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Analytical modelling of timber beams strengthened with composite materials

21 April, 2020 11 min reading
Based on the thesis by: Hamed Hoseinpour, MSc, E.I.T, Civil & Structural Engineer, Infrastructure Specialist

Analytical modelling of timber beams strengthened with composite materials

Wood has been always considered as a material for construction works, but during time it needs to be improved by strengthening through other materials such as steel or FRP.


The design of intervention of the timbers by the other materials needs to be studied in experimental and theoretical ways.


The research presented in this thesis by Hamed Hoseinpour results from a wide experimental work carried out at the University of Padova (Italy) concerning full-scale timber beams strengthened in flexure by means of natural flax fibers and a common unidirectional carbon and is analyzed by theory of the basic mechanics of materials.


The theoretical work was carried out by MATLAB programming code through developing the famous theories in beam analyzing, calibration of the model by pilot test and comparing the results with the results of the other tests which showed a good agreement. In addition during the calibration process, an amplification coefficient equation specifically for the employed wood type in this study was achieved which is similar to the rectangular stress block in concrete theory and can be used in future studies.

Wooden structures

Historical buildings are encountered to the problems coming from degradation in mechanical properties of the material due to the time, especially for wood elements. Wooden structures are always subjected to damage by earthquakes and decaying by the other environmental factors.


Structural elements in the wooden buildings can be strengthened or replaced with other kinds of materials like concrete, steel, but based on the codes and charters, damaged members should be strengthened, repaired, rehabilitated or replaced with the same material. So it is a big issue for the people who are doing research in this area.


As a light material in construction, wood has been always considered because of good performance in both compression and tension. Being light, easy to work and aesthetic appearance is among the wood properties which make it attractive to use in the construction industry.  Also, the nature of environmental friendly should be added to the characteristic.


On the other hand, unpredictable exactly the stiffness and strength in the same type of wood due to the natural defects and also slope of grains can be mentioned.  The main notable problem with wood is durability as after a while it should be replaced or reinforced with other materials like steel, concrete and recently composite materials to resist more for bending or shear loads.


Steel and aluminum bars or plates were the traditional techniques of reinforcing timber structures that have their own disadvantages like high dead load and low compatibility. So reinforcing with fiber strips can be an alternative to replace the old ways.


Use of FRP materials in the field of construction goes back to the beginning of the 1990s when FRP was being used widely for the strengthening of concrete and from then on it was started to use FRP for masonry, wood and steel structures.

Along with the continuous development of composite materials, there have been carried out a lot of research and development for concrete and much less for wood and masonry structures. Wooden Bridges' decks are of the places to use FRP materials for the strengthening of timber elements.


Once starting to think for strengthening it is very important to consider all aspects of the problem to select the proper way because each method can lead to different results. Considering the wide range of products and different mechanical properties of each one, make a selection between them is very difficult for the designer. Meanwhile, it proves the important role of an accurate analysis of the element's characteristics to have the most effective intervention. Strengthening with FRP material is notable in both terms of improving mechanical performance and also continuously decreasing material price as the main obstacle for using before that.


Experimental Campaign 

A wide experimental work was carried out on the timber elements reinforced with different patterns of FRPs and matrix. Tests specimens reinforced by composite fibers were put under a four-point loading test which is a standard way based on the famous codes. In each case, the predominant failure mode was considered as a very important factor in analyzing the test specimens.


Analysis Methodology

Considering the configuration of the experimental bending tests on the timber specimens, an analytical model based on the well-known beam theories so-called Bernoulli and Timoshenko was developed and it was calibrated with the results coming from pilot samples and then it was used to anticipate the behavior of the reinforced samples with a different type of used FRP and matrix and different patterns.


Results and Discussion

Considering the place of installed LVDTs a load-displacement diagram was generated in each case for the same point.


Due to the inhomogeneous characteristic of the wood samples in terms of the slope of grain, defects, etc. it is not possible to achieve all characteristics only from the direct tests and previous studies. So based on the results taken from the pilot test the analytical model was calibrated to get the raw character of the wood.


After calibration of the analytical model, the flexural behavior of this specific timber with different patterns of FRP layers and type, with different glue was anticipated. Following, the results of each experimental test and corresponding results from the analytical model are shown, Fig. 17-a.


In each diagram, the title from left to right shows the type of reinforcement (NR: None reinforced, CFRP: Carbon type FRP, FFRP: Flax (natural) type FRP), type of applied matrix (EP: Epoxy, V: Vinyl), number of FRP layer and test numbers respectively for that specific pattern of timber reinforcement.


The delicate lines in the first graph of each test show the results of the experimental data and thicker lines are representing the results coming from the analytical model. Corresponding lines related to the same LVDT are illustrated by the same color. In each diagram based on the test configuration, there are five LVDTs along the beam and two on the supports, all located on both sides. Regarding the small difference in the results of the LVDTs installed on both sides, an average was made between the outcome values for the corresponding LVDTs.


Also, between the symmetric LVDTs along the beams an average calculated to be compared to the results of the analytical model only for one side regarding the truth that analytical calculation of the displacement along the beam gives equal values for the symmetric points. The values of the LVDTs on the supports were subtracted from the results of the other ones by making a line equation between two points, Fig. 16.


For each test, there is another diagram representing the shape of the beam's deflection through loading. Continues lines are showing the results of the experimental tests and lines made by point pattern are the results of the analytical model for each level of loading. Corresponding lines related to the same level of loading are illustrated by the same color. Fig. 17-b.


First, start with the results of timber reinforcement with CFRP as the pilot test and then results for the other tests.

Based on the results taken from the mentioned pilot test and making a good agreement between theoretical and experimental graphs, the proposed characteristic for the wood material is as follows, Table 2.

In the case of reinforcement with Carbon FRPs due to the calibration of the model with that as the pilot test, there is very good agreement between the results of this test with the analytical model. To show how the model works, the results of the other tests should be illustrated. Fig. 18-a, 18-b.





As it can be seen from the results of the tests with different reinforcement and pattern, there is a very good agreement between results of the analytical and experimental tests which shows a selection of the wood material characteristic such as modulus of elasticity and yielding and ultimate strain points are quite reasonable.


Results from the experimental tests and theoretical analysis showed that in the case of without strengthening, specimens do not show high plastic behavior in compression and failure happens while the specimen is still in the elastic part or in some specimens with a little plastic behavior. But failure in the strengthened specimens was happened after showing complete plastic behavior except for some of the tests that some defects in the timber caused the failure to happen before reaching plastic behavior and they got far from theoretical results while incrementing of loading.


This means the tensile strength of the timber is not enough to utilize all compressive capacity of it and strengthening is a way to use maximum strength of the timber. Almost in all the cases that the experimental results are different from theoretical ones the failure happens in a load level less than what is shown in the theoretical results with more displacement, showing the truth that in analytical model taking into account the effects of the defects and slope of grains for each case is not possible and needs a wide statistical analysis on a high number of reinforced and unreinforced specimens to make reasonable average results.


In most of the cases reinforced with FFRP and using Vinyl glue as the matrix load-displacement graphs of the LVDTs become horizontal after going to the plastic behavior which is due to the stretching of the Vinyl glue along with loading while the theoretical graph stops far from the final point of the displacement. This shows the good deformation capacity of the vinyl glue compared to the specimens reinforced with epoxy which showed more brittle behavior. Based on the theory developed to predict the behavior of these beams under loading it was assumed that FRP and timber are fully connected and behavior of the glue under loading was not considered.


All the collapses observed in the specimens were due to the rapture of the wood in the region of the maximum bending moment combined with the overcoming of the bond shear strength in the wooden region close to the wood/epoxy interface and was propagated along the beams. In the case of high reinforcement, it helps the timber to bear less tensile strains in the same level of loading but due to the effect of shear, it starts to propagate up to the compression zone. This rapture in the timber causes the deboning of the reinforcement and it is mostly brittle.

Error calculation

In order to measure the precise of the analytical model, it needs to calculate the error between analytical and experimental results along the beam for all the corresponding points and also an error in maximum failure load. All the error results for each test are shown separately in Table 3.



On average the amount error is around 15 percent which shows the compatibility of the calibrated model to predict results of the other tests. Considering the error for the pilot test which is about 7 percent the value of the error for the other tests can be balanced and assumed more reasonable.



In conclusion, it is worth mentioning that the quality of doing the tests was high, regarding the reasonable values in deflection and good agreement between the results of the theoretical modeling and experimental tests. The average value of the error was around 15 percent which shows the precise of the performed tests.


The results of this experimental and theoretical work show that tensile strength of the wood is not enough in order to use the maximum capacity of the timber and non-reinforcement specimens fail mostly in the elastic area or at the beginning of the plastic area, but reinforcing of the timber in the tensile area by composite fibers is a very good way to reach the plastic behavior of the wood and utilize maximum capacity.


Considering the shape of deflection in the theoretical graphs, displacement of the point in the middle is more match compared to the points located on the beam sides. In theory, this area of the beam show more plastic behavior and that can be a reason.


Since there were only two pilot tests as none-reinforced beams in which one of them was stopped before reaching failure, calibration of the model only with the other one did not show good agreement with the results of the other tests. So it was decided to make calibration with the specimen reinforced with CFRP. This can be taken into notice for the future works that the number of pilot tests should be enough for the purpose of analyzing either for comparing the results of the other tests with trustable base results.


The results of both Bernoulli and Timoshenko’s theories, in this case, are the same with a very small difference. That shows the minor effect of the shear considering the test's configuration. The most important reason is the small dimension of the cross-section as with increasing the height, results coming from the Timoshenko theory are different than Bernoulli's ones and show more displacement.


The resulted properties of the wood are different from the values taken from the base experiment and the ones collected from the other literature. That is because, based on the codes which are approved in this study, flexure properties of the material are higher than the properties resulted from direct tensile and compressive tests and in some other papers it has been tried to amplify it by some coefficients.


Considering the good agreement of the results between calibrated model and the other tests with different reinforcement it shows for both of the cases (CFRP and FFRP) a unique design procedure can be used during calculation for intervention.


The other conclusion coming from the agreement of the analytical and experimental data, considering the selected wood properties in the calibration process which were the only parameters derived in this step, prove this truth that properties of the combination of the FRP and matrix which were taken from the direct tests, had high accuracy.


The main result of this study was the achievement of an equation to estimate wood plastic stress distribution by a rectangular stress block through Eq. 3, which is unique for this kind of wood and can be used in future studies.


Based on the experimental work done in (Valluzzi, et al., 2015), an increase in the flexural capacity for the CFRP reinforced case was about 46% (compared to the case of none-reinforced) and for the other cases, this increase was about 25-30%.


Basically, all the experimental works in this regard, are looking to show if natural fibers can be a proper alternative for more common carbon fibers which this matter was validated in this experimental work and an analytical model was developed here for the purposes of parametric studies regarding the truth that making specimens is expensive and time-consuming, so this model can be used to develop the theory for designing of the intervention using carbon or natural fibers.


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