MOISTURE-INDUCED INTERNAL STRESS WITHIN ADHESIVE-BONDED TIMBER CONCRETE COMPOSITES

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1 MOISURE-INDUCED INERNAL SRESS WIHIN ADHESIVE-BONDED IMBER CONCREE COMPOSIES Artur Ginz, Werner Seim 2 ABSRAC: Natural environmental conditions cause changes of moisture and temperature in wood, which lead to internal stress if the deformation caused by swelling and shrinkage is blocked. wo analysis methods are applied and compared with one another to determine the rolling shear stress resulting from blocked swelling deformation using the example of a bridge under natural climatic conditions. KEYWORDS: rolling shear stress, adhesive bond, relaxation, timber concrete composite. INRODUCION 2 Changes of moisture and temperature in wood lead to internal stress if the deformation caused by swelling and shrinkage is blocked. his situation occurs in adhesivebonded timber concrete composites (ACC) which are exposed to natural climate. he bridge cross-section, depicted in Figure, was taken as a reference to examine the level of the internal stress in the bonding zone and to check whether cracks in the timber are to be expected or not. he focus will be laid on rolling shear as large deformations are expected in the transverse direction perpendicular to the grain. 2. MOISURE RANSPOR IN WOOD 2. SIMULAION he moisture transfer takes place according to Eisenhut [] in Figure 2 in two ways: On the one hand, by the transport process q n, when the wood absorbs the moisture from the ambient climate over the surface or releases moisture from the timber to the ambient climate. On the other hand, there is the transport q b within the wood cross-section. Figure 2: Mechanisms of moisture transfer in wood used in the numerical simulation [] Figure : Cross-section of a bridge for analysis stresses due to moisture changes Artur Ginz, University of Kassel, Chair for Building Rehabilitation and imber Engineering, Kurt-Wolters-Straße 3, 3425 Kassel, Germany. aginz@uni-kassel.de 2 Werner Seim, University of Kassel, Chair for Building Rehabilitation and imber Engineering, Kurt-Wolters-Straße 3, 3425 Kassel, Germany. wseim@uni-kassel.de he moisture flow q b within the wood cross-section is based on Fick s law and is expressed by the concentration gradient c and the diffusion matrix D described in Equation (). his process measures the amount of water per unit of time through an area perpendicular to the transport direction. qb = D c () he diffusion matrix in Equation (2) represents the proportionality constants in the grain direction (D L) and perpendicular to the grain (D R, ). Constants in the radial

2 and the tangential direction can be assumed to be the same []. D D 0 0 L = 0 DR, D R, (2) Eisenhut [] has shown by comparison with the experimental investigations that the diffusion coefficients D R, perpendicular to the grain for natural environmental conditions can be applied by Equation (3) according to oratti [2]. D,, ,28u R = e (3) he diffusion coefficients for the moisture transport parallel to the gain are given in able. able : Coefficients of diffusion DL parallel to the grain, according to Sjödin [3] Wood moisture Coefficient of diffusion D L [%] [m²/s] u ( 273.5) ln ( h) ( ) + air = h ( ) 0.75 emperature in [ C] 0.0 RH (relative humidity) 2.2 APPLICAION FOR HE BRIDGE CROSS-SECION (5) Only a section of the ACC bridge was modelled for the simulation using the symmetry and storage conditions of the bridge shown in Figure 3. his reduces the computing time considerably without loss of accuracy. he boundary conditions were selected so that the displacement in the x-direction is blocked and the rotation in the y- and z-axis. he climate data according to Eisenhut [5], which were recorded in a watercourse in Riebelsdorf over a period of two years (see Figure 3 ), are used as the basis for determining the equilibrium moisture content of the timber at the bridge cross-section. he impact simulated from these climate data is shown in Figure 3. he red area with the arrows is the wood affected. concrete he transfer of moisture over the wood surface is described in Equation (4) []. q ( ) n = S 0 uair usurf (4) u surf S ρ 0 u air moisture content at the wood surface surface emissivity coefficient according to oratti [2] [m/s] density of the wood under dry conditions equilibrium moisture content of the wood [4] timber Figure 3: Recording climate data of Eisenhut [5] imber affected by the climate Figure 4 shows a section of the timber model with the FE mesh of the bridge. In this Finite Element (FE) model section, two node paths are marked which lie between the timber and the adhesive. he first (path ) runs directly at the end grain surface and the second (path ) runs 50 cm behind this surface. Figure 4 depicts the average moisture content profiles for these selected paths. welve per cent was chosen as the initial equilibrium moisture content of the timber, according to the

3 Keylwerth diagram [6], considering standardized production conditions ( = 20 C and 65 % relative humidity). path he grey curve in Figure 4 results from the nodes at the front (path ) and the blue from the end section of the timber model (path ). Both curves depict the moisture values which were determined as mean values from single contents along the path marked (Figure 4 ). he maximum difference between the first and last node was about 0.7 % for path and 2.4 % for path. It is noticeable that the grey gradient shows large fluctuations, because the front side is exposed to the ambient climate and the moisture can be emitted or absorbed via this surface. Daily and seasonal changes have a more intense effect in this area than further along the x-axis. By contrast, climate fluctuations are barely noticeable in path in comparison (blue gradient). In addition, it has emerged that 20 % of the moisture content in the wood is not exceeded. A continuous decline of the moisture content along the longitudinal axis can be seen. his non-uniform distribution is illustrated in Figure 4 c), which shows the moisture content of the bridge after 8.4 years along the x-axis. Paths were used for this evaluation with 5 cm between each path. he time point of 8.4 years was chosen because all the curves have reached the plateau by then. path 3. DEERMINAION OF ROLLING SHEAR SRESSES 3. MAERIAL MODELS hree-dimensional material models were adapted to describe the material behaviour of ACC numerically, taking into account the hygrothermal and the timedependent behaviour of the wood, the concrete and the adhesive. WOOD he material model depicted in Figure 5 is derived from the three-dimensional material model by Fortino [7]. Figure 5: Material model of the wood [] c) Figure 4: Node paths for moisture content determination; moisture content process at the bridge cross-section for path (grey) and path (blue); c) moisture content of the bridge section along the x-axis he material model of the wood is described by Equation (6), where the four deformation mechanisms are connected in series. p e u ve i i= = (6) ε e ε u ε ve ε i CONCREE elastic strains expansions due to moisture expansions due to temperature viscoelastic strains he material behaviour of the concrete is described with isotropic material properties by []. he deformation mechanisms considered for the concrete are presented in Figure 6 and Equation (7).

4 Figure 6: Material model of the concrete p e cs fl ve i i= = (7) ε cs ε fl, ε i ve ADHESIVE shrinking strains (consisting of strains due to drying shrinkage and autogenous shrinkage) viscoelastic strains Due to a lack of our own experimental investigations, the viscous and viscoplastic parameters for the rheological material model were derived from comparable investigations on epoxy adhesives according to Schmidt et al. [8]. he three-dimensional material model for the epoxy adhesive presented in Figure 7 is based on the linear viscoelastic Burgers model. in fluctuations of the level of rolling shear stresses. he course at node shows greater fluctuations than the course at the last node, because the changes in the seasons at this end of the cross-section have a more intensive effect. here is also a tendency for stresses to decrease from the sixth or rather the eighth year, which is probably due to viscoelastic effects. In addition to the decrease in annual fluctuations between the nodes, it is also clear that the magnitude of the rolling shear decreases along the x-axis. Figure 8 c) depicts the shear stress curve for the external nodes in the timber along the longitudinal axis after 8.4 years. Nodes were used for this evaluation with 5 cm between each node. node node Figure 7: Material model of the epoxy adhesive he deformation mechanisms of the epoxy adhesive are displayed in Equation (8). p e ve i i= = (8) ε η linear viscous strains 3.2 CALCULAION RESULS Figure 8 shows the rolling shear stresses in N/mm² at the surface of the timber body with the external nodes in the bonding joint. Figure 8 shows the development of the rolling shear stresses over time at node and. he graphs reveal that the rolling shear stress increases from zero and reaches values up to 0.6 N/mm². Seasonal changes result c) Figure 8: rolling shear stresses and selected nodes for evaluation; Rolling shear stress curves for node (grey) and (blue); c) Rolling shear stresses of the bridge section along the x-axis for external nodes (determined with the material models) 3.3 EQUIVALEN LOADING MEHOD A simplified method to validate the FE calculations with material models was developed to calculate the shear stress in the adhesive layer directly, based only on the values of the change of moisture content. he influence of temperature changes is negligible for the determination of the rolling shear stress.

5 A moisture difference u between the time t 0 and t x is required to determine the rolling shear stress between the timber and adhesive. his moisture content u was determined with the transfer simulation in section 2.2. In the next step, the reduced swelling strain is determined by Equation (0) considering a reduction factor of 0.5 because of the blocked deformation in the bond according to Steck [9] and Blaß et al. [0]. In the next step, the equivalent stress eq can be determined by Equation (), pre-assuming that it causes the same deformation in the timber as swelling (see Fig. 9). eq r, t = 0 (2) node node Figure 0: Rolling shear stresses τr,t=0 and selected nodes for evaluation with the equivalent loading method In the next step, the specified rolling shear stresses are halved due to the relaxation with the corresponding Equation (3) according to Steck [9] and Möhler and Maier [2] (see able 2). = 0,5 (3) r, t= r, t= 0 Figure 9: Equivalent loading to simulate swelling deformation Unrestricted swelling: = (9) S u, u Reduced swelling strain due to blocked deformation according to Steck [9] and Blaß et al. [0]: = 0,5 = 0,5 (0) ' S S u, u Equivalent tensile stress as swelling deformation: = () ' eq S E 90 with u, u E 90 shrinkage value tangential to the grain, according to Santaoja et al. []: set-up to 0.27 change of moisture elastic modulus perpendicular to the grain Stresses are calculated on two levels, which are based on the balance moisture content from Figure 4, to consider the effects of different swelling intensity in the timber. herefore, the mean equilibrium moisture content for path at the time of 8.4 years is about 9.5 % and for path about 7.5 %. According to the equivalent loading method, an equivalent stress of 4.56 N/mm² results for node and 3.34 N/mm² for node. In the next step, σ eq is applied as a trapezoidal load according to Figure 9 on the timber cross-section. Figure 0 shows the resulting rolling shear stress displayed from the equivalent tensile load at time t 0 according to Equation (2). he calculation was carried out with an FE programme. able 2: Results of the equivalent loading method for the bridge cross-section node node [ C] natural climatic conditions according RH [%] to Figure 3 u I[%] 2.0 u E [%] u [%] S [-] eq [N/mm²] τ t= [N/mm²] RH u I u E τ t= emperature relative humidity initial moisture content moisture content at the end rolling shear stress An evaluation of the rolling shear stresses τ r,t= is documented in Figure for the selected nodes in the longitudinal axis of the bridge following the path as depicted in Figure 0. Figure : Rolling shear stress τ r,t= for the external nodes along the longitudinal direction of the bridge (determined with the equivalent loading method)

6 3.4 COMPARISON OF ANALYSIS RE- SULS A comparison of the two analysis methods in Figure 5 shows that the results are very close. he simplified equivalent loading method overestimates stresses for about 5 % and shows a very good approximation with a high potential to avoid complex and timeintensive nonlinear modelling. Figure 2: Comparison of results for rolling shear stress in the longitudinal axis of the bridge 4. CONCLUSIONS AND OULOOK It is possible utilising the material model and the equivalent loading method as proposed in section 3 to determine the rolling shear stress in the bonding zone of ACC resulting from moisture changes under natural climatic conditions. For a typical situation rolling shear stresses reached values up to 0.60 N/mm². Characteristic values for rolling shear strength equal.0 N/mm² for solid timber according to [3] and.2 N/mm² for glulam GLh [4]. Regarding the design against rolling shear failure the situation is not clear if the stresses are resulting from moisture induced shrinkage or swelling. As for the action the German Annex to EC 0 [5] defines a partial safety factor of γ Q =.50. he German Annex to EC 2 [6] reduces this value to γ Q, =.00 if the stresses are due to temperature changes. Moreover, the partial safety factor for material properties γ m and the modification factor k mod to be used together with restraint stresses are unclear. Further research on material resistance against moisture induced rolling shear stresses is necessary. In addition, further investigations should be carried out regarding the superimposition of the stresses resulting from hygrothermal stress, dead load and live load. 5. REFERENCES [] Eisenhut, L.: Geklebter Verbund aus Holz und hochfestem Beton Untersuchungen zum Langzeitverhalten. Dissertation, University of Kassel, Institute of imber Engineering, 205. [2] oratti,.: Creep of timber beams in a variable environment. Dissertation, Helsinki University of echnology. Finland, Helsinki, 992. [3] Sjödin, J.: Steel-to-timber dowel joints influence of moisture induced stresses.växjö University. Växjö, Sweden, [4] Hanhijärvi, A.: Modelling of creep deformation mechanisms in wood. Dissertation, Finland, Helsinki. Helsinki University of echnology, 995. [5] Eisenhut, L.; Seim, W. Kühlborn, S: Adhesivebonded timber-concrete composites - Experimental and numerical investigation of hygro-thermal effects. Engineering Structures. 206 (25):67 78, 206. [6] Keylwerth, R.: Sorptionsgleichgewicht von Holz. Holz als Roh- und Werkstoff. 22 ():3, 964. [7] Fortino, S.; Mirianon, F.; oratti,.: A 3D moisture-stress FEM analysis for time dependent problems in timber structures. Mechanics of ime-dependent Materials. 3 : , [8] Schmidt, M.; Freisinger-Schadow, S.; Heim H.- P.; Mihm, K.-M.; Dilger, K.; Böhm, S.; Wisner, G.: Neue konstruktive Möglichkeiten im Betonbau durch Kleben von Bauteilen aus Ultra-Hochfestem Beton. Forschungsbericht, Industrielle Gemeinschaftsforschung Nr Z / [9] Steck, G.: Relaxationsversuche mit Brettschichtholzproben unter Querdruckbeanspruchung infolge Feuchtezu-nahme. Holz als Roh- und Werkstoff. 45(4) :37 40, 987. [0] Blaß, H. J.; Ehlbeck, J.; Kreuzinger, H.; Steck, G.: Erläuterungen zu DIN 052: : Entwurf, Berechnung und Bemessung von Holzbauwerken. Bruderverl., Karlsruhe [] Santaoja, K.; Leino,.; Ranta-Maunus, A.; Hanhi-järvi, A.: Mechano-sorptive structural analysis of wood by the ABAQUS finite element program. echnical Research Centre of Finland. Espoo, Finnland, 99. [2] Möhler, K.; Maier, G.: Kriech- und Relaxationsverhalten von lufttrockenem und nassem Fichtenholz bei Querdruckbeanspruchung. Holz als Roh- und Werkstoff. 28 :4 20, 970. [3] National Annex to Eurocode 5: Design of timber structures: General - Common rules and rules for buildings - EN 995--/NA German version, 203. [4] EN 4080: imber structures - Glued laminated timber and glued solid timber Requirements, 203. [5] National Annex Nationally determined parameters Eurocode: Basis of structural design - DIN EN 990/NA, 200. [6] National Annex Nationally determined parameters Eurocode 2: Design of concrete structures Part : General rules and rules for buildings - DIN EN 992--/NA, 203.