Analysis of holes in wooden rib panels

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IN THE FIELD OF TECHNOLOGY DEGREE PROJECT

CIVIL ENGINEERING AND URBAN MANAGEMENT AND THE MAIN FIELD OF STUDY

THE BUILT ENVIRONMENT, SECOND CYCLE, 30 CREDITS STOCKHOLM SWEDEN 2020,

Analysis of holes in

wooden rib panels

HANNA BERGMAN

LINA SKOG

KTH ROYAL INSTITUTE OF TECHNOLOGY

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Analysis of holes in

wooden rib panels

Hanna Bergman & Lina Skog

TRITA-ABE-MTB-20599

Department of Civil and Architectural Engineering Division of Structural Engineering and Bridges Stockholm, Sweden, July 2020

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Abstract

The concern for the environment is one of the leading aspects in material choice within the construction industry. According to the Swedish National Board of Housing, Building and Planning (2020) the construction industry is responsible for 19 percent of the total amount of greenhouse emissions in Sweden. Choosing wood over for example concrete or steel as building material would result in beneficial impacts on the environment. The research in the field of wood elements is ever growing and new materials are invented. A relatively new product on the market is the rib panel. The structure of the rib panel enables buildings with large spans and facilitates installations. Due to its properties and area of applications the rib panel could be a strong competitor among other flooring systems.

The objective of this thesis was to investigate the possibility of drilling holes aimed for air ducts through the ribs. Investigations of location of the holes, maximum possible hole

diameter at minimum possible rib height and influence of the cross sectional properties of the rib elements was performed.

A numerical model was designed to calculate minimum required rib height for eight different spans (6–13 m) according to EN 1995-1-1:2004 (2004). The model was constructed with specific requirements for beam deflection (L/500 and L/300) and natural frequency (8 Hz).

For each calculated rib height, the numerical model generated data of failure mode and usage ratio for each design requirement. Based on the evaluated rib heights, computer simulations were conducted in Abaqus FEA. From the computer simulation the maximum hole for specific positions and different load cases could be found.

The measured stresses in the vicinity of the hole was evaluated with Norris failure criterion.

The result from the simulations showed that relatively large holes at the midspan of the beams were possible with remaining bearing capacity according to SLS and ULS. High restrictions of SLS conditions caused a low usage ratio of stresses within the beam, which was a strong contributing factor for the possibility of large holes. Another contributing factor

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for the possibility of large holes was the influence by the flange. By placing the holes at a higher position, closer to the flange larger holes was possible.

Using another failure criterion or different limitations according to SLS could have generated a different result. The investigation is limited to simulations and calculations from numerical models, hence load tests in reality have not been conducted. Performing tests in reality might cover other aspects than in this thesis and possibly generate a more accurate result. The result in this thesis can be seen as a guidance of possible hole diameter, but should not be directly applied to real structures. Further investigations need to be done if the result from this thesis should be applied on real structures.

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Sammanfattning

En av de viktigaste aspekterna vid val av konstruktionsmaterial inom byggindustrin är idag dess påverkan på klimatet. Enligt Boverket (2020) är byggindustrin ansvariga för 19 procent av den totala mängden utsläpp av växthusgaser i Sverige. Användning av trä som

konstruktionsmaterial istället för betong eller stål skulle kunna leda till positiva effekter för klimatet. Forskning kring byggnadselement av trä är ständigt pågående och nya material blir möjliga att använda. En relativt ny produkt på marknaden är ribbdäck. Ribbdäckets

utformning möjliggör byggande med stora öppna ytor och underlättar för

ventilationsdragning genom bjälklaget. Utifrån dessa egenskaper finns möjlighet för ribbdäcket att konkurrera med andra konventionella bjälklag.

Syftet med denna uppsats är att undersöka möjligheten för håltagning genom ribborna. Vilket i sin tur ska möjliggöra ventilationsdragning genom dessa. Undersökningar gällande hålets placering, maximal storlek på hål och påverkan av tvärsnittets utformning utfördes.

En numerisk modell skapades för att beräkna minsta möjliga balkhöjd utifrån krav i EN 1995-1-1:2004 (2004) för åtta olika spännvidder (6–13 m). Specifika krav bestämdes för nedböjning (L/500 och L/300) och egenfrekvens (8 Hz). För varje framtagen balkhöjd genererade den numeriska modellen information om avgörande brottkriterium samt

utnyttjandegrad. Baserat på framtagna balkhöjder utfördes datorsimuleringar i Abaqus FEA.

Från simuleringarna kunde maximal håldiameter för specifika placeringar och lastfall tas fram.

Spänningarna som uppstod i närhet av hålet analyserades med Norris brottkriterium.

Resultatet från simuleringarna visade att relativt stora hål var möjliga när dessa var placerade på halva balkens längd. De höga kraven för bruksgränstillstånd ledde till att

utnyttjandegraden för spänningar i balkarna var låg, vilket var en stor bidragande faktor till att stora hål var möjliga. En annan bidragande faktor till möjligheten för stora hål var påverkan från flänsen. Genom att placera hålen högre upp på balken, närmare flänsen, var större hål möjliga att göra.

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Användning av ett annat brottkriterium eller andra bruksgränskrav skulle kunna ge upphov till ett annorlunda resultat. Undersökningarna i den här uppsatsen är begränsade till

simuleringar och beräkningar utifrån numeriska modeller, således har belastningstest på riktiga balkar inte utförts. Undersökning av riktiga balkar skulle möjligen beakta fler aspekter och resultera i ett mer noggrant och mer användbart resultat. Resultatet i denna uppsats kan ses som en vägledning till möjliga hålstorlekar, men bör inte direkt appliceras på verkliga balkar. Om resultatet från denna uppsats ska vara applicerbart på riktiga balkar bör ytterligare undersökningar utföras.

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Preface

This report is the final thesis for our master degree in Civil and Architectural Engineering at the school of Architecture and Built Environment at KTH Royal Institute of Technology in Stockholm, Sweden. The thesis was written in spring 2020 and has been carried out in collaboration with Dala Massivträ AB and Structor Byggteknik Dalarna AB.

During this master thesis many people have been to a lot of help. First of all we would like to address the biggest gratitude to our supervisor during this master thesis work, Bert Norlin at KTH. His knowledge has been very helpful for this thesis and Bert has also been a great inspiration to us during this spring and earlier years at KTH. We have really appreciated you showing an interest and spending a lot of your time to help us with our thesis work. Also thank you for all the concern you showed us during these special circumstances that it has been to write this master thesis during the spring of 2020.

Second of all, we would like to thank Mattias Brännström at Dala Massivträ for letting us write this thesis in collaboration with Dala Massivträ AB. Your time and great commitment in this thesis have been helpful. We have had a lot of enjoyable meetings during this spring and you have always been very engaged in the project. In addition, thank you to Adam Andersson at Structor Byggteknik Dalarna AB for taking your time for supervision.

Stockholm, June 2020.

Hanna Bergman and Lina Skog

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List of figures

Figure 1.1 Rib panel 2

Figure 3.1 Main directions in the tree trunk and the orthotropic constants 8 Figure 3.2 A five-layer CLT slab and its main directions 10 Figure 3.3 Member with one shear component parallel to grain (a), member

with both components perpendicular to grain (b) 12

Figure 3.4 Deflection components 13

Figure 3.5 Occurrence of crack planes and corresponding tension force F_t,90 16

Figure 3.6 Stress distribution perpendicular to the grain 18

Figure 4.1 Non-uniform stress distribution over the flange 24

Figure 4.2 Cross section of the rib panel 26

Figure 4.3 Z-distances. GC indicates the gravity center 26

Figure 4.4 Effective cross section of the rib panel 27

Figure 5.1 Assigned direction of the axes. Longitudinal (x), transverse and

horizontal(z) and transverse and vertical (y) 31

Figure 5.2 The flange as a separate part 32

Figure 5.3 The web as a separate part 32

Figure 5.4 Left support with slave node area and MPC point in the middle 33

Figure 5.5 Material orientations in the flange 34

Figure 5.6 Gravity load and pressure on top of the flange spread over the web width 36

Figure 5.7 Mesh assigned to the model 37

Figure 5.8 Largest normal stress in x-direction occurs in the lower edge of the hole 38 Figure 5.9 Largest normal stress in y-direction occurs at the lower left and right

edge of the hole 38

Figure 5.10 Largest shear stress in xy-direction occurs in the lower edge of the hole 39 Figure 6.1 Cross section (left) and loading of rib element (right) 43

Figure 6.2 Load and hole placement in a rib element 45

Figure 6.3 Percentage of web height that is allowed to be a hole if placed at the

upper position 46

Figure 6.4 Average required HU corresponding to each cover weight 47 Figure 6.5 Average S11 for a hole at the upper position for each span 47 Figure 6.6 Average S22 for a hole at the upper position for each span 48 Figure 6.7 Average S12 for a hole at the upper position for each span 48 Figure 6.8 Average deflection, U, for each span and cover weight for a beam with

a maximum allowed hole placed at the upper position 49 Figure 6.9 Average S11 for a hole at the middle position for each span 49 Figure 6.10 Average S22 for a hole at the middle position for each span 50 Figure 6.11 Average S12 for a hole at the middle position for each span 50

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Figure 6.12 Average deflection, U, for each span and cover weight for a beam with

a hole placed at the middle position 51

Figure 6.13 Difference in generated stress S11 at the upper and the middle position 51 Figure 6.14 Difference in generated stress S22 at the upper and the middle position 52 Figure 6.15 Difference in generated stress S12 at the upper and the middle position 52 Figure 6.16 The increase in Norris failure criterion if the maximum allowed hole is

moved from the upper position to the middle position 53 Figure 6.17 Percentage of the web that is allowed for a hole 53 Figure 6.18 Position of the hole when moved in the horizontal direction 54 Figure 7.1 Allowed hole size at 20, 40, 60, 80 and 100% utilization of the bending 59

stress

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List of tables

Table 3.1 Examples of limiting values for deflection 13

Table 5.1 Geometry of the flange and the web in the Abaqus model 32 Table 5.2 Material properties for assigning orthotropic materials 34 Table 5.3 Displacement and rotation for the left and the right support 36

Tabel 6.1 Maximum beam height of the web beam 43

Table 6.2 Height of the web beam, the distance under the hole, the diameter and

the position of the hole 45

Table 6.3 Maximum hole size at different horizontal positions along the beam 54 Table 7.1 Maximum allowed hole size at 20, 40, 60, 80 and 100% utilization of the

bending stress 58

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Nomenclature

The following list states the notions and abbreviations belonging to this thesis.

Symbols Description

Load and material

γ_M Partial Coefficient [–]

γ_d Partial Coefficient [–]

γ_G Partial Coefficient, unfavorable load [–]

γ_Q Partial Coefficient, unfavorable load [–]

ψ₀ Reduction factor [–]

ξ_j Reduction factor, unfavorable permanent load [–]

q_k Characteristic values of imposed load [kN/m ²]

C_w Characteristic values of floor cover weight [kN/m ²]

q_Ed.A Load combination for permanent action [kN/m ²]

q_Ed.B Load combination for permanent and variable action

[kN/m ²]

ρ Density [kg/m ³]

k_mod Modification factor [–]

k_def Creep factor [–]

ν Posson’s ratio [%]

Strength and stress

E_i,j Modulus of elasticity [MPa]

E_mean Modulus of elasticity, mean value [MPa]

E_inst Modulus of elasticity, instantaneous [MPa]

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E_{f in} Modulus of elasticity [MPa]

E_r Modulus of elasticity, reference material [MPa]

E_f Modulus of elasticity based on service class [MPa]

G_i,j Shear modulus [MPa]

f_k Strength, characteristic values [MPa]

f_d Strength, design values [MPa]

f_t Tensile strength [MPa]

f_c Compression strength [MPa]

f_v Shear strength [MPa]

f_t,90 Tensile strength parallel to the grain [MPa]

f_c,90 Compression strength parallel to the grain [MPa]

f_v,90 Shear strength flatwise [MPa]

f_{ef f} Effective tensile stress [MPa]

f_m Bending strength [MPa]

F_t,90 Tension force perpendicular to the grain [kN]

F_t,90,V Tension force caused by shear force [kN]

F_t,90,M Tension force caused by bending moment [kN]

M Bending moment [kNm]

M_y,Ed Maximum design bending moment [kNm]

V Shear force [kN]

V_z.Ed Maximum design shear force [kNm]

σ_cr Critical shear buckling stress [MPa]

σ_t Tensile stress [MPa]

σ_c Compression stress [MPa]

σ_t,90 Tensile stress perpendicular to the grain [MPa]

σ_d Stress, design value [MPa]

σ_m Bending stress [MPa]

σ_i, mean Stress in material i , mean value [MPa]

σ_V Stress from shear force perpendicular to the grain

[MPa]

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σ_M Stress from bending moment perpendicular to the grain [MPa]

τ_v,Ed Shear stress [MPa]

τ_mean.d Shear stress, mean [MPa]

k_{M V}_/ Section force combination factor [–]

k_size Size effect factor [m ³]

k_dis Shape factor [–]

k_kalib Calibration factor [–]

k_σ,orth Buckling coefficient [–]

λ_c Slenderness parameter [–]

χ_c Reduction factor [–]

Ω₀ Size effect factor, reference volume [m ³]

Ω Actually stresses volume [m ³]

k_t,90 Strength reduction caused by the height of the beam [–]

11

S Normal stress in longitudinal direction, X [MPa]

22

S Normal stress in transverse direction, Y [MPa]

12

S Shear stress in plane, XY [MPa]

Distance

h, h _w Height of the web beam [mm]

b_w Width of the web beam [mm]

h_f Height of the flange [mm]

, b

b_f Width of the flange [mm]

h_d Height of the hole [mm]

h_ro Distance from the upper beam edge to the hole [mm]

h_ru Distance from the lower beam edge to the hole [mm]

z_c Position of the neutral axis, distance [mm]

z_f Distance from the neutral axis to the flanges midpoint

[mm]

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z_t.edge Distance from the gravity center to the lower edge of the beam [mm]

z_t Distance from the gravity center to the center of the web [mm]

S

Δ _i First area moment of material i [mm ³]

b_i* Width of a CLT board layer [mm]

b_i Width of material i [mm]

b_{i.f ic} Fictive width of material i [mm]

b_{i,ef f} Effective width of material i [mm]

, L

l, l_tot _tot Total span length [mm]

L_depth Total depth of a rib element [mm]

l_t,90 Length of the stress distribution [m]

d Hole diameter [mm]

t_j Thickness of a CLT board layer [mm]

μ_i Transformation factor of material i [–]

β Coefficient for the effective width due to shear lag [–]

r_m Radius of the curvature at mid depth of the beam [mm]

w_slip Deflection due to slip [mm]

w_inst Instantaneous deflection [mm]

w_{f in} Final deflection [mm]

w_{f ca} Deflection in case of ful bonding [mm]

Uppercase constants

D_11... Engineering constants [–]

D Hole diameter [m]

U Deflection [mm]

R

U Rotation [mm]

S Stress [MPa]

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K Modification factor [–]

I Second moment of inertia [mm ⁴]

H Height of the web beam [mm]

U

H Distance from the lower edge of the beam to the hole

[mm]

O

H Distance from the upper edge of the beam to the hole

[mm]

B

U Utilization of the bending resistance [%]

M

N Norris criterion at mid position [–]

U

N Norris criterion at upper position [–]

Vibration

f₁ Natural frequency [Hz]

m Mass [kg]

v Unit impulse velocity [m/s]

n₄₀ Number of first-order modes with f ₁ ≤ 40 Hz

Abbreviation Description

LS

S Serviceability limit state

LS

U Ultimate limit state

A

N Elastic neutral axis

C

G Center of gravity

AT

C Category

ot

d The chosen position at a cross section

in

f Final

nst

i Instantaneous

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1. Introduction

The environment and the human impact on the environment is a current issue of today. The concern for the environment is one of the leading aspects in material choice within several industries, including the building construction industry. According to the Swedish National Board of Housing, Building and Planning (2020) the construction industry is responsible for 19 percent of the total amount of greenhouse emissions in Sweden. As part of a more climate neutral future wooden construction elements are widely discussed and the possibility to expand the applications are continually evolving. In the battle of reducing the concentration of carbon dioxide in the atmosphere, wooden structures can be a contributing part of the solution. As a part of the global cycle, living trees accumulate carbon dioxide in the biomass which creates a carbon sink (Sathare 2007). The storage capacity is continuous even after the conversion from living tree to construction element, consequently this creates a long-term carbon dioxide storage within wooden buildings with a lifespan of several decades. The research in the field of wood elements is ever growing, which has led to continuous

improvements of new wooden materials and extended the possibilities of utilizing wood in a wider range e.g., as load bearing frames or for wide spans in large buildings. This research is necessary if wooden building elements are to be fully utilized within the building

construction industry.

Requirements on shape, delivery time and fire protection needs to be met for wooden elements if the request on the material should be increased. Certain buildings require large open spaces to be adequate for their purpose, e.g., sports arenas, schools and office buildings.

New wooden building materials with high strength in relation to its self weight, such as cross laminated timber (CLT) is a strong competitor among conventionally used materials such as steel and concrete, even in constructions which require large open spaces. A relatively new product on the market is a building floor with underlying ribs; the rib panel, see Figure 1.1.

The rib and flange creates a T-cross section where the rib provides the stability needed for a floor element of large open spans. Cross laminated timber, glued laminated timber and laminated veneer lumber are all possible material combinations for the rib panel.

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Independently of the combination, the rib panel gives the possibility to utilize wood in constructions with large spans where support from columns are unwanted.

Figure 1.1. Rib panel (Dala Massivträ 2020).

1.1 Problem description

With upcoming new materials and structural elements, new issues and problems arise. When constructing a building floor several aspects regarding necessary installations, such as air ducts, must be resolved in an efficient way. To minimize the floor height, the air ducts can be placed within the floor structure. For the ventilation system it is favourable to place the air ducts in two directions, longitudinal and transverse to the ribs. To be able to place the ducts in the structure and in two directions it is necessary to perforate the ribs. This will imply

changes in the stress distribution and possibly lower the load resistance of the floor structure.

When drilling holes in a beam, stresses will be concentrated near the hole and perpendicular to grain. This can possibly lead to the development of cracks (Danielsson 2016). A hole in a wooden beam will imply changes in the stress distribution both in the beam and in the vicinity of the hole. Perpendicular tensile stresses will increase in the beam due to the hole and the investigation of the changes are of importance due to the fact that wood is very sensitive for stresses perpendicular to grain (Danielsson 2007). The failure that occurs due to perforation is very brittle and highly correlated to the size and the location of the hole.

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1.2 Objectives

The objective of this thesis is to propose a design for a wooden rib panel, with the possibility of placing air ducts in two directions. To place the air ducts transversal to the ribs, holes need to be drilled through the ribs. For the design proposal investigations on where the holes should be located, size of the hole, rib height and whether the cross sectional geometry will have influence on the size and placing of the holes will be performed. Stress analyses in the vicinity of the holes will be performed by using Abaqus FEA. The FE-results will be used in Norris failure criterion to investigate when the usage ratio for stresses in the material is reached. The final design needs to meet the requirements for resistance according to Eurocode. The results from analyses will be presented in a table clearly stating the dimensions and characteristics of the rib panel.

1.3 Limitations

To perform the research and investigations within a limited time frame, certain limitations are necessary:

● The flange is made out of a 100 mm thick CLT slab built up by five 20 mm thick layers, each layer has the timber grade C24

● The individual boards in each CLT layer are 120 mm wide

● The web is made out of a 140 mm thick glulam beam with varying height. The timber grade in the glulam beam is GL30c

● Sound propagation through the rib panel will not be considered

● Analysis of crack propagation will be not be performed

● In calculations and models, only circular holes will be investigated

● In all models where nothing else is mentioned the holes are placed at the mid span of the beams with their top edges 20 mm below the flange

● Simulations of hole positions in the horizontal direction is limited to only test a small sample of beam dimensions

● Economic aspects will not be considered in this thesis

● The beams will be considered as simply supported

● Full bonding is assumed between elements

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● Fire regulations is assumed to be met with cladding, but will not be investigated in this thesis

● The limit for the instantaneous deflection is set to be L/500 and the final deflection to L/300

● The limit for the natural frequency of the element is set to be at least 8 Hz

● The limit in Norris failure criterion is set to 0.5

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2. Methodology

A literature study has been conducted in order to achieve knowledge in the field of the research question and help with delimitations. While conducting the literature study it has been possible to investigate what has already been investigated and how we could learn from earlier attempts for solving problems with holes in wooden beams.

A numerical model has been constructed to be able to check the bearing capacity of beams with different dimensions, with respect to serviceability limit state (SLS) and ultimate limit state (ULS). The numerical model was used as a comparison and guideline for dimensions of the beams and possible hole sizes in the simulation models.

Finite element methods (FEM) have been used for conducting computer experiments. The advantage of computer experiments is the possibility to test the different hole sizes and positions in each beam, without being limited by the amount of calculations or complexity.

The FE-results gives a good approximation for a real structure, hence, the computer experiments are a good tool for drawing a conclusion applicable in reality.

2.1 Previous investigations

Information and research from previous investigations about holes in rib panels are limited.

Stora Enso (n.d.) and KLH (2019) are two manufactures of rib panels which produce the element in different sizes and spans. Stora Enso also offers their own calculation program, based on their products, called Calculatis. By investigation of these manufactures and their products and in addition previous research on the subject, conclusions about the calculation methods could be drawn. According to Samvik and Norén (2019), both Stora Enso and KLH utilizes a calculation model from the university in Gratz, Austria. This calculation model is developed for a wooden rib panel consisting of cross laminated timber in the flange and glulam in the web.

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Due to investigations of previous works and also the desire to create a numerical model which could be utilized for different material combinations, the model from Gratz was not utilized. Instead a model for composite wooden elements with full bonding presented in Design of timber structures (2019) was chosen to be suitable for this purpose, and therefore utilized in this thesis. After a period of time working with this thesis the limitations were changed to only focus on a material combination of cross laminated timber and glulam. This resulted in the numerical model being modified to solely process this material combination, nevertheless the model is based on procedures given in Design of timber structures (2019).

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3. Theory

3.1 Structure of wood

Wood is a complex material and differs in many aspects from other commonly used materials such as concrete and steel. The structure of wood makes it highly affected by environmental impacts, e.g., moisture, temperature and heat. Consequently, this affects the stability of the material in a wide range. Wood is a material typically characterised by its macro- and microstructure (Burström 2007). The macrostructure is visible to the eye, while the microstructure requiere aided observations to be visible, e.g., a microscope. The material characteristics are directly caused by the structure of the wood.

3.1.1 Macrostructure

In the macrostructure of a cross section in the tree trunk two sections are clearly visible; the core (heartwood) and the surrounding sapwood. The core starts to develop after 30 year.

When the core starts to develop it hinders transportation of nutrients within the tree trunk and resulting in a darker inner part (Burström 2007). The microstructure also shows the annual growth rings (almost circular in shape) and from which it is possible to identify three different orthogonal directions. The result of the anatomy is an anisotropic material, consequently with different material properties in different directions (Danielsson 2013).

Three main directions are important when discussing material properties such as strength or stiffness; longitudinal direction (L), radiell direction (R) and tangential direction (T). The three directions are located perpendicular to each other, as shown in Figure 3.1.

3.1.2 Microstructure

In the microstructure of wood the anatomy is similar to a bundle of pipes. This due to the numerous hollow cells oriented in the longitudinal direction of the tree trunk (Burström 2007). The microstructure of the wood cells helps identify nine orthotropic behaviour constants, e.g., elasticity, oriented in the grain direction, see Figure 3.1. These orthotropic constants regulate the behaviour of the microscopic structure (Astely, Harrington and Stol

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1997). With the microscopic and macroscopic behavior combined, wood can be seen as an anisotropic orthotropic material (Yingcheng et al. 2005).

Figure 3.1. Main directions in the tree trunk and the orthotropic constants (Swedish wood 2017).

3.2 Strength of wood

Due to the anisotropy of wood, the material is more or less prone to withstand stresses depending on the direction of its own fibers. The highest strength in wood is reached in the longitudinal direction, parallel to the grain. Depending on if the material is subjected to tension or compression the ability to withstand stresses differ. Wood is most prone to withstand tension in the direction of the grain and less prone to withstand compression perpendicular to the grain (Burström 2007). Compression perpendicular to the grain tends to flatten the walls of the cells resulting in a low strength. In addition, the strength is dependent on the density of the wood, its moisture content and by errors in the wood caused by knots.

For up to 50 % of the strength classification, wood follows Hooke's law of linear elasticity (Burström 2007). This is a generalisation and true for moderate loading but the deformation can for example be elasto-plastic for compression parallel to the grain. However, linear elasticity is the most utilized description of failure in timber engineering. This makes it possible to adopt a linear failure criterion which assumes that the strength of the observed element drops to zero at the point where the failure criterion is reached (Danielsson 2013).

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3.3 Rib panel

As of today, a few manufacturers produce rib panels as an alternative to more conventional floor slabs or roof structures. The rib panel is available in different material combinations, such as cross laminated timber (CLT), Laminated veneer lumber (LVL), plywood and glued laminated timber (glulam). The combinations and dimensions of the included materials, e.g., number of layers in the CLT board can vary. The panels can often be prefabricated and manufactured in long spans which allows building with open spaces. The elements are light weighted, hence, additional weight to the structure can be avoided meanwhile sufficient bearing capacity is fulfilled. The light weight facilitates the transportation of the panels which is advantageous in a climate perspective. The design of the panels are often architecturally pleasant and satisfy design demands without any cover.

3.4 Wood materials

3.4.1 Glued laminated timber

Glued laminated timber consists of boards glued together with the fibers in the longitudinal direction of the element and the glue joint perpendicular to the wide side of the cross section.

Glulam timber is commonly used as material in for example bearing frames, visible roof structures and wooden bridges (Gross 2016a). The most commonly used lumber is spruce, sometimes pine is used. The average glulam beam has a higher strength than solid

construction timber since the capacity is defined from the weakest section and almost always limited by knots or joints. When manufacturing a glulam beam, a number of lamellae are glued together. The likelihood that a concentration of knots and joints occurs through several lamellae will hence be lower than for a beam made of solid construction timber.

The bearing capacity of a glulam element is often higher than the bearing capacity of each lamella by itself, therefore a larger applied load with remaining safety can be accepted for the element than if each lamella was loaded separately (Gross 2016a). The elements can be designed either with lamellae of the same timber grade, a homogeneous element, or with different timber grade in the outer and inner lamellae, a combined element. In the combined

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element the outer lamellae has a higher strength classification than the inner. The material properties, e.g., the modulus of elasticity and the shear modulus is specified for each strength class according to the Swedish standard SS-EN-14080:2013 (2013).

3.4.2 Cross laminated timber

Cross laminated timber is a wood product made out of boards glued together. Each board layer is glued perpendicular to the adjacent layer, creating a cross like structure, as shown in Figure 3.2. CLT can be manufactured in large plane elements, with remaining high bearing capacity and stiffness. Due to its robustness CLT is mainly used as parts of the bearing structure in high-rise buildings, schools and industrial buildings, as well as small houses (Gustafsson 2017a).

Figure 3.2. A five-layer CLT slab and its main directions (Gustafsson 2017b).

Due to the cross like structure of CLT the strength of an element is higher than for a solid construction timber element with the same thickness. A CLT element is typically stiffer across the main span but not as stiff as a solid timber element along the main span

(Gustafsson 2017b). The main span can be seen as the direction of the two side layers placed with the fiber direction along the span, consequently placing the fiber direction of the second plate across the span. Due to the construction the bending capacity of the edge and middle board layer and the rolling shear of the second and fourth board is of importance in a five layer CLT element. Since the element can have different numbers of layers with different

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timber grade, the modulus of elasticity and the shear modulus need to be calculated for each layer based on characteristic values from laboratory experiments. The modulus of elasticity,

and shear modulus, are calculated for each layer where indicates the direction

E_i,j G_i,j, i

and the layer. Due to the orientation of the boards in each layer, some properties will be the j same, i.e., E_x,1 = E_x,3 = E_x,5, E _z,2 = E_z,4, G_x,1 = G_x,3 = G_x,5, G _z,2 = G_z,4. Based on this, to construct a solid element of the CLT, the modulus of elasticity and the shear modulus for all layers combined needs to be calculated.

3.5 Presentation of Eurocode 5 Section 6,7 and 9

Eurocode 5 includes information about design of timber structures. In sections 6 and 7 of Eurocode 5 the design in ultimate limit states, ULS, and serviceability limit states, SLS, are described. In section 9 of Eurocode 5 design of assembled or composite elements is

described. Eurocode 5 does not cover any design of holes in wooden beams. Consequently, this section will only describe design rules which are applicable for the design of the rib panel dimensions. All equations and figures in this section are obtained from sections 6, 7 and 9 in EN 1995-1-1:2004 (2004).

For a beam element the stresses due to compression, tension, bending and shearing needs to be checked in the ULS. In the SLS the deflection and vibration need to be checked. For a beam with a T-shaped cross section made of two different materials, checks due to failure caused by the interaction of the elements need to be performed, these are described in section 9.

For compression stress parallel to the grain in the flange (3.1) needs to be fulfilled.

σ_c,o,d ≤ f_c,o,d (3.1)

Where σ_c,o,dis the design compression stress parallel to grain in the flange and f_c,o,dis the design compressive strength parallel to grain in the flange.

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If the web beam is subjected to both bending and tension, the interaction between these two needs to be checked according to (3.2).

f_t,o,d σ_t,o,d

+ _f

m,d

σ_m,d

≤ 1 (3.2)

Where σ_t,o,d is the tensile stress at the center of the web beam and σ_m,d is the bending part of the stress, f_t,o,d and f_m,d are the design strengths for tension and bending.

The shear resistance with a stress component parallel to the grain and shear resistance with both stress components perpendicular to the grain, shown in Figure 3.3, need to be checked.

The shear stress with one stress component parallel to the grain needs to fulfill (3.3).

Figure 3.3. Member with one shear component parallel to grain (a), member with both components perpendicular to grain (b).

τ_d ≤ f_v,0,d (3.3)

Where is the design shear stress and τ_d f_v,0,d is the design shear stress for shear strength parallel to the grain.

For a composite T-shaped cross section, shear stress with both components perpendicular to grain may occur and needs to be checked for failure in or close to the glue line between the web and the flange. The shear stress in the most sensitive part of the flange needs to fulfill (3.4a) or (3.4b).

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for

τ_mean,d ≤ f_v,90,d b_w ≤ 8h _f (3.4a)

or

for τ_mean,d ≤ f_v,90,d

(

^bw

8h_f

)

^0.8 ^b^w ^{> 8}^h^f ^(3.4b)

Where τ_mean,d is the shear stress at the part of the flange most sensitive to rolling shear and is the design shear strength perpendicular to grain, i.e., for rolling shear.

f_v,90,d

The instantaneous and final deflection that must be taken into account, caused by loading and creep, are shown in Figure 3.4. Table 3.1 shows examples of limiting values for deflection.

Note that these values are only examples and the manufacturer, client or designer can choose different limiting values depending on specific cases.

Figure 3.4. Deflection components.

Table 3.1 Examples of limiting values for deflection.

w_inst w_{net,f in} w_{f in}

Beam on two supports l

/

300 to ^l

/

⁵⁰⁰ ^l

/

²⁵⁰^to^l

/

³⁵⁰ ^l

/

¹⁵⁰^to^l

/

³⁰⁰

For residential floors the fundamental frequency and vibrations needs to be considered in the design. The fundamental frequency is calculated by (3.5) and should be greater than 8 Hz.

f₁ = _2l^π2

√

^(EI)^m^l ^(3.5)

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Where m is the mass per unit area, l is the floor span and EI is the bending stiffness of the floor per unit width.

If the fundamental frequency is less than 8 Hz special investigations are required. For a fundamental frequency greater than 8 Hz, the condition (3.6) for unit impulse velocity response should be met.

v ≤ b^{(f ζ1)}¹ (3.6)

Where v is the unit impulse velocity response, b is the floor width, f ₁ is the fundamental frequency and ζ is the modal damping ratio. For rectangular floors, simply supported along all four edges, v can be approximated by (3.7).

v = m b l + 200

4(0,4 + 0,6 n )₄₀ (3.7)

Where m is the mass of the element, b is the floor width, l is the length of the floor span and n ₄₀ is the number of first-order modes with fundamental frequencies up to 40 Hz, the value can be calculated from (3.8).

n₄₀ =

{( ⁽

⁴⁰^f¹

⁾

²¹

) ⁽

^b^l

⁾

^{4 (EI)}^(EI)^b^l

}

^0,25 ^(3.8)

Where f ₁ is the fundamental frequency, b is the floor width, l is the length of the floor span, (EI) _land (EI) _b is the modulus of elasticity and second moment of inertia for the web

respective the flange part of a T-cross section element.

3.6 Hole in wooden beams

It can for many reasons be of interest to place round holes in the rib panel. Facilitating construction of for example ventilation or sewage systems round holes in the glulam beam is highly necessary. Design of an unreinforced hole in a timber beam is not as trivial as it is in other materials such as concrete or steel. As earlier mentioned Eurocode 5 does not cover

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design requirements or guidelines for holes in wooden structures. Studies available today are for the most part applicable to a specific structural design and not directly applied to other structures. This is because wood is an orthotropic material with different material properties in different directions. This generates widely spread mechanical properties which are able to withstand stresses to a varying extent due to the direction. This results in the need of every design approach being verified through experimental processes (Aicher and Höfflin 2008).

For wood, the most critical aspect is tensile stress perpendicular to the grain. Therefore this stress is of utmost importance in the design of a timber beam with holes (Danielsson 2007).

When drilling a hole in a beam which is subjected to bending the stress distribution in the fiber direction is disturbed. Firstly, the drilling leads to additional compression and tension stresses perpendicular to the grain. Secondly, additional shear forces appear in the vicinity of the hole. This results in decreased bearing capacity of the beam where the strength

perpendicular to the grain is of importance, since the associated failure is very brittle (Danielsson 2016).

3.6.1 Swedish glulam handbook

The Glulam Handbook (Gross 2016b) includes recommendations regarding drilling of holes in glulam beams, recommendations based on the German national annex DIN EN

1995-1-1/NA (2012) to Eurocode 5. In the Glulam handbook a number of recommendations regarding placement and size can be found in the case where a hole can not be avoided. The failure criterion (3.9), follows by the stress which occurs perpendicular to the grain, σ_t,90, in comparison with the corresponding strength class of the glulam, f_t,90, modified with the influence of the beam height. When perforating a loaded beam the occurrence of cracks along three parallel planes must be considered. The planes, shown in Figure 3.5, is subjected to triangular distributed tension stress perpendicular to the grain, σ_t,90, which is determined by the tension force, F_t,90,which is resulting from bending moment, M , and shear force, V , in (3.10).

f σ_t,90 = _0,5l^F^t,90_b

t,90 ≤ k_{t,90 t,90} (3.9)

where

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idth of the beam cross section b = w

in(1; ) ) k_t,90 = m (⁴⁵⁰_h ²

eight of the beam h = h

, 5h , h l_t,90 = 0 3 _d+ 0 5

iameter of the hole h_d = d

=

F_t,90 F_t,90,V + F_t,90,M = ^{V h}_4h^d(3 _h ) , 08

2

h_d²

+ 0 0 _h

r

M (3.10)

where

in(h , 5h ; h , 5h ) h_r = m _ru+ 0 1 _d _ro+ 0 1 _d

istance f rom upper edge of the beam to the upper edge of the hole h_ro= d

h_ru= istance f rom lower edge of the beam to the lower edge of the hole d

Figure 3.5. Occurrence of crack planes and corresponding tension force F_t,90(Danielsson 2017).

3.6.2 Aicher and Höfflin theory

Although there is no calculation model regarding holes in timber beams on which all scientists can agree, there are several different theories available, e.g. the theory of

unreinforced holes in glulam beams by Aicher and Höfflin (2018). The theory is applicable to rectangular glulam beams without flanges, i.e., this theory is not directly applicable to rib panels, as investigated in this thesis. The theory is experimentally derived by varying beam height, relative hole size, ratio of section force and beam shape in combination with Weibulls probability theory. According to Aicher and Höfflin the occurrence of additional tension and compressive strength perpendicular to the grain can be seen in the vicinity of the hole. If the hole is placed in an area with both bending moment, M , and shear force, V , forces in

diagonally opposite areas occur; two in tension, “af” and “an”, and two in compression, as

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shown in Figure 3.6. Aicher deems that the ratio of bending moment and shear force are in high correlation with the stress distribution in the vicinity of the hole. For ratios of

the distribution will be comparable to Figure 3.6. They also indicate that the V 0

M

/

^{≤ 1}

highest tensional stress always will occur in the bending compression zone, i.e. at the top right. Furthermore, Aicher and Höfflin states that the tension stress and strength ratio σ_y

/

ft,90 perpendicular to grain contributes to the stress interaction with more than 90%. Höfflin means that this is of great importance, hence a failure criterion is derived from the theory, (3.11). Where σ_t,90,dis the maximum design tension stress perpendicular to grain at the hole vicinity, resulting from bending moment and shear force, (3.12). ft,90,ef f ,dis the effective design tension strength perpendicular to grain (3.13).

σ_t,90,d≤ ft,90,ef f ,d (3.11)

σ )k

σ_t,90,d= ( _{t,V ,d}+ σ_{t,M ,d} _{M V}_/ (3.12)

where

(1, 3 , 2 ) σ_{t,V ,d}= ₂³^V_bh^d 2 + 0 8 ^d_h

(0, 3 , )

σ_{t,M ,d} = ⁶_b _h2

M_d

4 _r^h

m + 0 1^d_d

adius of curvature at mid depth of beam r_m = R

, f or M = , V = ; 1, f or V k_{M V}_/ = 0 9 _d

/

⁰ d

/

^{0 0} d = 0

k k k

ft,90,ef f ,d = ft,90,d size dis kalib (3.13)

where

f_t,90,d = _γ

M

f_{t,90,k mod}k

) ; Ω , 3 m k_size = (^Ω_Ω⁰ ² ₀ = 0 0 ³

, 9bd Ω = 0 1 ²

, ...2, k_dis≈ 1 6 0

, 3 k_kalib= 1 0

Analysis of holes in wooden rib panels

Analysis of holes in

wooden rib panels

HANNA BERGMAN

LINA SKOG

Analysis of holes in

wooden rib panels

Hanna Bergman & Lina Skog

Abstract

Sammanfattning

Preface

Contents

List of figures

List of tables

Nomenclature

Symbols Description

Abbreviation Description

1. Introduction

1.1 Problem description

1.2 Objectives

1.3 Limitations

2. Methodology

2.1 Previous investigations

3. Theory

3.1 Structure of wood

3.1.1 Macrostructure

3.1.2 Microstructure

3.2 Strength of wood

3.3 Rib panel

3.4 Wood materials

3.4.1 Glued laminated timber

3.4.2 Cross laminated timber

3.5 Presentation of Eurocode 5 Section 6,7 and 9

(

)

/

/

/

/

/

/

√

{( (

)

) (

)

}

3.6 Hole in wooden beams

3.6.1 Swedish glulam handbook

3.6.2 Aicher and Höfflin theory

/

/

/

/

{( ⁽

⁾

) ⁽

⁾