frame model A general and simple hysteresis model for timber structures with ten parameters was developed

Folz and Filiatrault [11]

Chui and Yantao [5] a b

Creating a hysteresis model for moment-resisting semi-rigid wood joints A general hysteresis model containing 13 parameters for single and multiple degree of freedom wood joints based on a modified Bouc-Wen-Baber-Noori model (BWBN) Development of a detailed nonlinear finite element model for a single-shear nailed wood joint under reversed cyclic loading

Development of a mathematical model based on the previously developed single-fastener finite element model (1998)

A hysteresis loop was divided into four segments, which are defined by different exponential equations with four boundary conditions, respectively Pinching and stiffness degradationb are included The hysteretic constitutive law can generate a smooth and versatile varying hysteresis shape that accounts for nonlinearity, strength and stiffness degradation, and pinching The nail was modeled as a beam element that incorporates the effects of large deformation and hysteretic nature. The embedment behavior of wood under the action of a nail was described using Dolan’s four exponential segments (1989) To achieve pinching behaviour as gaps were formed between the beam and the medium, the connector was modeled as an elastic– plastic beam in a nonlinear medium which acted in only compression

Developed for sheathing-to-framing connector accounts for Nonlinearity, strength and stiffness degradation, and pinching subjected to general cyclic loading were considered. This model has been incorporated into a program called CASHEW. It was developed for cyclic analysis of wood-framing shear walls It is used to predict the moment-rotation response of the timber connection containing multi-fasteners under general cyclic loading

Pinching is a sudden loss of stiffness. It is caused by loosening and slipping of the connection under repeated cyclic loading along with large deformations. Progressive loss of stiffness in each loading cycle.

dicting the behaviour of bracket type connections in combination with CLT. For generic application of the connections in hybrid structures, it is necessary to develop a component model of the connection for wall and building modeling. It is desirable to find a simple way to model the main features of the connection subjected to general monotonic and cyclic loading protocols. Compared to CLT connections, traditional wood-frame construction is a relatively mature system that can provide an important reference for modeling of CLT connections with the program OpenSees and its subroutine called Seismic Analysis of Wood frame Structures (SAWS). Modeling studies have ranged from simple models based on load–deformation relationship from cyclic tests to highly sophisticated models, including detailed nonlinear elements for each fastener [20]. Table 3 summarizes the model development over the course of the last decades. Although these mechanics-based models can capture some mechanical features of the joints, the real behavior of a nail joint is rather complicated under different loading situation and it is difficult to accurately capture those in a numerical model [31]. Meanwhile, the simple model generates the same level of accuracy as the sophisticated model and greater computational effort has to be considered with increasing model complexity [11]. In the following subsection, experimental work and load– displacement curves reported by Schneider et al. [25] will be used

to model the connections in OpenSees with a CUREE-10 parameters model. The finite element model (FEM) is used to predict the load–displacement response and energy dissipation characteristic of the connections under general monotonic and cyclic loading (Shen et al. [27]). The modeled results will be compared with the experimental results by using two different performance assessment methods. In the first approach, ductility ratio, elastic shear stiffness, and the equivalent energy elastic–plastic (EEEP) curve according to ASTM 2127-11 (2011) will be calculated and compared with the ASTM code provision. In the second method, the energy-based damage indices according to Kraetzig’s damage accumulation principle will be applied and compared. The proposed damage scale [25] for Kraetzig’s damage accumulation principle will be compared with the calculated damage indices generated from the model.

2. Experimental test and analytical models 2.1. Test outline Fig. 2 gives an overview of the procedure which was used for this study. The test series considers six connections. Two brackets and five fastener types were tested with three-ply CLT wall panels (94 mm total thickness). Fig. 3 summarizes the test combinations including the test ID. The test program comprises tests parallel and perpendicular to the outer grain direction of the CLT panels. ASTM 2127-11 (2011) was used to determine the loading protocol. All tests were performed with

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Assessment of CLT Connections

Connection Tests Parallel and perpendicular to the grain directions

Experimental Results

Finite Element Modelling of the Connections

Performance assessment calculations (static and dynamic)

Performance assessment calculations (dynamic)

EEEP Curve

Energy-based Damage Index

Comparison

Comparison

Evaluation of Performance Assessment Methods for FEM model

Fig. 2. Flowchart to describe the procedure of damage accumulation assessment.

a displacement controlled monotonic and cyclic loading protocol. The monotonic program is conducted with a unidirectional and downwards loading at a rate of 6.35 mm (1/400 ) per minute. The cyclic loading steps followed CUREE (Consortium of Universities for Research in Earthquake Engineering) loading protocol. The rate of displacement was chosen at 2.54 mm/s (0.100 ) per second. Time, displacement, and force were monitored at each incremental displacement step. The loading protocol for test parallel was modified compared to the original loading cycles. A bracket in CLT structures is mounted with one side to the floor and the other side to the wall. Based on the orientation, the wall can move up but cannot move down below the floor level. To acknowledge that restriction, the protocol for tests parallel to the grain was adjusted and cycles do not go in the negative range. Schematic drawings of the test set-ups are shown in Figs. 4 and 5. 2.2. SAWS hysteretic model SAWS model is derived from the load–deformation relationship based on hysteretic shapes obtained from general monotonic and cyclic tests. The required material properties were derived from the CLT handbook [14] and the report ‘‘Standard of performance-rated cross-laminated timber’’ [1]. SAWS model in OpenSees is a CUREE-10 parameter model, which can take into account highly nonlinear, stiffness and strength degradation and pinching behavior. It can produce smooth hysteretic loops. The envelope curve is defined by an exponential function curve and a linear line, which was proposed by Foschi [12]

F ¼ sgnðxÞ

ðF 0 þ R1 S0 jxjÞ

½1  expðS0 jxj=F 0 Þ;

F ¼ sgnðxÞ  F peak þ R2 S0 ½x  sgnðxÞ  Du ; F ¼ 0;

jxj > jDF j

jxj 6 jDu j

jDu j < jxj 6 jDF j

ð1Þ ð2Þ ð3Þ

The CUREE-10 parameters model was first described by Folz and Filiatrault [11]. Ten parameters are used to control the hysteretic constitutive law, seen from Fig. 6. F0 represents intercept strength for the asymptotic line to the envelope curve (F0 > FI > 0), Du stands for the displacement at peak load (Du > 0), and DF as the failure displacement. S0 represents the initial stiffness of the hysteretic curve (S0 > 0). The stiffness ratio of the asymptotic line to the envelope curve (0 < R1 < 1.0) is given by R1. R2 describes the stiffness ratio on the descending segment of the envelope curve (R2 < 0). R3 presents the stiffness ratio of the unloading segment off the envelope curve (R3 < 1). FI indicates intercept strength for the pinching part (FI > 0), R4

the stiffness ratio of the pinching part of the hysteretic curve (R4 > 0) where the pinching behavior is simplified to assuming a parallelogram. The parameters a (a > 0) and b (b > 0) control the stiffness degradation and energy degradation, respectively. The degrading stiffness KP is based on previous loading history, as given by:

K P ¼ S0 ½ðF 0 =S0 Þ=b  xun 

a

ð4Þ

where xun is the last unloading displacement off the envelop curve. 2.3. Analytical assessment methods In this paper, two performance assessment methods are applied to compare the modeled results with the test results. The first method uses only the envelope curve of the load–displacement graph to assess the performance and neglects influences of individual cycles. The second method, a damage accumulation method is an approach, where the performance of the connection is assessed under consideration of each loading cycle over time. The methods are explained in detail in the following sections. 2.4. Ductility and equivalent energy elastic–plastic curve Ductility and elastic shear stiffness are important numbers to assess and rate connections. Since the load–displacement curve does not provide an exact elastic and plastic section, the American Society of Testing Methods 2126-11 [2] provides a method to translate the irregular load–displacement curve into an ideally linear elastic–plastic curve, where ductility ratio, yielding force (Fyield) and related displacement, ultimate force (Fult) and related displacement, as well as elastic shear stiffness can be determined and compared exactly. The linear elastic–plastic curve is an idealized assumption of the connection behavior. The ductility ratio Dratio is calculated as the ratio of the ultimate displacement at 80% load of maximum load after reaching maximum load (Dult) and the displacement at yielding (Dyield).

Dratio ¼

Dult Dyield

ð5Þ

In order to find Dyield, the yield load Fyield and the plastic portion of the equivalent energy elastic–plastic (EEEP) curve has to be determined. The plastic portion is characterized with a horizontal line equal to Fyield. The equation to determine this yield plateau is given with

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Bracket Type

Fastener Type

Test ID parallel perpendicular to grain to grain (L) (P)

+ 10 Sprial nail 3.8 x 89mm (N)

B-N-L-C1 B-N-L-C2 B-N-L-C3 B-N-L-C4 B-N-L-C5

B-N-P-C2 B-N-P-C3 B-N-P-C4 B-N-P-C5 B-N-P-C7

A-R-L-C4 A-R-L-C5 A-R-L-C6 A-R-L-C7 A-R-L-C8

A-R-P-C1 A-R-P-C2 A-R-P-C6 A-R-P-C7 A-R-P-C8

A-r-L-C1 A-r-L-C2 A-r-L-C3 A-r-L-C4 A-r-L-C5

A-r-P-C3 A-r-P-C4 A-r-P-C5 A-r-P-C6 A-r-P-C7

A-S-L-C7 A-S-L-C8 A-S-L-C9 A-S-L-C10 A-S-L-C11

A-S-P-C5 A-S-P-C6 A-S-P-C8 A-S-P-C9 A-S-P-C10

A-s-L-C4 A-s-L-C5 A-s-L-C6 A-s-L-C7 A-s-L-C8

A-s-P-C3 A-s-P-C4 A-s-P-C7 A-s-P-C8 A-s-P-C9

A-N-L-C1 A-N-L-C2 A-N-L-C3 A-N-L-C4 A-N-L-C5 A-N-L-C6 A-N-L-C7

A-N-P-C2 A-N-P-C3 A-N-P-C4 A-N-P-C5 A-N-P-C6 A-N-P-C7

Bracket B

+ 12 Ring shank nail 3.4 x 76mm (R) Bracket A

+

12 Ring shank nail 3.8 x 60mm (r)

Bracket A

+ 18 Self-drilling screw 4 x 70mm (s)

Connections in CLT panels Bracket A

+ 9 Self-drilling screw 5 x 90mm (S) Bracket A

+ 18 Spiral nail 3.8 x 89mm (N) Bracket A

Fig. 3. Overview of tested connection combinations and test identifications.

F yield ¼

Dult 

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi! 2A D2ult  Ke Ke

ð6Þ

where A representing the area under the curve from zero to ultimate displacement (Dult) and Ke being the elastic shear stiffness which is given as:

Ke ¼

0:4F max De

ð7Þ

De = corresponding displacement at 0.4 Fmax. 2.5. Energy-based damage model Gosain et al. [16] formulated a model to describe damage by using energy absorption. The energy absorption is used to describe damage as follows:

X F i di De ¼ ; F y dy i

F i =F y P 0:75

ð8Þ

where De = energy-related damage index, Fi = force in i-th cycle, di = displacement in i-th cycle, Fy = force at yielding, and dy = displacement at yielding. Gosain et al. considered only hysteretic results as long as they have not dropped below 75% of the yielding point after reaching the maximum capacity. The first half-cycle of loading at given amplitude is called primary half-cycle (PHC). The subsequent part of the cycle after peak load is called follower (FHC) (Fig. 7). Based on previous research, Kraetzig et al. [18] developed a more complex energy-based formulation which considers half-cycles (Fig. 7). The response of the first loading cycle of given loading level is called primary half-cycle (PHC). The ensuing cycle at given load level called follower half-cycle (FHC). By including of the FHC in the formulation, stiffness and strength degradation can be captured. Kraetzig’s cumulative damage formulation has to be calculated individually for the positive (D+, tension) and negative side (D, compression) sides of the hysteresis loops. The overall damage index is defined as:

D ¼ Dþ þ D  Dþ D +

ð9Þ 

+



where D = damage in positive cycle, D = damage in negative cycle, D D = interaction of D+ and D.

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J. Schneider et al. / Construction and Building Materials 77 (2015) 197–212

Fig. 4. Schematic drawing of test set-up parallel to the grain.

Fig. 5. Schematic drawing of test-set-up perpendicular to the grain. +

The positive damage index D is defined as:

P Eþp;i þ Eþi D ¼ P Eþf þ Eþi þ

P

ð10Þ

where E+p,i = energy in a PHC, E+i = energy in a FHC, and E+f = energy in a monotonic test to failure. For the negative part of the response (D), the damage index is calculated using the same formula only with the negative parameters inserted (i.e. Ep,i, Ei, Ef). The inclusion of the FHC energy in the numerator as well as in the denominator limits the influence to a lower level compared to the primary term. As such, both deformation and fatigue-type damage are taken into account.

3. Results and comparison of test and model 3.1. SAWS hysteretic model results The monotonic and cyclic experimental results of the six connections are used to check the predictive capability of SAWS

model. Similar to the approach applied by Shen et al. [27], the parameter estimations for the present model applications are shown in Tables 4 and 5. 3.2. Hysteretic response Cyclic loadings were performed for all test combinations and for direction parallel and perpendicular to the grain. Besides generating the EEEP curves, ductility, elastic shear stiffness, maximum load and related displacement were analyzed. Figs. 8 and 9 illustrate the EEEP curves separated by direction, parallel and perpendicular to the grain. The summarized values are shown in Table 6. In the cyclic test results, Bracket A combined with 18 spiral nails showed highest ductility values in both directions (parallel to the grain D = 6.2 and perpendicular to the grain D = 4.9). The elastic shear stiffness is calculated at 0.4Fmax as the ratio between force and cor-

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Fig. 6. Hysteresis model for CLT connection.

M

PHC: Ep1+

FHC: E1-

m

фm

FHC: E2+ FHC: E1+

PHC: Ep1Fig. 7. Primary (PHC) and follower (FHC) half-cycles.

responding displacement. Bracket A with spiral nails shows the biggest elastic shear stiffness parallel to the grain (Ke = 8.7 kN/ mm), where bracket B shows the lowest value at 3.9 kN/mm. The long ring shank nails present the highest elastic shear stiffness value at 7.8 kN/mm (short ring shank nails Ke = 7.2 kN/mm). The ductility variation between test and model ranges from 2.8% (e.g. A-S-L) to 30.6% (A-N-L). The average variation over all 12 combinations was calculated to 16.8%. The greatest variation can be explained by examining the hysteresis curves (Figs. 8 and 9). In some cases the level of reaching the plastic plateau (horizontal part of the curve) varies between test and model up to 12% on the positive side (tension) and 18% on the negative side (compression) of the graph. The average variation is calculated to 7%. The model

lines up with the test result accurately until maximum load. After that point the test results show often irregular drops which can be created by cracks, abrupt fastener failure or wood degradation. Those events are not captured with the model. The model follows an overall linear degradation of a slope of –R2S0. Calculating the yield point, by using the EEEP curve approach, the sudden drops can lead to a bigger variation on the ultimate displacement (Du) between test and model which has a direct influence on the ductility. The elastic shear stiffness is presented by the initial slope between the origin and the yield point. The EEEP curves of tests and SAWS model for parallel to the grain direction match very well. Only in the cases of A-r-L and A-s-L, the level of the plastic plateau varies by about 10%. The positive branches of the curves perpendicular to the grain show good agreement between test and model. On the negative side it was found that the elastic shear stiffness is considerably higher than on the positive side. The reason can be found in the loading protocol. The next higher loading step is first applied on the positive side. When it then reverses the cycle into the negative side it has to overcome the plasticized bracket and fasteners which results in a higher force at similar displacement rate. Table 6 summarizes the measured maximum forces and the corresponding displacements from the performed tests and the model. In only one out of 12 combinations the variation of maximum load between test and model is over 10% (B-N-LC3). The related displacements show a good correlation between test and model. The average variation was calculated to 5.3%. In the case of A-r-L-C, the variation amounts to 12.5%. Overall, combinations A-N-L-C2, A-R-L-C4, A-S-L-C9, A-r-L-C3, and A-r-P-C5 provide the best agreement of the EEEP curve, elastic shear stiffness and ductility ratio. Figs. 10 and 11 represent the hysteretic curves obtained from test and model. The overall shape in all connection combinations on the positive (tension) side was captured in most cases with a high precision by the model. In Fig. 11 (perpendicular to the grain), certain variations between test and model can be observed. The reason behind that can be found in the loading protocol. The first loading cycle always starts in tension. In the reversed cycles around maximum load, big plastic deformations have to be overcome. That difference can be seen in the graph. The parameters of the model are the same in tension and compression, which results in a difference as it is expressed in Fig. 6. 3.3. Performance assessment using the damage accumulation index By applying Eqs. (9) and (10) to the obtained hysteretic response from testing and modelling, the cumulative damage index was computed at each time step. The comparative results are plotted in Figs. 12 and 13, respectively. The results will be discussed in the following subsections.

Table 4 Parameter estimation of SAWS model for monotonic connections tests. Connection type

B-N

Direction F0 [kN] FI [kN] Du [mm] S0 [kN/mm] R1 R2 R3 R4

L 30.43 – 21 4.442 0.001 0.566 – – – –

a b

A-R P 36.73 – 38 1.933 0.001 0.385 – – – –

L 34.49 – 15 7.051 0.0624 0.908 – – – –

A-r P 47.94 – 24 5.103 0.01 0.841 – – – –

L 38.69 – 16 8.332 0.01 1.068 – – – –

A-s P 36.11 – 18 7.089 0.03 0.844 – – – –

L 33.9 – 21 6.479 0.1311 1.522 – – – –

A-S P 47.85 – 25 5.825 0.01 0.932 – – – –

L 28.99 – 18 6.297 0.10 1.220 – – – –

A-N P 37.81 – 23 6.028 0.07 1.137 – – – –

A, B = bracket type, L = longitudinal to the grain, P = perpendicular to the grain, more information to the used fasteners can be found in Fig. 3.

L 56.47 – 21 7.179 0.01 1.120 – – – –

P 46.46 – 37 6.646 0.0256 0.530 – – – –

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Table 5 Parameter estimation of SAWS model for cyclic connections tests. Connection type

B-N

Direction F0 [kN] FI [kN] Du [mm] S0 [kN/mm] R1 R2 R3 R4

L 24.35 3.5 17 6.683 0.010 0.08 0.95 0.01 0.5 1.02

A b

A-R P 24.95 4 32 2.811 0.010 0.24 0.95 0.01 0.5 1.05

A-r

L 21.71 3 14 11.14 0.136 0.12 1 0.07 0.5 1.02

P 27.68 4 23 6.210 0.114 0.26 1 0.01 0.6 1.05

A-s

L 33.72 3 12 10.20 0.01 0.08 1 0.006 0.5 1.20

P 25.60 4 21 8.800 0.085 0.21 0.95 0.01 0.5 1.05

A-S

L 32.16 4 16 9.824 0.135 0.08 1 0.008 0.4 1.05

P 41.47 5 26 4.362 0.117 0.25 1.8 0.015 0.6 1.05

A-N

L 23.86 3 16 6.330 0.200 0.14 1 0.015 0.5 1.02

P 23.62 4 24 4.705 0.215 0.23 0.95 0.017 0.5 1.05

L 47.70 4 20 9.100 0.030 0.13 0.95 0.005 0.45 1.03

P 47.30 3 24 5.440 0.010 0.16 0.95 0.015 0.5 1.05

60

60

40

40

20

20 Load [kN]

Load [kN]

A, B = bracket type, L = longitudinal to the grain, P = perpendicular to the grain, more information to the used fasteners can be found in Fig. 3.

0

0 -20

-20 -40

-40

EEEP Test A-R-L-C4 EEEP Model A-R-L-C04

-60

-70

-50

-30

-10

10

30

50

EEEP Test A-r-L-C3 EEEP Model A-r-L-C03

-60

70

-70

-50

60

60

40

40

20

20

0 -20

-10

10

30

50

70

0 -20

-40

-40

EEEP Test A-s-L-C4 EEEP Model A-s-L-C04

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3.4. Results for connections parallel to the grain direction Each graph in Fig. 12 illustrates three curves, one damage accumulation curve generated with test results, the other damage accumulation curve generated with modeling results, and the loading curve of the connection. The plots show that all damage accumulation curves generated with model results are above the test result curves. In the first section of the curve up to D = 0.15 both curves show very little variation. In the following continuation of the curve the variation increases. The modeling curves show an overall stron-

ger increase in the damage index D. The shape of the modeling curve shows similarity to the equivalent test curve. The major increases created by the next loading step of the CUREE loading can be found in both curves. However, since Kraetzig’s principle considers and accumulates damage from earlier stages, smaller variations add up over time of the entire loading process. Table 7 summarizes and compares the times when D = 0.8 is reached in the test and model. The last two columns of the table presents the ratio between time at D = 0.8 and total length of the loading protocol. Reasons for that increase can be found by closer investigation of the hysteretic

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response. The envelope curve up to maximum load of the model and test match very well. Past maximum load, the model follows a linear degradation. The original tests results follow only a vague linear degradation. That behavior explains the differences of the greater increase of the damage index starting at around D = 0.5 and becoming continuously greater. Another factor for the variation can be found in the subsequent cycles of the loading procedure. To generate the observed pinching of the connection, the SAWS model rises at repetitive cycles with a slope of 1/R4S0 (Fig. 6). It is a linear approximation to the smooth curve seen at the test. By comparing those areas of the hysteretic response, a greater variation was identified. This effect causes a stronger increase of the damage curve between the linear jumps, which are created by the next primary loading step. The summations of those two parts, which were identified from the hysteretic response lead to the variation of DModel to DTest. However, the model overestimates the damage D and is therefore on a conservative side at all stages. 3.5. Results for connections perpendicular to the grain direction The damage accumulation curves and the applied CUREE loading protocol (red3 line) for all six connections perpendicular to the 3 For interpretation of color in Fig. 13, the reader is referred to the web version of this article.

grain for the test and model, respectively are presented in Fig. 13, while Table 8 describes how the loading steps are generated in detail. The value to define the amplitude of the initial cycle of each loading level is a percentage of Dult. The general characteristics of the damage accumulation curves can be found as well in the test curves as in the model curves. The steep increases represent the first loading cycle of each load level which lines up with the red curve. The following section of the damage curve, which increases with a lower slope represents the sub sequential cycles of the loading protocol. There are a few factors that influence the characteristics of the damage curve. To explain the variation between the two curves, the hysteretic response has to be analyzed in detail. The energy dissipation of test and model, which is described by the area enclosed by the hysteresis curves (Fig. 11), does not correlate perfectly at individual loading steps. On the tension side (positive quarter of graphs in Fig. 11), the hysteresis loops of SAWS model show similar behavior as the loops in the plots parallel to the grain. On the compression side of the graph, SAWS model does not accurately capture the test result. Except for A-r-P-C, the envelope curve of SAWS model is shifted towards left (more deformation). The contribution of bracket deflection towards the entire deflection is not considered adequately in the model. Hence, the calculated damage index of the test result reaches D = 0.8 at an earlier stage. In addition to that, the strength degradation on the compression side does not create a

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Table 6 Summary of ductility ratio, elastic shear stiffness, maximum forces, and displacement at maximum force of the connections under cyclic loading (test and model). Test ID

Cyclic loading Ductility ratio Du/Dyield [–]a

Elastic shear stiffness Ke [kN/mm]a

Maximum force Fmax [kN]

Displacement at maximum force DFmax [mm]

Parallel to the grain B-N-L-C1 B-N-L-C2 B-N-L-C3 B-N-L-C4 B-N-L-C5 Average B-N-L SAWS-B-N-L-C03

5.8 5.8 4.7 6.0 5.7 5.6 6.5

4.8 4.8 3.3 3.5 2.9 3.9 5.0

24.5 24.5 21.7 28.7 25.1 24.9 24.2

17.7 17.7 19.4 31.2 31.3 23.5 16.8

A-R-L-C4 A-R-L-C5 A-R-L-C6 A-R-L-C7 A-R-L-C8 Average A-R-L SAWS-A-R-L-C04

5.4 5.2 6.2 5.8 4.5 5.4 4.4

8.9 10.3 9.3 5.4 4.9 7.8 7.3

42.2 45.1 45.2 37.5 40.5 42.1 42.1

14.4 14.5 14.5 20.8 22.6 17.4 13.9

A-r-L-C1 A-r-L-C2 A-r-L-C3 A-r-L-C4 A-r-L-C5 Average A-r-L SAWS-A-r-L-C03

5.2 8.9 5.4 4.4 4.2 5.6 5.6

8.4 10.2 6.8 5.9 4.7 7.2 7.5

35.4 35.4 32.9 35.9 34.4 34.8 32.9

10.6 11.5 11.8 15.7 18.5 13.6 11.9

A-s-L-C4 A-s-L-C5 A-s-L-C6 A-s-L-C7 A-s-L-C8 Average A-s-L SAWS-A–s-L-C04

4.1 3.5 3.4 3.5 2.3 3.4 4.5

6.8 6.4 6.0 5.7 2.7 5.5 6.8

53.9 45.7 55.0 51.9 34.2 48.1 49.8

16.0 15.5 21.3 20.4 19.5 18.5 15.8

A-S-L-C7 A-S-L-C8 A-S-L-C9 A-S-L-C10 A-S-L-C11 Average A-S-L SAWS-A-S-L-C09

3.0 3.3 3.2 3.6 4.2 3.5 3.4

5.9 4.8 4.9 4.7 5.0 5.1 4.7

52.0 42.4 43.6 51.0 40.7 45.9 42.5

17.3 17.8 15.9 26.7 21.7 19.9 15.9

A-N-L-C1 A-N-L-C2 A-N-L-C3 A-N-L-C4 A-N-L-C5 A-N-L-C6 A-N-L-C7 Average A-N-L SAWS-A-N-L-C02

4.5 7.2 6.8 5.7 7.0 5.3 6.9 6.2 4.3

6.3 10.6 10.1 10.2 9.7 5.9 8.2 8.7 6.5

51.0 49.5 44.9 50.2 48.0 57.9 44.9 49.5 49.6

20.9 19.5 16.6 16.1 19.4 35.3 15.2 20.4 19.6

Perpendicular to the grain B-N-P-C2 B-N-P-C3 B-N-P-C4 B-N-P-C5 B-N-P-C7 Average B-N-P SAWS-B-N-P-C02

3.9 3.9 4.8 3.6 5.8 4.3 4.5

(6.9) (6.3) (4.1) (6.3) (7.3) (5.9) (4.5)

2.2 (4.6) 2.1 (4.1) 2.5 (2.4) 2.2 (4.2) 2.8 (5.4) 2.36 (4.1) 2.3 (2.3)

27.7 25.0 23.7 25.9 22.0 24.9 25.1

(29.4) (29.4) (26.0) (35.8) (34.5) (31.0) (25.1)

32.9 31.8 28.5 29.1 29.2 30.3 32.0

(16.6) (18.0) (17.8) (32.8) (32.0) (23.4) (32.0)

A-R-P-C1 A-R-P-C2 A-R-P-C6 A-R-P-C7 A-R-P-C8 Average A-R-P SAWS-A-R-P-C01

4.1 4.5 3.8 3.6 4.8 4.1 3.3

(5.9) (3.3) (4.1) (2.9) (3.0) (3.5) (3.4)

4.9 5.7 4.9 4.4 4.8 4.9 4.1

(7.7) (5.2) (6.9) (4.8) (3.9) (5.7) (4.7)

43.4 41.4 42.2 47.4 42.0 43.3 41.1

(40.9) (46.0) (49.7) (56.6) (51.0) (48.9) (45.9)

24.3 23.1 24.5 28.4 28.2 25.7 22.4

(17.6) (14.9) (14.6) (26.8) (27.2) (20.2) (23.2)

A-r-P-C3 A-r-P-C4 A-r-P-C5 A-r-P-C6 A-r-P-C7 Average A-r-P SAWS-A–r-P-C05

6.5 5.6 4.4 4.3 3.2 4.6 4.1

(4.7) (3.1) (5.5) (3.3) (3.0) (3.7) (4.4)

6.6 6.2 5.9 5.2 4.0 5.6 5.5

(5.9) (4.2) (7.3) (5.0) (4.1) (5.3) (6.1)

39.8 37.2 41.2 41.4 41.2 40.2 40.3

(48.9) (40.4) (41.3) (47.8) (47.9) (45.3) (42.2)

18.6 20.1 21.5 20.7 21.7 20.5 20.9

(20.8) (21.4) (21.9) (21.5) (21.5) (21.4) (21.1)

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J. Schneider et al. / Construction and Building Materials 77 (2015) 197–212 Table 6 (continued) Test ID

Elastic shear stiffness Ke [kN/mm]a

Maximum force Fmax [kN]

Displacement at maximum force DFmax [mm]

A-s-P-C3 A-s-P-C4 A-s-P-C7 A-s-P-C8 A-s-P-C9 Average A-s-P SAWS-A–s-P-C03

3.2 4.2 3.4 4.6 4.1 3.8 2.8

(4.3) (3.2) (3.1) (3.8) (3.8) (3.6) (2.9)

3.5 4.8 4.0 6.5 5.7 4.9 3.4

(8.1) (5.5) (5.0) (6.8) (6.3) (6.3) (3.6)

51.2 49.7 52.0 51.3 47.6 50.4 49.7

(58.3) (60.5) (64.8) (63.1) (62.4) (61.9) (52.7)

26.1 24.7 36.8 28.5 23.1 27.8 25.7

(20.2) (27.1) (26.8) (18.0) (20.3) (22.5) (26.4)

A-S-P-C5 A-S-P-C6 A-S-P-C8 A-S-P-C9 A-S-P-C10 Average A-S-P SAWS-A-S-P-C05

3.1 4.1 4.3 4.1 4.1 3.9 2.8

(3.7) (3.7) (3.9) (3.0) (3.2) (3.5) (2.9)

3.5 4.5 4.9 4.4 5.3 4.5 3.4

(5.7) (5.7) (6.1) (4.7) (5.5) (5.6) (3.6)

48.1 44.9 48.3 45.3 51.2 47.6 46.7

(53.0) (54.2) (52.6) (55.6) (56.8) (54.4) (48.3)

24.5 22.8 22.2 28.9 28.8 25.4 23.8

(19.5) (23.7) (24.5) (26.5) (24.9) (23.8) (24.2)

A-N-P-C2 A-N-P-C3 A-N-P-C4 A-N-P-C5 A-N-P-C6 A-N-P-C7 Average A-N-P SAWS-A-N-P-C04

5.2 6.2 4.6 6.1 4.6 3.7 4.9 3.4

(4.9) (4.1) (4.6) (4.0) (3.7) (5.6) (4.5) (3.8)

5.7 6.2 4.7 5.5 5.2 4.1 5.2 3.8

(6.7) (7.3) (7.1) (6.0) (6.1) (7.2) (6.7) (4.4)

43.4 48.6 44.8 52.0 52.4 51.1 48.7 43.0

(46.2) (49.6) (47.0) (54.8) (54.1) (54.6) (51.0) (47.9)

17.9 37.3 23.9 40.2 32.4 32.8 30.7 23.3

(19.7) (17.3) (19.8) (23.2) (18.0) (17.4) (19.2) (24.2)

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Values in brackets are generated with values from the negative branch of the curve.

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Fig. 10. Hysteretic response of connection tests and SAWS model parallel to the grain.

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Fig. 11. Hysteretic response of connection tests and SAWS model perpendicular to the grain.

smooth envelope curve. Often the following initial cycles of the next loading steps past maximum load are irregular, where the envelope curve of the model follows a linear degradation. Therefore, the model assumes more energy dissipation on the compression side than actually is achieved. The influence of the ‘‘initial cycle’’-factor is relatively small. Another factor causing the variation of DModel to DTest was investigated in the behavior of the subsequent cycles of the loading levels. The damage accumulation curves were obtained from the hysteretic responses perpendicular to the grain, which include loading in positive and negative directions (Fig. 11). In five out of six graphs, DModel is either equivalent or above DTest in the first section up to D = 0.25. A-r-P-C, A-s-P-C, AS-P-C, and A-N-P-C continue to show good correlation until D = 0.5 is reached. The envelope curve and loading cycles agree very well with the tests, resulting in good agreement of the damage curve. In the case of B-N-P-C, DModel is close to DTest, but stays at all sections below DTest. In the advanced part after D = 0.25, DModel increases slower than DTest so that the significant value of D = 0.8 is reached at a later point of the loading protocol. Only the connection combination A-N-P-C (Fig. 13f) shows small variation over the entire curve. The pinching of the connection is created by those two parallel lines. The loading and unloading of the connection follows the same path over the entire protocol. The model parameters are limited to capture the real pinching, which increases the slope

in the advanced cycles of the test. The limitation of SAWS model lead to an assumption that less energy is dissipated over the course of the subsequent cycles, as there is no variation to capture the test results accurately. Hence, the sections between the initial cycles in Fig. 13 (steep sloped lines) accent slower than the test curve. At the beginning of the test protocol, the influence of the subsequent cycles is insignificant and therefore good agreement between the two curves can be observed. In the advanced stage of the test, the increasing variation between test and model results in a greater difference, especially since Kraetzig’s model approach is an accumulation model, where previous events of the hysteresis curve are accumulated. It was found that the biggest difference between test and model of the subsequent cycles can be found at loading levels 5–7 of the CUREE protocol (Table 8). Even though the damage level of D = 0.8 in the model was reached at a later point of the loading protocol, in connection B-N-P, A-R-P, A-s-P, and A-N-P, DModel reached 0.8 before starting the next loading level. In that perspective, the differences of test and model are in reasonable range. Table 9 summarizes the times of model and test when D = 0.8 was reached and the ratio between time at D = 0.8 and total length of the loading protocol. Four out of six connections vary in a range from 1.5% to 9.5%. Connections A-r-P-C3 and A-s-PC4 show a higher variation of 14.6% and 11.2%. The average variation was calculated to 8.45%.

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A-R-L-C4

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Fig. 12. Cumulative damage index parallel to the grain with loading curve (red). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

3.6. Comparison of the model to the assessment method In this paper the test results of six CLT connections in two directions to the grain were used to generate a finite element model in OpenSees. To assess the accuracy of the obtained model results in comparison to the test results, two different assessment methods were chosen. The first method assessed ductility, elastic shear stiffness and maximum capacity. This method focuses on the envelope curve and neglects any influence from hysteretic cycles which occur at lower amplitude and do not contribute to the envelope curve of the load–displacement curve. The second method is a damage accumulation approach. The damage accumulation model considers each loading cycle not only the generated envelope curve. In addition to load and displacement, in this approach the relation between load, displacement, and time is tracked. The damage index D is calculated at incremental time steps, which requires knowledge of the load, displacement, and time relation. By using both approaches, both methods showed their strength and weaknesses in assessing the results. The EEEP curve, and herein calculated ductility, elastic shear stiffness and maximum capacity is a straight forward method, where its results can be

summarized and compared easily in a table. Test and model showed very good correlation. The observed differences are small and therefore it was interpreted that this model represents a good correlation to the testes connections. However, the damage accumulation method, where the damage index D was calculated in respect to the time, it was found that the subsequent cycles have a considerable influence on the accuracy of the damage results. The damage accumulation principle showed, in order to reproduce the exact load displacement relation the model needs to be modified to capture the behavior of the subsequent cycles. 4. Summary and conclusions In this research six connection combinations were tested and modeled in OpenSees. For the modeling, a CUREE-10 parameter model approach was chosen to reproduce the test curves. This paper has presented a comparison of the damage index computed through experimental and analytically model. Overall, there is a good trend between the two damage indices. However, since the analytical model is fitted and often under/overestimates at the

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Table 7 Time of the loading protocol (parallel to the grain) when damage index reached D = 0.8. Test ID

B-N-L-C3 A-R-L-C4 A-r-L-C3 A-s-L-C4 A-S-L-C9 A-N-L-C2 a b

Ratio between t0.8Da and tTotal b [%]

Time when reached Damage index 0.8 [s]

protocol

Testa

Modela

Test

Model

206 (480) 180 (366) 222 (387) 161 (489) 91 (400) 206 (473)

106 (480) 79 (366) 111 (387) 142 (489) 91 (400) 132 (473)

33.3 27.1 22.3 27.3 24.0 50.5

42.2 32.1 36.9 38.5 33.5 49.0

Time when damage level D = 0.8 is reached. Time when loading protocol is finished.

extreme points, there are apparent differences in the cumulative damage indices. Through establishing equivalency between the experimental and analytical result, however, for future performance assessment, this will furnish consistent results.

The obtained load–displacement results from both, test and model were analyzed according to the ASTM standard as well as to an energy-based damage accumulation principle. The two analyzing methods were used to assess and compare the results from testing and modeling to get a better understanding of the precision of the model. According to the ASTM analyzing method, the overall modeling result correlate with the test results very well. In the ASTM method 2126-11 [2], ductility ratio and elastic shear stiffness of the envelope curve of the hysteretic results are considered. Those values are represented in the EEEP curve (Figs. 10 and 11). For the energy-based damage accumulation principle, the load displacement results were processed to calculate a damage index at each incremental time step. The damage indices of test and model as well as the loading schedules are plotted in Figs. 12 and 13. The applied energy-based damage accumulation method showed a greater variation between test and model than the EEEP curves. It was observed, that the damage index curve of the model in parallel to the grain direction was increasing stronger for all six combinations. That can interpreted as being on the conservative side as var-

J. Schneider et al. / Construction and Building Materials 77 (2015) 197–212

Table 8 Amplitude of primary cycles for CUREE-protocol. Pattern

Step

Minimum number of cycles

Amplitude of primary cycle, %D

1 2

1 2 3 4 5 6 7 8 9 10

6 7 7 4 4 3 3 3 3 3

5 7.5 10 20 30 40 70 100 100 + 100aA (120) Additional increments of 100a (20%) up to 160

3 4

Table 9 Time of the loading protocol (perpendicular to the grain) when damage index reached D = 0.8. Test ID

B-N-P-C2 A-R-P-C1 A-r-P-C5 A-s-P-C3 A-S-P-C5 A-N-P-C4 a

Time when reached Damage index 0.8 [s]

Ratio between tD = 0.8 and tTotal protocol [%]

Testa

Modela

Test

Model

161 (483) 133 (489) 92 (412) 136 (499) 115 (480) 225 (445)

204 157 152 192 213 218

33.3 27.1 22.3 27.3 24.0 50.5

42.2 32.1 36.9 38.5 33.5 49.0

(483) (489) (412) (499) (480) (445)

Length of the entire loading protocol in brackets.

ious damage stages [25] are reached at an earlier point in the loading schedule. The results of the model perpendicular to the grain are mostly below the results of the test, which can be interpreted on the non-conservative side. Only in the case of A-N-P, the damage index curve follows closely the test results and can be found on the conservative side. Throughout all six combinations and both loading directions (parallel and perpendicular to the grain) a major difference was found in the damage index development generated by the subsequent cycles. Those parts increased slower than the index generated with the test results. The influence on the overall curve is significant and to a disadvantage in combinations perpendicular to the grain as it results in an overestimation of the performance of the connection. By only considering the envelope curve of the hysteretic response, the subsequent cycles are neglected completely. This research showed that the influence of subsequent cycles can be significant depending on the method of assessing the results. The EEEP method can achieve great correlation between test and model, but misses the influence of the subsequent cycles on the overall performance of the connections. The applied CUREE-10 parameter model showed good correlation with the test results. However, this model has limited abilities for modeling the subsequent cycles. Depending on the purpose of the model one or the other assessment method might be suitable. For an analysis of the overall ductility or elastic shear stiffness, applying the method provided by ASTM will give relatively accurate results to assess a hysteretic load–displacement model such as the SAWS model in this research. Since that approach considers only the envelope curve, which is mainly influenced by the first cycle of each loading step, the results showed good correlation for all six connections, as the initial loading cycle was captures relatively precise. If the model of the bracket is generated to be implemented into a bigger model to analyze the overall behaviour of a building, especially considering the

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time-history, it is important that to have the best possible correlation between test and model. In order to check for that, the damage accumulation method is a great tool, as the dissipated energy under the cyclic loading is considered. The energy dissipation is another indicator besides ductility and elastic shear stiffness to evaluate the model. By combining energy dissipation over time, the damage accumulation can help to analyze exactly where test and model vary and where good correlation can be found. The performed tests and generated models showed that the major inaccuracy was found in the subsequent cycles. The damage increase in those particular sections varied significantly, which caused a greater overall variation as Kraetzig’s approach is an accumulative model. Already small variation in an individual connection can change the performance result of an entire structure model as little variation will multiply with increasing number of levels of a building model. Connections are very important, as they contribute significantly to the deformation and performance of a building. Acknowledgements This research was supported through funding to the NSERC Strategic Network on Innovative Wood Products and Building Systems (NEWBuildS) and the Steel Structures Education Foundation (SSEF). References [1] ANSI A.N.. ANSI/APA PRG 320–2012: standard for performance-rated crosslaminated timber. APA – The Engineered Wood Association; 2012. [2] ASTM. Standard test methods for cyclic (reversed) load test for shear resistance of walls for buildings. ASTM E 2126-11. ASTM International; 2011. [3] BCBC. British Columbia building code. QP Publication Services; 2010. [4] Ceccotti A, Vignoli A. Engineering timber structures: an evaluation on their seismic behavior. Timber Engineering Conference, Tokyo; 1990, p. 946–53. [5] Chui Y, Yantao L. Modeling timber moment connection under reversed cyclic loading. J Strut Eng 2005;131(11):1757–63. [6] Chui Y, Ni C, Jiang L. Finite-element model for nailed wood joints under reversed cyclic load. J Struct Eng 1998;124(1):96–103. [7] Dickof C, Stiemer S, Tesfamariam, S, Wu, D. Wood-steel hybrid seismic force resisting systems: seismic ductility. World Conference for Timber Engineering. New Zealand Timber Design Society; 2012, p. 104–11. [8] Dolan J. The dynamic response of timber shear walls. Vancouver, British Columbia, Canada: University of British Columbia, Department of Civil Engineering; 1989. [9] Dujic B, Pucelj J, Zarnic R. Testing of racking behavior of massive wooden wall panels, Ljubljanar/Slovenia; 2004. [10] Foliente G. Hysteresis modeling of wood joints and structural systems. J Strut Eng 1995;121(6):1013–22. [11] Folz B, Filiatrault A. Cyclic analysis of wood shear walls. J Struct Eng 2001;127(4):433–41. [12] Foschi R. Analysis of wood diaphragms and trusses. Part 1: diaphragms. Can J Civ Eng 1977;4(3):345–62. [13] Foschi R. Modeling the hysteretic response of mechanical connections for wood structures. Vancouver: World Conference on Timber Engineering; 2000. [14] FPInnovations. CLT handbook: cross-laminated timber. Vancouver: FPInnovations; 2011. [15] Ghobarah A. Performance-based design in earthquake engineering: state of development. Eng Struct 2001;23:878–84. [16] Gosain N, Brown R, Jirsa J. Shear requirements for load reversals on RC members. J Struct Eng ASCE 1977;103(7):1461–76. [17] He M, Lam F, Foschi R. Modeling three-dimensional timber light-frame buildings. J Struct Eng 2001;127(8):901–12. [18] Kraetzig W, Meyer I, Meskouris K. Damage evolution in reinforced concrete members under cyclic loading. 5th international conference on structural safety and reliability, San Francisco; 1989, p. 795–02. [19] Liang H, Wen Y-K, Foliente GC. Damage modeling and damage limit state criterion for wood-frame buildings subjected to seismic loads. J Struct Eng 2011;137(1):41–8. [20] Lindt JW. Evolution of wood shear wall testing modelling and reliability analysis: bibliography. Pract Period 2004;9(1):44–53. [21] Lindt JW, Gupta R. Damage and damage prediction for wood shearwalls subjected to simulated earthquake loads. J Perform Constr Facil 2006:176–84. [22] Park YJ, Ang AH-S. Mechanistic seismis damage model for reinforced concrete. J Struct Eng ASCE 1985;111(4):722–39. [23] Polensek A, Laursen H. Seismic behavior of bending components and intercomponent connections of light-framed wood buildings. Oregon State University: Final Report to the National Science Foundation (Grant CEE8104626), Department of Forest Products; 1984.

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