Holes in Glulam Beams – Possible Methods of Reinforcement

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Holes in Glulam Beams – Possible Methods

of Reinforcement

VÄXJÖ June 2009 Thesis no: TD 056/2009 UTHMAN, Rawa Nawzad OTHMAN, Rawaz Najat Department of Technology and Design, TD

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Organisation/ Organization Författare/Author(s)

VÄXJÖ UNIVERSITET UTHMAN, Rawa Nawzad

Institutionen för teknik och design OTHMAN, Rawaz Najat Växjö University

School of Technology and Design

Dokumenttyp/Type of document Handledare/tutor Examinator/examiner

MasterThesis Prof. Erik Serrano Prof. Erik Serrano

Titel och undertitel/Title and subtitle

/Holes in Glulam Beams – Possible Methods of Reinforcement Sammanfattning (på svenska)

Denna rapport behandlar limträbalkar med hål. Olika hålgeometrier, cirkulära och kvadratiska hål, och olika metoder att förstärka balkarna vid hålet undersöktes. Totalt 24 enskilda provningar genomfördes med två olika förstärkningsmetoder (glasfiber och plywood) samt med balkar utan förstärkning. Vid provning av de oförstärkta balkarna användes ett system för beröringsfri deformationsmätning för att få en bild av deformationsmönstret. Ett kommersiellt finita elementprogram användes också för att analysera balkarnas respons och för att jämföra med provningsresultaten. Provningarna visade att förstärkningen med plywood var effektivare än förstärkningen med glasfiber. Vidare uppvisade de olika hålgeometrierna olika brottbeteenden, där de kvadratiska hålen gav mindre spröda brott, dock vid en i genomsnitt lägre brottlast än de cirkulära hålen.

Nyckelord

Abstract (in English)

This thesis deals with glued laminated beams with holes. Different hole geometries, circular and quadratic, and reinforcement methods were investigated. A total of 24 tests were performed using two types of reinforcements (glass fiber and plywood) and testing unreinforced beam. During testing of the beams without reinforcement a contact free deformation measurement system was used to capture the deformation pattern. A commercial finite element software package was used to perform numerical calculations of the response of the beams. The FE-analyses were also compared with the experimental results. The test results showed that the reinforcement with plywood was more efficient than the reinforcement with glass fiber. In addition, the two hole geometries showed different failure behaviors. The beams with quadratic holes showed a less brittle behavior, although at a lower load level than the beams with circular holes.

Key Words

Glulam beams, holes, contact free deformation analysis

Utgivningsår/Year of issue Språk/Language Antal sidor/Number of pages

2009 English 53

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Acknowledgements

This Master Thesis was written during 2009 at the School of Technology &

Design at Växjö University. First and foremost, we would like to thank our

supervisor Prof. Erik Serrano for giving us directions and responsibility, and

for trusting our choices during the work. We are also thankful to Mr. Bertil

Enquist for helping us during the experimental work.

Finally, we would like to express our thanks to our families for supporting us.

Växjö, May 2009

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Abstract

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1. Introduction

1.1 Background

Wood is a very useful and well-suited material in construction. It has many advantages in construction because of its high strength in relation to its weight. It has furthermore good resistance against environmental corrosion. A major drawback is the low strength in tension perpendicular to the grain. Glulam is a product manufactured by gluing a number of laminations on top of each other. It has many advantages in a number of applications, because of its fire resistance, its insulating properties, and because of the fact that it can be manufactured in almost any size or shape. As with solid timber, glulam has poor strength perpendicular to the grain and thus, under high stress, cracks can develop, typically parallel to the grain. Therefore; sometimes an efficient reinforcement method to give increased strength by preventing cracks can be vital. Holes in timber beams can be necessary in many cases, for example for accommodating ventilation pipes.

This thesis describes the effect of holes in a glulam beam. The glulam being used here was made from green-glued side boards. This means that the boards were glued to form the cross section before drying them. The holes are a starting point for fracture along the grain of the wood. The fracture often occurs suddenly and the failure of the beam is a brittle failure. The crack is initiated by shear stress or tension stress perpendicular to the grain or a combination. There are at the moment no calculation methods for holes in beams included in the European Timber design code EC5. There are, however, some older empirical methods available, methods that have been used before. If not applying these empirical methods, it would be necessary to use fracture mechanics methods to solve these problems. One way to increase both the strength and stiffness as well as to reduce the brittleness of these structures may be to reinforce the beam around the hole.

1.2 Aim and scope

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investigated, circular and quadratic holes. A total of twelve glulam beams have been used, six of them with reinforced holes and six of them without reinforcement. Each beam had two holes, one at each end of the beam. Thus three beams had circular holes and another three had quadratic holes, all without reinforcement. Three beams had circular holes and three beams had quadratic holes, all without reinforcement. The purpose of using reinforcement was to give a better ability to resist fracture when loading the beams.

1.3 Disposition

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2. Literature Review

2.1 General Remark

Several previous studies on glulam beam with holes can be found in the literature. Different configurations, like the geometry of the beam, location and type of holes, applied loads and type of reinforcement have been studied. Some of these investigations are briefly summarized below.

2.2 Bengtsson and Dahl, 1971

Bengtsson and Dahl tested glulam beams with different hole shapes and sizes, with and without reinforcement in the thesis Inverkan av hål nära upplag på hållfastheten hos

limträbalkar (Influence of holes near support on the strength of glulam beams) from

1971[1].They used 10 mm thick plywood for reinforcement, which was glue-nailed to both sides of the beams. The glulam beam samples were made from spruce of strength class L40. The results are presented in terms of failure loads and in addition it is stated that cracks appeared at load levels of 70-90 % of the ”failure loads” in most of the tests.

2.3 Kolb and Frech, 1977

Kolb and Frech tested glulam beams with holes with and without reinforcement in “Untersuchungen an durchbrochenen Bindern aus Brettschichtholz” (Analyses of glulam beams with holes) from 1977[2]. They tested 12 beams with 6 different configurations with respect to various shapes of holes, hole placements and reinforcements. The result indicated that for the holes near the point load, the crack growth was from the hole to the beam end, but for the beams with a hole placed in the zone with pure moment, the capacity was limited by bending failure at mid span.

2.4 Penttala, 1980

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initial cracking and load at failure. The results indicated that the load at initial cracking was typically 70% of the load at failure.

2.5 Hallström, 1995

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3. Experimental test methods and results

3.1 General

A total of 12 beams have been used. The beams were manufactured for a research project running at Växjö University in co-cooperation with Södra Timber AB. Each beam consists of 13 laminations glued together in the wet (green) state, that is before drying them. The beam dimensions are (5200X300X45) mm. In each beam two holes were made, each hole center placed 853.5mm from each end. The purpose of making two holes in one beam is to obtain a maximum number of tests, while using a minimum number of beams. The 24 holes were divided into two types: 12 circular with 100mm diameter and 12 quadratic 100X100mm in dimensions and with a corner radius of 10 mm. Each hole type was subdivided into three groups 6 holes without reinforcement, 3 holes reinforced by glass fiber mats with random orientation (165g/m2) glued with epoxy (NM275A and hardener NM275B) and 3 holes reinforced by birch plywood (12mm thickness made from nine sheets) glued by resorcinol (phenol) adhesive 1711+2622.

An Alvetron testing machine was used for testing the beams in 4-point bending at the 1/3 point of the span. 2 point loads were symmetrically applied, with the hole being centered between one of the point loads and the support as illustrated in figure 3.1. Two types of measurements were used. A contact free deformation measurement system to obtain deformation and strain fields (ARAMIS) and traditional potentiometers and load cell to measure deformations and load. The three potentiometers used were attached to three channels:

i. Ch1: measuring the deformation (crack opening) in the corner close to the support. ii. Ch2: measuring the deformation (crack opening) in the corner close to the load. iii. Ch3: measuring the deformation of beam between the two point loads.

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3.2 Test Setup

Three slightly different test setups have been used in this investigation. The reason for this is that the first two setups used did not work as expected, leading to the fact that it was not possible to test both ends of the beams. When performing the tests, one major aim has been to create a shear force in the area close to the support, without introducing too much bending moment. This means that the hole should be placed close to the support. At the same time the hole cannot be placed too close to the support since then, the stress and strain fields would be disturbed by the reaction force from the support

3.2.1 Test setup A

Figure 3.2 illustrates the details of the first setup used – setup A. One beam was tested with this setup, but during testing the crack developed when testing the first end. The crack passed the beam mid span, so that it was not possible to test the second hole at the other side. Since the set up was not completely symmetric approximately 51% of the total load passes the hole.

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3.2.2 Test Setup B

Figure 3.3 illustrates the second setup used. Three beams were tested with this setup, which included reinforcement in the middle (plywood on both sides of the beam). Unfortunately, due to high bending moment between the two point loads, cracking appeared at the tension side of the beams. Therefore the beams could not be used to test the second hole at the other end. Since the set up was not completely symmetric approximately 51% of the load passes through the hole.

Figure 3.3 Test setup B

3.2.3 Test setup C

Figure 3.4 details the configuration of the setup used for 9 beams. Reinforcement is used on both sides (the plywood in the middle). By increasing the distance between the point loads and decreasing the distance between the supports, the bending moment was reduced, leading to a higher shear force to bending moment ratio.

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3.3 Test Results and Analysis

3.3.1 Rectangular Holes

A total of twelve rectangular holes 100X100mm with a corner radius of 10mm were tested. Six without reinforcement, three reinforced with plywood on both sides and three reinforced with glass fiber on both sides. Setups A and C were used for testing.

Without Reinforcement

Four holes were tested with setup C and two holes were tested with setup A. During testing of the holes with setup C, crack initiation happened at approximately 15KN. The cracks appeared in the corners and developed slowly, the maximum load for these beams varied from 30 KN to 48 KN. One of the two beams tested with setup A (LBX03B01) gave a result similar to the one obtained with setup C. For the last specimen (LBX03B02) no cracking appeared before the beam failed due to the large bending moment. The difference in load levels recorded can be explained by the natural variability of the material. In figure 3.5 and 3.6 some typical results are shown. Table 3.1 presents the test results obtained, the loads indicated refer to the shear force passing the hole.

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Figure 3.6 Testing of rectangular hole without reinforcement. Table 3.1 Test results for rectangular holes without reinforcement

Rectangular without reinforcement Initiation Shear Force (KN) Maximum Shear Force(KN)

LBX-03-A-01 11 21.5 LBX-03-B-01 8.16 15.3 LBX-03-B-02 LBX-06-B-01 10.75 23 LBX-07-A-02 11.35 22.5 LBX-07-B-02 10 24 Setup A Setup C

Reinforcing with Glass Fiber

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Figure 3.7 Load vs. crack opening around the hole (left) and load vs. beam deformation (right)

Figure 3.8. Testing of rectangular holes reinforced with glass fiber. Table 3.2 Test results for rectangular holes with glass fiber reinforcement

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Reinforcing by Plywood

Three rectangular holes reinforced with plywood (12mm thickness, made from nine sheets) glued with resorcinol (phenol) adhesive were tested. Setups B and C were used for testing. From Fig 3.9 it is clear that the deformation is very small around the holes and the initial crack appears probably in the beam but not in the plywood. The applied load exceeded 47kN before the crack developed and the test was stopped since the fracture occurred between the loads in the tension side of the beam. Table 3.3 presents the test results obtained, the loads indicated refer to the shear force passing the hole.

Figure 3.10. Testing of rectangular holes reinforced with plywood

.

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Table 3.3. Test results for rectangular holes with plywood reinforcement

Rectangular with Plywood reinforcement Initiation shear _{Force (KN)} Maximum Shear _{Force (KN)}

LBX-05-A-02 17.85 23.97 LBX-06A-1 18.5 27 LBX-06-B-02 18.5 30 Setup B Setup C

3.3.2 Circular Holes

The two setups B and C were used for testing twelve circular holes with 100mm diameter. As mentioned above, six were without reinforcement, 3 were reinforced with glass fiber and three were reinforced with plywood (12mm thickness made from nine sheets) glued by resorcinol (phenol) adhesive.

Without Reinforcement

Six circular holes without any reinforcement were tested by using setups B and C, and in both cases initial cracks started approximately at (30-35) KN. The failure followed shortly after that and occurred suddenly. The crack developed and the final failure occurred when the load reached 35 KN. In figure 3.11 and 3.12 some typical results are shown. Table 3.4 presents the test results obtained, the loads indicated refer to the shear force passing the hole.

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Figure 3.12. Testing of circular holes without reinforcement. Table 3.4 Test results for circular holes without reinforcement

Circular without reinforcement Initiation Shear _{Force (KN)} Maximum Shear _{Force (KN)}

LBX-01B-02 16.5 25 LBX02A-01 17.85 18.36 LBX02A-02 20.145 20.655 LBX-07-A-01 15 21.5 LBX-07-B-01 20.25 20.5 LBX-01-A-01 18.5 21.75 Setup B Setup C

Reinforcing by Glass Fiber

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Figure 3.14. Testing of circular holes with glass fiber reinforcement. Table 3.5 Test results for circular holes with glass fiber reinforcement Circular with Glass fiber reinforcement Initiation Shear _{Force (KN)} Maximum Shear _{Force (KN)}

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Reinforcing by Plywood

Three circular holes reinforced with plywood (12mm thickness made from nine sheets) glued with resorcinol (phenol) adhesive were tested. From Figure 3.15 and 3.16 it is clear that the deformation is very small around the holes. The initial crack sometimes appeared in the beam but not in the plywood. The load reached 50kN, before the crack developed further and the test was stopped since the fracture occurred between the loads in the tension side of the beam. In one case the crack did develop at the hole and the final failure occurred (cracking around the hole) at 75kN. Table 3.6 presents the test results obtained, the loads indicated refer to the shear force passing the hole.

.

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Figure 3.16. Testing of circular holes with plywood reinforcement. Table 3.6 Test results for circular holes with plywood reinforcement

Circular with Plywood reinforcement Initiation Shear _{Force (KN)} Maximum Shear _{Force (KN)}

LBX-01-A-02 26.75 29

LBX-02-B-01 30 37.5

LBX-05-A-01 15.81 17.34

Setup B

Setup C

3.4 Result comparisons and Conclusion

3.4.1 comparing Rectangular holes with Circular Holes

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Figure 3.17 Load vs. crack opening for circular hole (left) and rectangular hole (right)

3.4.2 The effect of reinforcement

Twelve holes with reinforcements and twelve without reinforcements were tested. Comparing these two groups, some conclusions of the effect of the reinforcement can be drawn. As indicated from figure 3.18 the reinforced holes have a higher strength and stiffness against the shear force and are less brittle. As mentioned above, also in some cases the reinforcement prevents the crack to appear around the holes, or appears but at a larger load.

Figure 3.18 Load vs. crack opening for circular holes glass fiber reinforcement (Left) and (right) without reinforcement

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Comparing different types of reinforcement

Some differences can be noted between the different reinforcement materials. For the glass fiber, all cracks clearly appear around the holes. Using plywood only in one beam, and at a high load level, a crack appeared around the hole. Finally, the plywood reinforcement leads to stronger beams. Of course, the plywood is 12 mm thick, while the glass fiber is only about 1 mm thick and also has a more discrete appearance. See figure 3.18

Figure 3.19 Load vs. crack opening for circular holes with plywood (left) and with glass fiber (right) reinforcement

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4. Theoretical Calculation

4.1 Finite Element equation

The below derivation of finite element equations for two-dimension problems follows closely the one given in Ottosen & Petersson[5]

4.1.1 Equilibrium Equations

The basic equilibrium equations are

(4.1)

Where

σ

represents the stress, and b the body force. The traction, t, on the outer surface of the body is given by

(4.2)

Where n is the outwards pointing normal to the bending surface

.

The weak form in three dimensions is given by

_(4.3)

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And we obtain

(∇�𝑣𝑣)

𝑇𝑇

_{𝜎𝜎 =}

𝜕𝜕𝑣𝑣

𝑥𝑥

𝜕𝜕𝑥𝑥 𝜎𝜎

𝑥𝑥𝑥𝑥

+

𝜕𝜕𝑣𝑣

𝑦𝑦

𝜕𝜕𝑦𝑦 𝜎𝜎

𝑦𝑦𝑦𝑦

+ �

𝜕𝜕𝑣𝑣

𝑥𝑥

𝜕𝜕𝑥𝑥 +

𝜕𝜕𝑣𝑣

𝑦𝑦

𝜕𝜕𝑦𝑦 � 𝜎𝜎

𝑥𝑥𝑦𝑦

(4.4)

By defining the following matrices

∇�=

⎣

⎢

⎡

𝜕𝜕𝑥𝑥𝜕𝜕

0

_{𝜕𝜕𝑦𝑦}𝜕𝜕 𝜕𝜕 𝜕𝜕𝑦𝑦 𝜕𝜕 𝜕𝜕𝑥𝑥

⎦

⎥

⎤

;

_{𝑣𝑣 = �}

_𝑣𝑣

𝑣𝑣

𝑥𝑥 𝑦𝑦

�; 𝜎𝜎 = �

𝜎𝜎

𝑥𝑥𝑥𝑥

𝜎𝜎

𝑦𝑦𝑦𝑦

𝜎𝜎

𝑥𝑥𝑦𝑦

� (4.5)

We can, from the definition of ∇� note that it also can be used for plane strain. We define furthermore:

𝑡𝑡 = �

𝑡𝑡

_𝑡𝑡

𝑥𝑥

𝑦𝑦

�;

𝐛𝐛 = �

𝑏𝑏

𝑥𝑥

𝑏𝑏

𝑦𝑦

�;

(4.6)

With the definitions of matrices in 4.5 and 4.6 the weak form in equation 3.3 becomes

Here we can note that equation 4.7 look as equation 4.3 but with different definitions for 𝐯𝐯, 𝛁𝛁�, 𝝈𝝈, 𝐭𝐭 𝑎𝑎𝑛𝑛𝜎𝜎 𝒃𝒃 as defined in 4.5 and 4.6

y z

Y

_ℒ

x

�(∇�v)

𝑇𝑇

_{𝜎𝜎𝜎𝜎𝑣𝑣}

𝜎𝜎

= �v

𝑇𝑇

_{𝐭𝐭 𝜎𝜎𝑡𝑡}

𝑡𝑡

+ �v

𝑇𝑇

_{𝑏𝑏𝜎𝜎𝑣𝑣}

𝜎𝜎

(4.7)

t

A

b) Illustration of upper surface S+_,

lower surface S- and thickness t (a) Region A and boundary

ℒ for two dimensions

S

+

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-For two dimensional problem we introduce x and y coordinates, and here we denote the region in the XY-plane by A with boundary

ℒ

, see figure 4.1 (a). The thickness t is shown in figure 4.1 (b). Note the difference between the traction vector t and thickness t. The integrands in equation (4.6) are independent in the z-direction and the following equation can be obtain

�(𝛁𝛁�𝐯𝐯)

𝑻𝑻

_{𝝈𝝈𝜎𝜎𝜎𝜎}

𝜎𝜎

= � ��(∇�𝐯𝐯)

𝑇𝑇

_{𝜎𝜎𝜎𝜎𝑧𝑧}

𝑧𝑧

� 𝜎𝜎𝑑𝑑

𝑑𝑑

= �(𝛁𝛁�𝐯𝐯)

𝑻𝑻

_{𝝈𝝈𝑡𝑡𝜎𝜎𝑑𝑑 (4.8)}

𝑑𝑑

�𝐯𝐯

𝑻𝑻

_{𝒃𝒃 𝜎𝜎𝜎𝜎}

𝜎𝜎

= � ��𝐯𝐯

𝑻𝑻

_{𝒃𝒃 𝜎𝜎𝑧𝑧}

𝑧𝑧

� 𝜎𝜎𝑑𝑑

𝑑𝑑

= �𝐯𝐯

𝑻𝑻

_{𝒃𝒃𝑡𝑡𝜎𝜎𝑑𝑑}

𝑑𝑑

Referring to Figure 4.1 (b) we consider the surface integral in equation (4.7)

�𝐯𝐯

𝑻𝑻

_{𝐭𝐭 𝜎𝜎𝑡𝑡}

𝜎𝜎

= � 𝐯𝐯

𝑻𝑻

_{𝐭𝐭 𝜎𝜎𝑡𝑡}

𝑡𝑡+

+ � 𝐯𝐯

𝑻𝑻

_{𝐭𝐭 𝜎𝜎𝑡𝑡}

𝑡𝑡−

+ � ��𝐯𝐯

𝑻𝑻

_{𝐭𝐭𝜎𝜎𝑧𝑧}

𝑍𝑍

� 𝜎𝜎ℒ

ℒ

(4.9)

According to equation (4.6) the traction vector consists of two components tx and ty. Along S+ and S- we have nx=ny=0 and from equation (a), equation (4.2) gives

𝑡𝑡 = �

𝑡𝑡

_𝑡𝑡

𝑥𝑥

𝑦𝑦

� = �

𝜎𝜎

𝑥𝑥𝑧𝑧

𝑛𝑛

𝑧𝑧

𝜎𝜎

𝑦𝑦𝑧𝑧

𝑛𝑛

𝑧𝑧

�

The conditions for plane stress where by, definition we have σxz = σyz = 0, gives us for equation (1.9):

�𝐯𝐯

𝑻𝑻

_{𝐭𝐭 𝜎𝜎𝑡𝑡}

𝜎𝜎

= �𝐯𝐯

𝑻𝑻

_{𝐭𝐭𝑡𝑡𝜎𝜎ℒ (4.10)}

ℒ

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Then by insertion equation (4.10) and (4.8) in (4.7) we obtain

�(𝛁𝛁�𝐯𝐯)

𝑻𝑻

_{𝝈𝝈𝑡𝑡 𝜎𝜎𝑑𝑑}

𝑑𝑑

= �𝐯𝐯

𝑻𝑻

_{𝐭𝐭𝑡𝑡 𝜎𝜎ℒ +}

ℒ

�𝐯𝐯

𝑻𝑻

_{𝒃𝒃𝑡𝑡 𝜎𝜎𝑑𝑑}

𝑑𝑑

(4.11)

Which is the weak form for the two dimensional case. If the thickness of the body is constant then the weak form equation can be expressed as in equation (4.12)

�(𝛁𝛁�𝐯𝐯)

𝑻𝑻

_{𝝈𝝈 𝜎𝜎𝑑𝑑}

𝑑𝑑

= �𝐯𝐯

𝑻𝑻

_{𝐭𝐭 𝜎𝜎ℒ +}

ℒ

�𝐯𝐯

𝑻𝑻

_{𝒃𝒃 𝜎𝜎𝑑𝑑}

𝑑𝑑

(4.12)

FE formulation

The FE-formulation can be derived from (4.12). The displacement vector is

𝑢𝑢 = �

_𝑢𝑢

𝑢𝑢

_𝑦𝑦𝑥𝑥

� (4.13)

And is to be approximated by

𝑢𝑢 = 𝑵𝑵𝑵𝑵 (4.14)

Where N are the interpolation (shape) functions. We can then use the following expression for the arbitrary weight function v:

v = 𝑵𝑵𝑵𝑵 (4.15)

v and c are arbitrary. From equation (4.15) it follows that

𝛁𝛁

� 𝐯𝐯 = 𝐁𝐁𝐁𝐁

Where

𝑩𝑩 = 𝛁𝛁�𝐍𝐍 (4.16)

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As the c- matrix is arbitrary, we can conclude that

(4.18)

Plane strain can be formulated as

(4.19)

Where

𝜎𝜎 = �

𝜎𝜎

𝑥𝑥𝑥𝑥

𝜎𝜎

𝑦𝑦𝑦𝑦

𝜎𝜎

𝑥𝑥𝑦𝑦

�; 𝜀𝜀 = �

𝜀𝜀

𝑥𝑥𝑥𝑥

𝜀𝜀

𝑦𝑦𝑦𝑦

𝜀𝜀

𝑥𝑥𝑦𝑦

�

(4.20)

By using the kinematic relation for strain ε we can derive from displacement

𝜺𝜺 = 𝛁𝛁�𝐮𝐮

From equation 4.14 and 4.16 we obtain

𝜺𝜺 = 𝑩𝑩𝑵𝑵 (4.21)

By inserting the value of 𝛆𝛆 into equation (4.19) the result is

𝝈𝝈 = 𝐃𝐃𝐁𝐁𝐃𝐃 (4.22)

By inserting equation (4.22) into equation (4.17) we obtain

The unit vector n, which is normal to the boundary of the body, bounded by

ℒ

and is located in the xy-plane. The traction vector t along

ℒ

is given by equation (4.6). Thus, the traction boundary conditions, equation (4.2), can be written as

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t = 𝑡𝑡𝑛𝑛 (4.24)

Where

𝑡𝑡 = �

𝜎𝜎

_𝜎𝜎

𝑥𝑥𝑥𝑥_{𝑦𝑦𝑥𝑥}

_𝜎𝜎

𝜎𝜎

𝑥𝑥𝑦𝑦_{𝑦𝑦𝑦𝑦}

� 𝑛𝑛 = �

𝑛𝑛

_𝑛𝑛

𝑥𝑥_𝑦𝑦

� (4.25)

Thus all boundary conditions can be expressed as

(4.26)

Where h and g are known vectors.

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5. Numerical analysis

5.1 ABAQUS program

ABAQUS is computer software solving finite element problems, including dynamics, power statics and electrical applications. In this chapter, a model of the beams is defined. The model contains the different hole shapes as used in the tests. The model is used to calculate the strain around the holes and to show the location of maximum strain, see below figure.

Figure 5.1 Beams with circular holes and quadratic holes. Calculation performed with ABAQUS

5.2 Model Description

The dimensions of the beams were set to (5200X300X45) mm which is the dimensions of the tested beams. A 2D deformable model was created in ABAQUS. Table (5.1) shows the material properties used in the calculations for describing the mechanical properties of the glued laminated beams. E1 young’s modulus in the X direction, E2 is young’s modulus in Y direction, G12 shear modulus in XY direction, G23 shear modulus in YZ direction, G13 shear modulus in XZ direction and V12 is Poisson’s ratio in XY direction.

Table 5.1 Mechanical properties for timber beam

E1 E2 G12 G13 G23 V12

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Two rigid bodies, 150mm in length, were used to model the supports. The rigid body reference points were used to apply boundary conditions. The beams are simply supported, and thus, at the reference points, one side has zero displacement in X and Y directions and the other has zero displacement in the Y direction. Both supports were free to rotate. Two other rigid bodies, 240mm in length, were used to model the plates used in the tests for applying the loads. The interaction between the rigid plates and the beam was modeled with friction, and the coefficient of friction was set to 0.3. After defining the local orientation of the material, the interaction between the rigid bodies and the beam and meshing, the model is ready for solving

5.3 Evaluation of results

Of all data available from the analyses we concentrate on the strain distribution, especially around the holes. Strains in all directions X, Y and XY around both the circular and the rectangular holes are of interest. All evaluations are made in the elastic range. Figure5.1 shows the maximum strain around the holes. The color scale is set such that red is maximum and dark blue is minimum.

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Figure 5.2B Strain in Y direction at a load level of 25.62KN

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In Figure 5.3 strains are shown for the rectangular hole in the elastic range. It can be noted that the maximum strain (red) appears close to the corner

Figure 5.3A Strain in X direction at load level 21.88KN

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6. Results Comparison

The present works includes two main parts, practical and theoretical work. The results show some differences between practical and theoretical (ABAQUS) part. Elastic, plastic and fracture point can be seen during experimental work but in ABAQUS it is not possible to see crack or fracture point, since the model is linear elastics. At the same time, by help of Aramis, measuring the strain around the holes, gives us this information. However by ABAQUS we can get a theoretical (finite element) calculation for strain that it is much different when compared to real strain.

• Here some pictures are shown to clarify the differences and similarity. All figures show the comparison at the same load.

• The reason of this difference is meaning that the FE-model is highly idealized including a perfect orthotropic, homogeneous, material.

i. Photo from ARAMIS ii. Photo from ABAQUS

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Other factors leading to the difference between measured and calculated strain include: the property of the wood, the orientation of the grain, the adhesive layers. When painting the surface ARAMIS as in figure 6.1 can be seen that some points are not useful, since the camera couldn’t follow those points. Generally ABAQUS can give a general idea or expectation about the location of high tension, high compression or fracture, but with the highly idealized modeling used here the differences are rather larger.

i. Photo from ARAMIS _ii. _{Photo from ABAQU}

iii. Photo from ARAMIS iv. Photo from ABAQUS

Figure 6.2 Strain in XY direction

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i. Photo from ARAMIS ii. Photo from ABAQUS

Figure 6.3 Strain in Y direction

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Table 6.1 Strain calculated by ABAQUS

Table 6.2 Shear Force measured during Testing

Hole shear force (KN) Initiation crack Maximum Shear Force (KN)

1.76E+01 2.140E+01

1.08E+01 2.083E+01

Hole Max. E22 Max. E12

8.19E-06 1.083E-05

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7. Concluding Remarks

The present thesis has shown the differences between hole geometry and type of reinforcement, and also the effect of using reinforcement on the beams. These parameters have an effect on the crack initiation around the holes. From our work we can say that cracking depends upon:

I. Hole geometry

II. Using reinforcement or not. III. Type of reinforcement IV. Test setup

V. Beam properties.

For rectangular holes the initial crack appeared at approximately 50% of maximum load due to the sharp corner .These make cracking start early and prevents the energy being stored. However for circular holes, the time between initial crack and final failure is short. The reason is that the circular hole prevents early cracking. This results in more energy being stored around the holes and causes a sudden crack. The different types of reinforcement used to increase the strength and stiffness and the brittleness of the glued laminated beams worked well. Using glass fiber (1 mm thickness) the crack appeared around the holes at lower loads when comparing with plywood reinforcement. However, the glass fiber is more acceptable from an aesthetical point of view. Finally the ABAQUS software results show different results when comparing to the experimental results because of.

I. Material in homogeneities

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8. References

[1] Bengtsson S., Dahl G.

Inverkan av hål nära upplag påa hållfastheten hos limträbalkar. (In Swedish)

(Influence of holes near support on the strength of glulam beams.) Master’s Thesis, Byggnadsteknik II, LTH, Lund University, 1971 [2] Kolb H., Frech P.

Untersuchungen an durchbrochenen Bindern aus Brettschichtholz. (In German)

(Analyses of glulam beams with holes.) Holz als Roh- und Werkstoff 35, p. 125-134, 1977.

[3] Penttala V.

Reiällinen liimapuupalkki. (In Finnish) (Glulam beams with holes.)

Publication 33, Division of Structural Engineering, Helsinki Univeristy of Technology, Otaniemi, 1980.

[4] Hallström S.

Glass fibre reinforcement around holes in laminated timber beams. Report 95-14, Department of Lightweight Structures,

Royal Institute of Technology (KTH), Stockholm, 1995

[5] Niels Ottosen & Hans Petersson,

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1.1. Relation between Ch1 and Ch2(Deformation) with Ch7(Load) in Circular Holes Without reinforcement and showing the deformation around holes

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1.1.1. Relation between Ch3 and Ch7 Load Circular holes 1.1.1.1. Circular holes Without reinforcement

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1.1.2. Rectangular holes

1.1.2.1. Rectangular holes Without reinforcement

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Results For Rectangular

Beam number _{Initiation (KN)}Crack Maximum Load _(KN)

Setup

Status

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Results for Circular

Beam number Crack Initiation _(KN) Maximum Load _(KN) Setup Status

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Rectangular Plywood

reinforcement Circular Plywood reinforcement

_{Rectangular Glass}

Fiber reinforcement

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School of Technology and Design SE- 351 95 Växjö

Sweden

Holes in Glulam Beams – Possible Methods of Reinforcement