TESTING AND MODELLING OF PRESTRESSED TIMBER BEAMS USING A MULTI SURFACE PLASTICITY MODEL

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1 TESTING AND MODELLING OF PRESTRESSED TIMBER BEAMS USING A MULTI SURFACE PLASTICITY MODEL Martin Lehmann 1, Till Vallée 2, Karl Rautenstrauch 3 ABSTRACT: The refurbishment of old buildings often comes hand in hand with an increase of the dead- and live loads. The latter, combined with the higher safety factors often make a reinforcement of the old structures necessary. FEM calculations are a helpful tool to understand the complex stress sate in member with externally bonded prestressed reinforcement. The linear orthotropic elasticity does not allow considering, plasticity, softening or hardening. As in prestressed timber bending beams significant crushing can appear numerical modelling of the ultimate load should allow for plasticity on the compression side. The authors undertook extensive numerical and experimental investigations of the failure modes for reinforced glued laminated timber made of Picea Abies. Reinforcement was achieved with pre-stressed CFRP-lamellas. KEYWORDS: reinforcement, prestressing, multi surface plasticity 1 INTRODUCTION 123 Timber is a natural, anisotropic and inhomogeneous material. Although the structure of wood is very complex, for numerical modelling it is often assumed to be homogeneous and free of defects, ignoring natural imperfections such as knots and distortions in the alignment of grain. For samples cut far from the tree centre and small in size in relation to the distance to the pith, the growth ring curvature can be ignored and properties are regarded as orthotropic with three orthogonal planes of material symmetry: longitudinal, radial and tangential. The resulting nine independent parameters can be determined experimentally. While standard procedures allow a relatively high accuracy about the longitudinal elastic modulus, less certainty exists about the transverse modules and shear modules, and very little research has been carried out determining the Poisson s ratios. In addition to having different values for tension and compression stresses, each value 1 Martin Lehmann, Bern University of Applied Sciences, Architecture, Wood and Civil Engineering BFH-AHB, Solothurnstrasse 102, P.O.Box, CH-2500 Biel-Bienne 6, Switzerland. martin.lehmann@bfh.ch 2 Till Vallée, College of Engineering and Architecture of Fribourg, Bd de Péeolles, P.O.Pox 32, CH-1705 Fribourg. Switzerland, till.vallee@hefr.ch 3 Karl Rautenstrauch, Chair of Timber and Masonry Engineering, Bauhaus-University Weimar Marienstraße 13 A, D Weimar, Germany. karl.rautenstrauch@bauing.uni-weimar.de may be non-linearly dependent on strain and also dependent on the specimen size as indicated by Madsen [1]. Failure modes of timber vary depending on member geometry as well as material type and its associated failure modes. Eberhardsteiner [2] identified four basic failure modes for softwoods: I) brittle tensile failure in fibre direction; II) brittle tensile failure perpendicular to grain; III) ductile compressive failure perpendicular to grain; and IV) ductile compressive failure in fibre direction. The stress-strain behaviour of clear spruce wood under multi-axial loading covering the whole set of distinguishable stress states for an orthotropic material under plane stress was experimentally determined in [2]; the observed interactions were subsequently micromechanically explained [3]. 2 EXPERIMENTAL STUDIES The experimental work included prestressing the beams, and testing the specimen in bending subsequently. The prestressing was achieved as follows: the timber beam was cambered with a single force at midspan before the CFRP lamella was bonded to the timber. The force was released after the adhesive had fully cured. Because of the simplicity, the method can be readily used in-situ (Figure 1).

Figure 1: The solid drawing shows the timber beam prior to intervention. The dashed line is the cambered beam after installation of a prop which can be adjusted in height.

2 Figure 1: The solid drawing shows the timber beam prior to intervention. The dashed line is the cambered beam after installation of a prop which can be adjusted in height. The prestressing force in the system is not constant. It peaks in the middle of the beam were it is mostly needed and is zero towards the ends. The moment introduced into the beam has a triangular shape. Therefore the shear stress in the glue line is constant and quite low: in effect the prestressing force is anchored over half the beam length, which is a great help against debonding (Figure 2). The camber also makes a positive contribution to the service limit state. Figure 2: system with installed reinforcement and after removal of the force. The internal forces due to P 0 in the CFRP and the adhesive are not shown. 2.1 SERIES 1 The experimental work was divided in series 1 and 2. Series 1 was done using nearly clear timber and relatively small specimens. In this series the applied level of stress in timber during bonding of the CFRPlamella was varied and three different adhesives were tested. For each sample five specimens were tested. Table 1: Samples tested in series 1 sample adhesive induced stress* [MPa] timber section CFRP section Control x 53 - A C x x 15 B B x x 15 C A x x 15 D A x x 15 E A x x 15 F A 0 40 x x 15 *Bending stress in timber during the bonding of the carbon lamella The prestressed specimens were tested in four point bending. Strain gauges on the CFRP allowed conclusions about the stress in the CFRP due to prestressing and during the bending tests. F 53/ = strain gauge = dial gauge = CFRP lamella Figure 3: Four-point bending setup as used for series 1 to test the reinforced specimens. The reinforcing using CFRP lamellas leads to a significant increase on the bending capacity. The adhesive had no significant influence on the achieved prestress force. The induced stress during bonding was clearly governing the prestress level. However no significant influence of the prestress level on the loading capacity could be determined. The first failure mode of the timber was crushing on the compressive side. This was almost independent on the parameters used to reinforce the timber. Even some of the controls showed some crushing this was due to the clear timber in the tension zone. Table 2: Overview of the results of series 1 Sample prestress measured camber M max [MPa] COV COV [knm] COV Control % A % % 1.9 7% B 154 7% % % C % % % D 79 13% % % E % % % F 4 66% % 2.2 SERIES 2 In series 2, ten full scale specimens were produced using GL24h and the most promising parameters of series 1. The induced stress during bonding was set to 20 MPa, which is below the 5% percentile and about 50% of the load bearing capacity. Table 3: parameters of the specimens in series 2 adhesive induced stress* [MPa] timber section 53 CFRP section B x x 50 *Bending stress in timber during the bonding of the carbon lamella

Stain gauges were used in order to measure the strain on the CFRP and timber during the prestressing and the four point bending tests of the reinforced beams [4].

3 Stain gauges were used in order to measure the strain on the CFRP and timber during the prestressing and the four point bending tests of the reinforced beams [4]. The strain measurement on the CFRP-Lamella confirmed the triangular distribution of the prestress force. The reinforcement of timber beams using prestressed CFRP leads to a significant increase of the load bearing capacity. The residual camber after prestressing and the increased bending stiffness is a significant contribution to the service limit state F = strain gauge = dial gauge = CFRP lamella Figure 4: Four-point bending setup as used for series 2 to test the reinforced beams /160 Table 4: Overview of the results of series 2 # EI local camber prestress measured M max [Nmm 2 ] [MPa] [knm] E E E E E E E E E E average 523.4E COV 10% 39% 8% 19% NUMERICAL INVESTIGATIONS A timber material model that includes multi-surface plasticity developed at the University of Weimar [5] allowed studying the phenomena. The model uses softening rules to model the post failure behaviour of timber in each failure mode. The model is implemented in Ansys. Seven conditions in order to describe a 3d failure criterion for soft wood are used. Rupture of the fibres (surface 1) Crushing of the fibres (surface 2) Crack development in the LT plane (surface 3 and 4) Compression radial (surface 5) Crack development in the LR plane (surface 6) Compression tangential (surface 7) The surfaces 1, 2, 5 and 7 are maximal stress criterions therefore multi axial stress states have no influence on those surfaces. On the other hand tension in radial direction has a clear influence on the shear capacity LRplane (τ RL,u ). Compression in radial direction has no influence on the shear capacity in the LR-plane (τ RL,u ). (Figure 6) The shear capacity in the LT-plane is clearly higher than the tension capacity in radial direction and also higher than capacity in compression radial. Contrary to non-reinforced bending members, local failure in the compression zone is the first failure mode before splitting in the tension zone occurs (Figure 5). This splitting leads to complete failure of the composite beam. Figure 6: Multi surface plasticity criterion for softwood for stress in the LR-plane [5] Figure 5: Local failure in the compression zone of reinforced timber beam The interaction between shear capacity in the LT-plane (τ TL,u ) and tension or compression (σ T ) in the tangential direction is different as shown above. Tension tangential leads to a reduction of the shear capacity while compression tangential leads to an increase of the shear capacity in the LT-plane (Figure 7).

As the multi surface plasticity model requests the input of the strength properties they were determined using small clear specimen of Picea Abies (Table 6).

4 As the multi surface plasticity model requests the input of the strength properties they were determined using small clear specimen of Picea Abies (Table 6). For the modelling of the full size specimen the influence of the fibre angle and the knots had to be considered. Therefore in longitudinal direction the ultimate stress determined during the bending tests was used. For further information how the stress was determined see Lehmann et al. [4]. Table 6: strength properties of Picea Abies determined using small clear specimen Figure 7: Multi surface plasticity criterion for softwood for stress in the LT-plane [5] The different failure modes are described by different softening and hardening functions for all six loading direction. The more or less brittle tension and shear softening is expressed by a linear function based on the dissipated fracture energy. The softening and hardening functions for the ductile compression failure are more complex functions. For compression longitudinal timber reaches a maximum followed by a slight decrease which leads to a plateau and after the timber is completely crushed a rapidly increasing branch represents the behaviour of compacted cell material. For compression perpendicular to the grain qualitatively the same function are used in radial and tangential direction. Timber does not have a clear maximum in transversal compression but goes smoothly from elastic behaviour over to a slightly increasing branch which represents the buckling and finally crushing of the cell walls. After the timber is completely crushed a rapidly increasing branch represents the behaviour of compacted cell material. The interaction between the different yield criteria was taken into account using multi-surface plasticity and the strength-reduction as result of shear or tension failure was described as dependent of fracture-energy dissipated during crack formation. The single span bending beams were modelled using three-dimensional 8-node orthotropic elements. Symmetry conditions were used to reduce the modelling to one quarter of the beam. The relevant elastic material properties were taken from literature [6] (Table 5) except the modulus of elasticity was taken from the experiments described above. tension compression shear [MPa] [MPa] [MPa] long. (f Lt ) 93.4 long. (f Lc ) 37.9 f RLs 11.7 rad. (f Rt ) 3.9 rad. (f Rc ) 3.7 f RTs 3.5 tang. (f Tt ) 3.5 tang. (f Tc ) 5 f TLs 11.2 f TRs 2.7 Figure 8 to Figure 10 shows the stress strain relation resulting from the multi surface plasticity timber model using the mechanical parameters for Picea Abies glulam with the quality GL24h (5% percentile in bending is 24 MPa) as was used in the full scale experiments. Figure 8: stress strain relationship in fibre direction (longitudinal) yielded by the used multi surface plasticity model Table 5: elastic coefficients for Picea Abies according to Neuhaus [6] for a moister content of 12 % MOE shear modulus poison's ratio [MPa] [MPa] [-] longitudinal (L) 11'990 RL 623 TL radial (R) 817 RT 42 RT tangential (T) 419 TL 722 RL Figure 9: stress strain relationship perpendicular to the fibre direction (radial) yielded by the used multi surface plasticity model

Figure 10: stress strain relationship perpendicular to the fibre direction (tangential) yielded by the used multi surface plasticity model The CFRP laminates are modelled as orthotropic, linear

5 Figure 10: stress strain relationship perpendicular to the fibre direction (tangential) yielded by the used multi surface plasticity model The CFRP laminates are modelled as orthotropic, linear elastic material. The modulus of elasticity in longitudinal direction was set as stated by the producer [7]. The modulus of elasticity across, the shear modulus (across / longitudinal) and the poison s ratio of the CFRPlamellas were determined by using the mixing rules according to Meier [8]. The rolling shear modulus was set to the shear modulus of the matrix. The elastic constants for the CFRP-lamella used in the experiments are presented in the table below. Table 7: Elastic constants used in the numerical modelling for the CFRP-lamella MOE shear modulus poison's ratio [GPa] [GPa] [-] long. (L) 165 L / P L / P perp. (P) P / P P / P 0.3 As the adhesive showed some influence on the failure behaviour of the small specimen therefore the adhesive layer was modelled using three-dimensional 8-node brick elements. In reference to de Castro San Román [9] the epoxy based adhesives were modelled as isotropic linear elastic materials. Therefore only two elastic constants are needed to describe the material (Table 8). timber using a dummy material layer. This dummy material has the MOE of not cured adhesive. Between the timer and the dummy material and between the dummy material and the CFRP contact elements were used. The contact elements had a tangential contact stiffness of nearly zero. At the end of load step one the timber was cambered and the CFRP lamella had the same shape as the beam. The stresses and its distribution in the timber and the CFRP are equal to the stress resulting from the curvature. This proves that the dummy material and its contact element do not transmit any forces but still ensure that the CFRP has the same camber as the timber. During the second load step no deformations or forces are introduced but the elements of the dummy material and its contact elements are set inactive and the elements of the adhesive are set active. These yields in an adhesive layer with the MOE of cured adhesive and the same camber as the timber but no stress is present in the material. The stresses and its distribution in the timber and CFRP did not change during this load step. This behaviour of the model corresponds with the expected material behaviour during the bonding process In the third load step all applied forces were removed. The residual camber of 3.3 mm corresponds well with the experiments. The fourth load step models the four-point bending until failure. In this step the presented timber model allowed the determination of the failure load and the deformation at ultimate load. Good agreement between numerical and experimental results was achieved. The zone between the loading points shows clearly the plastic strain of the timber in the compression zone the largest plastic strain occurs near the loading points (Figure 11). The plastic strain at the tension face indicates the beginning of the splitting which leads to complete failure of the specimens. Table 8: Modulus of elasticity and poison s ratio used for the different adhesives adhesive type MOE poison's ratio [MPa] [-] A B C The prestressing was modelled as done in the experiments. Therefore the first load step was to introduce the camber in the timber. During this load step the elements of the adhesive layer were inactive. The elements of the CFRP-lamella were connected to the Figure 11: computed plastic strain distribution (only one quarter of the timber beam is shown). Not only the qualitative plastic strain distribution corresponded well with the experiments but also the ultimate load and the deformation could be modelled with a satisfying accuracy. As the specimen showed a

6 quite abrupt failure the deformations measuring devices had to be removed before complete failure. Therefore the crosshead movement was taken for comparison with the numerical modelling. The deformation of the testing equipment was considered for the comparison. force [N] crosshead movement Figure 12: comparison of the experiments and the modelling of series 1 (black. experiments red: numerical calculation) For both series the maximal force and the deformation during the four point bending tests could be modelled with a high accuracy (Figure 12 and Figure 13). This was achieved using only parameters that could be measured by experiments. Figure 13: comparison of the experiments and the modelling of series 2 (black. experiments red: numerical calculation) The comparison of the tension strain measurement on the timber done during the bending tests in series 2 showed a good correlation to the numerical calculations (Figure 14). load [kn] % 0.1% 0.2% 0.3% 0.4% 0.5% 0.6% 0.7% strain [%] Figure 14: comparison of the experiments and the modelling of series 2 (black. experiments red: numerical calculation) 4 CONCLUSIONS The experiments showed that the presented method is suitable to reinforce timber beams. Furthermore it was shown that delaminating of a prestressed CFRP-lamella can be prevented by using this cost efficient method. The numerical calculations showed good agreement with the experiments. Especially the non linear part of the force deflection graph could be modelled using only the nine engineering constants and the strength as input data for the numerical model. The reported approach allows for the safe design of reinforced glued laminated timber beams. ACKNOWLEDGEMENT The authors like to thank D. Roder for his support during the experimental work. REFERENCES [1] Madsen, B.: Structural Behaviour of Timber American Society of Civil Engineers, [2] Eberhardsteiner, J.: Mechanisches Verhalten von Fichtenholz : experimentelle Bestimmung der biaxialen Festigkeitseigenschaften, Springer Wien, Wien, [3] Grosse, M., Rautenstrauch, K. and Schlegel, R.: Numerische Modellierung von Holz und Verbindungselementen in Holz-Beton- Verbundkonstruktionen. Bautechnik, 82(6): , [4] Lehmann, M., Properzi, M. and Pichelin, F., Strengthening of timber structures using pre-stressed carbon fibre lamellas, in 1st MEDACHS 08 Conference. 2008: Lisbon. [5] Grosse, M.: Zur numerischen Simulation des physikalisch nichtlinearen Kurzzeittragverhaltens von Nadelholz am Beispiel von Holz-Beton- Verbundkonstruktionen, Dissertation, Fakultät Bauingenieurwesen, Bauhaus-Universität Weimar, Weimar, 2005 [6] Neuhaus, F.-H.: Elastizitätszahlen von Fichtenholz in Abhängigkeit von der Holzfeuchtigkeit, Dissertation, lnstitut für Konstruktiven lngenieurbau, Ruhr-Universität Bochum, Bochum, 1981 [7] Sika CarboDur Lamellen, Hochfestes CFK- Lamellen-Verstärkungssystem. 2008, Sika Schweiz AG. [8] Meier, U.: Grundlagen zur Bemessung von Kunststoffbauteilen. Skriptum zur ETH Vorlesung Teil 1, ETH Zürich, Zürich, [9] de Castro San Román, J.: Experiments on Epoxy, Polyurethane and ADP Adhesives. technical report. CCLab2000.1b/1. École Polytechnique Fédéralede Lausanne. 2005

Pre-stressed FRP for the in-situ strengthening of timber structures

Pre-stressed FRP for the in-situ strengthening of timber structures Lehmann Martin 1*, Milena Properzi 1, Frédéric Pichelin 1, Pascal Triboulot 3 1 University of Applied Sciences Bern HSB, Biel. Switzerland