Cross laminated timber (CLT) diaphragms under shear: Test configuration, properties and design

Construction and Building Materials 147 (2017) 312–327

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Cross laminated timber (CLT) diaphragms under shear: Test configuration, properties and design Reinhard Brandner a,⇑,1, Philipp Dietsch b,1, Julia Dröscher a, Michael Schulte-Wrede b, Heinrich Kreuzinger b, Mike Sieder c a b c

Institute of Timber Engineering and Wood Technology, Graz University of Technology, Inffeldgasse 24/I, 8010 Graz, Austria Chair of Timber Structures and Building Construction, Technical University of Munich, Arcisstraße 21, 80333 München, Germany Institute for Building Construction and Timber Structures, Technische Universität Braunschweig, Schleinitzstraße 21 A, 38106 Braunschweig, Germany

h i g h l i g h t s
Verification of a novel test configuration for in-plane shear properties of CLT.
Conclusive examination procedure for net-, gross-shear and torsion.
Identification of main influencing parameters from a comprehensive parameter study.
Proposal for characteristic shear properties for CLT with/without edge bonding.
Conclusive design concept for in-plane shear of CLT.

a r t i c l e

i n f o

Article history: Received 12 December 2016 Received in revised form 13 April 2017 Accepted 15 April 2017

Keywords: Cross laminated timber CLT Shear in-plane Failure mechanisms Gross-shear Net-shear Test configuration Parameter study Characteristic properties Design concept

a b s t r a c t The orthogonal structure of cross laminated timber (CLT) diaphragms under shear can cause three possible shear failure mechanisms: (i) gross-shear (in case of narrow-face bonded laminations), (ii) netshear and (iii) torsion. While the resistance against torsion has been investigated comprehensively, the determination of in-plane gross- and net-shear strength remains a challenging task. Whereas grossshear properties are proposed in analogy to glulam, for net-shear only properties derived from testing single CLT nodes are available. The verification of these approaches for full CLT elements has yet to be confirmed. We aim on verifying the applicability of a corresponding novel test configuration. For this aim and for evaluation of net- and gross-shear strength and modulus, an experimental study comprising in total 23 series featuring different parameter settings was conducted. In doing so, the operational efficiency of the test configuration together with reliable shear failure of all tested CLT elements was observed. With regard to the conducted parameter study, results qualitatively correspond with tests on single CLT nodes. Gap execution and layer thickness are confirmed to be the main parameters significantly influencing in-plane shear properties. Based on gathered experiences, characteristic shear properties and a conclusive design concept are proposed. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction Cross laminated timber (CLT) is a two-dimensional laminated engineered timber product, commonly composed of an uneven number of orthogonally and rigidly connected layers (see Fig. 1).

⇑ Corresponding author. E-mail addresses: [email protected] (R. Brandner), [email protected] (P. Dietsch). URLs: http://www.lignum.at (R. Brandner), http://www.hb.bgu.tum.de (P. Dietsch). 1 Joint first authorship. http://dx.doi.org/10.1016/j.conbuildmat.2017.04.153 0950-0618/Ó 2017 Elsevier Ltd. All rights reserved.

High resistances in- and out-of-plane predestines it for numerous applications, e.g. for floor and wall elements, shear walls, folded panels and beams. With respect to resistances and properties as a structural product, it is differentiated between out-of-plane and in-plane loading. For CLT under out-of-plane loading, test configurations, characteristic values and design procedures are well agreed. For CLT diaphragms under in-plane loading, some properties are still under discussion, presently resulting in conservative regulations, e.g. tension and compression in direction of the top layers, where homogenization effects, due to common action of several lamellas and layers, are not taken into account. The same is valid for CLT under in-plane shear. To fully profit from the high

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between the layers (Fig. 2; [5,6,24,8]). All failure mechanisms can be achieved if a corresponding test configuration is applied. Properties for the mechanism (III) ‘‘torsion”, based on Blaß and Görlacher [2], Jeitler [30] and Jöbstl et al. [31], are well accepted [12,41]. Apart from some influences on torsional resistance, e.g. annual ring pattern and surface area stressed in torsion [30,31], a characteristic (5%-quantile) value of ftor,k = 2.5 N/mm2 is commonly agreed. In contrast, the determination of the properties (I) grossshear and (II) net-shear by testing is challenging, as it is practically impossible to secure larger fields of pure shear. Up to now, the properties for in-plane net-shear provided in technical approvals are based on testing single nodes. The resulting strength values seem partly to be high (average values up to 14 N/mm2) and feature a higher variability than expected for diaphragms (coefficient of variation, CV[fv,net], of 13.5% for tests of [32], and between 4.2 and 15.1% for tests of [28] (values biased; specimen partly from the same board); see Brandner et al. [10]). Associated investigations include Wallner [51], Jöbstl et al. [32] and Hirschmann [28]. After re-evaluating and summarizing previous findings, Brandner et al. [10] proposed fv,net,05 = 5.5 N/mm2 as 5%-quantile of

capacities of CLT in-plane, a detailed knowledge of all relevant mechanical properties, which are dependent on the geometrical layup of the elements, as well as the development and verification of practicable test configurations to determine these properties are indispensable. Consolidated knowledge of CLT properties under in-plane shear is crucial for typical structural applications such as wall and floor diaphragms, cantilevered CLT walls and CLT used as (deep) beams, in all cases potentially featuring holes or notches. The current technical approvals and assessment documents for CLT products contain differing regulations to determine their load-carrying capacities in-plane. Generally they imply a verification of the torsional stresses in the cross-section of the cross-wise glued elements as well as a verification of the shear stresses in the boards of the top and cross layers. The basis of theoretical and practical considerations are the following three basic failure mechanisms for a CLT element under in-plane shear: (I) gross-shear (longitudinal shearing in all layers), (II) net-shear (exceedance of shear resistance perpendicular to grain in all layers in weak plane direction), and (III) torsion failure in the gluing interfaces (side face bonding)

side face

tℓ,ML

tCLT

tℓ,TL tℓ,CL

top layer (TL) cross layer (CL) middle layer (ML)

wℓ

narrow faces

wgap

wCLT

Fig. 1. Example of five-layer cross laminated timber (CLT) element: (left) photo; (right) technical drawing & specification of main terms and dimensions.

gross-shear (I) narrow face bonded CLT without cracks

net-shear (II) torsion (III) CLT with gaps, cracks and / or reliefs

τxy

τyx

τyx

τyx τyx

τyx

τxy

τyx

τxy

τxy

a = wℓ

a = wℓ

a = wℓ

y z

τxy

τxy

y

y a = wℓ

x tℓ

z

a = wℓ

x tℓ

z

Mtor x

a = wℓ

tℓ / 2

Fig. 2. Potential in-plane shear mechanisms in a CLT element & internal sub-element: schematic representation of deformed CLT and corresponding shear failures: (left) gross-shear; (middle) net-shear; (right) torsion (see also [6].

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net-shear strength for a reference CLT node in conjunction with the test configuration ‘‘EN” of Hirschmann [28]. Board thickness, gap width and annual ring pattern were identified as parameters with significant influence on shear resistance. For narrow face bonded (edge-glued) CLT elements prone to fail in gross-shear (I), characteristic shear strengths equal that of the base material boards without cracks are proposed, see Blaß and Flaig [4] and Flaig and Blaß [24]. In general and in particular for in-plane shear mechanisms (II) net-shear and (III) torsion, tests on single nodes are able to produce separated stress conditions; hence all test configurations on single nodes can represent and therefore lead to separate failure mechanisms in CLT under in-plane shear. The full stress state within a full-scale CLT-element under in-plane shear, however, cannot be represented by them. Several efforts were made to determine shear properties on fullscale CLT diaphragms, e.g. Bosl [7], Bogensperger et al. [5] and Andreolli et al. [1]. Apart from their rather costly implementation, the main challenges within the tested configurations were (i) to realize a continuous load introduction, (ii) to receive a field of pure shear, and (iii) to achieve failure under in-plane shear. It is expected that these challenges are also encountered when applying the standardized test configuration, which is used to determine the racking strength and stiffness of timber frame wall panels, see EN 594 [21]. The determination of shear strength based on fourpoint bending tests, e.g. given in EN 16351 [25] (based on CUAP 03.04/06 2005 [11]), has to be critically analyzed as well. Here,

the determination of shear strength is based on the beam theory considering the total thickness of all cross layers for the evaluation. The typical stress states within CLT diaphragms under in-plane shear are not represented by this approach. In the context of an approval in the individual case, a proposal for a test configuration and evaluation procedure for CLT diaphragms under shear stress was published in Kreuzinger and Sieder [39]. The approach to determine shear strength out of a combined stress state with transverse stresses can already be found in Szalai [49]. The approach proposed is based on a simple compression test; the test results, assuming gross-shear failures, are evaluated using theoretical approaches from the plate theory (in-plane stresses). In this publication, the test configuration and evaluation procedure are extended for net-shear failures, see Chapter 2.

2. Test configuration and evaluation procedure 2.1. Description of test configuration In the test configuration according to Kreuzinger and Sieder [39], column-shaped rectangular specimen, which are cut out under 45° rotated to the main orientation of CLT elements, are tested in compression, see Fig. 3. The stress state in a differential CLT section rotated by 45° constitutes pure shear combined with pure compression, see Fig. 4.

τxM,yM F

ACLT = wCLT tCLT

τyM,xM

yM

τyM,xM

ACLT

y

xM α

F

τxM,yM σyM

x

τxM,yM Fig. 3. System & internal stresses and external loading.

σx/2 σy σyM

σx/2

σx/2

σxM τyM,xM

τyM,xM

τxM,yM

=

τxM,yM

τyM,xM

τyM,xM

τxM,yM

σyM

shear & compression

σx/2 σy/2

σy/2

τxM,yM

σxM

σy/2

σy/2

σy

pure shear

σyM

σxM

σxM

σyM

+

pure compression

Fig. 4. Stress state in differential column & differential CLT-section rotated by 45°.

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This circumstance requires consideration when evaluating shear properties; see Section 2.2.

(CL) and top layers (TL); standardized value or value determined by testing), respectively. The approach is based on

and The stresses on the column as well as on a differential CLT section are given in Figs. 3 and 4. Fig. 5 contains a scheme of a specimen featuring five layers to highlight notation of important CLT parameters used throughout the text. For an arbitrary angle a and based on the Cartesian coordinate system of the column cross-section (x, y), the principal stresses are:

rx ¼ 0; ry ¼  rxM ¼

F F ¼ ACLT wCLT t CLT

F 2 sin ðaÞ; ACLT

ryM ¼

F cos2 ðaÞ; ACLT

ð1Þ

sxM;yM ¼

F sinðaÞcosðaÞ ACLT ð2Þ

For the proposed angle a = 45° expressions in Eq. (2) reduce to

rxM ¼ ryM ¼

ry 2

;

sxM;yM ¼

ry 2

ð3Þ

In this case, the shear stress at maximum load Fmax is determined according to

sxM;yM ¼

1 F max F max ¼ 2 ACLT 2wCLT t CLT

ð4Þ

In general, the shear resistance is influenced by stresses perpendicular to the grain, see Spengler [48] and Hemmer [27]. Compressive stresses perpendicular to the grain result in an increase of shear resistance. Consequently, in the given test setup (see Fig. 3), the obtained maximum shear stresses sxM,yM are higher than the actual shear strength fv. For a = 45° the test setup leads to compressive stresses rxM and ryM, which equal the shear stresses sxM,yM, see Fig. 3. In case of a gross-shear failure in a CLT element with uneven number of equally thick layers, the compressive stresses ryM are primarily transferred by the layers featuring a board direction yM. The compressive stresses perpendicular to the grain, r90, which reach in case of gross-shear failure their maximum in that layers oriented in xM-direction (see also Fig. 5), can be calculated as

r90 ¼ ryM

E90 E90 ¼ sxM;yM EyM EyM

ð5Þ

Their magnitude is reduced by the relationship E90/EyM, given as

P

EyM ¼

P t‘;yM E0 þ t ‘;xM E90 t CLT

X

tCLT EyM ¼

2.2. Determination of in-plane shear strength

ð6Þ

with EyM as weighted modulus of elasticity in yM-direction (CLT cross layers (CL); standardized value or preferably value determined by testing), E0 and E90 as modulus of elasticity parallel and perpendicular to the grain of the base material (CLT cross layers

tCLT ¼

X

t‘;yM E0 þ

t ‘;xM þ

X

X

ð7Þ

t‘;xM E90

t‘;yM and

X

t ‘;L P

X

t ‘;T

ð8Þ

P P with t‘,L and t‘,T as sum of layer thicknesses in strong and weak plane direction, respectively. Assuming softwood of typical strength classes according to EN 338 [18] with C16 to C30 and layup parameters (ratios between P the sum of layer thicknesses in weak plane direction, t‘,T, to that P P P in strong plane direction, t‘,L) of 0.25  t‘,T/ t‘,L  1.0, this leads to values r90 = sxM,yM (0.06–0.25), and considering C24 only to r90 = sxM,yM (0.07–0.17). Using the test results reported in Spengler [48], an empirical attempt to estimate this influence is given by the approach taken by Blaß and Krüger [3], which modifies the obtained shear resistances as follows:

f v;gross ¼ sxM;yM þ 1:15 r90 þ 0:13 r290

ð9Þ

whereby r90 is negative if representing compression stresses. To determine the shear strength fv,gross, the obtained shear stresses sxM,yM should be reduced in the range of fv,gross = sxM,yM (0.75–0.94) (C16–C30) and fv,gross = sxM,yM (0.83–0.93) (C24 only). The higher the layup parameters, P P t‘,T/ t‘,L, the smaller the reduction. In case of a net-shear failure in principle the same considerations can be made. In doing so the layers relevant for transferring compression stresses perpendicular to the grain change, and the number of layers which fail in transverse shear is equal to the number of layers in the weak plane direction of the CLT element. Consequently, the following relationship applies:

P

ExM ¼

P t‘;xM E0 þ t‘;yM E90 t CLT

ð10Þ

with ExM as weighted modulus of elasticity in xM-direction (CLT top layer (TL); standardized value or value determined by testing). The amount of stresses in compression perpendicular to the grain can be calculated according to Eq. (11); the net-shear strength according to Eq. (12)

r90 ¼ rxM

E90 E90 ¼ sxM;yM ExM ExM

ð11Þ

f v;net ¼ sxM;yM ttCLT þ 1:15 r90 þ 0:13 r290 P net with tnet ¼ t ‘;T

ð12Þ

whereby r90 is negative if representing compression stresses. The resistances in net- and gross-shear in case of gross- and net-shear failure, respectively, can be calculated by considering the relevant P ratio between t‘,T and tCLT. 2.3. Determination of in-plane shear stiffness The shear modulus G can be determined using the flexibility matrix and its transformation. Using the constitutive equation e = S r, a simplified flexibility matrix describing the state of plane stress (neglecting the off-diagonal elements related to Poisson’s ratio vxM,yM)

2

6 6 S xM;yM ¼ 6 6 4 Fig. 5. Schematic cross section of a five-layer CLT element and notation of some parameters.

1 ExM

0 1 EyM

symm:

0

3

7 7 0 7 7 5

1 GxM;yM

ð13Þ

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can be transformed from the coordinates (xM, yM) to (x, y) by the angle 360° – a following

S x;y ¼ T S xM;yM T T

ð14Þ

with

2 6 T ¼6 4

cos2 ðaÞ

sin ðaÞ 2

sinðaÞcosðaÞ

sin ðaÞ

cos2 ðaÞ

sinðaÞcosðaÞ

2

2sinðaÞcosðaÞ 2sinðaÞcosðaÞ cos2 ðaÞ  sin ðaÞ

3 7 7 5

3.2. Test program

2

ð15Þ For example, the flexibility in y-direction is given as

1 sin ðaÞ cos4 ðaÞ sin ðaÞcos2 ðaÞ ¼ þ þ Ey ExM EyM GxM;yM 4

S x;y ð2; 2Þ ¼

2

ð16Þ

For the proposed angle a = 45° transformation to Sx,y according to Eqs. (13)–(15) gives

2 0:25 6 S x;y ¼ 6 4

ExM

þ 0:25 þ G0:25 EyM xM;yM

0:25 ExM

þ 0:25  G0:25 EyM xM;yM

0:5 ExM

0:25 ExM

þ 0:25 þ G0:25 EyM xM;yM

0:5 ExM 1

symm:

ExM

 E0:5 yM

3

7 7  E0:5 yM 5

ð17Þ

þ EyM 1

From the load-deformation characteristics of the columnsection, the load F and the modulus of elasticity Ey, e.g. based on centric local deformation measurements in vertical direction, can be determined. For a = 45°, a discrete stress state ry with associated strain ey and by using the constitutive equations e = S r and ry = Ey ey, the following relationship can be derived:

  1 1 1 1 ¼ 0:25 þ þ Ey ExM EyM GxM;yM

ð18Þ

The shear modulus GxM,yM given a = 45° can then be determined according to

GxM;yM ¼ 

4 Ey

1 1 1  ExM  EyM



ð19Þ

Another approach to determine the shear modulus is based on a procedure standardized in EN 408 [20]. This approach requires the local measurement of shear deformations by means of measurement crosses, applied on both side faces of the specimen. The shear modulus can then be calculated as

G090;CLT;xM;yM;EN ¼ G090;EN

h0 DF=2 ¼ aG wCLT t CLT DwG

To prove the robustness of the test configuration and evaluation procedure with respect to a varying angle a between the grain orientation of the top layer and the horizontal (see Fig. 3), five series, denominated to group and producer ‘‘D”, featuring a = 15°, 30°, 45°, 60° and 75°, were tested. The main parameters of narrow and side face bonded CLT elements of pine (Pinus sylvestris) featuring nominal strength class C24 according to EN 338 [18] are presented in Table 1. All specimen featured P P three equally thick layers (t‘ = 30 mm; tCLT = 90 mm; t‘,T/ t‘,L = 0.50) of equally wide lamellas (w‘ = 120 mm) without reliefs.

ð20Þ

with h0 as measurement length and DF/D wG as relationship between load and shear deformation, determined in the linear elastic range between 0.1 and 0.4 Fmax, and aG as correction factor which adjusts the shear deformation measurement according to the theoretical shear stress distribution within the measurement field. 3. Materials and methods 3.1. Preliminary investigations First tests conducted at the Technische Universität München (TUM) and Graz University of Technology (TU Graz) in 2013 indicated the functional and operational efficiency of this novel test configuration. Motivated by these promising results, a joint research project between TUM and TU Graz was initiated with the aim
to prove the applicability and suitability of the test configuration for a wider range of parameter settings,
to investigate and quantify possible influences on the shear properties, and
to answer the open question of a possible transfer from single node outcomes to CLT diaphragms.

The test program was developed in consideration of all relevant product parameters and their common range found in current European Technical Approvals (ETAs) of Central European CLT products. Only CLT products featuring side face bonded layers were investigated. Table 2 and Fig. 6 give an overview of the tested parameters and their range of values. The parameters of each series are given in Table 3. In this test program only CLT from Norway spruce (Picea abies) was used which was provided by three producers, leading to three groups of specimen, A, B and C. For the boards used for group A, strength class C24 according to EN 338 [18] was agreed. The boards for all series within group A were delivered in one stack with the exception of the boards of series A4 and A5, which were delivered at a later stage. Due to production limits on the part of the producer, series A1 and A3 were produced in the laboratories at TU Graz, see Dröscher [17] for further details. All specimen within groups B and C were produced according to the specific Technical Approvals of the producers, allowing the use of boards of strength class C16 according to EN 338 [18] at a share 10% together with C24. Series A1 was the only test series with narrow-face bonded specimen, to be used for example as reference series for comparison with all other series featuring no narrow-face bonding. The series in groups A and B consisted of six, the series in group C of seven specimen. The specimen were generally retrieved consecutively from one CLT plate. Thus it is expected that the variability of the parameters within one series is reduced due to partly the same base material within these series. To evaluate this influence, a stochastic simulation was conducted, see Section 4.4.3. 3.3. Test configuration The test configuration (see Figs. 7 and 9) was realized according to the configuration described in Chapter 2. The geometric relationship was set to hCLT/ wCLT = 3/1, more specifically to hCLT/wCLT = 1,500 mm/500 mm. This results in a field of pure shear outside the quadratic area potentially influenced by the support conditions while eliminating the potential for stability failure in most configurations. The assumption of a field of constant shear was verified by means of a FiniteElement (FE) study, in which geometric and stiffness parameters were varied in a practical range, see Fig. 8 and Silly [47] for further details. The potential influence of friction between the support (surface of load application) and the test specimen was experimentally investigated by using (i) lubricated narrow faces, (ii) Teflon intermediate layers, (iii) roller bearing, and (iv) blank steel to timber contact. The differences in determined transverse strains were evaluated by measurements of

Table 1 Preliminary test program for investigating the influence of a; overview of test series and parameters. Series (TUM)

D1

D2

D3

D4

D5

No. of Spec. No. of layers N a [°]

1 3 75

3 3 60

6 3 45

3 3 30

1 3 15

Table 2 Overview of tested parameters and their values (range). Parameter [–]

Values [–]

Gap execution

narrow face bonded (edge-glued; NFB); not narrow face bonded, gap width wgap = {0; 5} mm w‘ = {80; 160; (230) 240} mm

Board (lamella) width Layer thickness No. of layers N Stress relief Layup parameter Producer

t‘ = {20; 30; 40} mm N = {3; 5; 7} layers {Yes; No} P P t‘,T/ t‘,L = {0.32; 0.35; 0.46; 0.50; 0.68; 0.75; 0.86}, P P with t‘,T  t‘,L {A; B; C}

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R. Brandner et al. / Construction and Building Materials 147 (2017) 312–327

wℓ C3

B5 | C2

C4

tℓ

B1

B2

wℓ

A2 | B3

A3

B4

A1

width wℓ & thickness tℓ A6

A8

A7

Ref. A5

layup parameter ∑tℓ,T / ∑ tℓ,L A9

gap exec.

C1

No. of layers N

relief

tℓ

A4

Fig. 6. Overview of test program and parameter variation.

Table 3 Test program; overview of test series including all necessary parameters. Institute

TU Graz 1)

Series

A1

No. of spec. No. of layers N Layup t‘ [mm]

6 3 30 30 – 90 0.50 160 NFB N 90 all

tCLT [mm] P P t‘,T/ t‘,L [–] w‘ [mm] Gap execution Stress relief 4) t‘,fail [mm] Layer failing

TL CL ML

3)

TUM 1)

A2

A3

6 3 29 29 – 87 0.50 160 0 N 29 CL

6 3 30 30 – 90 0.50 160 5 N 30 CL

A4

2)

A5

6 5 17/19 32 19 119 0.86 160 0 N 17 L

2)

6 5 28/30 30 30 148 0.68 160 0 N 30 CL

A6

A7

A8

A9

B1

B2

B3

B4

B5

C1

C2

C3

C4

6 5 40 19 30 148 0.35 160 0 N 19 CL

6 5 31 19 20 120 0.46 160 0 N 19 CL

6 5 40 19 40 158 0.32 160 0 N 19 CL

6 7 30 30 30 210 0.75 160 0 N 30 CL

6 3 20 20 – 60 0.50 80 0 N 20 CL

6 3 20 20 – 60 0.50 160 0 N 20 CL

6 3 30 30 – 90 0.50 160 0 N 30 CL

6 3 30 30 – 90 0.50 160 0 Y 30 CL

6 3 40 40 – 120 0.50 240 0 Y 40 CL

7 3 30 30 – 90 0.50 230 0 N 30 CL

7 3 30 30 – 90 0.50 230 0 Y 30 CL

7 3 40 40 – 120 0.50 230 0 N 40 CL

7 3 40 40 – 120 0.50 230 0 Y 40 CL

TL . . . Top Layer; CL . . . Cross Layer; ML . . . Middle Layer; L . . . Longitudinal Layers (TL & ML); T . . . Transverse Layers (CL); t‘,fail . . . thickness of failed layer(s) where shear failure(s) was (were) observed. 1 produced in laboratory. 2 boards delivered at later stage. 3 NFB . . . narrow face bonded (edge-glued); 0 resp. 5 . . . gap width wgap [mm]. 4 Yes (Y), No (N).

the horizontal deformation near the load application and found to be not of practical relevance. However, all tests within group A were realized using Teflon intermediate layers, all tests within groups B, C and D were conducted with a roller-bearing at the bottom support and steel plate to timber contact at the load introduction. In all cases, the load was applied at a constant rate to achieve failure within

hCLT = 1,500 mm 400 550

F

300 ± 120 s according to EN 408 [20]. The tests within group A were realized in the 4 MN four-column test frame of the Laboratory for Structural Engineering (LKI) at TU Graz. All tests of groups B, C and D were conducted in the Zwick Z-600 testing machine at the MPA BAU at TUM. In case of very slender test specimen, one horizontal support was added to each side face of the specimen

series A: teflon series B & C: steel-timber contact yM

y

xM α=45°

series A: teflon series B & C: roller bearing

x

wCLT = 500 mm Fig. 7. Test configuration (schematic), local and global coordinate system.

Fig. 8. Stress distribution from FE-study [47]: hCLT/wCLT/tCLT = 1,200/600/120 mm3, Dx/Dy = 1, F = 600 kN, l . . . coefficient of friction for steel-timber-contact zone.

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R. Brandner et al. / Construction and Building Materials 147 (2017) 312–327

Fig. 9. Impressions from testing at TU Graz (left) and TUM (right).

and with load-free contact to the specimen’s surface to effectively prevent premature buckling. The in-plane deformation on both side faces of the specimen was determined using centrically placed measurement crosses featuring a measuring distance of h0 = 400 mm. For this, the specimen of group A were equipped with compact strain transducers of type DD1, which were removed at approximately 50% of Fmax. The specimen of groups B, C and D were equipped with rope extensometers on one side face. On the other side face, the contact-free optical measurement system GOM with software PONTOS [42] was used. 3.4. Determination of parameters 3.4.1. Moisture content and density For each specimen, the mean density as well as the mean moisture content (group A: kiln drying, groups B, C and D: resistance method) were determined. In the case of moisture contents differing from the reference moisture content uref = 12%, the mean density at 12% moisture content, q12, was determined according to EN 384 [19]. 3.4.2. Shear strength and maximum torsional stresses The shear strength in case of gross- and net-shear failure was determined according to Eqs. (9) and (12), respectively. The (low) influence of compressive stresses perpendicular to the grain on shear strength was taken into account using the regression formula from Blaß and Krüger [3], applying compressive stresses perpendicular to the grain determined with Eqs. (5) and (11). The torsional stresses stor;i at the time of failure in gross- or net-shear were determined on the basis of polar torsion, considering a finite number of layers N and a heterogeneous layup with thicknesses t‘;i by establishing ideal layer thicknesses t ‘;i to take into account bonded areas in the outer and core region of the CLT elements, with

t‘;1 ¼ minð2t‘;1 ; t‘;2 Þ; ;t ‘;N1 ¼ minðt ‘;N1 ; 2t‘;N Þ and t‘;26i6N1 ¼ minðt ‘;i ; t ‘;iþ1 Þ

ð21Þ

with t ‘;i as thickness of the layer i = 1, 2, . . ., N – 1, and the relationship

t

CLT stor;i ¼ 3f v;gross PN1 i¼1

t‘;i



t ‘;i w‘ or a

 ð22Þ

see Bogensperger et al. [6], with w‘ and a as board width and spacing or edge distance of reliefs, respectively. To determine the shear strength at the reference moisture content uref = 12%, an adjustment factor of 3% per percent change in moisture content was applied; see Gerhards [26], Kretschmann and Green [38] and Brandner et al. [8]. 3.4.3. In-plane shear stiffness of the CLT elements The shear modulus G090,CLT of the CLT elements under in-plane shear was determined with two approaches; see Section 2.3. The first approach is based on the measured vertical deformation in the local measurement field and standardized moduli of elasticity E0,mean and E90,mean according to the strength class of the boards, considering a strength class of C24 according to EN 338 [18], with E0,mean = 11,000 N/mm2 and E90,mean = 370 N/mm2. The shear modulus G090,CLT,xM,yM,KS = G090,KS is determined according to Eq. (19).

The second applied approach follows EN 408 [20]. Considering the geometric and stiffness relationships in our investigations (see Section 3.3), it could be shown by means of a Finite-Element (FE) study, that the differences between ideal and real stress distribution within the measurement field are negligible (< 1%); hence, a correction factor aG = 1.0 was applied, see Dröscher [17] for further details. To determine the shear modulus at reference moisture content uref = 12% an adjustment factor of 2% per percent change in moisture content was applied. This correction is based on own experiences and supported by recent investigations on the influence of moisture on the initial stiffness of axially-loaded self-tapping screws; see Ringhofer et al. [45].

4. Results and discussion 4.1. General Four groups with a total of 23 series (five preliminary test series and 18 series in the main test program) featuring different product configurations or test specifications were tested. The statistics of the main parameters in each series are given in Table 4; the outcomes are illustrated as box-plots in Fig. 10. The statistical analyses as well as stochastic simulations were carried out in R [43]. The moisture content u of all specimen was in the range of 12 ± 2%. Regarding the average density q12,mean of all groups in the test program it can be noted that it decreases from group A to C (A: 463, B: 437, C: 419 kg/m3; coefficients of variation CV [q12] in the range of 1–3%, on average 1.6%). Only series B5 exhibited a density below the expected range for series within group B. The average density in group D, featuring CLT made of pine, was 525 kg/m3. In addition to the high amount of homogenization that is to be expected for density of CLT elements, deriving all specimen from the same CLT element was concluded to be another factor leading to low coefficients of variation (CVs) in density; more on homogenization and the determination of the expected range in Section 4.4. The low CVs of the shear strength (2%  CV[fv,net,12]  8%, on average 5%) in combination with the very reliable failure in gross- and net-shear, independent of the multitude of tested parameters and their range, affirmed the very robust test configuration. No differences in results were identified between the testing institutes despite the fact that different testing machines and setups were used. However, as already mentioned, these low CVs are biased by the applied sampling approach. To estimate the influence of sampling on the observed CVs, some simple stochastic simulations were conducted; see Section 4.4.3.

1 10.1 517 – 568 1) 8.31) 2.0 1) 7.9 1) – – 1,571 – – – – 2.2 1) 3 10.7 534 0.2 414 8.4 3.2 10.8 3.8 10.2 749 2) 4.7 – – – 3.6 6 9.9 519 2.8 350 7.4 3.3 10.6 4.8 9.8 747 3) 4.9 751 3) – – 3.7 3 10.5 532 2.1 420 7.0 3.6 11.4 7.5 10.0 929 2) 9.3 – – – 4.1 1 10.6 518 – 584 1) 6.4 1) 3.0 1) 9.2 1) – – 1,560 – – – – 3.4 1) 7 14.1 433 1.4 268 8.4 2.3 7.0 4.3 6.5 440 11.8 510 10.7 470 3.6

4.2. Shear strength

7 12.7 411 1.6 230 8.1 2.6 7.7 4.7 7.1 470 9.9 520 6.2 510 3.0 7 12.4 423 1.3 244 8.3 2.7 8.1 6.1 7.3 480 14.2 560 10.8 510 1.6 wf,app,mean . . . apparent fracture deformation corresponding to maximum load, based on global measurement from the testing device. 1 Test stopped; maximum value reached without shear failure; only one specimen tested. 2 Outcomes of only two of three specimen usable. 3 Outcomes of only four of six specimen usable.

6 10.4 414 2.7 217 8.2 1.7 5.1 5.5 4.6 310 12.4 380 4.8 480 1.3 6 10.8 445 1.2 214 8.8 2.3 6.7 2.1 6.5 430 12.3 480 10.0 460 3.8 6 11.6 443 1.3 247 9.0 2.7 8.0 5.2 7.3 420 7.2 490 5.5 460 2.3 6 10.1 450 1.1 226 7.7 3.5 10.5 4.1 9.8 600 12.2 590 9.7 520 2.0 6 10.5 434 1.1 178 9.1 2.8 8.4 1.8 8.1 500 7.7 500 8.1 410 3.1 6 10.6 471 1.4 570 9.5 2.5 5.9 7.7 5.2 460 6.6 510 5.3 500 1.7 6 11.3 445 0.7 353 7.9 2.2 9.0 7.1 8.0 410 9.1 460 12.4 540 1.6 6 10.9 461 1.4 339 9.0 2.7 8.5 6.3 7.6 490 13.3 540 10.0 540 1.5 6 11.2 455 1.0 353 8.1 2.3 8.9 3.5 8.4 460 4.0 490 2.6 540 1.6 6 11.6 459 1.9 431 9.9 2.8 6.9 3.2 6.6 510 6.3 550 5.9 490 2.0 6 12.5 472 1.9 379 10.4 3.1 6.8 4.1 6.3 520 4.8 540 6.9 540 2.2 6 12.2 461 2.6 177 8.6 1.9 5.8 3.3 5.5 300 5.8 320 5.8 460 1.6 6 12.2 478 1.4 194 7.9 2.2 6.6 5.3 6.0 460 11.8 490 10.0 460 1.8 6 12.3 470 1.4 378 8.7 3.8 11.5 7.4 10.1 640 11.0 650 7.5 – 3.3 No. of spec. [–] umean [%] q12,mean [kg/m3] CV[q12] [%] Fmax,u,mean [kN] wf,app,mean [mm] fv,gross,mean,12 [N/mm2] fv,net,mean,12 [N/mm2] CV[fv,net,12] [%] fv,net,12,05,LND [N/mm2] G090,KS,12,mean [N/mm2] CV[G090,KS,12] [%] G090,EN,12,mean [N/mm2] CV[G090,EN,12] [%] G090,CLT,mean,est [N/mm2] stor,12,mean [N/mm2]

319

In contrast to common expectation, the shear modulus features higher CVs than the shear strength (3%  CV[G090,EN,12]  12%, on average 8%), although these values are based on averaged measurements taken on both specimen’s side faces. Observed differences between both measurements are within the expected bandwidth and can be attributed to inhomogeneities in the specimen as well as imperfections in loading. Bias caused by the measurement system used and specimen’s positioning within the testing device was not determined. Thus, the high variabilities are attributed to epistemic uncertainties, well known difficulties in deriving distinct values from deformation curves, which are the result of measurements of very small deformations (range of DwG within 0.1–0.4 Fmax: 0.4– 1.2 mm, mostly between 0.4 and 0.7 mm).

7 13.1 410 2.6 264 7.8 2.2 6.7 2.3 6.5 450 10.8 530 7.3 470 1.8

D2 D1 C1 B5 B4 B3 B2 B1

TUM

A9 A8 A7 A6 A5 A4 A3 A1 Statistics

A2 TU Graz Institute

Table 4 Statistics of tested series: moisture content, density, maximum load, apparent fracture deformation, shear strength, shear modulus, torsional stresses.

C2

C3

C4

D3

D4

D5

R. Brandner et al. / Construction and Building Materials 147 (2017) 312–327

4.2.1. General observations All specimen within group D and series A1, featuring narrow face bonded boards, failed in gross-shear. All specimen without narrow face bonding showed lower stiffness and failed in netshear; see Fig. 11. Average shear strengths within group D were analyzed, comprising series featuring the same parameters but tested at various angles a. The outcomes are comparable, apart from series D1 and D5 where testing was interrupted due to limits of the testing device before the maximum load was reached. In general, the failure in gross-shear was followed by a failure in net-shear and corresponding softening to a plateau of about 30– 60% of net-shear strength, see Fig. 11. This can be seen in analogy to concrete; change from the state of uncracked cross sections to the state of cracked cross sections. The development of cracks when exceeding Fmax in gross-shear resulted in a change in shear stress distribution as now, equal to CLT without narrow face bonding, only a shear transfer via the lamella’s cross sections within the layers and the gluing interfaces between the layers was possible. The load-deformation relationship appeared linear-elastic until about 80% of Fmax, followed by a non-linear decline until Fmax. The non-linearity was a result of local exceedance in shear parallel to grain, with fractures in the transition zone between early- and latewood, combined with local exceedance in torsion. The regressive softening after reaching Fmax was characterized by a successive dissolution of the shear fracture zone leading to an agglomeration of fixed-end annual ring beams which were stressed in bending and tension parallel to grain; see Fig. 12 (left) which shows local failure (left) as well as load-displacement curves from single-node tests (right) as reported e.g. in Jöbstl et al. [32] and Brandner et al. [10]. Because of the chosen layups, all series without narrow face bonded boards failed due to a net-shear failure in the cross layer (s) with the exception of series A4 in which all specimen exhibited a net-shear failure in layers oriented in direction of the top layers. Two specimen within series B1 experienced a stability failure (second eigenmode due to horizontal support) before net-shear failure. A comparison to the strength values of the other specimen within that series did not show any influence of stability failure on shear properties. The mean vertical deformations at time of failure, independent of the type of failure, featured a low range (7.7 mm  wf,app,mean  9.5 mm). Fig. 10 shows the net-shear strength of individual series arranged by certain parameters to enable examination of parameters relevant for shear strength. In the following sections, these parameters will be discussed with respect to their influence on shear strength. 4.2.2. Gap execution Series A1, A2 and A3 from the test program were used to analyze the influence of gap execution. The narrow face bonded

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gap exec. param. NFB 0 5 wℓ 160 160 a 1) 30 tℓ,fail 2) .18 tℓ,fail / a

a = min(wℓ; trelief), trelief as edge distance of relief thickness of failed layer(s), rounded to 10

500 450 range CLT | C24 1)

400

1)

CLT | C24: 420 kg/m³ ± 3 σ; σ … standard deviation fv,net,12,05,LND

12 10 8 6

4.0 3.5 3.0 2.5 2.0 1.5 G090,CLT,mean,est

700 600 500

C4

B5

A8 A6 A7 A2 A5 A9 A4 A2 B3

C3

C4

B4

B3

C1 C2

B5

A2 A5 A9

B3

B5 B2

B2

B1

400 300 A3

G090,EN,12 [N/mm²] fv,gross,12 [N/mm²]

fv,net,12 [N/mm²]

ρ12 [kg/m³]

2)

A1 A2

1)

tℓ layers stress relief ∑tℓ,T / ∑tℓ,L producer wℓ 80 160 240 20 30 40 3 5 7 N Y N Y N Y .32.35.46 .50 .68.75.86 A B B C 80 160 240 160 240 160 230 160 230 160 160 240 230 80 160 120 160 120 160 230 115 160 80 230 115 160 160 120 115 20 40 20 30 40 30 30 30 40 20 30 20 30 40 .25 .13 .33 .13 .19 .33 .19 .13 .26 .19 .38 .17 .35 .13 .19 .13 .19 .17

Series [-] Fig. 10. Box-plots of density, net- and gross-shear strength and shear modulus, for identification of relevant parameters; box-plots and properties in ‘‘grey” mark series which can be used only to a limited extent for specified parameter investigations.

Fig. 11. (left) load-displacement curves of series A1 (with) & A2 (without narrow face bonding); (right) typical impressions of net- and gross-shear failure mechanism.

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Fig. 12. (left) net-shear fracture zone in cross layer (centrically sawn) in detail; (right) typical single and average load-deformation curves of net-shear failure mechanism from testing single nodes; see e.g. Brandner et al. [10].

4.2.3. Board width To analyze the parameter board width w‘ respectively gap or relief spacing or edge distance a, the results of series B1 and B2 could be used directly whereas series B5 could be used to a limited extent due to its board thickness and stress reliefs. Taking into account the pronounced influence of the parameter board thickness (see Section 4.2.4), the results given in Fig. 10 and Table 4 indicate a regressive relation between board width and shear properties. Jöbstl et al. [32], Hirschmann [28] and Brandner et al. [10] state that the failure in net-shear happens as a result of a local interaction of torsional and longitudinal shear failure at the lamella’s narrow faces. From this it can be expected that increasing board width and hence decreasing torsional stresses due to a decreasing relation (t‘/a) or (t‘/w‘) has a positive effect on shear strength. On the other hand, wider boards are usually cut close to the core (pith) of logs, leading to a higher proportion of rift or half-rift cuts. The shear strength in the longitudinal-tangential plane, fv,LR (failure usually in transition zone between early- and latewood), is lower than in the longitudinal-radial plane, fv,LT (failure usually by shearing early- and latewood); see e.g. Keenan et al. [35], Denzler and Glos [13] and Brandner et al. [8]. With respect to knots and cracks,

a reciprocal relation is expected. Due to the very local formation of failure, the influence of these timber characteristics is expected to be low. Taking into account the very heterogeneous densities of the series compared and the comparable outcomes of C1 vs. C3 and C2 vs. C4, both pairs without and with reliefs, no clear influence of the board width on shear properties could be derived. In accordance with the results from tests on single CLT nodes [10], the influence of board width on the shear parameters was identified as low in the data evaluation, thus it is proposed to disregard this parameter for practical applications. 4.2.4. Board (layer) thickness This parameter was evaluated by comparing series B2 & B3 (to a limited extent also B5) as well as C1 & C3 and C2 & C4. With increasing layer thickness, a distinct decrease in net-shear strength could be identified. This is in accordance with results from tests on single CLT nodes, and apart from the tendency that the decrease of shear strength in CLT elements is slightly stronger ([10]; see Fig. 13). The observed relationship between board (layer) thickness and the shear strength can be attributed to the locking effect due to the orthogonal arrangement of layers, as well as the tendency of thicker boards featuring an increased proportion of timber prone to fail in the longitudinal-tangential shear plane, resulting in a lower shear strength, fv,LR, see Section 4.2.3. Another potential influence is the size effect of timber under shear stress, i.e. the zone available in which the shear failure (e.g. cracking) is likely to develop. Thicker boards exhibit a larger zone at their narrow faces featuring half-rift or rift orientation in addition to the circumstance that thicker boards, equal to wider boards, are usually cut close to the pith. This type of size effect is thus mainly attributed to a so called ‘‘structural size effect”. 12

fv,net,12,mean [N/mm²]

specimen in series A1 exhibited increased stiffness and a failure in gross-shear, followed by failure in net-shear. The parameters determined for series A1, fv,gross,12,05 = 3.4 N/mm2 (based on lognormal distribution) and G090,EN,12,mean = 650 N/mm2, are comparable to those of glulam GL24 h, according to EN 14080 [23], with fv,g,k = 3.5 N/mm2 and Gg,mean = 650 N/mm2. Although A1 is the only series with narrow face bonding, evident analogies with glulam as rigid composite support these comparable properties. Series A2 and A3, without narrow face bonding, like all other remaining series, failed in net-shear. The shear strength of series A2 and A3, compared to series A1 featuring narrow face bonding, is almost halved. The higher shear parameters of series A2 in comparison to series A3 can mainly be attributed to the unintended but common narrow face bonding of CLT with closed gaps due to the penetration of adhesive from the side faces into the gaps between the boards during the production process. Another effect is the activation of friction between the boards in contact. Current technical approvals allow gaps up to 4 or 6 mm. The resulting reduction in cross-section is, however, negligible for practical applications ( max[wgap]/min[w‘] = 6 mm/80 mm ?  8%). Although the higher shear properties could be attributed to CLT elements with closed gaps and/or narrow face bonding, this implies, however, that the closed gaps and even more the narrow face bonding are preserved throughout the lifetime of the structure. Cracks due to climatic changes are at least to be expected in the top layers.

fv,net,12,mean = 28.8 tℓ,fail –0.39

11

r² = 0.82

10

CIB EN C1; C3 C2; C4 B2; B3; B5 A2,5,9; A6,7,8

9 8 7 6 5 10

20

30

40

tℓ,fail [mm] Fig. 13. Net-shear strength vs. thickness of failed layer(s): average test values from single nodes [28]; CIB | B, C & EN | B, C, D) & CLT elements (selected series from groups A, B, C); power regression models.

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The shear values of the series within group A were lower compared to that of series within groups B and C. However, the relative differences between series featuring board thicknesses t‘ = 20 mm and 30 mm were comparable. A comparison of the series within group B showed that the shear strength of series B5 is unexpectedly low, accompanied by very low densities and unexpectedly high CV. Although specimen, test parameters, protocols and all results gained from this series where checked in detail, no reason for the low values could be identified. Therefore, this series has been disregarded when determining characteristic shear strength. For quantification of the relationship between shear strength and board (layer) thickness, average shear strengths of all series which reliably failed in net-shear, comprising tests on single nodes [28], [10] and herein presented tests on CLT elements, are illustrated in Fig. 13. For the description of size effects in timber engineering, power regression models are frequently applied. Such a model, weighted in respect to the number of tests per series, was calibrated to the data points and reflected a power of 0.39 (neglecting series B5) which outlined a very pronounced dependency of the average net-shear strength on the layer thickness. Calibration to 5%-quantile values gave a power of 0.38, only slightly lower than found for the average relationship. This underlines the necessity to take the influence of layer thickness into account in determination of characteristic values as well as in design procedures. 4.2.5. Number of layers A comparison of series A2 (three layers), A5 (five layers) and A9 (seven layers) showed, inversed to the density, a slightly concave relationship between the shear strength, fv,net,12, and the number of layers, N. It should be noted that the boards used within series A5 were delivered at a later stage; a corresponding influence cannot be excluded. Due to the relatively small differences between the series and the circumstance that all these elements failed in the cross layers, so that boundary effects can be excluded, the parameter ‘‘number of layers in CLT elements prone to net-shear failure in the cross layers” was evaluated negligible for practical applications. For CLT elements prone to net-shear failure in layers oriented in direction of top layers please see Section 4.2.7. 4.2.6. Stress relief For an assessment of this parameter, three pairs of series with/ without stress reliefs (C1 vs. C2, C3 vs. C4 and B3 vs. B4) were compared. Due to the local interaction of shear and torsional stresses in case of net-shear failure, it was expected that higher ratios of (t‘/a), in particular in cases where this ratio exceeds 0.25, lead to lower shear properties. Apart from one exception (B3 vs. B4), only small differences could be found in this comparison. Based on these outcomes, with respect to building practice and regarding the potential question of how to define individual shear parameters for CLT with stress reliefs, it is proposed to disregard this parameter. 4.2.7. Layup parameter In general, the layup parameter (ratio between the sum of layer thicknesses in weak plane direction to that in the strong plane P P direction; t‘,T/ t‘,L) of CLT elements featuring layer thicknesses t‘ = 20, 30 and 40 mm can exhibit 0.25–1.00. This study represents a range of 0.32–0.86. The results of the series of group A, grouped according to the thickness of the failing layer, t‘,fail, showed a progressive trend of gross-shear strength fv,gross,12 while the net-shear strengths, fv,net,12, were rather constant for given failing layer thickness, t‘,fail. This outlines that the net-shear strength does not directly depend on the layup parameter but, as demonstrated in Section 4.2.4, on the thickness of the failing layer. Series A4 exhibited comparatively low net-shear strengths. In this series, not the cross but the top and middle layers failed. CLT elements with layup parameters close to 1.0 can exhibit failure

of the top and middle layers; series A4 featured a comparatively high ratio of 0.86. Comparable outcomes were observed in a smaller test series comprising three specimen with layer thicknesses (from top to bottom) 20 | 30 | 20| 30 | 20 mm and layup parameter 1.0; see Dröscher and Brandner [16]. In this series two specimen failed in top and middle layers, whereas one specimen failed in the cross layers, suggesting a balanced failure probability in both plane directions. It is expected that the missing locking effect at the outer side faces of the top layers leads to a lower shear strength than observed from net-shear failures of equally thick cross layers. Taking these observations and the relationship between net-shear strength and thickness of the failing layer into account (see Section 4.2.4), as well considering the few test results currently available with CLT elements with top layers prone to fail in net-shear, a 20% reduction of net-shear strength should be considered, i.e. in top layers a net-shear strength equal to 80% of the shear strength of equally-thick core lamellas can be applied. For the design process, it is suggested to reduce the applicable top layer thickness by 20% instead of reducing the net-shear strength. 4.3. Shear modulus A comparison of the shear moduli from the test program determined with the approach in Eq. (19) and the approach given in EN 408 [20], Eq. (20), showed that the values determined with latter approach were on average about 10% higher. The reason is the imposed and considerably higher vertical deformation, caused by the deformation-controlled compression test setup, in comparison to the horizontal deformation. The approach by Kreuzinger and Sieder [39], Eq. (19), only takes into account the vertical deformation. Furthermore, the application of standardized values for E0, mean and E90,mean leads to higher CVs (+28%) for shear moduli according to Kreuzinger and Sieder [39] compared to shear moduli determined according to EN 408 [20]. A comparison between shear moduli within group D showed unrealistically high values for series D1 (a = 75°) and D5 (a = 15°). Without overrating these single realizations, these high values are the result of the restricted shear deformations caused by very steep middle layers (D1) and top layers (D5). Apart from this it should generally be discussed how both approaches, the approach of EN 408 [20] and that of Kreuzinger and Sieder [39], could be adapted to better eliminate the influence of deformations from other stresses than shear stresses. For the time being, the approach according to EN 408 [20] is preferred as it returns more stable results. Table 4 contains also values G090,CLT,mean,est for series without narrow face bonded CLT calculated with the formalism given in Bogensperger et al. [6], with G0;‘;mean

G090;CLT;mean;est ¼ with aT ¼ p





1þ6 aT

t ‘;mean w‘

q

t‘;mean w‘

2

and t‘;mean ¼

ð23Þ tCLT N

with G0,‘,mean as average shear modulus of the lamellas, t‘,mean = tCLT/ N as average layer thickness, p and q as parameters of function aT, see Table 5. Compared to G090,EN,12,mean overall congruent shear moduli, with deviations within ±10% and only for some series within ±20%, are found, apart from A3 (wgap = 5 mm). Fig. 14 shows a comparison between an effective shear modulus based on tests (average outcomes) and the mechanical model according to Bogensperger et al. [6], derived for CLT with gaps or cracks, without (N ? 1) and with consideration of boundary effects (N = 3, 5 and 7 layers). Apart from some series with stress reliefs (w‘ = a; a as edge distance or spacing between two or more reliefs in the same lamella) the results are overall coherent. Rea-

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R. Brandner et al. / Construction and Building Materials 147 (2017) 312–327 Table 5 Parameters p and q for aT from Dröscher [17].

Table 6 Variabilities of density and shear properties per producer (group); CLT without narrow face bonding.

No. of layers N [–]

3

5

7

p [–] q [–]

0.53 –0.79

0.43 –0.79

0.39 –0.79

CV[q12] [%] CV[fv,net,12] [%] CV[G090,EN,12] [%]

sons for additional stiffness, indicated by underestimated effective shear modulus in case of CLT with stress reliefs, are (i) the residual bridge at the groove of the relief, and (ii) the adhesive which unintentionally penetrated into the relief. 4.4. Discussion on homogenization and stochastic simulation studies 4.4.1. Discussion on homogenization of density As briefly outlined in Section 4.1, a distinctive homogenization can be observed in the density of tested CLT elements. The density values, with coefficients of variation 0.7%  CV[q12]  2.6%, on average 1.6%, are based on volume and mass taken from the whole specimen. Taking into account a reference lamella or board width of w‘ = 150 mm, overall and for each layer seven independent boards can be considered. With CV[q‘] = 8%, as coefficient of variation of density of boards/lamellas, and according to the Central Limit Theorem, the coefficient of variation of the density of CLT elements can be determined as

CV½q  CV½qCLT  ¼ pffiffiffiffiffiffi‘ffi 7N

ð24Þ

For N = 3, 5 and 7 this leads to CV[qCLT] = 1.7, 1.4 and 1.1%. Considering that two thirds of all specimen featured three layers, a good agreement between observed and calculated values can be stated.

40 mm / 80 mm

20 mm / 240 mm

0.10

C

1.6 4.0 8.3

2.2 4.7 9.0

4.4.3. Stochastic simulations for estimating variabilities of shear properties For estimating unbiased variabilities of shear modulus and strength of CLT elements without narrow face bonding, prone to fail in net-shear, a simple stochastic simulation was conducted. The basis was a reference CLT element with N = 5 equally thick layers, each with four boards (lamellas) and w‘ = 150 mm, representing the central shear field in tested CLT elements. Each board (lamella) was divided in four equally long segments; thus, each layer consisted of four times four nodes or 16 board segments. By assigning values of shear strength and modulus to each of these segments, a two-level hierarchical model was applied. This model, frequently used for timber and other hierarchical materials (e.g. [44,50,52,33,40,34,14,15,29,36], allows differentiating explicitly between variability of shear properties within and between boards. Equicorrelation coefficients, as ratio of variance within boards to total variance, of 0.40 and 0.50 for shear strength and shear modulus, respectively, as summarized for other timber properties in Brandner [9], were applied. The shear properties of the board segments were modelled as lognormal variates assuming CV[fv,net,segment] = 30% and CV[G090,segment] = 20%. Between shear strength and modulus a Pearson correlation coefficient of 0.60 was assumed. The shear properties, being system properties of the reference CLT element, were determined by simulating a system of parallel and serial interacting nodes and board segments, assuming linear-elastic material behavior and global load sharing (GLS). The simulations comprised two steps: In the first step, the parallel, and in the second step the serial interaction between elements and sub-systems was addressed. Firstly, as net-shear failure in such CLT elements can only develop in the cross layers and only when all cross sections of all cross layers along a gap between the longitudinal layers exceed their resistance against shear, the number of parallel acting elements is given as the number of boards in the top layer times the number of boards in the cross layer (equals the number of nodes) times the number of cross layers, in the reference case as 4  4  2 = 32. Secondly, as net-shear failure

model | N → ∞ model | N = 3 model | N = 5 model | N = 7 /

B

product properties that become independent of the producer; see also Kohler et al. [37].

tests | N = 3 without / with reliefs tests | N = 5 tests | N = 7

lower limit

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.01

upper limit

G090,CLT,mean,est / G0,ℓ,mean [–]

4.4.2. Influence of producer on variability of properties Testing CLT elements from three producers predestines investigations on potential differences. As shear properties, in particular average values, are influenced by the set parameters, in this comparative investigation only variabilities are treated; see Table 6. Between the three producers (groups) overall congruent coefficients of variation are found. However, differences in the average values, e.g. as observed for density, have an influence on the overall coefficients of variation representing the population ‘‘CLT made of Norway spruce boards of nominal strength class C24 according to EN 338 [18]”. This circumstance requires more general discussions on how these aspects can and should be dealt with in the design of engineered structures. For CLT and other engineered timber products this circumstance outlines the necessity to harmonize the production process and base material used to guarantee very homogeneous

A 1.6 5.0 7.7

1.00 0.95 0.90 0.85 0.80 0.75

1.00

tℓ,mean / wℓ [–]

10.0

0.70 0.10

1.00

tℓ,mean / wℓ [–]

Fig. 14. Effective shear modulus in-plane of CLT with gaps or cracks vs. geometric ratio t‘,mean/w‘: model from Bogensperger et al. [6] compared to average values from test program (excluded series: A3 & B5); (left) overview; (right) outcomes in detail.

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can develop along several gaps, the number of serial acting parallel sub-systems is given as the number of boards in the top layer plus one (in reference case 4 + 1 = 5). For each parameter setting, 10,000 systems were generated and statistics of system properties determined. A sensitivity analysis on this stochastic model, performed with focus on CV[fv,net] and CV[G090], reflected a dependency on CV[fv,net,segment] and CV[G090,segment], to some amount also on N, but negligible for equicorrelation and Pearson correlation coefficients. Given N = 3, 5, 7 values for CV[fv,net] = 8.5, 6.2 and 5.1% were found. These values are comparable to values found by testing although the specimen within one series were consecutively taken from the same CLT element. Reasons for the low influence of applied sampling approach on statistics of variability are the heterogeneity induced by finger-jointing board segments to lamellas, the orthogonal layering, and variation indirectly caused by the 45° rotated positioning of specimen in produced CLT elements. In view of these outcomes and the distinctive non-linear behavior of CLT failing in net-shear, which is not taken into account in the simulation but has a positive effect on net-shear variability, overall a value CV[fv,net] = 6.0% is suggested. However, additional variation in shear properties of CLT elements, i.e. caused by varying process parameters, are not considered, neither in testing (within one series) nor in the stochastic model. For CV[G090], given N = 3, 5 and 7, values of 3.6, 2.6 and 2.1%, were found. These values were much lower than observed from tests but correspond to typical outcomes known from testing glulam beams featuring a comparable cross section in bending. Reasons for the high coefficients of variation in tested series are given in Section 4.1. For the in-plane shear modulus of CLT with/ without narrow face bonding consideration of variabilities equal to glulam appears applicable. 5. Design proposal The results of the test series described in the preceding sections have shown that the main parameters influencing the shear properties are the layer thickness, t‘,fail, (decreasing properties with increasing thickness) and the gap execution (narrow face bonded (edge-glued), not narrow face bonded (not edge-glued) and without/with gaps, with decreasing properties in mentioned order); see Table 7. The distinct relationship between layer thickness and net-shear strength leads to a dependency of the calculated gross-shear strength on the layup parameter. Therefore, the most practical approach for CLT elements prone to fail in net-shear would be to define a design concept based on the net-shear strength and the associated layers prone to fail. Such a concept would allow for a design independent of the above mentioned layup parameter. In addition, it would mirror the approach applied for the verification of longitudinal stresses in CLT elements under in-plane loads. Based on presented test outcomes and results from stochastic simulations, a characteristic reference net-shear strength of fv,net,k,ref = 5.5 N/mm2 is proposed. Here, layer thicknesses up to 40 mm and gap widths up to 6 mm are taken into account. For layers in weak plane direction with thicknesses between 20 mm  t‘,fail < 40 mm and without gaps or reliefs, higher strength values are expected. Also taking into account the results from single CLT nodes [10], the relationship

h i f v;net;k ¼ f v;net;k;ref min ð40=t‘;fail Þ0:4 ; ; 1:3

ð25Þ

according to the average weighted power regression model described in Section 4.2.4, is proposed. In case of CLT elements in which the sum of layer thicknesses oriented transverse to the top P layers ( t‘,T) exceeds 80% of the sum of layer thicknesses oriented P in direction of top layers ( t‘,L), indicating a potential failure of the

Table 7 Impact of investigated parameters on shear properties: qualitative summary. Parameter

Investigated range

Impact on fv,net

Impact on G090

Layer no. Layup param. Gap exec. Board thickness Board width Stress reliefs

{3; 5; 7} {0.32–0.86} {NFB; wgap {0; 5 mm}} {20; 30; 40 mm} {80; 160; 240 mm} {Y; N}

0 0 << << 0 0

0 0 < < >> 0

P P top and middle layer(s), i.e. t‘,T/ t‘,L  0.8, verification of netshear has to be met for both plane directions. The reason is the potential failure of the weaker top layers. In doing so, a reduced shear resistance of the top layers, considered by a 20% reduction of applicable top layer thickness, following the approach in Section 4.2.7, shall be considered, i.e. only 80% of the top layer thickness shall be applied. For CLT elements that are expected to fail in net-shear, the verification of torsional stresses, i.e. the potential failure between two layers in the vicinity of the adhesive bond, has to be met, in addition to the verification of net-shear. Following Schickhofer et al. [46], i.e. considering a characteristic torsional strength fv,tor,k = 2.5 N/mm2 in combination with the proposed values for fv,net,k presented in this paper, it can be concluded that the torsional failure mechanism can potentially govern only in cases of CLT diaphragms featuring a ratio between board thickness to board width/ spacing or edge distance of reliefs, (t‘/w‘) or (t‘/a), exceeding 0.25. In CLT elements with lamellas featuring equal widths but heterogeneous layer thicknesses, the thickest layer governs the design in torsion. This is because the shear stress in torsion depends on the geometric ratio (t‘/w‘) or (t‘/a). The shear modulus of CLT elements without narrow face bonding can be determined according to Eq. (18); see Bogensperger et al. [6]. For simplification, a value of G090,mean = 450 N/mm2 is proposed. For CLT elements with expected gross-shear failure, verification on the basis of gross-shear strength and assuming the full element thickness, tCLT, is feasible. For such elements, the shear properties known from glulam, fv,gross,k = 3.5 N/mm2 and G0,mean = 650 N/ mm2 are proposed. This necessitates, however, the consideration of potential influences during the lifetime of the structure, e.g. crack formation and delamination. Consequently, the narrow face bonding and the uncracked state shall be preserved throughout the lifetime of the structure. Cracks due to climatic changes are at least to be expected in the top layers. The approach given in EN 1995-1-1 + A1 [22], implying the reduction factor kcr to take into account shrinkage cracks in solid timber and glulam, could be translated to narrow face bonded CLT elements. Following this approach, the cross-section utilized for verification, Ashear, would be reduced by a certain proportion of the top layer thickness, hence by considering only 50% of t‘,TL. For some layups, this approach, which focuses on CLT in use, can lead to lower resistances compared to CLT without narrow face bonding. Reasons are differences in the resistances in net- and gross-shear, as consequence of significantly different failure modes, as well as system and size or volume effects for shear, which are not taken into account for grossshear failures in this proposal. Additional investigations to better quantify this approach are required. Securing the full potential utilization of the core layers over the lifetime of the structure implies as well, that the load-carrying capacity of the narrow face bond, i.e. the certified applicability of the utilized adhesive and the correct execution of the bond, is ensured and controlled. Further research could include a comparison of shear properties of intact narrow face bonded specimen to narrow face bonded specimen featuring pronounced shrinkage cracking.

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Table 8 Design concept for CLT diaphragms with/without narrow face bonding under shear; basis: Norway spruce, lamella/board strength class C24 acc. to EN 338 (2009). Narrow face bonded CLT

CLT without narrow face bonding

failure: gross-shear

failure: net-shear torsion

basic properties

basic properties for t‘,fail  40 mm & wgap  6 mm


fv,gross,k = 3.5 N/mm2
G090,mean = 650 N/mm2

gross-shear: Ashear
Ashear = [tCLT – t‘,TL] wCLT


fv,net,k = fv,net,k,ref min[(40/t‘,fail)0.4; 1.3] with fv,net,k,ref = 5.5 N/mm2
fv,tor,k = 2.5 N/mm2
G090,mean = 450 N/mm2 or acc. to Eq. (23) net-shear: Ashear P P t‘,T/ t‘,L < 0.8 P Ashear = t‘,T wCLT, with t‘,fail = max[t‘,T,i] P P
for t‘,T/ t‘,L  0.8 P (i) Ashear = t‘,T wCLT, with t‘,fail = max[t‘,T,i] P P (ii) Ashear = (0.8 t‘,TL + t‘,ML) wCLT, with t‘,fail = max[t‘,L,i]


for

torsion: Ator & verification acc. to Eq. (21); see Bogensperger et al. [6] note: load-carrying capacity of narrow face bonding shall be secured over the whole lifetime

note: verification against torsion only required in cases of (t‘/a) or (t‘/w‘) > 0.25

Vk . . . characteristic shear force in-plane [N; kN]. Ashear . . . cross section applied in verification [mm2].

A summary of the proposed design concept for CLT with/without narrow face bonding is provided in Table 8. For notation of parameters, reference is given to Fig. 5. 6. Conclusions The novel shear test configuration, given in Kreuzinger and Sieder [39], was successfully applied to the full spectrum of tested configurations, demonstrating its functional and operational efficiency and reliable shear failures of all tested CLT diaphragms. All specimen with layers of boards bonded at their narrow faces (edge-glued) failed in gross-shear followed by a net-shear failure. All specimen without narrow face bonding failed in net-shear. Consequently, we propose this robust and reliable test configuration for implementation in EN 16351 [25] or an appropriate test and evaluation standard. The examination procedure, originally intended for determining shear properties from CLT elements failing in gross-shear, was slightly amended and extended for calculating in-plane shear properties also for CLT elements failing in net-shear. It is proposed to include the presented conclusive examination procedure, by considering all three potential failure mechanisms of CLT diaphragms under shear stress, in EN 16351 [25] or an appropriate test and evaluation standard. Regarding the investigated parameters, qualitatively congruent results to experiences made on single CLT nodes were achieved. Gap execution and board/layer thickness were identified as the main influencing parameters for both, in-plane shear strength and shear modulus. Based on herein presented outcomes and appreciating characteristic shear properties of previous investigations, for net-shear: fv,net,k,ref = 5.5 N/mm2 and G090,mean = 450 N/mm2, and for grossshear: fv,gross,k = 3.5 N/mm2 and G090,mean = 650 N/mm2, are proposed. Their incorporation together with size effect models in [25] is recommended. Based on previous observations and experiences made during this comprehensive joint research project, its results, as well as already existing approaches given in current European Technical

Approvals for CLT products, a conclusive and practicable design concept was derived. This concept differentiates explicitly between CLT elements prone to fail in net-shear and elements prone to fail in gross-shear and takes into account a reduced resistance of narrow-face bonded CLT elements caused by shrinkage cracks that are to be expected at least in the top layers. The design concept for net-shear, as presented in Table 8, leads to degrees of utilization comparable to the design procedure presented in Bogensperger et al. [6]. Because of its ease of use, mirroring also the design of CLT diaphragms in case of normal stresses, we propose to include this design concept in Eurocode 5 [22]. The presented characteristic in-plane shear properties derived for CLT diaphragms can also be applied in the design of CLT beams exposed to in-plane shear stresses. It is recognized that the shear stress distribution over the cross section in CLT beams differs from that in CLT diaphragms, and that the peak shear stresses in CLT beams apply more to single nodes. However and following the conclusions in Brandner et al. [10], the characteristic shear properties for single nodes shear compare well with the shear properties of CLT diaphragms. It is rather a question of what base material properties should be considered in particular in CLT beams randomly cut from larger CLT elements. In such cases there is a high probability that the lengthwise cuts parallel to CLT layers, mainly responsible for load bearing, are not in the gap between but rather within lamellas. The position of this cut significantly affects the residual resistance of these lamellas and hence of the whole CLT beam. In any case, a quadratic parabolic shear stress distribution over the depth of such beams should be considered. 7. Outlook Considering in-plane shear of CLT diaphragms, there are some points which leave space for additional investigations. There is still some lack of knowledge with respect to the locking effect which accounts for half of the power parameter of the power regression model derived and used for adapting net-shear strength, fv,net, with respect to t‘,fail (see [10]). This statement also holds for the more distinctive decrease of fv,net with increasing t‘,fail in CLT elements

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compared to CLT nodes. Secondly, so far only two test series are P P available that cover the ratio t‘,T/ t‘,L > 0.8 leading to netshear failure of top and middle layers instead of the most common failure of the cross layers. Limited knowledge about the influence of the missing locking effect at the outer side faces of top layers is the reason for the proposed 20% reduction of strength or top layer thickness in design. Although this reduction is conform to test outcomes it misses a stronger database as well as mechanical basis. Another question is the influence of shrinkage cracks, system as well as size and volume effects on the gross-shear strength and modulus of CLT featuring narrow face bonding. Although the authors are currently not aware of producers offering CLT featuring narrow face bonding in all layers by using adhesive systems certified for load-carrying purposes, it might become a question of relevance for future CLT productions. In general, it is seen of utmost importance to proceed with standardization and harmonization of CLT as a structural building product. Advances in harmonizing the layer thicknesses have already been achieved. Apart from harmonizing layups, as relevant for technical specifications, construction tenders and design procedures, it is also required to harmonize the production processes, quality assurance procedures and the base material used for CLT. This to enable regulating reliable and robust characteristic CLT properties in- and out-of-plane, making CLT competitive vis-à-vis to mineral based solid building products, like concrete and masonry, without leaving the focus on meaningful fields of application; this to push further the initiated renaissance of timber in our cities, in our built environment.

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Acknowledgements This research project originated from a cooperation project between the holz.bau forschungs gmbh, in the frame of the FFG COMET K-Project ,,focus_sts‘‘, the Graz University of Technology, Institute of Timber Engineering and Wood Technology, and the Technische Universität München (TUM), Chair of Timber Structures and Building Construction, in cooperation with the Glued Laminated Timber Research Association inc., Wuppertal. The support by the funding bodies and project partners as well as the funding of a short-term scientific mission in the frame of COST Action FP1402 is gratefully acknowledged.

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