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Electronic Journal of Polish Agricultural Universities (EJPAU) founded by all Polish Agriculture Universities presents original papers and review articles relevant to all aspects of agricultural sciences. It is target for persons working both in science and industry,regulatory agencies or teaching in agricultural sector. Covered by IFIS Publishing (Food Science and Technology Abstracts), ELSEVIER Science - Food Science and Technology Program, CAS USA (Chemical Abstracts), CABI Publishing UK and ALPSP (Association of Learned and Professional Society Publisher - full membership). Presented in the Master List of Thomson ISI.

Volume 9
Issue 4
Topic:
ELECTRONIC
JOURNAL OF
POLISH
AGRICULTURAL
UNIVERSITIES
. , EJPAU 9(4), #37.
Available Online: http://www.ejpau.media.pl/volume9/issue4/art-37.html


 

ABSTRACT

The article presents results of analytical and numerical investigations on the effect of reinforcement on the load-carrying capacity and bending rigidity of combined I-beams made of timber and OSB board. The reinforcement effect was achieved by combining, with the assistance of the gluing technique, of a CFRP type carbon composite with wooden elements of the beam. The obtained results were presented in the form of fields of combined states of stresses and deformations in individual beam elements. Calculations were performed on numerical models employing the finite elements method (FEM).

Key words: .

INTRODUCTION

The reinforcement of structural elements used in civil engineering industry is achieved more and more often employing composite materials. The best known of these materials with which considerable hopes are associated include carbon or glass fibres [2, 3, 8]. These materials are characterised by very good specific tensile strength (ratio of the tensile strength to density), high elasticity modulus, deformation linearity practically up to destruction as well as viscosity and resistance to chemical agents. However, the disadvantages of these materials include: poor fire resistance, sensitivity to mechanical damage and a certain amount of rheological properties. Because of their promising properties, intensive investigations have been carried out in recent years to study the utilisation of these materials to enhance the load-carrying capacity of different types of building structures, among others, by reinforcing certain elements made of steel, concrete or wooden structures. In this way, it is possible to improve strength parameters without affecting significantly the dimensions or weight of the structure itself. The improvement of the load-carrying capacity can be achieved, among others, by gluing the composite in the form of bands or mats to the base or by gluing inside the reinforced element. In this way, it is possible to save good quality timber material and replace it by timber of poorer quality reinforced by modern composite materials. However, these solutions have recently been facing some technological-practical as well as economical problems.

RESEARCH OBJECTIVE

The aim of the experiments was to determine, on the basis of theoretical and numerical calculations, the impact of the reinforcement with Carbon Fibre Reinforced Polymer (CFRP) bands of the combined wood and OSB board I-beams on their load-carrying capacity and rigidity. In addition, the investigations aimed to determine the values of stresses and deformations, primarily, in the zone of the connection of the composite and wood as well as in the jointing area of the OSB board, as the web of the I-beam, and wood flanges of the beam.

DESCRIPTION OF THE STRUCTURE OF NUMERICAL MODELS AND RESEARCH METHODS

The required numerical calculations were conducted using computer techniques employing, a professional calculation program of an American company Algor® which carries out calculations based on the finite elements method (FEM) [11, 12, 13]. The type of the examined beams as well as the boundary conditions and loading type are presented in Figure 1. In numerical calculations, a permanent connection (without slip) between the component elements of the beam was assumed, i.e. between the wood flanges and the web board and the carbon composite. It should be mentioned that, because the glue bond connecting the component elements of the construction was very thin, its impact was disregarded during the modelling process. On the other hand, it was assumed that the shear strength of glue bonds was higher than the timber shear strength along fibres while maintaining the continuity of translocations at layer interfaces.

Fig. 1. Types of beams and way of loading: a) model beam of O-type; b), c) reinforced types of beams;
d) e) f) FEM models

Because of the orthogonal anisotropy of the wood material and the OSB board, they were discretised creating a structural mesh of 8-node brick elements and 6-node prism elements of the Linear Brick type. After the discretisation, the beam model consisted of the following quantities of finite elements: 8640 – the OSB board; 14 256 – wood flanges; 1920 – bracing brackets; 864 – carbon composite. The total of approximately 25 680 finite elements containing 30 735 nodes were used in the discretised model of the reinforced beam. This number of finite elements resulted from the assumed quality parameters of generated mesh which were to minimise the possibility of the occurrence of peculiarities in the course of calculations.

Taking into account empirical data and literature analysis [4, 15], wood elasticity constants, were selected as estimate values corresponding to the C30 class of softwood according to the PN-B-03150:2000 standard [9]. The elasticity constants for the domestic OSB board were adopted from literature data [1, 14, 15] and the appropriate standard – PN-EN300:2000. Technical properties of the applied materials are presented in Figure 2.

Fig. 2. Values of the adopted material constants of timber of OSB board

The straps manufactured as a CFRP composite have many advantages. Some of their most important properties include: high elasticity modulus (1.5-4.8 x 105 MPa), linearity of strains (maintained until destruction), high tensile strength and negligible volume weight (1.6-2.0 g*(cm3)-1 as well as resistance to alkali and corrosion [10]. Two types of carbon fibres S and M of the Sika® CarboDur Company were used in the performed numerical analysis. Their characteristic properties are given in Table 1 [9].

Table 1. Characteristic data of the employed carbon composites

Parameters

Types of Sika® CarboDur® straps

S

M

Young’s modulus of elasticity [GPa]


160-165


200-210

Tensile strength
[MPa]


2800


2800

Mean strain at break
[MPa]


2800


3100

Strain at break
[%]


1.70


1.35

The reinforcement of the combined beams made of wood and OSB board consisted in gluing CFRP straps in regions where the tensile stresses occurred. The way of positioning of the two types of composites are shown in Figures 1b and c. In order to compare the strength parameters, the author made an assumption that there were identical contact areas between the composite and wood. Theoretical calculations of the rigidity of the reinforced combined beams, taking into account material diversity of the composite, were carried out according to the classical elasticity theory referring to deformable materials [4, 10]. Limiting the calculations to the linear elasticity and small displacements, the maximum deflections of the beam axis were expressed with the formula:

           (1)

Analytical calculations of the deflection of reinforced beams were carried out taking into account the following relations:

Aequiv.D = Ad + n1 Ap            (2)

Aequiv.DR = Ad + n1 Ap +n:S;M AW:I,II           (3)

           (4)

where:

n1= Ep / Ed; n:S,M = Ew:S,M / Ed,
Ed
elasticity modulus of wooden flanges,
Ew:S.Melasticity modulus of the S, M types of composites
ApEp web’s modulus of elasticity,
web cross section area,
Ad – flanges cross section area,
Aw: I, II – cross section of the composite straps,
Jd – axial moment of inertia of flanges,
Jp – web’s axial moment of inertia,
Jw:I,II – axial moments of inertia of composite straps.

Calculations of the geometric characteristics of cross sections of beams are presented in Table 2.

Table 2. Geometric characteristics of the cross section area of beams

Beam type

Composite modulus of elasticity
[GPa]

Composite cross section
Aw: I, II,
[mm2]

Beam cross section reduced to timber
Aequiv.DR
[mm2]

Equivalent moment
of inertia
Jequiv.D
10-3 [mm4]

0

-

-

4739.0

3266.1

I S

165

63

9861.3

4327.7

I M

210

63

9861.5

4617.2

II S

165

30.8

9181.7

3614.9

II M

210

30.8

9297.2

3719.1


CALCULATIONS AND ANALYSIS OF RESULTS

In order to perform numerical calculations, two types of virtual beam models differing with regard to their construction and strength parameters of the composite were prepared. Figure 3 presents a schematic diagram of the load distribution of concentrated forces as well as the boundary conditions.

Fig. 3. Application of concentrated forces of the beam model

Figure 4 shows a perspective view of an exemplar model after its discretisation as well as the mutual contact of solid finite elements at the contact interface of materials.

Fig. 4. View of the solid model of the reinforced beam type ll S

The geometry of the model used for the simulation calculations was determined in the global system of coordinates (Fig. 5). On the other hand, material properties were determined in local systems of individual component materials. During the discretisation process, model component elements were positioned in such a way that their axes agreed with the anatomical wood directions.

Fig. 5. Axis orientation of the adopted system of coordinates

Numerical calculations of deflections of the combined beam models were carried out at two ranges of loads: 9.0 kN and 11.2 kN. The results of numerical analyses for the selected models are presented in Figure 6 in the form of fields of displacements. Table 3 presents results of deflections of all types of beam models in the central area both for analytical and numerical calculations.

Fig. 6. Form of deformations of selected beam models at the loading P = 9 kN: a) type-0, b) type-IS, c) type-IIS

Table 3. Maximum vertical displacement (deflection) of beams f [mm]

Load
P
[kN]

Types of beams

0

I S

I M

II S

II M

Theor.acc. to form. 5

FEM

Theor.acc. to form. 5

FEM

Theor.acc. to form. 5

FEM

Theor.acc. to form. 5

FEM

Theor.acc. to form. 5

FEM

f [mm]

9.0

11.78

13.52

8.89

10.66

8.33

10.21

10.64

12.40

10.34

12.29

11.2

14.66

16.82

11.06

13.27

10.37

12.71

13.24

15.43

12.87

15.09

The presented shape of the deformation at the adopted type of support and load shows that the greatest beam deflection occurs in its central part in the region of pure bending. The analysis of the form of deflections of individual models revealed, that the deflection line takes the form of a parabolic curve deflected more or less depending on the parameters of the carbon fibre. This result confirms that there is the impact of the reinforcing element (composite) on the stiffening of the reinforced element. The analysis of numerical calculations of the displacement confirms that the rigidity of reinforced beams increases in comparison with the rigidity of the non-reinforced beams. The value of deflections in the central parts of both types of reinforced beams increased by about 24% in comparison with the beams which were not reinforced. The results of numerical calculations of stress distributions are presented in Figures 7 and 8 as isolines of equivalent stresses.

Fig. 7. Distribution of reduced stresses in the beam type – 0: a) selection of the cross section, b) stress distribution in the cross section

Fig. 8. Distribution of equivalent stresses at the 9 kN load in the central cross sections of beams: a) type l M, b) type II S

Equivalent stresses, in accordance with the Huber-Mises hypothesis, in the special state of stress are expressed using the relation:

        (5)

Values of the calculated reduced stresses in selected points of Figure 9 in the central cross section plane are presented in Table 4.

Fig. 9. Identification of estimated points on the cross section

Table 4. Equivalent stresses in estimated points σequiv. [MPa]

Beam type

P
[kN]

Estimated points

Top timber flange

Bottom timber flange

Composite

a

b

c

d

f

g

h

i

k

m

n

p

0

9.0

17.38

17.38

10.29

10.29

10.29

10.29

17.41

17.41

       

11.2

21.63

21.63

12.81

12.81

12.80

12.80

21.66

21.66

       

I S

9.0

15.68

15.68

10.18

10.18

5.82

5.82

59.83

59.83

   

157.2

157.2

11.2

19.52

19.52

12.67

12.67

7.22

7.22

74.45

74.45

   

197.3

197.3

I M

9.0

15.41

15.41

10.17

10.17

5.07

5.07

67.69

67.69

   

183.2

183.2

11.2

19.18

19.18

12.66

12.66

6.32

6.32

84.22

84.22

   

228.3

228.3

II S

9.0

16.83

16.83

10.40

10.40

8.24

8.24

14.72

14.72

172.9

172.9

   

11.2

20.97

20.97

12.97

12.97

10.27

10.27

18.31

18.31

214.9

214.9

   

II M

9.0

16.72

16.72

10.45

10.45

7.78

7.78

14.08

14.08

209.7

209.7

 

 

11.2

20.81

20.81

13.01

13.01

9.67

9.67

17.52

17.52

260.9

260.9

 

 

It is quite obvious from the distribution of the equivalent stresses in individual beam models that the values of equivalent stresses in the reinforced beams declined in comparison with beams which were not reinforced. The stress reduction increased with the increase of the longitudinal elasticity coefficient of the composite. It was found that with the increase of the composite elasticity coefficient, about 20% decline in the equivalent stresses in the reinforced elements occurred. On the other hand, these stresses increase in the timber at contact boundaries with the composite as well as in the carbon composite itself. Maximum stresses occur in the pure bending zone and they reach the values close to the limiting normal stresses for timber (the mean value for softwood along fibres amounts to about 90 MPa) [4]. Also the values of acceptable normal compression stresses were not exceeded in any of the examined beams. The maximum value of these stresses at the load of 11.2 kN in the region of pure bending in the top wood flanges amounted to about 20.81 MPa (beam type II M). This constitutes nearly half of the mean allowable values of compression stresses (maximum 30-45 MPa for coniferous wood along fibres). From the analysis of stresses of beams subjected to bending it is evident that the highest shear stresses occur in the central part of the beam along the neutral bending axis which amounts to 3.2 MPa.

Fig. 10. Distribution of reduced stresses in the composite

Based on the literature review related to experiments on both timber and concrete beams reinforced with carbon composite, it can be concluded that the destruction mechanisms are similar [1, 3, 4, 7, 10]. It is possible to prognosticate these mechanisms, from the distribution of the fields of reduced stresses shown in Figures 7, 8 and 10, the areas of damage caused by the loosening of the composite from the timber surface or as a result of exhaustion of the load carrying capacity of the compressed zones in the beams.

CONCLUSIONS

On the basis of the performed analysis of numerical calculations it can be concluded that CFRP straps can be successfully applied to reinforce elements of wood structural in civil engineering. Noticeable increments of load-carrying capacity and rigidity of reinforced beams regions of the maximum effort of the material and the form of deformations at a specified level of were found depending on the degree of the applied reinforcement. The analysis of deformations of the numerical models, as well as the distribution of stresses, allow to initially determine the load. The introduction of the reinforcing element into the construction exerts an optimal effect on the distribution of stresses between individual elements of the structural. The introduction of reinforcing composites, especially in zones where tensile stresses occur, significantly improves the mechanical properties of timber in the direction perpendicular to the direction of loading forces. This effect refers to the unification of mechanical properties in relation to wood defects, e.g. heterogeneity of annual rings etc. The performed simulation investigations, thanks to their abundant graphic part, create comfortable conditions for analyses using various types of loads, fixation, modification of mechanical properties of individual materials etc. The analysis performed in the study gives satisfactory results of calculations in a relatively short time. However, not all questions connected with the strength of the examined reinforced materials were answered. Therefore, it appears appropriate to carry out further experiments and investigations with the aim to determine the response of reinforced elements under long-term loads, taking into account the existence of different rheological properties of the structure of the component elements.

REFERENCES

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  3. Fiorelli J., Alves Dias A., 2003. Analysis of the strength and stiffness of timber beams reinforced with carbon fiber and glass fiber. Mater. Res. 2, 193-202.

  4. Lis Zb., Rapp P., 2002. Badanie belek drewnianych wzmocnionych tasmami z włókien węglowych [Investigation of timber beams strengthened by carbon fibers reinforcing strips]. Inż. Budown. 7, 309-392 [in Polish].

  5. Makowski A., 2005. Wykorzystanie metody elementów skończonych do analizy dystrybucji naprężeń w belce zespolonej [The analysis of stress distribution with use of finite elements method in joint beam]. Przem. Drzew. 7-8, 36-41 [in Polish].

  6. Neuhaus H., 2004. Budownictwo drewniane [The timber construction]. Polskie Wydawnictwo Techniczne, Rzeszów [in Polish].

  7. Spyrakos C.C., 1994. Finite Element Analysis in Engineering Practice. Algor Inc. Publishing Division Pittsburgh. PA USA.

  8. Spyrakos C.C., Raftoyiannis J., 1997. Linear and nonlinear finite element analysis in engineering practice. Algor Inc. Publishing Division, Pittsburgh PA USA 1997.

  9. Leichti R.J., Falk R.H., Lauffenberg T.L., 1990. Prefabricated wood composite I-beam-a literature review. Wood Fiber Sci. 22, 1, 62-79.

  10. Mielczarek Zb., 2001. Nowoczesne konstrukcje w budownictwie ogólnym [Modern construction in civil building]. Arkady, Warsaw.

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  12. Wilczyński A., Gogolin M., 1999. Ortotropia własciwosci sprężystych płyty OSB [Orthotropy of elastic properties of oriented strand board]. Konf. Nauk. Drewno i materiały drewnopochodne w konstrukcjach budowlanych. Szczecin-Swinoujscie, 103-109 [in Polish].

  13. Wood as an engineering material. 1999. Wood handbook. Forest Products Laboratory.

  14. www.sika.pl

  15. PN-B-03150:2000. Konstrukcje z drewna i materiałów drewnopochodnych. Obliczenia statyczne i projektowanie [Timber structures. Design rules. Materials].

 

Accepted for print: 29.11.2006



Responses to this article, comments are invited and should be submitted within three months of the publication of the article. If accepted for publication, they will be published in the chapter headed 'Discussions' and hyperlinked to the article.


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