TEMTIS Horsens, A Design Model of Shear Wall Elements with Plaster Boards Assoc. Prof. Dr. Miroslav Premrov University of Maribor, Faculty of Civil Engineering TEMTIS Horsens, A Design Model of Shear Wall Elements with Plaster Boards Assoc. Prof. Dr. Miroslav Premrov University of Maribor, Faculty of Civil Engineering

1.Current Tendency in Timber Building in the World  Tendency to multi-story prefabricated timber-frame houses.  At least F + 3  It is important to assure beside fire resistance also a construction resistance stability.

Different Systems in Multi-Story Building a.) Platform Building b.) Balloon System c.) Massive System Frame System Space Frame System Multi-layer Panels Macro-panel System

2. Timber-Framed Wall System 2. Timber-Framed Wall System  Although timber-framed walls are meantime connected they can be in static design considered as separated cantilever elements (Eurocode 5-1-1) Static Design

2.2. Composition of Timber- Framed Walls - timber frame, - timber frame, - fibreboards (as sheathing boards) - fibreboards (as sheathing boards) - fiber-plaster boards, - fiber-plaster boards, - plaster-cardboards, - OSB (Oriented Standard Board, North America,....)

timber frame timber frame Composition of a Timber Panel Shear Wall boards

3. Strengthening of FPB Ussing additional fibre-plaster boards (FPB) – very popular by producers Ussing additional fibre-plaster boards (FPB) – very popular by producers By reinforcing with classical steel diagonals in the tensile area of FPB By reinforcing with classical steel diagonals in the tensile area of FPB By reinforcing with carbon or high-strength syntetic fibres in the tensile area of FPB By reinforcing with carbon or high-strength syntetic fibres in the tensile area of FPB

3.1. Additional Boards  The simplest case of reinforcing.  Usually used by producers.  Boards can be added: - symmetric, - symmetric, - asymmetric. - asymmetric.  Resistance of boards is increased, but ductility is practically not changed.

What was increased?  The force forming the first crack for 35,82%.  The crack extended by only for 9% bigger force to the internal board.  Destruction force for 25,65%. What was decreased?  “Ductility” for 7,41%

3.2. Reinforcing with Steel Diagonal Elements Static System of the Test Samples

Destruction force unreinforced: 20,18 kN; reinforced: 35,73 kN ratio = 1.77 Ductility Ductility was increased for 39,64%!

Comparison of the Measured Vertical Displacements F [kN] v [mm] unreinforcedreinforced

Hotel Terme Zreče (3+M)

3.3. Reinforcing with CFRP Diagonal Strips

Test Configuration 1. The first group (G1) of three test samples was additionally reinforced with two CFRP diagonal strips (one in each FPB) of width 300 mm which were glued on the FPB using Sikadur-330 LVP. The strips were additionally glued to the timber frame to ensure the transmission of the force from FPB to the timber frame. of three test samples was additionally reinforced with two CFRP diagonal strips (one in each FPB) of width 300 mm which were glued on the FPB using Sikadur-330 LVP. The strips were additionally glued to the timber frame to ensure the transmission of the force from FPB to the timber frame.

2. The second group (G2) of three test samples was additionally reinforced with two CFRP diagonal strips of width 600 mm. The strips were glued on FPB and to the timber frame as in G1. of three test samples was additionally reinforced with two CFRP diagonal strips of width 600 mm. The strips were glued on FPB and to the timber frame as in G1. 3. The third group (G3) 3. The third group (G3) of three test samples was additionally reinforced with two CFRP diagonal strips of width 300 mm as in G1 but they were not glued to the timber frame. of three test samples was additionally reinforced with two CFRP diagonal strips of width 300 mm as in G1 but they were not glued to the timber frame.

Properties of the used materials E 0,m [N/mm 2 ] G m [N/mm 2 ] f m,k [N/mm 2 ] f t,0,k [N/mm 2 ] f c,0,k [N/mm 2 ] f v,k [N/mm 2 ] ρ m [kg/m 3 ] Timber C Fibre-plaster board SikaWrap- 230C //4100//1920

Test Results Average force forming the first crack in FPB unreinforced: kN G1: 24,28 kN G2: 32,13 kN G3: 35,90 kN

Average destruction force unreinforced: 26,02 kN G1: 40,33 kN G2: 46,27 kN G3: 36,26 kN

Test samples behaviour Further information on the behaviour of tested elements can be obtained by calculation of the "safety " (ci) and "ductility coefficients of FPB" (di) in the following forms: Further information on the behaviour of tested elements can be obtained by calculation of the "safety " (ci) and "ductility coefficients of FPB" (di) in the following forms:

Measured bending deflections under the force F (mm) un-strengthened samples G1 samples G2 samples G3

It is evident from figure that, similarly to the classical reinforcement with BMF steel diagonals presented in Dobrila and Premrov (2003), there is practically no influence on stiffness of any reinforcement before appearance of cracks in the un-strengthened FPB. It is evident from figure that, similarly to the classical reinforcement with BMF steel diagonals presented in Dobrila and Premrov (2003), there is practically no influence on stiffness of any reinforcement before appearance of cracks in the un-strengthened FPB. This is logical because in this case the reinforcement is practically not activated at all and its stiffness in comparison to the stiffness of un-cracked FPB is small. After appearance of the first crack in the un-strengthened test samples (Fcr,uns = kN) the influence of the CFRP strips is obvious and it depends on the strip’s dimensions as well as on the boundary conditions between the strips and the timber frame. This is logical because in this case the reinforcement is practically not activated at all and its stiffness in comparison to the stiffness of un-cracked FPB is small. After appearance of the first crack in the un-strengthened test samples (Fcr,uns = kN) the influence of the CFRP strips is obvious and it depends on the strip’s dimensions as well as on the boundary conditions between the strips and the timber frame.

Measured average slips in the connecting area (mm) samples G1 samples G2 samples G3

Conclusions for G1 and G2 test groups Beside the fact that samples G1 and especially G2 demonstrated higher load-carrying capacity than samples G3, it is important to mention that samples G1 and G2 produced substantially smaller slip than samples G3, which never exceeded 1mm at the first crack forming. Beside the fact that samples G1 and especially G2 demonstrated higher load-carrying capacity than samples G3, it is important to mention that samples G1 and G2 produced substantially smaller slip than samples G3, which never exceeded 1mm at the first crack forming. Therefore it can be assumed that the yield point of the fasteners was not achieved before cracks appeared at all! Therefore it can be assumed that the yield point of the fasteners was not achieved before cracks appeared at all! Consequently, the walls tend to fail because of the crack forming in FPB. In this case of strengthening the ductility of the whole wall element (see Fig. 6 for samples G1 and G2) practically coincides with the “ductility” of FPB, as proposed with d1 and d2 coefficients. Consequently, the walls tend to fail because of the crack forming in FPB. In this case of strengthening the ductility of the whole wall element (see Fig. 6 for samples G1 and G2) practically coincides with the “ductility” of FPB, as proposed with d1 and d2 coefficients.

In contrast, in G3 model, where the CFRP strips were unconnected to the timber frame, the slip (Δ) between the FPB and the timber frame was evidently higher than in samples G1 and G2, and exceeded 3mm when the first crack in FPB appeared. In contrast, in G3 model, where the CFRP strips were unconnected to the timber frame, the slip (Δ) between the FPB and the timber frame was evidently higher than in samples G1 and G2, and exceeded 3mm when the first crack in FPB appeared. The load-displacement relation (F-Δ) of the fasteners was in this case at the force which produced first cracks almost completely plastic. The load-displacement relation (F-Δ) of the fasteners was in this case at the force which produced first cracks almost completely plastic. Since the tensile strength of FPB is essentially improved, the walls tend to fail because of fastener yielding. Although the fibreboards in samples G3 demonstrated practically no deformation capacity (d3 ≈ 1.0, Eq.14) the ductility is formed (F-w diagram) over the fasteners yielding. Since the tensile strength of FPB is essentially improved, the walls tend to fail because of fastener yielding. Although the fibreboards in samples G3 demonstrated practically no deformation capacity (d3 ≈ 1.0, Eq.14) the ductility is formed (F-w diagram) over the fasteners yielding. Conclusions for G3 test group

4. Design Models Shear model (EC 5) Shear model (EC 5) Composite Beam Model Composite Beam Model

4.1. Modelling of walls with wood-based sheathing boards - Shear Model (EC 5)

«Lower bound plastic method« Källsner and Lam (1995) a.) behaviour of the joints between the sheet and the frame members is assumed to be linear-elastic until failure, b.) the frame members and the sheets are assumed to be rigid and hinged to each other.

Shear resistance - Method A Shear resistance - Method B

4.2. Modelling of walls with fibre - plaster sheathing boards - Composite Beam Model

»γ-method« (EC 5) Basic assumptions: Bernoulli`s hypothesis is valid for each sub- component, Bernoulli`s hypothesis is valid for each sub- component, slip stiffness is constant along the element, slip stiffness is constant along the element, material behaviour of all sub-components is linear elastic. material behaviour of all sub-components is linear elastic.

Effective bending stiffness (EI y ) eff of mechanically jointed beams

Influnce of steel (CFPR) diagonal reinforcing

Shear deformation in one fiberboard is: Horizontal displacement of the fiberboard is: Axial force in the tensile steel diagonal is :

total cross section of the fictive fiberboard: If we consider continuity of horizontal displacements u b = u s, we get for the total cross section of the fictive fiberboard: Horizontal displacement of the tensile steel diagonal is thus:

Proposed Models:  Model with the fictive thickness of the board:  Model with the fictive width of the board:

a.) Normal panel (without reinforcement) b.) Panel with the fictive width c.) Panel with the fictive thickness

Modelling of fasteners flexibility

Definition of slip modulus K

Modelling of cracks in FPB Force forming the first crack in FPB:

Major assumptions of the cracked cross-section: The tensile area of the fibreboards is neglected after the first crack formation. The tensile area of the fibreboards is neglected after the first crack formation. The stiffness coefficient of the fasteners in the tensile connecting area (γ yt ) is assumed to be constant and equal to the value by appearing the first crack. The stiffness coefficient of the fasteners in the tensile connecting area (γ yt ) is assumed to be constant and equal to the value by appearing the first crack. The stiffness coefficient of the fasteners in the compressed connecting area (γ yc ) is not constant and depends on the lateral force acting on one fastener. The stiffness coefficient of the fasteners in the compressed connecting area (γ yc ) is not constant and depends on the lateral force acting on one fastener. The normal stress distribution is assumed to be linear. This simplification can be used only by assumption that behaviour of timber frame in tension is almost elastic until failure and that the compressive normal stress in timber and in FPB is under the belonging yield point. The normal stress distribution is assumed to be linear. This simplification can be used only by assumption that behaviour of timber frame in tension is almost elastic until failure and that the compressive normal stress in timber and in FPB is under the belonging yield point.

Characteristic horizontal destruction force (according to the tensile stress in the timber stud)

5. Numerical Example 5.1 Geometrical and material properties

Height of the wall: Height of the wall: h = cm h = cm Staples: Staples: Φ1.53 mm, Φ1.53 mm, length l = 35 mm, length l = 35 mm, constant spacing s = 75 mm constant spacing s = 75 mm

Timber C22 FPB Knauf Swedian (S) Plywood * E 0,m [N/mm 2 ] f m,k [N/mm 2 ] f t,0,k [N/mm 2 ] f c,0,k [N/mm 2 ] ρ k [kg/m 3 ] ρ m [kg/m 3 ] * The values are given for 12mm typical thickness of the board.

5.2 Results a.) Lateral load-bearing capacity of the staples (Johansen expressions): (Johansen expressions): FPB: FPB: F f,Rk = N F f,Rk = N F f,Rd = N F f,Rd = N WBB (plywood): WBB (plywood): F f,Rk = N F f,Rk = N F f,Rd = N F f,Rd = N

b.) Slip modulus (K ser ) of the staples: FPB:

WBB:

c.) Stiffness coefficient γ yi before any cracks appearing in the boards (Composite model):

d.) Effective bending stiffness (EI y ) eff of the un- cracked cross-section (Composite model):

e.) Horizontal force (F H,cr ) forming the first tensile crack in board (Composite model):

f.) Characteristic horizontal load-carrying capacity (F H,k ): FPB (Composite model, timber condition): FPB (Shear model, fastener‘s yielding criteria) WBB (Shear model, fastener‘s yielding criteria)

F H [kN] F 1 (FPB) [N] F 1 (WBB) [N] Δ FPB [mm] Δ WBB [mm] = F (FPB) H,cr < N al = F (FPB) H,k < F f,Rd = F (WBB) H,cr / ≈ N al /1.384

Conclusions FPB FPB Shear model (EC5) is not recommended! Practical use  Reinforcing of FPB by multi-storey buildings (steel diagonals, CFRP diagonals)

Experimental results for FPB P. Dobrila, M. Premrov, Reinforcing Methods for Composite Timber Frame – Fibreboard Wall Panels. Engineering Structures, Vol.25, No.11, 2003, pp P. Dobrila, M. Premrov, Reinforcing Methods for Composite Timber Frame – Fibreboard Wall Panels. Engineering Structures, Vol.25, No.11, 2003, pp M. Premrov, P. Dobrila, B.S. Bedenik, Analysis of timber-framed walls coated with CFRP strips strengthened fibre-plaster boards, International Journal of Solids and Structures, Vol.41, No. 24/25, 2004, pp. 7035–7048. M. Premrov, P. Dobrila, B.S. Bedenik, Analysis of timber-framed walls coated with CFRP strips strengthened fibre-plaster boards, International Journal of Solids and Structures, Vol.41, No. 24/25, 2004, pp. 7035–7048.

WBB WBB Shear model (EC5) is recommended! Practical use  No need of any board´s reinforcing,  decreasing of fastener´s spacing

6. Numerical Example for G1 CFRP Test Sample Fasteners slip modulus (Kser) can be computed using Eurocode 5: Fasteners slip modulus (Kser) can be computed using Eurocode 5:

The stiffness coefficient of the fasteners (γy) is computed using EC 5[3]

The horizontal force (FH,cr) forming the first tensile crack in FPB is: measured: FH,cr,meas = kN

The crushing horizontal force (FH,u): Numerical: FH,u = kN measured: FH,u = kN

7. Conclusions WBB → Shear (EC 5 ) model WBB → Shear (EC 5 ) model Fasteners yielding appear before cracks forming in the tensile area of boards. Fasteners yielding appear before cracks forming in the tensile area of boards. FBP → Composite model FBP → Composite model It was presented that by forming first tensile craks in boards stresses in fasteners are tolerably under the yield points. It was presented that by forming first tensile craks in boards stresses in fasteners are tolerably under the yield points.