


REINFORCED PREFABRICATED TIMBER SHEAR WALLS
Miroslav Premrov & ^{ }Peter Dobrila
University of Maribor, Faculty of Civil Engineering, Smetanova ulica 17, SI2000 Maribor, Slovenia
Email: miroslav.premrov@unimb.si
Abstract
The paper presents results of shearbending experiments performed on panel shear walls used as loadcarrying capacity walls in the construction of prefabricated timber structures. The aim of research is to determine the difference in resistance and ductility between panel shear walls, reinforced with two different methods. While the first, reinforcing with additional fiberboard, was not improve resistance and especially ductility in the contended sense, we tried to find a solution by inserting diagonal steel strips, which were fixed to the timber frame. Additionally, analytical solutions of those by mathematical modeling with the fictive thickness and height of fiberplaster boards are proposed. Presented design models are simple and show a good coincidence with the measured results
Keywords: Timber structures, shear walls, measured results, mathematical modelling.
The presented panel shear walls are usually used as loadcarrying capacity walls in the construction of prefabricated timber houses. In structural analysis they can be regarded separated for design purposes as vertical cantilever beams. A compressed and a tensional support represent actual boundary conditions of neighboring panel walls and assure an elasticclamped boundary condition for the treated wall (Figure 1).
Figure 1: Static design of panel shear walls
The treated wall is a composite system, composed of a timber frame and fiberplaster boards, which are fixed by mechanical fasteners to one or both sides of a timber frame. In such walls a greater part of a vertical load is usually beard with the timber frame. In engineering design a contribution of fiberboards is usually not considered in a horizontal stiffness of the shear wall, which does not coincide with the real state. A horizontal load namely shifts a part of the force over the mechanical fasteners to the fiberboard. The boards thus also contribute to the shear stiffness of the wall and it should be regarded as an integral part of the both elements. Thus the total shear stiffness of the wall can be written in the form:
(1)
The bending stiffness (EI)_{eff} can be also considered in a such form. The coefficient γ represents a stiffness of the mechanical fasteners, connecting the timber frame and the boards. For a static analyse it is very important. Bigger it is, a bigger part of the horizontal load is transmitted from the boards to the timber frame. As a consequence a resistance and also a ductility of the composed wall is bigger. The total resistance of the wall can be written as a sume of the timber frame resistance (R_{t}) and the resistance of the boards (R_{b}):
(2)
While strength of the boards is usually smaller than strength of the timber frame, the boards are usually a weaker part of the presented composite system. Thus, especially by multistory buildings located on the seismic or wind areas, we have usually problems with cracks, which appear in fiberplaster boards. In this case the boards are losing their stiffness and the second term in Eq.(2) of course should not be considered. Stresses in the timber frame under a horizontal load are usually not so critical.
2. POSSIBILITIES OF REINFORCING THE FIBREBOARDS
Producers have different possibilities how to reinforce the panel shear walls and to avoid cracks in the fiberboard:
▫ In using additional boards. The boards are usually doubled:
▫ In reinforcing boards with carbon or highstrength synthetic fibers.
▫ In reinforcing boards with steel diagonals.
2.1 Using Additional Boards
This is the simplest way to reinforce fiberboard. Some solutions can be found in [13]. The influence of the added boards strongly depends on the stiffness coefficient of fasteners (γ), which connect the boards to the timber frame. By this reinforcement the elasticity behavior of the wall is high improved, but the panels do not prove higher ductility. Test results are presented in Section 4.
2.2 Reinforcing with Carbon or HighStrength Synthetic Fibers
By this reinforcing higher ductility is assured as in the first case. Some test results by using carbon fibers in laminated beams are presented in [4]. Investigation results of fiber reinforced hollow wood beams are presented in [5]. They show that fiber reinforcement increase the average strength and stiffness of the beams, compared to the unreinforced control samples, by 22% and 5%, respectively.
2.3 Reinforcing with Steel Diagonals
In a sense to assure essential increasing of resistance and ductility of a fiberboard we tried to find another solutions by reinforcing panels with diagonal steel elements. In this way a part of the horizontal force is shifted from fiberboard to the tensional steel diagonal. The aim of our research was computationally and experimentally to determine the difference in the resistance and stiffness between panels shear walls reinforced with steel diagonals and the unreinforced panels. Test results are presented in Section 4.
Solving such diagonal reinforced panels with the finite element method can be very complicated. In this way it is necessary to develop some simple mathematical models. They are presented in the analytical form in Section 5.
3. EXPERIMENTS
The investigation was performed on nine test samples. Three of them were “normal” (unreinforced) panel shear walls without any reinforcement (T1). Another three were reinforced by additional symmetric boards (T2, Subsection 2.1). The last three were ductility reinforced with the steel diagonal strips 2x(2x60)mm (T3, Subsection 2.3), which were fixed to the timber frame with three additional bolts. All of the test samples were rigidly clamped into a support by bolts and INP steel profiles. The test samples were at the free edge loaded with the vertical force F_{v}, which just symbolically represented the lateral force in a real design (rotation for 90^{0}).
3.1 Dimensions of the Test Samples
All test samples were 255 cm long and 125 cm high. The cross section of the samples is composed of (Figure 2):
 a timber frame made of:
timber columns (2x8.5x12 + 1x4.5x12) cm, and
timber beams (2x8.5x12) cm,
 Knauf fibreplaster boards with the thickness of 1.5 cm. They are fixed to the timber frame by steel staples Φ1.53 mm at the constant average distance s_{ }= 9.1 cm.
Figure 2: Scheme of the static system and of the composed cross section of the test samples
3.2 Material Properties
Considered timber properties were of the class C22 according to the Eurocode5 classification [6]. We assumed for the modification factor (k_{mod}) the value 0.9 (for a shortterm load). The relative humidity of timber was less than 20%. While the fibreplaster boards were of the Knauf type, material properties of the boards were taken from [7]. Table 1 presents all material properties of the test samples.
Table 1 Material properties of the timber and of the Knauf fibreplaster boards
timber 
E_{0,mean} [MPa] 
E_{90,mean} [MPa] 
G_{mean} [MPa] 
f_{m,k} [MPa] 
f_{t,0,k} [MPa] 
f_{c,0,k} [MPa] 
f_{v,k} [MPa] 
ρ_{mean} [kg/m^{3}] 
10 000 
330 
630 
22 
13 
20 
2.4 
410 

fiberboard 
3000 
/ 
/ 
4.0 
2.5 
20 
5.0 
1050 
4. TEST RESULTS
4.1 Cracks
The curve of the first crack in fibreplaster boards in all test samples propagated from the most tensioned fibre at the connection of the first bolt to the neutral axis of the composed cross section. At the same time we also noticed that the crack in the opposite diagonal corner was not formed at all, not even before destruction. This indicates that the panel shear walls under great loads behave like a thinwall (L/H>2) and not like a truss. Let us compare the measured cracks in all test samples. The obtained average force forming the first crack (F_{cr}) was by:
 Unreinforced test samples (T1): F_{cr,1} = 14.59 kN
 Reinforced test samples with additional symmetric boards (T2): F_{cr,2} = 19.82 kN
 Reinforced test samples with steel diagonals (T3): F_{cr,3} = 18.50 kN
It is evident that in this case is the best solution in reinforcing with additional symmetric boards, but a difference in reinforcing possibilities is not especially evident.
4.2 Destruction
The measured destruction force (F_{u}) of the test samples was by:
 Unreinforced test samples (T1): F_{u,1} = 20.18 kN
 Reinforced test samples with additional symmetric boards (T2): F_{u,2} = 25.36 kN
 Reinforced test samples with steel diagonals (T3): F_{u,3} = 35.73 kN
This means that the resistance of the steel reinforced test samples was in average 77% bigger as by the normal ones. In this case the solution with using additional symmetric boards is not so convenient. The conclusions from the both measured characteristics are now clear. In a sense to increase only elasticity of the wall it is a little better to use additional boards, but in a view to improve a resistance and also ductility it is recommendable to insert steel diagonal strips.
4.3 Vertical Displacements
Figure 3 presents measured average vertical displacements on all test samples. It is evident that the stiffness of the reinforced test samples T2 and T3 is greater than by unreinforced elements (T1). More about the measured results on test samples T1 and T3 can be found in [8].
F [kN]
v [mm]
Figure 3: Comparison of measured vertical displacements
It is easy to see from the figure that behaviour of T1 and T2 is practically in the similar form, only stiffness is not the same. On the other hand behaviour of T3 is more ductility and applicable for heavy loads. It is also interesting that by uncracked elements it is practically no need to insert steel diagonals. This is logical, while we declared that the tensional diagonal takes the part of the force from the board, when the first crack in the board appears. A heavy horizontal load recommends as a consequence reinforcing with steel diagonals when cracks in the boards are expected. If we wish the boards to be without any cracks, then it is more convenient just to add additional boards.
5. MATHEMATICAL MODELLING OF DIAGONAL REINFORCED ELEMENTS
According to the classical mechanical theory we developed new mathematical models for computation of such reinforced panels. It is especially important to consider the contribution of steel diagonals to the whole stiffness and resistance of the walls. Derivation of the mathematical model is based on continuity of a horizontal displacement of the reinforced panel with the fictive normal (unreinforced) panel (Figure 4).
Figure 4: Computational scheme of the model
The obtained total fictive cross section of one reinforced fiberboard is then:
(3)
In the upper form it means:
t … thickness of one fiberboard,
E_{s} … modulus of elasticity of the inserted steel diagonals,
G_{b} … shear modulus of the fiberboard,
A^{0}_{1s} … netto cross section of the inserted steel diagonal,
a … incline angle of the inserted steel diagonal (according to the Figure 4).
It is evident that the fictive cross section of a reinforced panel (A_{1b}^{*})_{ }is bigger than by a normal one (A_{1b}). To get the fictive cross section are now two possibilities:
a.) To use the fictive "height" of a fiberboard:
(4)
b.) To use the fictive thickness of a fiberboard:
(5)
According to the first possibility the height of developed fictive fibreboard is of course bigger than by a normal one. The thickness is not changed. The same is by considering the fictive thickness of the fibreboard. But it is very important that by the both proposed models dimensions of a timber frame are not changed.
5.1 Comparison with the Measured Results
The results obtained with the proposed mathematical models show a good coincidence with the measured results. By considering the dimensions of the test samples from Subsection 3.1 the ratio in a bending stiffness (EI)_{eff} between the diagonally reinforced and the normal test samples is by the slip modulus of the staples K=K_{ser}:
But if we consider K=2/3K_{ser} the ratio is:
By considering the tensional stiffness of the board from Table 1 f_{t,0,k}=2.5 MPa we can compute a force forming the first crack (F_{cr}) in the board:
 by the model with the fictive thickness: F_{cr,t} = 16.678 kN
 by the model with the fictive height: F_{cr,h} = 20.096 kN
The measured force was 18.50 kN.
Also computed destruction forces of the whole element prove a good coincidence with the measured value. Obtained values are:
 by the model with the fictive thickness: F_{u,t} = 32.90 kN
 by the model with the fictive height: F_{u,h} = 38.60 kN
The measured value was 35.73 kN.
Figure 5 presents a comparison between displacements, obtained with the both proposed mathematical models.
F [kN]
v[mm]
Figure 5: Comparison of computed vertical displacements
It is evident from the obtained results that the resistance and stiffness of the model with the fictive height are bigger. As a consequence we propose to use the model with the fictive thickness by a load before the first crack appears. After that the model with the fictive height is more advisable. Results, obtained with such “mixed” model, are compared with the measured displacements and presented in Figure 6.
F [kN]
v[mm]
Figure 6: Comparison of measured and computed vertical displacements
6. CONCLUSIONS
In a sense to assure essential increasing of resistance and ductility of fiberboard, which are used in loadcarrying capacity walls in the construction of prefabricated timber structures, we tried to find a solution by reinforcing the panels with two completely different methods. The first, reinforcing with additional fiberboard, attested higher elasticity of the element, but a resistance and especially ductility were not improved in the contended sense. In this way we tried to find another solution by inserting diagonal steel strips, which were fixed to the timber frame. The idea was in somehow to shift a part of the horizontal force from inductility fiberboard to the tensional steel diagonal. From the relation between the measured forces forming the first crack it was evident that the inserted steel diagonals were not very important. The maximum load can be namely only 27% greater than by unreinforced test samples. But the proportion between the measured destruction forces showed that the resistance of the reinforced panels is 77% higher. Consequently, we recommend the steel diagonals in the construction of multistory buildings located on the seismic or wind areas.
Measured results showed a good coincidence with the results obtained with the proposed mathematical models. Analytical models with the fictive height and thickness of fibreboards are presented in the analysis. We recommend a mathematical model with the fictive thickness by a load before the first crack appears. After that it is more advisable to use the model with the fictive height.
REFERENCES
[1] Brüninghoff, H. (1988), Eine Ausführliche Erläuterung zu DIN 1052, Teil 1 bis Teil 3, Beuth Kommentare, Beuth Bauverlag.
[2] Faherty, K.F. and Williamson, G. (1989), Wood Engineering and Construction Handbook, Mc GrawHill Publishing Company.
[3] Schulze, H. (1996), Holzbau: Wände – Decken  Dächer, B.G. Teubner, Stuttgart.
[4] Bergmeister, K. and Luggin, W. (2001), "Innovative Strenthening of Timber Structures Using Carbon Fibres", Proceedings of the IABSE Conference Innovative Wooden Structures and Bridges, pp. 367372, Lahti.
[5] Kent, S., Tingley, D. (2001), "Structural Evaluation of Fiber Reinforced Hollow Wood Beams", Proceedings of the IABSE Conference Innovative Woooden Structures and Bridges, pp. 361366, Lahti.
[6] British Standard Institutions (1995), Eurocode 5: Design of Timber Structures, Part 1.1 General rules and rules for buildings, DD ENV 199511:1994.
[7] Knauf Gipsfaserplatten Vidivall/Vidifloor 2002.
[8] Dobrila, P. and Premrov, M. (2001), "Bending Tests of Panel Shear Walls", Proceedings of the IABSE Conference Innovative Woooden Structures and Bridges, pp. 373378, Lahti.