A pseudo-ductile approach design of glued laminated timber beams

A pseudo-ductile approach design of glued laminated timber beams
Massimo DEL SENNO
First Researcher
ITL CNR
S. Michele a/Adige, Trento,
Italy
Maurizio PIAZZA
Associated Professor
Department of Mechanical &
Structural Engineering,
Trento, Italy
Roberto TOMASI
Post Graduated Student
Department of Mechanical &
Structural Engineering,
Trento, Italy
Massimo Del Senno, born 1944,
got his electronic engineering
degree in Bologna, 1969. He is first
researcher at the Institute for Wood
Technology since 1974. His
research activity is currently
oriented towards wood structure
fire behaviour and rehabilitation of
ancient timber structures.
Maurizio Piazza, born 1953, got his
civil engineering degree in Padova,
1978. Researcher at the University
of Padova since 1978, he is
professor at the University of
Trento since 1992. His research
activity is currently oriented
towards timber structures, and to
strengthening of existing ones.
Roberto Tomasi, born 1973, got his
civil engineering degree in Trento,
2000. He got his PhD degree on the
subject "Design, restoration and
monitoring of conventional and
innovative structures", 2004.
Summary
Wood is a brittle material, with a poor attitude to dissipate energy: this fact, when comparing timber
with other building materials such as steel or reinforced concrete, is a severe obstacle in using
timber in seismic areas, because failure can suddenly occur, without any warning. On the other
hand the excellent ratio between strength and dead weight can be considered optimum in order to
reduce the effect of dynamic loads. Traditionally to obtain energy dissipation in timber structures it
has been resorted to plastic deformations occurring in the mechanical joints manufactured with
mechanical connectors (dowel, nail, etc.).
The research reported in this paper aims to identify and implement means to improve the dissipative
behaviour of timber structures, particularly when brittle behaviour of wooden elements can
represent an obstacle to the choice of timber structures. Two technological approach solutions are
under investigation within the frame of a three-year national research project: the mixed glulam
beam manufactured by coupling laminations of different wood species, featuring a better
performance as far the global ductile behaviour is concerned; homogeneous glulam beam reinforced
with steel bars. The basic assumption of these technologies is the strengthening of the tension side
of the beam, in order to allow the compression side to develop a plastic behaviour before the brittle
failure occurs in the tension zone: the global behaviour of these beams has been indicated by the
authors as pseudo-ductile.
A numerical iterative model has been worked out in order to determine the moment-curvature
relationship in the plastic field up to failure.
The tests on mixed species glued laminated timber beams confirmed the predicted pseudo-ductile
behaviour. The behaviour of glulam beams reinforced with steel bars are currently under
investigation.
1.
Introduction
Several solutions have been already proposed by several authors, in which the tension zones of the
timber elements are reinforced, externally or internally, by means of other more resistant materials
in order to improve the global stiffness and strength properties of timber beams. Steel re-bars have
been used by Lantos [1]. In recent years, the increase of the fiber-reinforced polymer materials
industry has encouraged several researchers in the application of FRPs for strengthening timber
structures [2]. A new solution technology, analogous to the reinforce concrete with steel re–bars,
whit the commercial name Armalam®, has been proposed [3], and attained a patent in Europe.
On the contrary, there are few examples, in the scientific literature, of investigations on the failure
behaviour of wooden beams in bending, regarding the brittle behaviour of fibers in tension.
Buchanan [4] has investigated the possible failure modes of lumber beams, suggesting numerical
models in order to study the moment-curvature pattern. Krueger et al. [5] tried to experimentally
verify the feasibility of a limit design approach for “reinforced” wood structures, investigating the
possibility of a ductile bending failure of elements both of solid wood and glued laminate beams
reinforced by means of steel plates.
Mixed species glulam beams have been proposed and their behaviour investigated by several
authors in the past [6]: in these solutions, laminations of two different species are placed
symmetrically, with the more resistant species in the outermost areas of the section. Currently this
kind of beams are ordinary produced and utilized in many countries. Recently, some researchers [7]
have proposed solutions based on mixed species beams with laminations of poplar clones from fast
growth plantations.
Poplar has never had an important role in structural use notwithstanding a great availability of raw
material coming mainly from Euro-American poplar plantations. In particular, the interest for clone
‘I 214’, the most cultivated in Italy, lies in its low density (about 320 kg/m3), and in its favourable
shear behaviour, comparable to that of Norway spruce (Picea excelsa Link), the most important
species in Europe for structural destinations. This feature led to introduce poplar laminations near
the neutral axis, in mixed species beams (eucalyptus-poplar, spruce-poplar and larch-poplar), thus
improving both the structural efficiency and the behaviour at failure. Moreover, the easy
impregnability together with the reliability of bonding of this fast growing species, have suggested
possible utilizations for structural purposes.
2.
Numerical modeling
In this paper the non-linear behaviour of glued laminated timber beams composed of two wood
species and subjected to simple bending action is studied through an analytical method whose basic
assumptions are: 1) the cross-sections remain plane in bending; 2) there is no slip between adjacent
laminations, and between wood and steel bars (glued line thickness deformations are neglected); 3)
the stress-strain relationship is known both for wood in tension, (linear elastic behaviour up to
failure), and for wood in compression (non-linear plastic behaviour).
According to the third assumption, different material
stress
models have been adopted for wood in compression:
tension
ft,0,m
I) a linear elastic-perfectly plastic stress-strain
relationship;
Em,0
II) a bilinear relationship with a softening branch [8];
Htu
Hcu
Hcy
strain
III) a more general stress-strain relationship, as
obtained directly from experimental data [9].
II)
III)
fc,0,m
I)
compression
The stress-strain patterns are shown in Figure 1.
The non-linear pattern of M-F relationship of the beam
cross-section has been therefore analyzed
incrementally applying a prescribed curvature to the
section, starting from F0 = 0. For a given curvature,
the strains in the section have been evaluated starting
from an assumed position, or the last one, of the
neutral axis.
Fig. 1 Different stress-strain diagrams
with patterns in compression
characterized by a plastic plateau (I),
by a softening branch according to
Buchanan (II), or by a shape directly
obtained through physical tests
(O’Halloran, III).
From the evaluated strain values, the corresponding stresses in wood can be worked out according
to the previously assumed stress-strain relationship. The control of the equilibrium along the beam
axis allows to adjust the position of the neutral axis. Finally, the resisting bending moment can be
evaluated by means of the equilibrium condition around, for instance, the neutral axis. The
procedure can be iterated for different couples of values (F, M), until the condition ¨H¨ ¨Hultimate ¨
is satisfied for both wood, in compression and in tension, and steel. As a result of the previously
described procedure, a moment-curvature relationship like the one for spruce-poplar mixed beam
reported in fig. 5 (shown in the next page) can be obtained.
3.
Experimental tests
The behaviour of compression stressed poplar has been preliminarily investigated, in order to
establish an experimental pattern for the constitutive relationship, to validate the different models
reported in the literature and described in the previous paragraph.
Fig. 2 Test set-up for compression parallel to fibres in
clear poplar test pieces.
The experimental results showed that
the Bazan curve, characterized by a
downwards slope after the elastic
phase is the one that best fits the
experimental pattern. (see fig. 2) .
O’Halloran’s curve instead does not
give good fits; it is close to the
experimental curve for only a short
portion of the plastic phase, up to the
compression failure.
Several types of mixed glulam beams
have been produced, assembled by
means of 11 laminations 80 mm × 10,5
mm × 2000 mm, glued with
resorcinolic resin, and tested in
bending using the so-called “four
point loading” system.
diminishing
strength quality
Two different composition criteria have been assumed, as reported in fig. 3a: some beams have
been produced using a single wood species, but with different strength grades from the lower to the
upper side of the section; in other beams lamellas of the more resistant species (spruce and larch),
have been coupled with the less resistant poplar lamellas.
Two differently steel reinforced glulam beams have been produced (fig. 3b). The beam indicated as
AR2+2I12, was reinforced in order to achieve a balanced type of failure, with plastic deformation
in the compression zone and yielding of the bar; in the beam indicated as AR1+1+2I12, there were
some notches had been machined in the tension zone of the wood, in order to artificially to
reproduce the cracking of the brittle material, as it happens in a steel reinforced concrete beam, and
to allow plastic deformation in the bars. A third “regular glulam” beam, in the following referred to
as LL 330, has been moreover tested as a reference.
poplar
4 IFeB44k
4 IFeB44k
115
115
spruce
or larch
80
80
notches
a
b
Fig. 3 Tested pseudo-ductile behaving sections.
In the first testing configuration, some strain gauges had been glued to the faces of the beam. Such
a mixed measure system did not give satisfactory results, since extensometers could not accurately
read strains in the phase of plasticization of compressed fibres, therefore another testing
configuration has been adopted, in which the strain gauges have been replaced by LVDT devices
(linear variable differential transformers).
b
a
Fig. 4 a) Plastic hinge in compression zone, not registered by the strain gauge; b) an Armalam®
specimen, with the new measuring set-up, utilising the LVDT transducers.
4.
Results and conclusions
The experimental campaign aimed to verify, for both the analysed techniques, the possibility of a
ductile bending behaviour. To describe in term of plastic deformation and strength, the failure
behaviour of the element, the parameters of table 1 were utilised:
Tab. 1 Parameters utilised to describe the experimental results
Curvature ductility
Slip ductility
PF
Fu
Fe
PG
Gu
Ge
Modulus of rupture
MOR
Mu
W
where:
Fu, Fe, ultimate bending and elastic bending;
Gu, Gu, ultimate deflection and elastic deflection.
W
section failure modulus.
Test results are shown in diagrams reported in fig. 5, and lead to the following conclusions.
x Best results in terms of “pseudoductility” have been obtained with mixed construction, single
species (Norway spruce) beams.
x The reinforced glulam beam, referred to as AR2+2I12, has shown poor ductile behaviour, since
the fibres shear failure did not allow the reinforcing bars to reach plasticization.
x The notched reinforced glulam beam, referred to as AR1+1+2I12, has shown very good ductile
performances as foreseen by the numerical model, based on the unrealistic hypothesis of non
tension resisting material. A better ductily, however, was obtained at expenses of the beam
strength and stiffness.
70
5
60
40
3
30
2
MOR
50
4
20
0
AR
AR
1+
1+
2+
LL
2F
I1
33
2
0
e
la
r
-S
p
ru
c
ar
c
Po
p
Po
pl
ar
-L
La
Sp
curvature ductility
2F
I1
2
0
h
10
rc
h
1
ru
ce
Ductility
6
slip ductility
Spruce beams 115x80x2050 mm
MOR
3
Bending moment (kNm)
12
10
8
6
4
2
S1
S2
S3
S4
S5
numerical model
0
0
0,00005
0,0001
0,00015
0,0002
0,00025
0,0003
0,00035
curvature 1/r (1/mm)
®
Armalam beams 120x165x3300 mm
3
Bending moment (kNm)
35
30
25
20
15
LL330
ar2+2
ar1+1+2notches
LL330_numerical
ar2+2_numerical
ar1+1+2_numerical
10
5
0
0
0,00005
0,0001
0,00015
0,0002
0,00025
0,0003
0,00035
curvature 1/r (1/mm)
Fig. 5 Failure behaviour results according to the different analysed techniques (mixed species
upper, armalam® lower)
5.
Acknowledgements
The authors wish to thank dr. Gaetano Castro of “Istituto di Sperimentazione per la Pioppicoltura”
Casale Monferrato (Italy), for providing poplar raw material, and prof. Maria Adelaide Parisi of
Department of Structural Engineering, Politecnico di Milano for precious discussions and advises.
They moreover appreciated the substantial contribution of mr. Franco Paganini during the
preliminary phases of the research; a special mention is deserved also by undergraduate student
Alessandro Fontanari for its important help in the realization of this research.The research is partly
financed by the Administration of the Provincia Autonoma di Trento, through the Research Project
named CODULE.
6.
References
[1]
Lantos, G. (1970). “The flexural behavior of steel reinforced laminated timber beams.” Wood
Sci., 2(3), 136-143.
Gentile, C., Dagmar, S., and Rizkalla, S. H. (2002). “Timber beams strengthened with GFRP
bars: development and applications”, Journal of Composites for Construction, 6(1), 11-20.
www.armalam.it
Buchanan, A. H. (1990). “Bending strength of lumber.” J. Struct. Eng., 116(5), 1213-1229.
Krueger, G. P. and Eddy, F.M., Jr. (1974), Ultimate-strength design of reinforced timber:
Moment-rotation characteristics, Wood Sci., 6(4), 330-344.
Biblis, E.J. (1965). Analysis of wood-fiberglass composite beams within and beyond the
elastic region. Forest Prod. J., 15(2), 81-88
Castro, G., and Paganini, F. (2003),Mixed glued laminated timber of poplar and Eucalyptus
grandis clones, accepted for publication on Holz als Roh- und Werkstoff.
Buchanan A. H., (1990) Bendig Strength of Lumber, J. Struct. Eng., Vol. 116, n.5, May 1990,
1213-1229
O’Halloran, M. R. (1973), A curvilinear stress-strain model for wood in compression, Ph.D.
Diss., Colorado State Univ., Fort Collins, CO.
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]

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