Glulam beams reinforced with FRP externally-bonded: theoretical and experimental evaluation

ORIGINAL ARTICLE

Glulam beams reinforced with FRP externally-bonded:theoretical and experimental evaluation

Juliano Fiorelli • Antonio Alves Dias

Received: 8 March 2010 / Accepted: 28 January 2011 / Published online: 11 February 2011

� RILEM 2011

Abstract The glued- laminated lumber (glulam)

technique is an efficient process for the rational use of

wood. Fiber-reinforced polymer (FRPs) associated

with glulam beams provide significant improvements

in strength and stiffness and alter the failure mode of

these structural elements. In this context, this paper

presents guidance for glulam beam production, an

experimental analysis of glulam beams made of Pinus

caribea var. hondurensis species without and with

externally-bonded FRP and theoretical models to

evaluate reinforced glulam beams (bending strength

and stiffness). Concerning the bending strength of the

beams, this paper aims only to analyze the limit state

of ultimate strength in compression and tension. A

specific disposal was used in order to avoid lateral

buckling, once the tested beams have a higher ratio

height-to-width. The results indicate the need of

production control so as to guarantee a higher

efficiency of the glulam beams. The FRP introduced

in the tensile section of glulam beams resulted in

improvements on their bending strength and stiffness

due to the reinforcement thickness increase. During

the beams testing, two failure stages were observed.

The first was a tensile failure on the sheet positioned

under the reinforcement layer, while the second

occurred as a result of a preliminary compression

yielding on the upper side of the lumber, followed by

both a shear failure on the fiber-lumber interface and a

tensile failure in wood. The model shows a good

correlation between the experimental and estimated

results.

Keywords Glulam � FRP � Reinforcement

1 Introduction

When applied to structural elements, the term glued-

laminated lumber (glulam) refers to the material

produced by gluing the edges and faces of wood

sheets along with the wood grain parallel to the axis

of the piece. Long sheets are obtained by joining

boards together longitudinally, gluing them face to

face and edge to edge to obtain the desired height and

width. The sheets can also be bent to produce a

curved shape during the gluing. All these factors

provide a wide variety of design choices, subjected

only to production and/or application cost constraints.

The use of FRP to reinforce beams not only

ensures improvements in the structural strength and

J. Fiorelli (&)

Sao Paulo University—USP, Pirassununga,

Av. Duque de Caxias Norte, 225,

CEP:13635-900 Pirassununga, SP, Brazil

e-mail: [email protected]

A. A. Dias

Sao Carlos School of Engineering—USP,

Av. Trabalhador Saocarlense, 400, Sao Carlos,

SP, Brazil

Materials and Structures (2011) 44:1431–1440

DOI 10.1617/s11527-011-9708-y

stiffness of the element, but also alters its failure

mode. Fiber reinforced polymers (FRP) are formed

from the linking of fibers to a adhesive, making a

composite which presents mechanical properties of

strength and stiffness higher than from each material

by itself. According to Norris and Saadatmanesh [1],

the fibers are responsible for the strength of the

composite, while the adhesive is responsible for the

stress transmissions.

Dagher [2] studied the reinforcement of glulam

beams with carbon fiber blades (1.5 mm thick),

aiming to evaluate the load capacity of these elements.

The fiber provided a better structural behavior to the

parts, leading to a broader use in civil engineering

applications. The carbon fiber blades were applied in

the bottom glue layer on the tensioned section,

resulting in strength increases. For the beams rein-

forced at 1.1% of their height, it was observed a 25%

increase in their load capacity, whereas for those

reinforced at 3.3%, a 60% increase was observed.

Fiorelli and Dias [3] presented a deterministic

model to calculate the stiffness and strength of fiber-

reinforced solid lumber beams. The stiffness was based

on the ‘‘transformed-section’’ analysis. When calcu-

lating the failure mode, the model considers compres-

sive failure of the upper fibers or tensile failure of the

lower fibers. To evaluate the ultimate moment, the

model considers the ultimate tensile and compressive

strength of the lumber. This model is based on the

Navier/Bernoulli hypothesis (plane sections remain

plane after straining). A comparison between the

experimental and estimated results demonstrated very

similar values for bending strength and stiffness.

Triantafillou and Deskovic [4] evaluated the

strength of solid wood beams reinforced with unidi-

rectional carbon fibers fixed with epoxy adhesive. It

was used a reinforcement varying from 0.55 to

0.75 mm thick, which resulted in a 20–40% increase

in the load capacity, respectively.

Lindyberg [5] evaluated 96 glulam beams with

dimensions of 13 9 30 9 670 cm, made of Western

Hemlock Lamstock and Douglas-fir, reinforced with

fiberglass at 1.1 and 3.3% of its height. The fiber was

applied to the last line of glue in the tensioned

section. The bending test was performed according to

ASTM D 198-96 Standard Test Methods of Static

Tests of Lumber in Structural Sizes. The author

pointed that the reinforcement above 3.3% is not

economically feasible since the increase in strength

and stiffness does not justify the investment.

Romani and Blab [6] present a model for design-

ing MLC fiber-reinforced beams, containing different

failure modes for the reinforced MLC beams. There

were assumed constant modulus of elasticity and

strength in tension and compression parallel to the

grain, as well as a linear elastic–plastic ideal behav-

iour. The authors state that the proposed model is

quite conservative, once the theoretical values were

up to 35% lower than the experimental ones. For the

theoretical calculation of the stiffness, the authors

used the transformed section method. Comparing

these results to those obtained experimentally, a good

agreement between these values could be noticed,

with variations of 5%, approximately.

Bergmeister and Luggin [7] studied carbon fiber-

reinforced glulam beams. During the trials, they

observed two stages of failure. The first was a tensile

failure on the sheet positioned under the reinforce-

ment layer, while the second consisted on a combi-

nation of compressive and shear failure.

Tingley and Kent [8] evaluated timber box beams

reinforced with aramid fibers. These fibers presented

modulus of elasticity of 59,000 MPa and tensile

strength exceeding 1,034 MPa. As a result, it was

observed a 21.5% increase in strength and 4.69%

increase in stiffness, compared to the results obtained

for beams without reinforcement. A compressive

failure occurred on the upper fibers of the reinforced

beams, after a large plastic deformation. On the other

hand, a tensile failure was observed for those with no

reinforcement.

Yahyaei-Moayyed and Taheri [9] present a study

about wooden beams reinforced with aramid fiber-

reinforced polymer (AFRP) composites. An extensive

experimental program was carried out to characterize

the creep response of both plain southern yellow pine

(SYP) and Douglas-fir (DF) wood species and

unidirectional aramid fiber-reinforced polymer

(AFRP) composites. AFRP reinforcement was suc-

cessfully used for flexural strengthening of timbers,

the maximum load-carrying capacity of reinforced

timber was dominant with the shear capacity of the

AFRP layer/wood bond interface, the flexural

strength of SYP and DF species were improved by

an average amount of 74 and 31%, respectively, and

the stiffness was increased by approximately 20 and

1432 Materials and Structures (2011) 44:1431–1440

11%. Additionally, a more desirable compressive

failure was observed, especially in DF woods.

On this context, the objective of this work is to

present a glulam beam fabrication method, a theo-

retical model to evaluate reinforced glulam beams

and an experimental analysis of timber beams made

of Pinus caribea var. hondurensis species without

and with FRP.

2 Glulam beam fabrication method

The beams were produced with Pinus caribaea var.

hondurensis wood with a mean density of 0.54 g/cm3

and mean moisture content of around 12%. The

boards were graded visually, following the Southern

Pine Inspection Bureau (SPIB) recommendations

[10] and subsequently submitted to a mechanical

classification, where the modulus of elasticity for

each lumber was determined. Lumbers of better

quality (fewer defects and higher elasticity modulus)

were placed on the region of maximum compressive

and tensile stress, according to the American Ply-

wood Association [11]. Finger-joints were used for

gluing the sheets according to DIN 68 140/1971 [12].

A phenol–resorcinol adhesive was used to glue the

beams, which were then submitted to pressures

ranging from 0.8 MPa to 1.0 MPa for 12 h, as well

as temperatures under 20�C and a 65% relative

humidity. Afterwards, the Glulam Fiber Reinforced

Polymer (GFRP) reinforcement was applied, using

epoxy adhesive AR-300. A lumber sheet was placed

under the reinforcement, not only to obtain fire

protection but also a better esthetic result.

3 Theoretical models

The theoretical models presented here refer to the

bending stiffness and strength of the glulam beams

concerning failure by tension and compression,

without considering lateral buckling.

3.1 Bending stiffness

Considering the linear range of stress–strain, the

bending stiffness of the beam (EI) can be calculated

through the transformed section method (Eq. 1),

using the beam width (b), and the properties of each

lumber sheet: their modulus of elasticity (Ei), thick-

ness (hi) and distance from the centre of the sheet to

the neutral axis (di):

EI ¼X Eibh3

i

12þ Eibhid

2i

� �ð1Þ

3.2 Bending strength

The theoretical model to evaluate the ultimate bend-

ing moment related to tension or compression failure

in the materials, which considers a realistic behavior

for the lumber and fibers, is based in Buchanan [13]

and Lindyberg [4]. The lumber under compression

parallel to the grain has an initial linear elastic

behavior, reaching strength in compression parallel to

the grain (fc), followed by decreasing levels of stress,

until failure, as the strains increase; where ‘‘m’’ is the

relation between the modulus of elasticity on the

plastic and elastic stages. The lumber under tension

parallel to the grain has a linear elastic behavior until

failure (ft). Figure 1 shows the stress–strain relation of

the lumber. The fiberglass reinforced polymer behav-

ior is considered linear elastic until failure.

The strain values on the levels of stress corre-

sponding to strength in tension and compression are

obtained according to Eq. 2.

etu ¼ft0

Eecy ¼

fc0

Eð2Þ

To evaluate the ultimate bending moment of the

beams, it was considered a linear distribution of

strains, both in the lumber and FRP, over the height

Compression

mE 1 1

E

εtu

ε

Tension

ft

εcy εcu

fc

Fig. 1 Stress–strain relation of lumber under compression and

tension parallel to the grain

Materials and Structures (2011) 44:1431–1440 1433

of the beam until failure. Two failure modes were

considered for the lumber: compression and tension

ones in lumber. Failure in FPR was not considered

because its maximum stress level is always lower

than its strength. Figures 2 and 3 show the strain and

stress distribution at failure, considering that the

lumber sheets have the same modulus of elasticity.

However, to calculate the bending strength, the

modulus of elasticity used for each lumber sheet

were the ones obtained through static bending tests.

A software was developed, based on Lindyberg

[5], to calculate the bending strength. Firstly, an

initial strains are considered and the neutral axis

(NA) is positioned at half-height of the beam so that

the forces in each layer (lumber sheets and glass

fibers) can be determined. The real position of the

neutral axis is achieved through an iterative process,

so the resultant force is null. After that, the bending

moment is calculated.

A new step is started by increasing the strains. At

the end of each step, it is verified whether the bending

moment calculated led to a limit state. Regarding to

the failure mode in tension, the limit state occurs

when the maximum stress on the lumber reaches the

tensile strength (ft).

As for the compressive rupture mode, after the

strain at the compressed side reaches the value of ecy,

a gradual compression yielding starts. The bending

moment increases until it reaches a maximum and it

starts decreasing. The limit state for compression is

considered at the point where the calculated bending

moment reaches its maximum value.

4 Experimental program

To evaluate the strength and stiffness of the FRP

reinforced glulam beams, 6 prototypes were prepared

using Pinus caribaea var. hondurensis lumber. The

glulam beams were reinforced with fiberglass along

the last glue line from the tensioned section. The

percentage of fiber employed was either 1.2 or 3.3%

of the height of the beam. The wood was glued with

Phenol–resorcinol (Axo-Nobel) adhesive and the

unidirectional fiberglass fabric (UF 0900, FIBER-

TEX) was glued with AR-300 epoxy adhesive. Two

beams were not reinforced. The beams had a nominal

section of 7 9 30 9 400 cm and 3.3 cm-thick sheets.

The size of each beam, number of sheets and

reinforcement thickness studied are described in

Table 1.

4.1 Classification of the lumber sheets

The lumber sheets used to prepare the glulam beams

were mechanically classified through static tests. A

visual grading was performed according to SPIB [10].

The modulus of elasticity determined here for each

sheet was used in the theoretical model to evaluate

the strength and stiffness of the beams.

Table 2 presents the cross-section, visual grades,

and modulus of elasticity for the each lumber sheet.

h

b

Y

e

εcy

fc

α

Strain (ε) Stress (σ)

NA

Cross section

Fig. 2 Strain and stress diagrams—failure mode in compression

f tf tb

h

εtu

YYe e

α

tensile failure with compression yielding

tensile failure with no compression yielding

Strain (ε) Stress (σ) Stress (σ)

NA

Cross section

Fig. 3 Strain and stress diagrams—failure mode in tension

Table 1 Glulam beams information

Glulam

beam

Number of

lumber sheets

w (cm) h (cm) Reinforcement

thickness (cm)

01 9 7.7 28.9 –

02 9 7.5 28.7 –

03 9 7.6 30.4 0.35

04 9 7.0 30.2 0.35

05 9 6.9 30.8 0.90

06 9 7.0 30.6 0.90


4.2 Characterization of the fiberglass

The mechanical properties of strength and stiffness

(Table 3) of the fiberglass were determined according

to ASTM D 3039-95 [14] Standard Test Method for

Tensile Properties of Polymer Matrix Composite

Material, of the American Society for Testing and

Materials.

4.3 Glulam beam bending test

The beams were subjected to a bending test with

loads applied at one-third intervals along the span

(Fig. 4), according to the ASTM D198-97 [15]

Standard Test Methods of Static Tests of Lumber in

Structural Sizes.

Table 2 Cross-section, visual grade (VG) and modulus of elasticity (E) for each lumber sheet

30 maeB 20 maeB 10 maeBCross section VG E (MPa) Cross section VG E (MPa) Cross section VG E (MPa)

SS-ND 11,178 SS-D 11,077

SS-D 11,522

Nº1-D 10,886 Nº1-ND 11,077 SS-ND 10,201

Nº2-D 10,614 Nº3-ND 11,027 Nº2-D 10,553

Nº2-ND 8,374 Nº3-D 10,382 Nº3-ND 7,521

Nº3-ND 5,229 Nº3-ND 6,667 Nº3-D 8,631

Nº2-ND 9,273 SS-ND 9,017 Nº3-ND 9,416

SS-ND 9,239 Nº2-ND 13,162 Nº1-ND 9,951

Nº1-D 1,278 Nº1-D 12,872 Nº1-D 12,302

SS-D 13,816 SS-D 12,823 SS-ND 13,358

60 maeB 50 maeB 40 maeBCross section VG E (MPa) Cross section VG E (MPa) Cross section VG E (MPa)

SS-ND 11,077

SS-D 11,755

SS-ND 10,372

SS-ND 10,298 Nº1-D 11,636 Nº3-D 11,331

Nº3-ND 10,047 Nº2-ND 11,547 Nº1-ND 11,529

531,9 D-3ºN 461,8 DN-3ºN 240,9 DN-3ºN

084,8 D-3ºN 061,8 DN-3ºN 647,7 DN-3ºN

873,9 D-3ºN 492,11 DN-3ºN 131,8 D-3ºN

Nº2-D 11,769 Nº2-D 11,982 Nº1-ND 9,428

Nº1-ND 13,519 Nº1-D 12,156 SS-D 12,751

SS-D 13,210 SS-D 12,897 SS-D 14,590

Table 3 Strength and Stiffness values of the fiberglass

Strength Stiffness

Mean (MPa) 1,247 56,154

Coefficient of variation (%) 2.24 2.25

Fig. 4 Bending test


The displacement was measured in the central

region of the beam with a dial indicator. The loading

speed was 10 MPa per minute, considering the

maximum stress. A specific disposal was used in

the load points in order to avoid lateral buckling,

once the tested beams have a higher ratio height-to-

width.

Strain gages were installed in the center of the

span, on beams 2, 4 and 6, as shown on Fig. 5.

5 Results and discussion

Beams without reinforcement were tested until fail-

ure and the bending moment at failure was denoted as

M1. For the reinforced beams, two failure stages were

observed. Firstly, there was a tensile failure on the

bottom sheet, located under the FRP layer (the

bending moment at this failure stage was denoted

as M1). After that, another failure starts after a

gradual compression yielding at the upper side of the

E2 E3

E1

E4

FRP

Fig. 5 Position of the

strain gages

Fig. 6 Strains distribution

along the height of the

beams for various levels of

loading


beam, followed by both a shear failure on the FRP-

timber interface and a tension failure in the wood (the

bending moment at this second failure stage was

denoted as M2).

5.1 Analysis of the strains

Figure 6 presents the values of the deformations

along the height of the beams, for different levels of

loading. The values of the experimental strains are

being marked as dots, with straight dashed lines

connecting the dots related to the same level of

loading. The continuous lines represent the values of

the strains which were obtained through the theoret-

ical model. On each figure, lines with the same color

refer to the same level of loading. For the level of

loading corresponding to the first tensile failure (M1),

there are only being shown the theoretical values of

the strains, once the experimental values could not be

measured.

On Fig. 7, there are being presented the values of

the strains on both the upper and lower sides in

relation to the bending moment applied. Likewise,

continuous and dashed lines refer to theoretical and

experimental values, respectively.

By looking at Figs. 6 and 7, it is possible to state

that, in general, there is a good agreement between

the theoretical and the experimental values. However,

probably due to imperfections on the bonding

between the reinforcement and the bottom sheet,

the experimental values obtained for beam 06 are

considerably different from the expected results.

5.2 Bending stiffness and strength of the beams

Table 4 indicates experimental values for compres-

sion and tension strength (fc0 and ft0) determined by

testing in clear wood specimens, extracted from the

top and bottom sheet of each tested beam.

Table 5 indicates theoretical and experimental

values for bending stiffness and strength. Theoretical

(estimated) values were determined according to the

theoretical models presented in Sect. 3. Concerning

the bending strength calculated, was used a value of

m = 0.31 (evaluated through compression tests), and

0.64 ft0 for strength in tension (a preliminary

calibration of the model indicated the use of 0.64

ft0, in order to consider the transposition to the

structural element and the existence of joints in the

sheets [16]). For the reinforced beams are presented

two bending moment at failure: concerning to the two

failures stages, M1 and M2.

Based on Table 5, the estimated values have good

agreement with the ones experimentally observed for

the bending stiffness. The estimated failure moment

(using 0.64 ft0 for the tension strength in the model)

has good correlation with the experimental value

Fig. 7 Bending moment–strain relationship

Table 4 Experimental values for compression and tension

strength

Beam fc0 (MPa) ft0 (MPa)

01 44.4 42.4

02 47.2 37.5

03 54.6 50.0

04 51.4 57.6

05 61.3 48.8

06 54.0 62.8


(M1) in the first failure stage, presenting a maximum

variation of 29%.

Reinforced beams with a lumber sheet under the

reinforcement layer present an additional safety

after the tension failure in this sheet, as can be

seen on the results obtained in the second failure

stage (M2).

Figure 8 shows the failure mode for the beams

without reinforcement and Fig. 9 shows the failures

modes of the reinforced beams, that have presented

two failure stages.

6 Conclusion

Based on the current results, it is possible to conclude

that the method used to produce glulam beams led to

a higher efficiency of the structural elements.

The GFRP introduced in the tensioned side of

glulam beams improved strength and stiffness as the

percentage of reinforcement increased.

The analysis of the strains on the experimentally

evaluated beams leads to the statement that, for most

beams, the theoretical deformations determined by

the proposed model of calculation are close to the

experimental deformations, which ensures the valid-

ity of the initial hypotheses.

Reinforced beams have presented two failure

stages. The first one was caused by the tension on

the sheet positioned under the reinforcement layer,

while the second occurred as a result of a compres-

sion yielding on the upper side of the beam, followed

by both a shear failure on the fiber-lumber interface

and a tensile failure on the wood.

The theoretical models show a good correlation

between the experimental and estimated results. For

the bending stiffness (EI), the experimental and

estimated values (transformed section method)

showed a difference of approximately 5%. Bending

strength could be safely estimated for the six tested

beams using 64% of the strength in tension parallel to

the grain, evaluated through clear wood specimens

extracted from the bottom lumber sheet of each beam.

The beams built on this way—with a sheet after

each reinforcement layer—present an extra safety

after tensile failures in the lower lumber sheet.

Table 5 Experimental and estimated values for flexural stiffness and failure moment

Beam EI (kN cm2) EIexp./EIest. Bending moment at failure (kN cm) M2/M1 M1/Mest

Exp. Estimated M1 M2 Estimated

01 16,826,463 18,179,793 0.92 3,824 – 3,888 – 0.98

02 17,179,260 17,458,861 0.98 4,220 – 3,655 – 1.15

03 22,050,998 20,186,708 1.09 6,200 7,835 5,249 1.26 1.18

04 19,278,948 20,080,207 0.96 6,143 6,875 6,161 1.12 0.99

05 24,255,268 23,300,058 1.04 8,173 8,906 6,291 1.09 1.29

06 21,978,306 22,844,327 0.96 7,948 8,568 7,280 1.08 1.09

Fig. 8 Beams 01 and 02—(without reinforcement)—tensile failure began at the lower lumber sheet and spread to finger-joints


Acknowledgment The authors gratefully acknowledge the

financial support of the Brazilian research financing institution

FAPESP—Fundacao de Amparo a Pesquisa do Estado de Sao

Paulo.

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Glulam beams reinforced with FRP externally-bonded: theoretical and experimental evaluation

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