Modelling and testing of CLT panels for evaluation of stiffness Master Thesis

(1)

Modelling and testing of CLT

panels for evaluation of

stiffness

Master Thesis

Authors: Sebastian Svensson Meulmann Egzon Latifi

(2)

(3)

Acknowledgement

Many people have contributed to making this work what it is. We would like to thank Associate senior lecturer Min Hu for her help with the software Abaqus, Research engineer Anders Alrutz for his help with the four-point bending tests, Lecturer Whokko Schirén for her help with the DIC-testing and Senior

specialist Dr. Kristoffer Segerholm of Södra for investigations on wood material and manufacturing of CLT elements for testing. Our special thanks go to our main supervisor, Professor Anders Olsson who has helped us all along the way. Your ambition and drive really helped to motivate us to make this work as good as possible.

We have learned a great number of things related to both CLT, and also research in general. We look forward to seeing what this research can be used for in the future.

(4)

Abstract

The use of timber in building structures is steadily increasing. cross laminated timber (CLT) is an engineered wood product made of an uneven number of layers of lamellas glued at an angle of 90 degrees to each other. This gives CLT high stiffness and strength to bending in all directions, and capability of taking load both in-plane and out-of-plane. Due to the large size of CLT elements, they allow for quick assembly of strong structures. Due to both economic and environmental reasons it is important for producers of CLT to optimize the use of the wood material by using the timber with higher stiffness and strength where it is most needed. This thesis is about evaluating the bending and shear stiffness of CLT elements, when used as plates, depending on the quality of wood used in the different layers. Four-point bending tests are carried out on elements of different compositions and a parametrized finite element model is created. Thus, the model is validated on the basis of experimental tests to evaluate the influence of different quality of different layers. The measured dynamic MoE proved to have good potential to be used as the longitudinal bending stiffness in an FE-model, with a deviation from the experimental tests of less than 1%. There is a strong correlation between the bending stiffness and bending strength of the plates. The effective rolling shear modulus in pine was calculated to be around 170 MPa for pine of dimension 40 x 195 mm2_{. Grading} the boards into two different classes used for different layers proved to increase the MoE of the plates by 11-17% for 3- and 5-layer CLT.

Keywords: Cross-laminated timber (CLT), Four-point bending, Bending

(5)

5.3 Potential element bending stiffness by optimized utilization of lamellas 56 5.3.1 3-layer CLT Package 1 ... 57 5.3.1.1 Non-sorted ... 57 5.3.1.2 Sorted ... 57 5.3.2 5-layer CLT Package 1 ... 58 5.3.2.1 Non-sorted ... 58 5.3.2.2 Sorted ... 59 5.3.3 3-layer CLT Package 2 ... 59 6 Discussion ... 61

6.1 Use of dynamic MoE as longitudinal stiffness in FE-model ... 61

6.2 Effective rolling shear modulus in the centric layer ... 61

6.3 Influence of timber grade sorting ... 61

6.4 Evaluation of strength ... 62

6.4.1 Relation between bending stiffness and strength ... 62

6.4.2 Rolling shear strength ... 62

6.5 System effect ... 63

6.6 Sources of error ... 63

6.6.1 Four-point bending test ... 63

6.6.2 FE-model ... 64

6.7 Future work ... 64

(7)

1 Introduction

This chapter will give a short introduction to cross laminated timber (CLT) as a construction material and the current use and further prospects. The aims and purposes of this work will also be presented along with the limitations.

1.1 Background

In a world that is constantly growing and developing, in terms of population and material standard, alternative solutions to problems that were previously solved by using non-renewable materials to a high degree need to be solved in a more sustainable manner. This is necessary in order to make sure that the needs in today’s society are, to the highest possible degree, met without the use of non-renewable materials. Not only does a dependency on non-renewable materials eventually result in a scarcity of materials, but extraction and production of these materials also causes emissions of greenhouse gases. The building and construction sector accounts for 39% of the energy use and process-related CO2 emissions worldwide, of which 11% comes from manufacturing of building materials such as steel and cement (IEA, 2019). Since construction materials need to be available for building, more sustainable materials need to be used to fulfill sustainability goals.

Wood is a well-known construction material that has been used all over the world throughout history. However, as science progressed in the 20th_century, materials such as reinforced concrete became more and more commercially available and inexpensive, wood as a construction material fell out of favor (Schickhofer, et al. 2010). One main factor that caused this was that that the resistance to fire was better in material such as reinforced concrete. As the issue of climate change has become more prevalent, the minimization of reliance of non-renewable sources has become more sought after and timber has once again become an important material for construction. It is the only material for construction that is renewable (Svenskt trä, 2020).

(8)

to be distributed over the element, thereby minimizing local points of weakness. This is referred to as the system effect.

1.2 Problem description

The global usage of CLT increases at a very high rate (Muszynski et al. 2017) and it becomes increasingly important to optimize the use of the wood material to produce strong and stiff CLT elements, at a minimum use of raw material. It is evident that this can be accomplished by placing the timber with best

mechanical properties in the outermost layers of the CLT panels, as this increases the stiffness and strength to out-of-plane bending, which is a very important property for CLT. Today, however, the same grade of wood is often used for all layers which means that there is potential for improvement and utilization of the wood material. However, optimized design of CLT-elements requires knowledge of the statistical distributions of the important mechanical properties of the available wood material, as well as models by which

knowledge of lamella properties can be transferred to mechanical properties of CLT-elements.

1.3 Purpose and aims

The purpose of the thesis is to contribute to better utilization of raw material in production of CLT-panels. The aims are to evaluate, and suggest a way to increase, the effective bending stiffness of CLT elements. This will be done by experimental examination of CLT-elements, manufactured of lamellas with known stiffness properties, and by creating a finite element model by which experimental tests can be simulated and statistical parameter studies performed. Specific objectives are to:

- Investigate if the dynamic MoE of lamellae can be used for longitudinal MoE in the layers of a finite element model of a CLT-element, i.e. investigate if simulations using the model give the same stiffness to bending as corresponding experimental bending tests do, or if the model must be calibrated.

- Evaluate, using the FE model and experiments, the effective rolling shear modulus of the timber used in transversal layers of investigated CLT-elements.

- Show the potential to increase the effective bending stiffness of three- and five-layer CLT-element by grading lamellae in two different grades, one with higher and one with lower dynamic MoE.

- Investigate experimentally the relationship between stiffness and strength of narrow three-layer CLT-plates.

- Evaluate the impact of the system effect in the CLT-plates, when using a varying number of lamellas in the longitudinal direction.

1.4 Limitations

(9)

Experiments will only be carried out through a four-point bending test.

(10)

2 Theory

This chapter will give the theoretical background for this thesis work. It begins with a short summary of the main terminology to familiarize the reader to the context and facilitate further reading and understanding of the work. This is followed by a short introduction to CLT as a material, to the calculation methods used herein and to the relevant standards. Thereafter, an introduction to finite element modeling is given. The last part of this chapter gives a summary of the literature that has been studied in preparation for the present work.

2.1 Terminology

Bending stiffness An elements resistance against bending deformation.

Coefficient of variation The ratio of the standard deviation and the mean value of a sample.

Cross-laminated timber Timber lamellas glued together in layers cross-wise to each other, often referred to as CLT in this thesis work. Degrees of freedom (DOF) Number of values in a node (of a

calculation model) free to vary.

Digital image correlation (DIC) Image tracking often used to determine strains and deformations in a material. Failure mode The mode in which the material breaks

(bending, rolling shear etc.).

Finger joint A type of joint used in woodworking to interlock two pieces of wood.

Four-point bending A test setup with two point loads and two supports creating a section with pure bending between the point loads. LVDT sensor Device used to convert mechanical

motion into a variable electrical current. Mean value The central tendency of a set of values Modulus of elasticity (MoE) A materials ability to resist elastic

deformation

(11)

Pith The original tree stem at the center of the log. It is surrounded by wood of poor structural characteristics.

Poisson’s ratio The ratio of the transversal strain to the axial strain in uniaxial loading.

Rolling shear failure Cracking due to shear strains in directions perpendicular to the wood fiber direction.

Shear modulus A materials ability to resist shear deformation.

Shear stiffness An elements resistance against shear deformation.

Softwood Wood from gymnosperms often grown quickly (e.g. spruce and pine)

Standard deviation Measurement of the variation of a set of values

Timoshenko beam theory A beam model taking shear

deformation into consideration and thus being suitable for beams with large height to length ratio.

2.2 Cross laminated timber

Cross laminated timber (CLT) is an engineered timber product consisting of an uneven number of layers glued crosswise to the next layer. This creates a high dimensional stability in plane due to the minimization of swelling and

shrinkage (Brandner et al. 2016).

CLT is a versatile building material with many different applications thanks to its many different ways of composition. 3- and 5-layer CLT is mostly used in walls and floors while a larger number of layers is more suitable for bridge decks and flooring (Brandner et al. 2016). The large dimensions of CLT makes it highly viable to be used in markets that were previously dominated by mineral-based construction material.

(12)

CLT is mainly used as large surface panels in floors and walls, the high stiffness and load-bearing capacity also makes the panels useful as stabilizing elements of a structure (Swedish Wood 2019). The CLT-handbook lists many useful properties of CLT, such as: High strength to self-weight ratio, good dimensional stability and good load-bearing capacity in fire. Besides this, CLT is highly flexible in its production which allows many different shapes to be produced, such as curved surfaces.

CLT is generally produced within the thickness span 80-300 mm but can be produced in other dimensions if this is necessary. The most common width of CLT-panels is in the range 1.2-3.0 m. The number of layers can be set to up to 25, but the most common amount is 3, 5, 7 and 9. The timber strength classes used are normally in the span C14-C30 (Swedish Wood 2019).

2.2.1 Material properties of CLT

Because of how CLT is manufactured, the material properties of the individual boards even out over the whole plate. This means that the strength properties are highly dependent on the cross section of the plate (Swedish Wood 2019). For CLT the most important properties for ultimate load are the tensile strength in the outermost layers and the effective rolling shear modulus in the mid layers. In the same way, the very most important property for the effective bending stiffness is the tensile stiffness of the lamellas in the outermost layers. Another rather important stiffness parameter is the effective rolling shear stiffness of the lamellas in the mid layers.

2.2.2 Effective bending stiffness of CLT

A study by (Fellmoser & Blass 2004) tested the rolling shear modulus influence on strength and stiffness of bonded timber elements. The results gathered showed that elements with a span to depth ratio off less than 30 were influenced by the rolling shear modulus when analyzing the effective bending MoE. The influence was increased the lower the ratio between the span and depth got. As this ratio increased the influence of the rolling shear modulus could be neglected and the effective bending stiffness was close to the pure bending stiffness.

2.2.3 System effect

(13)

accurate result. This factor is based on how many individual boards there are in each layer, where more layers create a higher system effect and more

homogenized layer. The system effect is more obvious in terms of bending strength and tension strength where multiple parallel boards can co-operate. The CLT have higher characteristic strength because more than one board is exposed to bending or tension at the same time (Swedish Wood 2019). The system effect, 𝑘_!"! is the minimum value of the equations below (Swedish Wood 2019):

𝑘𝑠𝑦𝑠= min"_{1 + 0.1𝑏}1.15 (1) where b is the width of the element cross section in meters.

2.3 Hand calculations

The CLT handbook (Swedish Wood 2019) contains construction standards that refer both to European standards and Eurocodes in a more condensed way only applicable for CLT-elements. Besides providing ways of checking different stresses, to make sure the element can withstand the applied stresses, it also includes general information about CLT as a material.

2.3.1 Prediction of maximum load capacity

Hand calculations can be performed to predict the maximum capacity to point loads in, for example, a four-point bending test.

The following design criteria are considered in this work:

In-plane bending stress

𝜎𝑚,𝑥,𝑑= 𝑀𝑥,𝑑 𝑊_{𝑦,𝑛𝑒𝑡}≤ 𝑓𝑚,𝑦𝑙𝑎𝑦,𝑑 = 𝑘𝑠𝑦𝑠∙ 𝑘𝑚𝑜𝑑 ∙ 𝑓_{𝑚,𝑦𝑙𝑎𝑦,𝑘} 𝛾_𝑀 (2) where:

𝑀",$ moment design value about the y-axis

𝑊_%,&'( panel’s net moment of resistance 𝑓_),*,%+,",$ bending strength design value 𝑓_),*,%+,",- characteristic bending strength

𝑘!"! system factor

𝑘_).$ modification factor

𝛾/ partial factor for the material

(14)

𝜏0,%1,$ =2!,#$%₅ ∙4!&,'

!,#$%∙6! ≤ 𝑓0,7*,"+,",$ = 𝑘).$∙

8(,)*),+,-+,.

9/ (3)

where:

V_:;,< design shear force

S:,=>? panel’s net static moment

f_@,7*,ABCA,< design value for the longitudinal shear strength of the boards

f@,*7*,ABCA,D characteristic longitudinal shear strength of the boards

kEF< modification factor

γ_G partial factor

Rolling shear strength perpendicular to the grain

𝜏./,01,2= 3-,.,/01∙5.2,3 6_.,/01∙7_. ≤ 𝑓/,8989,:;<0,2 = 𝑘=>2∙ ?4,5656,789.,: @_; (4) where:

𝑉"1,$ design shear force

𝑆_H,",&'( panel’s net static moment

f_{@,7*7*,:BCA,<} design value for the rolling shear strength of the boards

f_{@,7*7*,:BCA,D} characteristic value for the rolling shear strength of the boards

2.3.2 Dynamic E-modulus

The following equation is used to determine the lamellas elastic modulus at 12 % moisture content:

𝐸20A.C>DD= 𝐸20A41 −EFGHI_H99 6 (5) where:

𝐸20A= 4 𝜌 𝐿I 𝑓I (6)

where:

(15)

𝑓 axial resonance frequency of the lamella [Hz] 𝑀𝐶 moisture Content [%]

2.3.3 Shear strain

When the plate is exposed to a four-point bending test the shear force, i.e., the sum of shear stresses over the cross section, will be constant, i.e., independent of the position, between the support and the point load. Thereby the

displacements of four different positions or nodes within one layer of the plate can be picked to determine the shear stress in that layer as

𝜏:0= 𝐺:0 𝛾:0 (7)

where Gxy is the effective shear modulus and the engineering strain γ:A is

calculated as

𝛾:0=<<_2:G<=+<>₂₀G<? (8) in which a1, a2, a4 and a5 are displacements and dx and dy are distances as defined in Figure 3.

If the shear stress varies over the section, a mean value over the sections area can be used for evaluation. If the shear stress is constant over the section, a single element within the section (not too close to a support or point load) can be analyzed since the shear deformations will be nearly identical for all elements within the section. The location of the nodes and behavior of an element is shown in Figure 1.

Figure 1: Infinitesimal element with deformation from shear stresses.

2.4 Four-point bending test

(16)

distance from the support on each side creating a symmetric loading. This creates three different sections on the testing piece where the section in the center is subjected to pure bending while the two outermost sections are subjected both to shear forces and to bending, see Figure 2 and Figure 3 for a graphical description of this.

Figure 2: Shear force diagram of a four-point bending test. The shear force between the loads is zero.

Figure 3: Moment diagram of a four-point bending test. The moment is distributed linearly in the first and last section while the maximum moment is constant in the

center.

When analysing the local stiffness, the section where pure bending is acting is considered. For the global stiffness, the entire plate or beam is considered.

2.4.1 SS-EN 408

(17)

2.4.1.1 Determination of local and global modulus of elasticity

For determination of local modulus of elasticity, the following lay-up is proposed, see

Figure 4

.

Figure 4: Lay-up for determining local modulus of elasticity in bending according to SS-EN 408.

The local modulus of elasticity can then be calculated with the following expression:

𝐸𝑚,𝑙=

𝑎𝑙₁2(𝐹₂−𝐹₁)

16𝐼(𝑤₂−𝑤₁) (9)

where

𝐹_K− 𝐹_L load increment with correlation coefficient of 0.99 or better [N]

𝑤K− 𝑤L the increment corresponding to 𝐹K− 𝐹L [mm]

(18)

Figure 5: Lay-up for determining global modulus of elasticity in bending according to SS-EN 408.

The global modulus of elasticity is then determined by the following expression: 𝐸𝑚.𝑔 = 3𝑎𝑙2−4𝑎3 2𝑏ℎ3!2𝑤2−𝑤1 𝐹2−𝐹1− 6𝑎 5𝐺𝑏ℎ"

(10) where

𝐹K− 𝐹L the load increment with correlation coefficient of 0.99

or better [N]

𝑤_K− 𝑤_L is the displacement increment corresponding to 𝐹_K− 𝐹_L [mm]

𝐺 is the shear modulus [MPa] 2.4.1.2 Inclusions in the test report

In order to make the test easy to comprehend and repeat, information has to be given about many different specific details of the test piece and the methods. The information that should be given according to SS-EN 408 are listed below:

Information about the test piece:

a) Description of the test piece and specification of quality and species etc. b) Dimensions, type of glue used and number of laminations.

(19)

f) Other information that could affect results.

Information about test method:

a) Reference of test methods applied.

b) Temperature and relative humidity at the time of testing. c) Description of equipment used and testing device. d) Other information that could affect results.

Information about test results:

a) Moisture content at time of testing. b) Actual dimensions.

c) Strength and/or stiffness values. d) Failure mode and location of cracks. e) Time to reach maximum load.

f) Other information that could affect results.

2.4.2 CEN-EN-16351

CEN-EN-16351 is a draft not yet accepted by the CEN board. It contains guidelines mainly applicable for laboratory testing on CLT-elements.

(20)

Figure 6: The layup according to CEN-EN-16351. F/2 is a point load which is applied in two different points with 6h between. The local displacement is measured at a distance of 5h and the span between the support and the force can vary between

9h-12h.

This set-up shall be used when applying the following formula to determine the bending stiffness: (𝐸𝐼)FV,;>W<;,AXY= 𝐸;>W<; 𝐼FV,7XY= ;=∙;? = HZ [₌G[_? \=G\? (11) Where:

(EI)MN,BFOCB,=>? bending stiffness of the CLT element [NmmK]

I_MN,P>? moment of inertia considering layers parallel to the span [mmQ_]

E_BFOCB modulus of elasticity [MPa]

lK distance between the force and closest support [mm]

l_L gauge length for w_BFOCB [mm] FL, FK point loads on the plate [N]

w_L, w_K displacements corresponding to the loads F_L, F_K [mm] If rolling shear failure is to be avoided, the span between the supports and loads can be increased. 15 specimens should be tested for all strength classes of timber layers.

(21)

If the test pieces have a moisture content of 𝑢 = (12 ± 3) % the tests can be made without conditioning the specimens.

Test report should be given as basis of EN 408 where relevant information such as layup of specimen, test setup, testing and analysis of results should be included.

2.4.2.1 Governing assumptions in CEN-EN-16351

The following assumptions should be considered when determining the strength, stiffness and density properties of layers from full scale tests:

a) Calculations are done with net cross sections, cross layers are disregarded. b) Bonds shall be taken as rigid, non-structural edge bonds shall be taken as

non-existent.

c) Linear elastic theory shall be considered. d) Timoshenko beam theory shall be applied.

2.5 Finite element modeling

The finite element method is a numerical method to solve differential equations in an approximate manner (Ottosen & Petersson 1992). The differential

equations are assumed to be valid for a certain region which can be 1-, 2- or 3-dimensional. The differential equations are applied to finite elements within the specified region and approximated for each element. By dividing the region into finite elements, linear or other approximations that might not be very accurate over the entire region will be more accurate if the linearity is only assumed within the elements themselves. This means that each element has an approximation which might not be very accurate for the element itself but will give a decent approximation for the entire region once the elements have been bound together (Ottosen & Petersson 1992).

2.5.1 Monte Carlo simulation

The Monte Carlo simulation is a mathematical tool that can be used to verify a model. The method is used among different systems such as financial, physical and mathematical models. The process is that a randomly generated input, N is picked, the simulation is then performed and result is extracted. The simulation will then restart with new random input, N parameters. The number of

(22)

2.6 Digital image correlation

By digital image correlation (DIC) the displacements of points on the surfaces of an object can be followed as function of loads applied on the object. Aramis is a 3D DIC measurement system for static and dynamic testing. The software is able to establish coordinates on a 3D-surface, but also calculate 3D-strains, velocities and how strains vary over the object surface. Aramis also includes a function which can verify FE-analysis, deciding the material parameters (Cascade 2021).

The software identifies points on the object surface with a specific resolution. The points on the object will be followed in the software making it possible to calculate stress- and deformation related values over the field.

2.7 Literature review

In the study “Shear Stress and Interlaminar Shear Strength Tests of Cross-Laminated Timber Beams” by Lu et al. (2018), the authors calculated

interlaminar shear stresses for three different types of CLT-plates; three-layer, five-layer and seven-layer. The short span beams were subjected to a three-point bending test which resulted in three different failure modes,

perpendicular layer rolling shear failure, interlaminar shear failure and parallel layer bending failure. The method of using a three-point bending test for short span beams effectively tested the strength to rolling shear failure. Some of the failure modes found in this study were confirmed by the paper

“Cross-laminated Timber Plates Subjected to Concentrated Loading” by Hochreiner et al. (2014). The failure modes found inside the plate were, shear failure, tensile failure and delamination. The rolling shear modulus turned out to highly affect the overall stiffness of the plate.

A study carried out by Zhou et al. (2014) concluded that the design of CLT is strongly influenced by the rolling shear properties of the lamellae. Therefore, it is important to accurately define the rolling shear properties in the CLT in order to carry out tests of the performance of the material. In the same study it was also mentioned that the bending tests carried out with a single point load showed that the specimen width did not have any significant effect on the apparent modulus of elasticity.

(23)

strength graded Norway spruce planks showed that the strongest relationship between the bending strength and the MoE could be found in the local static MoE in edgewise bending. The local static MoE was proved to be a better estimator than other assessment methods of MoE such as, dynamic axial excitation.

The work “Bending strength predictions of cross-laminated timber plates subjected to concentrated loading using 3D finite-element-based limit analysis approaches” by Füssl et al. (2019), used limit analysis approaches to predict the bending strength in CLT plates. Because of the inhomogeneities in wood a scatter of strength can be found in the material. This was investigated using a stochastic approach. The results showed that the analytical methods suitably approximated both the mean loading capacity and the scatter of strength. In a study carried out by Sikora (2016) several tests of three- and five-layer CLT panels were analyzed. The material was Irish-grown Sitka spruce. The conclusions drawn from this article is that the bending strength decreased with thicker panels. The same phenomena could be seen for the rolling shear strength. The global deformation of the panels gave results that were close to the theoretical stiffnesses.

The study “Experimental Study and Finite Element Simulation Analysis of the Bending Properties of Cross-Laminated Timber (CLT) Two-Way Plates” by Wang et al. (2020) compared two different stacking methods of the lamellae in CLT and how these affect the bending performance. Layups were made up of three- and four-layer CLT. The study showed that the overall bending capacity could be improved by using four lamellae instead of three, although the optimal number of layers was five, when considering bending properties.

In a study by Gülzow et al. (2011) it is shown that the moisture content of CLT has a big impact on the stiffness. An increase in moisture content led to a decrease in stiffness properties, although the swelling caused the gap between the middle layers to close increasing internal friction, which increases the stiffness at low deflections. A low moisture content will lead to cracks in the CLT which causes a reduction in the bending stiffness in the grain direction of the face layers.

(24)

3 Material and preparation of CLT-elements for

testing

In this chapter, the process of how the test pieces used for four-point bending tests were manufactured, which quality and what type of wood was used, is described. The chapter begins with a description of the different types of wood used. Afterwards a table and describing text of the different measured data is presented. Lastly the procedure of how the company Södra prepared and manufactured the different plate groups and a table of which plate groups that were included in the testing procedure will be presented. When referring to the test pieces and the groups into which they are sorted, three different terms will be used.

Package – The package of timber boards that were used to produce the plates. Plate group – The group in which the plates have the same lay-up.

Plate/Specimen – A single plate within a certain plate group.

3.1 Material overview

The plates used for experimental tests were manufactured from four different packages of sawn timber, consisting of two different wood species, spruce and pine. Three of the packages consisted of pine and one consisted of spruce. In chapter 3.1.1, the different packages and their measured parameters will be displayed.

3.1.1 Measurement parameters of packages

Four different packages were used when producing the test pieces. The different packages of lamellas, their quality, the number of lamellas in every package and how they will be denoted in this thesis is shown in Table 1. Table 1: Overview of lamellas quality, number of lamellas in every package and denotation.

(25)

The longitudinal resonance frequency, mass and dimensions of the timber boards of the different packages is displayed in Table 2.

Table 2: Measurement data of the packages. Package Frequency [Hz] Mass [kg] Length [m] Width [mm] Thickness [mm] Moisture Content [%]

Mean Std.dev Mean Std.dev

P1 506 38 22 2 4.8 196 45 12.3

P2 504 35 23 2 4.8 195.6 45 13.2

Pc16 484 32.5 22.3 2.1 4.8 195.6 45 12.6

S2 545 37 19 2.35 4.8 195.5 45 13.7 The frequency, mass and length were measured for every lamella. However,

the measurement for width, thickness and moisture content was only performed on every tenth lamella.

3.2 Specimen

In this section is described how the plates were manufactured. Summary of the different plate groups and what timber packages that were used for the different groups are given as well.

Three-layer plates with dimension 3 x 6 meters were assembled from lamellas of either spruce or pine, each layer was 40 mm thick, giving a total element thickness of 120 mm, see Figure 7. In total four large elements with layers consisting of either spruce or pine were manufactured and examined.

(26)

Before gluing the elements/plates, properties of the lamellas were investigated by company employees of Södra in Värö, Southwest Sweden. During the manufacturing of the plates the position of each lamella is specified in what layer and what CLT-element they are positioned in. No glue was used between the lamellas in the same layer. Originally each lamella was 4.8 meters long, but the lamellas were connected by finger joints to give longer members. After manufacturing of four large plates, each of these was sawn into seven 4 m long and seven 2 m long elements with a width of 390 millimetres. However, the 2-meter-long elements were later sawn to 1.6 meters. This is done to create the correct span with no overhang, seen later on in Figure 10b. Figure 8 shows how a plate was sawn into smaller specimen.

Figure 8: Overview of saw procedure of the original plate.

(27)

Table 3: Specimen included in the four-point bending tests.

Elements Plate group

1 2 3 4

Element type 1 102-108 202-208 302-308 402-408

Element type 2 111-117 211-217 - - In total four different plate groups will be used for testing. In Table 2 the different notations of packages used for creating the plates is shown. Table 3 shows what kind of elements are included in the different plate groups. Which package of timber boards that was used for the different plate groups can be seen in Figure 9.

Figure 9: Layup of the different plate groups.

(28)

4 Methods & Implementation

This chapter explains the different methods that have been used in order to achieve the aims of this thesis. This chapter begins with an explanation of the experimental evaluation procedure of the pieces, this includes how the experiments were set up, what results were extracted and how these results were extracted. After this the usage and purposes of the FE-model will be explained.

4.1 Experimental evaluation of stiffness and strength

This includes an explanation of the setup used for all the four-point bending tests and how they differed between the 4 m-elements and the 1.6 m-elements. The setup will be used when analyzing global and local stiffness of the plates, but also when performing the DIC analysis to obtain shear strains which are needed to determine the effective rolling shear modulus. The test setup was done in accordance with CEN-16351 and SS-EN 408 which were covered in sections 2.4.2 and 2.4.1, respectively.

4.1.1 Setup for four-point bending test

The tests have been done in the laboratory hall in the M-building at Linnaeus University in Växjö using an electromechanical testing machine of make Alwetron. The experiments were carried out by performing a four-point bending test. The tested element was simply supported in both ends and exposed to two concentrated loads. Two different spans were used in the tests. Plate group 1-4 were performed as bending test where the space between the loads is 6h and the distance from support to load is 12h, where h is the total height of the plate, see Figure 10a. This creates a span of 3.6 m between the supports, since the long plates are 4 meters long, there was an overhang of 200 mm on each side.

(29)

Figure 10: (a) Bending test setup, (b) Shear test setup.

Figure 11: (a) support plate used in the tests, (b) LVDT sensor, (c) potentiometer used for global displacement measurement, (d) Moisture content meter.

(30)

The global displacement was measured with the help of a potentiometer, see Figure 11c. The sensor was placed underneath the plate and in the middle of the test piece, as seen in Figure 5 and Figure 6. The spring should be as straight and far inserted as possible to enable measurement of large displacements. The sensor has a capacity to measure up to 100 millimeters. The positioning of the LVDT sensor and potentiometer are shown in Figure 12.

(31)

Figure 13: Measurement points for moisture content on the plate.

The loads acting on the test specimen were applied at two different speeds. For 4-meter specimens, the load V1 for the 4-meter specimens was 15 mm/s. The 1.6-meter specimens were exerted to a speed of V1 = 3.75 mm/minute. The test procedure was carried out as follows:

• To ensure that the support and specimen has full contact the force from the testing machine is a few newtons above zero.

• The load, V1 begins to be applied, when 100 N is reached, all measurement instruments are set to zero.

• When the testing machine reaches approximately 40% of the characteristic load capacity the displacement speed is changed to the load V2, a speed of 1 mm/minute, to ensure a safe removal of the LVDT sensor.

• The speed is changed to V1 and continues at a constant rate until reaching 50% of the total characteristic load capacity in the plate. For

non-destructive tests, the test ends here.

• For destructive tests, the load is increased until failure is reached. The ultimate load is defined as the maximum load applied when the plate loses its ability to withstand the loading.

(32)

Figure 14: Graphical description of the test procedure. 4.1.2 Digital image correlation

To determine the effective rolling shear modulus 𝐺%", the camera system

Aramis from Gom was used. This system can follow the deformations in all three directions but herein it is the deformations in the xy-plane in the mid-layer of the CLT-elements that are of interest. The deformations correlate to the load being applied when the photo is taken. This can then be used to calculate the strains at a given load. The equipment used in the tests was two cameras, which were positioned 50 centimeters from the specimen and a LED light, placed behind the camera to give better light to the specimen which was tested. The setup that was used can be seen in Figure 15.

After this, the shear deformations are to be picked from the middle layer of the lamellas and compared between Aramis and Abaqus results. The shear

(33)

Figure 15: Setup of the Aramis system.

A speckle pattern is applied/sprayed on the side of the plate. This is done to enable the system to follow displacements of a high number of positions on the surface as loading increase such that the shear strain in the painted sections can be calculated for different load levels. Figure 16 shows how the pattern inside a studied window should look like, approximately 50% should be colored with a light touch of spray, creating small dots within the section.

(34)

The specimens were tested in two different sections, section A and B, of each examined element. This can be seen in Figure 17. Section A is located from 540 mm from the edge to 940 from the edge, while section B starts 920 mm from the edge and ends at 1320 mm. In total seven specimens were tested with the Aramis system. The specimens included were 202, 203, 104, 205, 206, 207 and 208. The plates were divided into different groups, even and uneven numbers. The even numbers were analyzed from lamella 15 to 19, uneven numbers and 104 were measured between lamella 4 to 7. This was done to give a variety of investigated lamellas, since the same lamellas appear in the mid layers of elements that are cut from the same big plate. Investigated sections should comprise lamellas with a variety of pith location. Lamellas with pith inside the cross section were included in investigated sections of element 104 (lamella 6), element 202 (lamella 16) and element 203 (lamella 16).

Figure 17: Section A and B on the different specimens.

(35)

Figure 18: Example of engineering shear strains calculated on basis of DIC. The specimens contain imperfections, such as knots. By picking a single point on the section, the shear strain will become inaccurate when comparing it with the Abaqus results. Therefore, a mean shear strain over a certain area in the section needs to be considered. The white rectangle in the figure above shows the considered area. Further on the example image of a DIC-scan shows how the dark red vertical stripes represent the gap between the lamellas. These stripes appear since no glue is used between the lamellas. The oblique dark red stripes symbolize crack openings, what is notable is that the shear strains are lower next to the crack openings. In the results from the DIC, which will be shown in 5.1.2 the pith can be identified in several lamellas. However, the pith is located by locating the maximum shear strain in the scan. The crack

openings often point towards the pith as well.

4.1.3 Determined displacements and strains

The four-point bending test was used to extract global and local displacements (𝑤_R,STU and 𝑤_+,STU) to be used to evaluate the stiffness. The DIC has been used to extract the rolling shear strain 𝛾%",STU.

4.2 Finite element modelling and simulations

In this section the FE-model used to simulate the four-point bending tests is described. In subsection 4.2.1 some graphical results from a plate with standard material parameters are presented, in order to provide insight of the behavior of the model. A convergence study to determine the best mesh size for the model is included as well. Lastly how to evaluate system effect, the influence of effective rolling shear modulus and relationships between dynamic longitudinal lamella stiffness and static element bending stiffness are discussed.

4.2.1 Design of FEM model

The model was developed using the general finite element software Abaqus. Abaqus is able to run scripts that are created through software such as

(36)

Figure 19: The model as seen in Abaqus with force- and support plates added for better visual presentation.

The mesh size can be chosen by the user at an early stage, after the dimensions of the entire CLT-plate have been added the script will then divide the entire plate into small elements at the size of the user input. The mesh is created so that the element limits always coincide with the edges of the layer. This is necessary in order to apply different material properties and orientations in the different layers since the material properties are assigned to the elements. The elements used are linear brick elements with 8 nodes, see Figure 20.

Figure 20: Linear brick element with 8 nodes.

(37)

The model was created to resemble the laboratory testing as far as possible. The support is defined in both ends of the beam as a node on top of the CLT. The steel plate is then represented by constraining an area the size of the steel plate to the node, making all the nodes below the “steel plate” move and rotate according to the same given boundary conditions as the node with the boundary conditions defined. See Figure 21 and Table 4 for how the boundary conditions were defined.

Table 4: The boundary conditions for the model. Roller support in the right support and fixed in the left. Both supports are free to rotate around the Z-axis.

DOF Left support Right support

Displacement X (U1) Locked Free

Displacement Y (U2) Locked Locked

Displacement Z (U3) Locked Locked

Rotation X (UR1) Locked Locked

Rotation Y (UR2) Locked Locked

Rotation Z UR3) Free Free

The same principle was applied for the point load. Since in reality, the load was applied via a steel frame from bottom of the plate, the same situation had to be emulated in the FE-model. A node was selected in the center of the load application zone to which a point load was applied. This entire zone was then constrained to the node with the force in order to spread out the force

application in the same manner as the laboratory testing, see Figure 21.

(38)

mid lamella, in this report also referred to as Gxy. 𝑙𝑎𝑚₊ = ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎡_𝐸𝐸+ V 𝐸₍ 𝐺_V+ 𝐺₍₊ 𝐺_(V 𝑢₍₊ 𝑢(V 𝑢_+V 𝜌 ⎦⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎤ = ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎡12000₄₀₀ 400 690 690 170 0.622 0.38 0.31 340 ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎤ 𝑙𝑎𝑚₍= ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎡𝐸_𝐸V + 𝐸₍ 𝐺_V+ 𝐺_(V 𝐺₍₊ 𝑢₍₊ 𝑢(V 𝑢_+V 𝜌 ⎦⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎤ = ⎣ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎡₁₂₀₀₀400 400 690 170 690 0.025 0.38 0.31 340 ⎦ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎤

The following results presented graphically (results in general from FE-model are presented in the results 5.2) were extracted by loading the generated .imp file into Abaqus CAE and creating a job. The total load applied was set to 12 kN. All results used the material parameters specified above. See Figure 22 for the displacement in z-direction over the entire plate.

Figure 22: The displacement in y-direction of the plate with 12 kN load applied. In order to see that the displacement was constant along the y-direction, a path was created to see if and how the displacement in z-direction changes. See the placement of the path in Figure 23 along which the displacement was found to be constant.

(39)

Figure 24: The shear strains 𝛾:0,[]E over the plate at a load of 12 kN. Section 1 shows the shear strains on the left side of the plate and section 3 shows the shear strains on

the right side. Only small shear strains appear in the part between the point loads (section 2) where the shear force is equal to zero.

4.2.2 Element mesh and convergence of global displacement

In order to prove that the results gained from the finite element analysis are accurate, it is necessary to prove that the model converges as the element mesh is refined. When further refinement only gives negligible changes of results, in the present case displacements, the mesh no longer needs to be refined and it can be concluded that the results are accurate (XCEED 2017).

(40)

Table 5: Convergence study with different mesh sizes.

Element size [mm]

Displacements

[mm]

Height Length Width Local Global

40 40 40 0.6429 15.2654

20 20 20 0.6193 14.9205

10 10 10 0.6152 14.9646

5 5 5 0.6140 15.0067

The solution can be said to occur when the difference between the current solution and the previous solution is close to zero. As seen in Figure 25: Deviation in local displacement in different element sizes compared to 5 mm., the difference between the local displacement, for an element size of 10 mm, only deviates less than 0,2% from the local displacement within the solution using 5 mm element size. The displacement achieved with an element size of 20 mm is still within 1% of the displacement using the 5 mm elements which shows that it is not as accurate as 10 mm but can be used for some purposes if corrected with the same factor.

Figure 25: Deviation in local displacement in different element sizes compared to 5 mm.

4.2.3 Calculated displacements and stresses

The model has been used partly to extract the global and local displacement (𝑤_R,WS/ and 𝑤_+,WS/) with different material parameters applied. It was also used to extract and calibrate the rolling shear strain 𝛾_%",WS/. The shear stress 𝜏_%"was extracted when evaluating the rolling shear strength in the elements of 1.6 m length. 4.2.4 System effect 0 1 2 3 4 5 40 20 10

(41)

longitudinal lamellas that were used in the outer layers. In total four different layups were investigated, with 2, 4, 8 and 16 lamellas used in each of the outer layers. This is done because the lamellas have different stiffnesses and it is not until a large number of lamellas in width that the layers stiffness will be a close approximation of the mean stiffness of the sample, i.e., the standard deviation decreases as the number of lamellas used are increased.

To evaluate the system effect, the longitudinal bending stiffness from package 1, P1 was used, i.e., the 𝐸+ from the 84 different lamellas. Afterwards 1000

simulations were performed on each of the four different layups. The

simulation was performed in a way that different stiffnesses were applied to the lamellas, mean value and standard deviation for that simulation were

calculated. When all 1000 simulations were performed the mean value and standard deviation was calculated for all the different combinations. However due to the fact that two lamellas in width will give a high standard deviation a Monte Carlo simulation will be performed to verify the mean value and standard deviation.

4.3 Evaluation of effective rolling shear modulus and shear

strength

For test pieces 111-117 and 211-217 with 1.6 meters length an attempt to analyze shear strength was performed. A characteristic rolling shear strength of τxy = 1.1 MPa implied that the characteristic ultimate load should be about 60 kN. The setup for the rolling shear test is shown in Figure 10b. The reason why a much shorter span was used is to reduce the bending moment in the plate and eliminate the risk for failure in bending. For these two different tests the mesh size used was 10 x 10 x 10 mm3_{. The MoE of the lamellas in the longitudinal} layers was set to the mean value of the dynamic MoE of the timber boards of the package used to manufacture the large plates from which the tested plates were sawn. For plate group 1 this mean value was 12.5 GPa and for plate group 2 it was 13 GPa. 𝐺_V( was set to 170 MPa for both plates. Since the shear stress is very close to constant in the middle layer between a support and a point load (except very close to the support or the point load) the shear stress considered was obtained from a single point in position (x, y, z) = (260 mm, 60 mm, 0 mm).

(42)

4.4 Potential element bending stiffness by optimized utilization of

lamellas

Monte Carlo simulations were carried out for two different purposes. Firstly, to verify the FE model with the results from four-point bending tests and secondly to investigate the potential of increasing the bending stiffness by grading lamellas with respect to dynamic MoE and use the lamellas with higher MoE in outer, longitudinal layers and lamellas with lower MoE in inner and transversal layers. For all simulations a mesh with element size 10 x 10 x 10 mm3_was used. Each layer has a height of 40 mm and the plates are built up of either 3 or 5 layers. The tests had similar measurement points as in the four-point bending tests, one point underneath the plate placed at (x, y, z) = (2000, 0, 190) and a point on top of the plate simulated to represent the local displacement. The local measuring points can be seen in Figure 4.

When calibrating the FE-model with test results each package was analyzed separately, package 1 and 2 was used for the different simulations. The dynamic MoE for each lamella was calculated as shown in page 14. For the simulations two lamellas in width were used in the outer layers.

The first Monte Carlo simulation was for an assembly process where no classification is made the plate layup was unsorted randomly. This was done for both 3 and 5 layers. The process in the following:

- Random dynamic MoE will be picked from one of the packages used for the top layer, same process is then performed for the bottom layer. Different layups can be seen in Figure 9.

- The MoE of the outer layers is randomized and differs between the upper and lower layer. For these unsorted simulations the dynamic MoE in the middle layers will be set to 12 500 MPa.

- Once the dynamic MoE have been picked for bottom- and top layer the simulation was performed with a load of 12 kN, the local- and global displacement was saved when using the parameters above.

- This process was then redone with different randomized dynamic MoE for the outer layers. The number of simulations varied depending on the package, Table 6 shows the number of simulations done per plate. - Once all simulations had been carried out, the mean value of the

displacement in all the unsorted simulations was extracted and the stiffness ratio dP/dw was used.

(43)

package 1 were applied. This is due to the fact that the dynamic MoE needs to be consistent when using different classifications so a validated comparison can be performed.

In total two different combinations were analyzed, three layers and five layers. The lamellas MoE will be divided into two different classifications, class 1 and 2. The classification of the boards will be determined by a percentage. The ratio in the different classifications can be seen in Table 7.

Table 7: Sorted Monte Carlo simulations with 𝐸; of package 1.

Package Number

of layers Percentage in class 1 [%]

Percentage in

class 2 [%] of simulations Number

1 3 67 33 1000

5 40 60 1000

The boards in class 1 will be denoted for the stiffest boards in the package. The lamellas in class 1 will be used in the outer layers and class 2 will be inserted in the middle layers. For plate 1 with three layers 2/3 of the stiffest boards will be included in class 1 and the remaining boards will belong in class 2. Lamellas in the 5-layer CLT will be divided with the percentage of 40% into class 1 and the remaining 60% in class 2. The simulations were performed in the following way:

- The lamellas in package one was divided into two classifications depending on the desired ratio between class 1 and 2.

- The outer layers dynamic MoE were randomized in the same manner as unsorted simulations.

- The middle layers dynamic MoE was randomized from the lamellas in class 2. All the lamellas considered in the middle layer had the same dynamic MoE.

- The simulations were then repeated 1000 times were different dynamic MoE were used in each of the simulations, the load used for these simulations was 12 kN.

(44)

5 Results and analysis

In this chapter, all results gathered from the experiments, calculations and simulations are presented. It will also include calibrations that use the results to calibrate the FE-model.

5.1 Four-point bending test

This sub-section will present all the results from the four-point bending test. This includes the results from the displacements when analyzing the local and global stiffness of the plate, the test of the shear modulus in Aramis and the ultimate loads for the destructive tests.

5.1.1 Evaluation of stiffness

The results shown in this sub-chapter show the local and global stiffness for both the specimen of length 4 m and 1.6 m. The factor $U

$X012 is a factor of the load 12 kN and the displacement related to that force.

4-meter plates:

For plate group 1 (pine in all the three layers) the following results were obtained:

Table 8: Results from specimens in plate group 1.

Specimen 𝒅𝑷 𝒅𝒘𝒈,𝑬𝑿𝑷 [Pa] 𝒅𝑷 𝒅𝒘𝒍,𝑬𝑿𝑷 [N/m] 102 7.66 ∙ 10\ _{2.62 ∙ 10}] 103 6.07 ∙ 10\ _{1.96 ∙ 10}] 104 7.00 ∙ 10\ _{2.44 ∙ 10}] 105 6.41 ∙ 10\ _{2.09 ∙ 10}] 106 5.74 ∙ 10\ _{1.85 ∙ 10}] 107 6.16 ∙ 10\ _{2.13 ∙ 10}] 108 5.75 ∙ 10\ _{1.82 ∙ 10}] Mean value 6.40 ∙ 10\ _{2.13 ∙ 10}] Std. deviation 0.706 ∙ 10\ _{0.299 ∙ 10}]

(45)

Table 9: Results from specimens in plate group 2. Specimen 𝒅𝑷 𝒅𝒘𝒈,𝑬𝑿𝑷 [Pa] 𝒅𝑷 𝒅𝒘𝒍,𝑬𝑿𝑷 [N/m] 202 7.68 ∙ 10\ _{2.61 ∙ 10}] 203 8.19 ∙ 10\ _{2.83 ∙ 10}] 204 8.49 ∙ 10\ _{2.73 ∙ 10}] 205 8.50 ∙ 10\ _{2.83 ∙ 10}] 206 6.11 ∙ 10\ _{2.06 ∙ 10}] 207 7.04 ∙ 10\ _{2.24 ∙ 10}] 208 9.76 ∙ 10\ _{3.23 ∙ 10}] Mean value 7.97 ∙ 10\ _{2.65 ∙ 10}] Std. deviation 1.17 ∙ 10\ _{0.392 ∙ 10}]

For plate group 3 (spruce in the longitudinal layers and pine in the transversal layer) the following results were obtained:

Table 10: Results from specimens in plate group 3.

Specimen 𝒅𝑷 𝒅𝒘𝒈,𝑬𝑿𝑷 [Pa] 𝒅𝑷 𝒅𝒘𝒍,𝑬𝑿𝑷 [N/m] 302 8.37 ∙ 10\ _{2.41 ∙ 10}] 303 8.02 ∙ 10\ _{2.48 ∙ 10}] 304 8.47 ∙ 10\ _{2.41 ∙ 10}] 305 8.06 ∙ 10\ _{2.77 ∙ 10}] 306 9.59 ∙ 10\ _{3.00 ∙ 10}] 307 6.98 ∙ 10\ _{1.99 ∙ 10}] 308 8.85 ∙ 10\ _{2.71 ∙ 10}] Mean value 8.33 ∙ 10\ _{2.54 ∙ 10}] Std. deviation 0.803 ∙ 10\ _{0.323 ∙ 10}]

(46)

Table 11: Results from specimens in plate group 4. Specimen 𝒅𝑷 𝒅𝒘𝒈,𝑬𝑿𝑷 [Pa] 𝒅𝑷 𝒅𝒘𝒍,𝑬𝑿𝑷 [N/m] 402 7.69 ∙ 10\ _{2.36 ∙ 10}] 403 8.06 ∙ 10\ _{2.63 ∙ 10}] 404 8.02 ∙ 10\ _{2.50 ∙ 10}] 405 9.05 ∙ 10\ _{2.82 ∙ 10}] 406 9.36 ∙ 10\ _{2.90 ∙ 10}] 407 8.32 ∙ 10\ _{2.52 ∙ 10}] 408 7.52 ∙ 10\ _{2.38 ∙ 10}] Mean value 8.29 ∙ 10\ _{2.59 ∙ 10}] Std. deviation 0.683 ∙ 10\ _{0.209 ∙ 10}]

Analyzing all plates with 4 m length gives the following results: Table 12: Results from all long plates.

𝒅𝑷 𝒅𝒘𝒈,𝑬𝑿𝑷 [Pa] 𝒅𝑷 𝒅𝒘𝒍,𝑬𝑿𝑷 [N/m] Mean value 7.82 ∙ 10\ _{2.50 ∙ 10}] Std. deviation 1.10 ∙ 10\ _{0.343 ∙ 10}]

See Figure 26 and Figure 27 for graphic results of the stiffness distribution in the elements.

(47)

Figure 27: Distribution of _2\2^

8,LMN over all long elements.

1.6-meter elements:

The following results show the local and global stiffnesses achieved in the short elements, all of the elements are from plate group 1 & 2 consisting of only pine in all layers.

Table 13: Results for all short length elements

(48)

See the distribution of the stiffness in all the short elements in Figure 28 and Figure 29.

K,LMN over all short elements.

8,LMN over all short elements.

5.1.2 Shear modulus

Results from Aramis containing specimen 104A. 104B, 202A and 202B are presented in Figure 30, Figure 31, Figure 32 and Figure 33 respectively.

(49)

with poor structural characteristics. 202A shows that no piths were located in that section, however, the crack openings are all pointing towards the same position, namely the pith. Thus, the inclinations of the cracks indicate the location of the pith in relation to the lamella.

If the local effects, such as crack openings and gaps between the lamellas are neglected, the typical shear strains differ between the sections and lamellas. 202A has the maximum shear strain around 2.5 ∙ 10^__{located around x = 300}

mm meanwhile the maximum shear strain in 202B is approximated to 4.0 ∙ 10^__{occurring near the section end at x = 400 mm.}

Figure 30: Engineering shear strain, 𝛾:0,]_^, testing 104A with load 20 kN.

(50)

Figure 32: Engineering shear strain, 𝛾:0,]_^, testing 202A with load 20 kN.

Figure 33: Engineering shear strains, 𝛾:0,]_^, testing 202B with load 20 kN.

5.1.3 Maximum load and failure type

(51)

Table 14: Different specimen and their maximum force application. Specimen Maximum force

[kN] 102 67.2 103 48.1 105 53.1 106 37.0 107 46.2 204 58.1 302 37,7 303 50.9 304 33.5 305 48.1 306 58.1 307 30.6 308 53.9 Mean value 47.9 Std. deviation 10.7

All the plates above broke due to bending failure. See Figure 34 for typical failure types where failure is initiated around a local weakness in the CLT. This was the case for all of the elements that were loaded until failure.

Figure 34: (a) Failure concentrated around a knot in the board. (b) Location of failure at a finger joint.

(52)

acting on the specimens for the destructive test. The trendline shows that as the local MoE increases, so does the strength. The coefficient of determination was calculated to 𝑅K_{= 0.68.}

Figure 35: Graph showing the local MoE and maximum force for the destructive tests.

5.2 Results from finite element simulations and comparisons

This chapter contains both results obtained from Abaqus and the influence of the rolling shear modulus for deformation.

5.2.1 Calibration of finite element model

The model was calibrated in three different ways. The first calibration was to see the minimum mesh size in order to achieve good approximations of the results, this is covered in section 4.2.2. The model was also calibrated based on the rolling shear modulus and longitudinal bending stiffness. These calibrations were partly carried out in order to determine the correct material parameters to use for future simulations. But also, to enable an investigation of if accurate results of bending stiffness are obtained when using the dynamic MoE of lamellas as MoE for longitudinal layers in a FE model, i.e., if the same load-deflection relationship is obtained in simulation as in laboratory tests. 5.2.1.1 Calibration of rolling shear modulus

(53)

Table 15: Shear modulus of 7 specimens. Specimen Section Aramis

Ratio 𝒅𝑷 𝒅𝜸 [𝟏𝟎𝟕_] Abaqus Ratio 𝒅𝑷 𝒅𝜸 [𝟏𝟎𝟕_] Corresponding shear modulus [MPa] 202 A 1.4034 1.4107 218 B 0.7478 0.7478 117 203 A 1.1812 1.1833 184 B 0.9323 0.9259 145 104 A 0.7341 0.7306 115 B 0.7386 0.7371 116 205 A 1.2776 1.2765 198 B 1.0275 1.0245 160 206 A 1.4698 1.4714 227 B 1.1205 1.1169 174 207 A 1.4098 1.4107 218 B 1.1669 1.1634 181 208 A 1.2435 1.2431 193 B 1.0143 1.0113 158 Mean Value 1.1048 1.1038 172 Standard deviation 0.2507 0.2526 38.3

The span of rolling shear moduli is between 115-227 MPa which shows a large deviation in values for plates of the same layup and material. All of the

examined plates had more than double the characteristic value often used for calculation of 𝐺_V( = 50 MPa.

5.2.1.2 Calibration of longitudinal bending stiffness

The basis of the calibration will be stiffnesses achieved with an unsorted layup of 3-layer CLT. The mean value of the global and local stiffness of the package will be compared to see how much the FE-model deviates from physical testing.

(54)

Table 16: The results and differences in mean value of 2^

2\8 local stiffness between the four-point bending and numerical simulation.

Numerical simulation Four-point bending Difference [%] Package 1 1.88 ∙ 10] _{1.92 ∙ 10}] _2.1 Package 2 1.95 ∙ 10] _{1.93 ∙ 10}] _-1.0 Mean value 𝟏. 𝟗𝟏𝟓 ∙ 𝟏𝟎𝟕 _{𝟏. 𝟗𝟐𝟓 ∙ 𝟏𝟎}𝟕 _0.6

5.2.2 Maximum force and Rolling shear modulus

The rolling shear stress in plate group 1 and 2 was analyzed when exposed to a load of 100kN, corresponding to the maximum force in the four-point bending test when trying to achieve a rolling shear failure. Since no shear failure was achieved, the tests were simulated in the FE-model to extract the shear stresses and strains corresponding to a force of 100 kN. These strains and stresses are presented in Table 17 and it is shown that the strength to rolling shear failure was higher than 1.5 MPa for all 14 elements investigated.

Table 17: Rolling shear stress in package 1 and 2 with 100kN force applied in FE-model.

𝜸_𝒙𝒚 𝝉_𝒙𝒚 [MPa]

Package 1 8.90 ∙ 10^_ _1.513

Package 2 8.86 ∙ 10^_ _1.506

The calculations made before the analysis predicted the plates to fail in rolling shear when a shear stress of 0.968 MPa was reached. This shear stress

correlates to a total load of 67.95 kN applied to the plate. Based on hand calculations, the ability to resist at least 100 kN of force shows that the characteristic rolling shear strength of the sample was at least 1.619 MPa. For the calculation of this, see Appendix C.

5.2.3 The rolling shear modulus influence on bending stiffness

The influence of how the rolling shear modulus effect on the overall stiffness of the plate was evaluated by using different values for 𝐺V( in the FE-model

(55)

Table 18: The global and local displacement for different rolling shear moduli. 𝑮_𝒓𝒕 [MPa] Local displacement [mm] Global displacement

[mm] 50 -0.747 18.824 75 -0.705 18.062 100 -0.683 17.673 125 -0.670 17.435 150 -0.661 17.275 175 -0.654 17.159 200 -0.649 17.072 225 -0.645 17.003 250 -0.642 16.948

The percentage difference of local and global displacement when using 50 MPa versus 250 MPa was 14.1% for local- and 10% for global displacement. The increase in stiffness can be seen in Figure 36 and Figure 37 where the applied load through the local and global displacement are considered.

(56)

Figure 37: The influence of different values for 𝐺DY for global stiffness.

5.2.4 System effect

Table 19 shows how the mean value and coefficient of variation for the longitudinal bending stiffness varies depending to the number of lamellas used in longitudinal direction.

Table 19: System effect for different number of lamellas used as width. Number of lamellas Number of calculations Mean value of 𝑬_𝒍 [MPa] Coefficient of variation 2 1000 12 500 0.1527 4 1000 12 500 0.1110 8 1000 12 500 0.0744 16 1000 12 500 0.0548 32 1000 12 500 0.0387

Modelling and testing of CLT panels for evaluation of stiffness Master Thesis