Maurizio PIAZZA Associated Professor Department of Mechanical & Structural Engineering, Trento, Italy

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1 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, He is first researcher at the Institute for Wood Technology since 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, Researcher at the University of Padova since 1978, he is professor at the University of Trento since 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, 2. He got his PhD degree on the subject "Design, restoration and monitoring of conventional and innovative structures", 24. 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.

2 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 32 kg/m 3 ), 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). cu II) III) I) stress cy f t,,m compression E m, tu f c,,m tension strain 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). According to the third assumption, different material models have been adopted for wood in compression: I) a linear elastic-perfectly plastic stress-strain relationship; II) a bilinear relationship with a softening branch [8]; III) a more general stress-strain relationship, as obtained directly from experimental data [9]. The stress-strain patterns are shown in Figure 1. The non-linear pattern of M- relationship of the beam cross-section has been therefore analyzed incrementally applying a prescribed curvature to the section, starting from =. 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. 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 (, M), until the condition ultimate 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.

3 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 8 mm 1,5 mm 2 mm, glued with resorcinolic resin, and tested in bending using the so-called four point loading system. 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+212, 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 AR , 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 33, has been moreover tested as a reference. diminishing strength quality poplar spruce or larch 4 FeB44k 4 FeB44k 8 8 notches a Fig. 3 Tested pseudo-ductile behaving sections. b 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).

4 a b 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 Modulus of rupture u e where: u, e, ultimate bending and elastic bending; u, u, ultimate deflection and elastic deflection. W section failure modulus. u e M MOR W u Test results are shown in diagrams reported in fig. 5, and lead to the following conclusions. Best results in terms of pseudoductility have been obtained with mixed construction, single species (Norway spruce) beams. The reinforced glulam beam, referred to as AR2+212, has shown poor ductile behaviour, since the fibres shear failure did not allow the reinforcing bars to reach plasticization. The notched reinforced glulam beam, referred to as AR , 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.

5 Ductility Spruce Larch Poplar-Larch Poplar-Spruce LL33 AR2+2FI12 AR1+1+2FI12 curvature ductility slip ductility MOR MOR Spruce beams 115x8x25 mm 3 12 Bending moment (knm) S1 S3 S5 S2 S4 numerical model,5,1,15,2,25,3,35 curvature 1/r (1/mm) 35 Armalam beams 12x165x33 mm 3 Bending moment (knm) LL33 ar2+2 ar1+1+2notches LL33_numerical ar2+2_numerical ar1+1+2_numerical,5,1,15,2,25,3,35 curvature 1/r (1/mm) Fig. 5 Failure behaviour results according to the different analysed techniques (mixed species upper, armalam lower)

6 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. (197). The flexural behavior of steel reinforced laminated timber beams. Wood Sci., 2(3), [2] Gentile, C., Dagmar, S., and Rizkalla, S. H. (22). Timber beams strengthened with GFRP bars: development and applications, Journal of Composites for Construction, 6(1), [3] [4] Buchanan, A. H. (199). Bending strength of lumber. J. Struct. Eng., 116(5), [5] Krueger, G. P. and Eddy, F.M., Jr. (1974), Ultimate-strength design of reinforced timber: Moment-rotation characteristics, Wood Sci., 6(4), [6] Biblis, E.J. (1965). Analysis of wood-fiberglass composite beams within and beyond the elastic region. Forest Prod. J., 15(2), [7] Castro, G., and Paganini, F. (23),Mixed glued laminated timber of poplar and Eucalyptus grandis clones, accepted for publication on Holz als Roh- und Werkstoff. [8] Buchanan A. H., (199) Bendig Strength of Lumber, J. Struct. Eng., Vol. 116, n.5, May 199, [9] O Halloran, M. R. (1973), A curvilinear stress-strain model for wood in compression, Ph.D. Diss., Colorado State Univ., Fort Collins, CO.