Volume 9
Issue 4
JOURNAL OF
POLISH
AGRICULTURAL
UNIVERSITIES
Available Online: http://www.ejpau.media.pl/volume9/issue4/art37.html
The article presents results of analytical and numerical investigations on the effect of reinforcement on the loadcarrying capacity and bending rigidity of combined Ibeams 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 loadcarrying 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 loadcarrying 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 technologicalpractical 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 Ibeams on their loadcarrying 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 Ibeam, 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 Otype; 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 8node brick elements and 6node 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 PNB03150:2000 standard [9]. The elasticity constants for the domestic OSB board were adopted from literature data [1, 14, 15] and the appropriate standard – PNEN300:2000. 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 (1.54.8 x 10^{5} MPa), linearity of strains (maintained until destruction), high tensile strength and negligible volume weight (1.62.0 g*(cm^{3})^{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] 


Tensile strength 


Mean strain at break 


Strain at break 


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:
Cross section area of the combined beam reduced to wood
A_{equiv.D }= A_{d }+ n_{1} A_{p } (2)
Cross section area of the reinforced beam reduced to wood
A_{equiv.DR }= A_{d }+ n_{1} A_{p }+n:_{S;M} A_{W:I,II} (3)
Equivalent moment of inertia of the combined cross section in relation to the central main axis
(4) 
where:
n_{1}= E_{p }/ E_{d}; n_{:S,M} = E_{w:S,M }/ E_{d},
E_{d} – elasticity modulus of wooden flanges,
E_{w:S.M} – elasticity modulus of the S, M types of composites
A_{p}– E_{p }– web’s modulus of elasticity,
web cross section area,
A_{d} – flanges cross section area,
A_{w: I, II} – cross section of the composite straps,
J_{d} – axial moment of inertia of flanges,
J_{p} – web’s axial moment of inertia,
J_{w: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 
Composite cross section 
Beam cross section reduced to timber 
Equivalent moment 
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) type0, b) typeIS, c) typeIIS 
Table 3. Maximum vertical displacement (deflection) of beams f [mm] 
Load 
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 nonreinforced 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 HuberMises 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 σ_{equiv.} [MPa] 
Beam type 
P 
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 3045 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 loadcarrying 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 longterm loads, taking into account the existence of different rheological properties of the structure of the component elements.
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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.