TEMTIS 06-08TEMTIS 06-08Horsens, 11.09.2008Horsens, 11.09.2008

A Design Model of Shear A Design Model of Shear Wall Elements with Wall Elements with

Plaster BoardsPlaster Boards AssAssococ. Prof. Dr. Miroslav Premrov. Prof. Dr. Miroslav Premrov

University of MariborUniversity of Maribor, , Faculty of Civil EngineeringFaculty of Civil Engineering

1.1. Current Tendency in Timber Current Tendency in Timber Building in the WorldBuilding in the World

Tendency to multi-story prefabricated Tendency to multi-story prefabricated timbertimber-frame-frame houses. houses.

At least At least F + 3F + 3 It is important to assure beside fire It is important to assure beside fire

resistance also a construction resistance also a construction resistance resistance stabilitstabilityy..

Different Systems in Multi-Story BuildingDifferent 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

22. Timber-Framed Wall. Timber-Framed Wall System System

Although Although timber-framedtimber-framed walls are walls are meantime connected they can be in static meantime connected they can be in static design considered as design considered as separated separated cantilever elementscantilever elements (Eurocode 5-1-1)(Eurocode 5-1-1)..

22.1. .1. Static DesignStatic Design

FH,tot FH

h

b b

n·b y

n

FF tot,H

H

timber frame (the studs)

coating boards

22.2. .2. Composition of Composition of Timber-Timber-FramedFramed Walls Walls

- - timber frametimber frame,,

- - fibreboards fibreboards (as (as sheathing boardssheathing boards))

- - fiber-plaster boardsfiber-plaster boards, ,

- - plaster-cardboardsplaster-cardboards,,

- OSB (- OSB (Oriented Standard Board, Oriented Standard Board, North AmericaNorth America,....),....)

timber frametimber frame

Composition of a Timber Panel Shear Wall

boards

timber gird thermo- isolation timber stud fasteners 2s sheathing board

3. Strengthening of FPB3. Strengthening of FPB

Ussing additional fibre-plaster boards Ussing additional fibre-plaster boards (FPB) (FPB) – very popular by producers– very popular by producers

By reinforcing with classical steel diagonals By reinforcing with classical steel diagonals in the tensile area of FPBin the tensile area of FPB

By reinforcing with carbon or high-strength By reinforcing with carbon or high-strength syntetic fibres in the tensile area of FPBsyntetic fibres in the tensile area of FPB

3.1. 3.1. Additional BoardsAdditional Boards

The simplest case of reinforcingThe simplest case of reinforcing.. Usually used by producers.Usually used by producers. Boards can be addedBoards can be added: : - s- symmetric,ymmetric, - - asymmetric.asymmetric. Resistance of boards is increased, but Resistance of boards is increased, but

ductility is practically not changed.ductility is practically not changed.

What was increased?What was increased?

The force forming the first crack forThe force forming the first crack for 35,82%.35,82%. The crack extended by The crack extended by only foronly for 9%9% bigger forcebigger force to the to the

internal board.internal board. Destruction force forDestruction force for 25,65%.25,65%.

What was decreased?What was decreased?

““Ductility”Ductility” forfor 7,41% 7,41%

3.3.2. Reinforcing with Steel 2. Reinforcing with Steel Diagonal ElementsDiagonal Elements

Static System of the Test Samples

FH,tot FH

x h steel (CFRP) strips α bd

b b

n·b y

n

FF tot,H

H zt

timber frame

coating board

Destruction force

unreinforced: 20,18 kN;

reinforced: 35,73 kN ratio = 1.77

Ductility

Ductility was increased forDuctility was increased for 39,64%! 39,64%!

Comparison of the Measured Vertical Comparison of the Measured Vertical DisplacementsDisplacements

F [kN]

v [mm]

unreinforced reinforced

Hotel Terme Zreče (3+M)

3.33.3. Reinforcing with . Reinforcing with CFRPCFRP Diagonal Diagonal StripsStrips

3.3.1. Test Configuration3.3.1. Test Configuration

1. The first group (G1)1. The first group (G1)

of three test samples was of three test samples was additionally reinforced with two additionally reinforced with two CFRP CFRP diagonal strips (one in each FPB) of width diagonal strips (one in each FPB) of width 300 mm300 mm which were glued on the FPB using Sikadur-330 LVP. The which were glued on the FPB using Sikadur-330 LVP. The strips were additionally glued to the timber frame to ensure the strips were additionally glued to the timber frame to ensure the transmission of the force from FPB to the timber frame. transmission of the force from FPB to the timber frame.

2. The second group (G2)2. The second group (G2)

of three test samples was of three test samples was additionally reinforced with two additionally reinforced with two CFRP CFRP diagonal strips of width diagonal strips of width 600 mm600 mm. The strips were glued . The strips were glued on FPB and to the timber frame as in G1. 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 of three test samples was additionally reinforced with two additionally reinforced with two CFRP CFRP diagonal strips of width diagonal strips of width 300 mm300 mm as in G1 but they were as in G1 but they were not glued to the timber frame.not glued to the timber frame.

Properties of the used materialsProperties of the used materials

  

EE0,m0,m

[N/mm[N/mm22]]

GGmm

[N/mm[N/mm22]]

ffm,km,k

[N/mm[N/mm22]]

fft,0,kt,0,k

[N/mm[N/mm22]]

ffc,0,kc,0,k

[N/mm[N/mm22]]

ffv,kv,k

[N/mm[N/mm22]]

ρρmm

[kg/m[kg/m33]]

Timber C22Timber C22 1000010000 630630 2222 1313 2020 2.42.4 410410

Fibre-plaster Fibre-plaster board board

30003000 12001200 4.04.0 2.52.5 2020 5.05.0 10501050

SikaWrap-SikaWrap-230C230C

231000231000 // // 41004100 // // 19201920

3.3.2. Test Results

Average force forming the first crack in FPB

unreinforced: 17.67 kN

G1: 24,28 kN

G2: 32,13 kN

G3: 35,90 kN

Average destruction forceAverage destruction force

unreinforcedunreinforced: 26,02 kN: 26,02 kN

G1: 40,33 kNG1: 40,33 kN

G2: 46,27 kNG2: 46,27 kN

G3: 36,26 kNG3: 36,26 kN

Test samples behaviourTest samples behaviour

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

47.1c;01.1F

Fc,44.1

F

Fc,66.1

F

Fc uns

3,cr

3,u3

2,cr

2,u2

1,cr

1,u1

71.2d;0.1

u

ud,66.2

71.23

15.63

u

ud,80.2

67.19

06.55

u

ud uns

F

F

3F

F

2F

F

1

3,cr

3,u

2,cr

2,u

2,cr

2,u

Measured bending deflections under the force F Measured bending deflections under the force F (mm)(mm)

un-strengthened

samples G1

samples G2

samples G3

It is evident from It is evident from figure figure that, similarly to the classical that, similarly to the classical reinforcement with BMF steel diagonals presented in Dobrila reinforcement with BMF steel diagonals presented in Dobrila and Premrov (2003), and Premrov (2003), there is practically no influence on there is practically no influence on stiffness of any reinforcement before appearance of cracks stiffness of any reinforcement before appearance of cracks in the un-strengthened FPBin the un-strengthened FPB. .

This is logical because in this case the reinforcement is This is logical because in this case the reinforcement is practically not activated at all and its stiffness in comparison practically not activated at all and its stiffness in comparison to the stiffness of un-cracked FPB is small. After appearance to the stiffness of un-cracked FPB is small. After appearance of the first crack in the un-strengthened test samples (of the first crack in the un-strengthened test samples (Fcr,uns Fcr,uns = 17.67 kN)= 17.67 kN) the influence of the CFRP strips is obvious and it the influence of the CFRP strips is obvious and it depends on the strip’s dimensions as well as on the boundary depends on the strip’s dimensions as well as on the boundary conditions between the strips and the timber frame.conditions between the strips and the timber frame.

Measured average slips in the connecting area Measured average slips in the connecting area (mm)(mm)

samples G1

samples G2

samples G3

Conclusions for G1 and G2 test groupsConclusions for G1 and G2 test groups

Beside the fact that samples G1 and especially G2 Beside the fact that samples G1 and especially G2 demonstrated higher load-carrying capacity than samples G3, demonstrated higher load-carrying capacity than samples G3, it is important to mention that samples it is important to mention that samples G1 and G2 produced G1 and G2 produced substantially smaller slip than samples G3, which never substantially smaller slip than samples G3, which never exceeded 1mm at the first crack forming. exceeded 1mm at the first crack forming.

Therefore it can be assumed that the yield point of the Therefore it can be assumed that the yield point of the

fasteners was not achieved before cracks appeared at allfasteners was not achieved before cracks appeared at all!! Consequently, the walls tend to fail because of the crack Consequently, the walls tend to fail because of the crack

forming in FPB. In this case of strengthening the ductility forming in FPB. In this case of strengthening the ductility of the whole wall element (see Fig. 6 for samples G1 and of the whole wall element (see Fig. 6 for samples G1 and G2) practically coincides with the “ductility” of FPB, as G2) practically coincides with the “ductility” of FPB, as proposed with d1 and d2 coefficients. proposed with d1 and d2 coefficients.

In contrast, in In contrast, in G3 G3 model, where the CFRP strips were unconnected to the model, where the CFRP strips were unconnected to the timber frame, the slip (timber frame, the slip (Δ)Δ) between the FPB and the timber frame was between the FPB and the timber frame was evidently higher than in samples G1 and G2, and exceeded 3mm when the evidently higher than in samples G1 and G2, and exceeded 3mm when the first crack in FPB appeared. first crack in FPB appeared.

The load-displacement relation (F-Δ) of the fasteners was in this case at The load-displacement relation (F-Δ) of the fasteners was in this case at the force which produced first cracks almost completely plastic.the force which produced first cracks almost completely plastic.

Since the tensile strength of FPB is essentially improved, the walls tend Since the tensile strength of FPB is essentially improved, the walls tend

to fail because of fastener yielding. to fail because of fastener yielding. Although the fibreboards in Although the fibreboards in samples G3 demonstrated practically no deformation capacitysamples G3 demonstrated practically no deformation capacity (d3 ≈ (d3 ≈ 1.0, Eq.14) the ductility is formed (F-w diagram) over the fasteners 1.0, Eq.14) the ductility is formed (F-w diagram) over the fasteners yielding. yielding.

Conclusions for G3 test groupConclusions for G3 test group

4. Design Models4. Design Models

Shear model (EC 5)Shear model (EC 5) Composite Beam ModelComposite Beam Model

4.1. Modelling of walls with wood-based sheathing boards -

Shear Model (EC 5)

««Lower bound plastic methodLower bound plastic method««

Källsner and LamKällsner and Lam (1995) (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.

s

b

b

bFF i

Rkfkv1

2

1

,,

Shear resistance - Method AShear resistance - Method A

Shear resistance - Method B

nsqidii

Rkfkv kkkkcs

bFF ,

0,,

4.2. Modelling of walls with fibre - plaster sheathing boards -

Composite Beam Model

4.2.1. 4.2.1. »γ-method«»γ-method« (EC 5)(EC 5) Basic assumptions:Basic assumptions:

Bernoulli`s hypothesis is valid for each sub-Bernoulli`s hypothesis is valid for each sub-component, component,

slip stiffness is constant along the element, slip stiffness is constant along the element, material behaviour of all sub-components is material behaviour of all sub-components is

linear elastic.linear elastic.

Effective bending stiffness (Effective bending stiffness (EIEIyy))effeff of of

mechanically jointed beamsmechanically jointed beams

.

1 1.

2

1

2)(

timber boardn

i

n

jFPByiitimbiiyiiyii

n

iiiyiyiieffy

IEaAEIE

aAIEEI

steel diagonals u

F F α L γ h timber frame fibreboards

4.2.2. Influnce of steel (CFPR) diagonal reinforcing

Shear deformation in one fiberboard is:Shear deformation in one fiberboard is:

bb1bb1b

xy

G)dA(109

2

F

G)dA(2

F

Gx

v

y

utg

Horizontal displacement of the fiberboard is:

bb1

bb

G)dA(109

2

LFu

L

utg

Axial force in the tensile steel diagonal is:Sin2

FS

If we consider continuity of horizontal displacements ub = us, we get for the total cross section of the fictive fiberboard:total cross section of the fictive fiberboard:

l s1s2

sss AECosSin2

LFdx

AE

SSu

0s1

3

b

sb1b1

*b1 ACosCos

G

E

9

10htdAAA

Horizontal displacement of the tensile steel diagonal is thus:

Proposed ModelsProposed Models::

Model Model with the with the fictive thicknessfictive thickness of the board: of the board:

Model Model with the with the fictive fictive widthwidth of the board: of the board:

h

1ACosCos

G

E

9

10t

h

At 0

s13

b

s*b1*

t

1ACosCos

G

E

9

10h

t

Ah 0

s13

b

s*b1*

a.) b.) fictive board c.) fictive board

h h* h

t t t*

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

44..2.3. 2.3. ModellingModelling of fasteners flexibility of fasteners flexibility

yy k1

1

KL

sEAk

2eff

t1t2

y

Definition of slip modulus KDefinition of slip modulus K

a.) F1[N] Ku b.) F1 [N] Kser

dF1/dΔ = 0 Ff,Rk

Ff,Rd

Ku Nal

Kser

Δ [mm] K [N/mm]

zeffy

effy1 V

2

s

)EI(

)ES(F

seruRdf KKFF 3

2,1

4.1.4. 4.1.4. ModellingModelling of cracks in FPB of cracks in FPB

Force forming the first crack in FPB:Force forming the first crack in FPB:

db

effybtcr,H hbE

)EI(f2F

MMajor assumptions of the cracked cross-section:ajor assumptions of the cracked cross-section: The tensile area of the fibreboards is neglected after the The tensile area of the fibreboards is neglected after the

first crack formation. first crack formation.

The stiffness coefficient of the fasteners in the tensile The stiffness coefficient of the fasteners in the tensile connecting area (connecting area (γγytyt) is assumed to be constant) is assumed to be constant and equal to and equal to the value by appearing the first crack. the value by appearing the first crack.

The stiffness coefficient of the fasteners in the compressed The stiffness coefficient of the fasteners in the compressed connecting area (connecting area (γγycyc) is not constant) is not constant and depends on the and depends on the lateral force acting on one fastenerlateral force acting on one fastener..

The normal stress distribution is assumed to be linear.The normal stress distribution is assumed to be linear. This This simplification can be used only by assumption that behaviour simplification can be used only by assumption that behaviour of timber frame in tension is almost elastic until failure and of timber frame in tension is almost elastic until failure and that the compressive normal stress in timber and in FPB is that the compressive normal stress in timber and in FPB is under the belonging yield point.under the belonging yield point.

yI yII

xII Ab1, Eb t At1, Et

At1, Et At2, Et z c

t

a d a ztII zcII

bd = 2 zp

b

My

yc

ctc

n

σcb,max

σcb

yt

ttc

n

Fcb Fct

Ftt

Characteristic horizontal destruction forceCharacteristic horizontal destruction force

(according to the tensile stress in the timber stud)(according to the tensile stress in the timber stud)

h2

azE

)EI(fF

tIIytt

effII

yk,0,tk,H

5. Numerical Example5. Numerical Example

55.1 Geometrical and material properties.1 Geometrical and material properties

yi At, Et y Ab, Eb yi t =1.5

9.0 9.0 4.4 9.0 ai = 58 b =125 cm

Height of the wall:Height of the wall:

h = 263.5 cmh = 263.5 cm

Staples:Staples:

Φ1.53 mm, Φ1.53 mm,

length length l = 35 mm,l = 35 mm,

constant spacing constant spacing s = 75 mms = 75 mm

Timber C22FPB

Knauf Swedian (S)

Plywood*

E0,m

[N/mm2]10000 3000 9200

fm,k

[N/mm2]22.0 4.0 23.0

ft,0,k

[N/mm2]13.0 2.5 15.0

fc,0,k

[N/mm2]20.0 20.0 15.0

ρk

[kg/m3]340 1050 410

ρm

[kg/m3]410 1050 410

* The values are given for 12mm typical thickness of the board.

5.2 Results5.2 Results

a.)a.) Lateral load-bearing capacity of the staples Lateral load-bearing capacity of the staples (Johansen expressions)(Johansen expressions)::

FPB: FPB: FFf,Rkf,Rk = 659.69 N = 659.69 N FFf,Rdf,Rd = 456.71 N = 456.71 N

WBB (plywood):WBB (plywood): FFf,Rkf,Rk = 516.74 N = 516.74 N FFf,Rdf,Rd = 357.74 N = 357.74 N

b.) Slip modulus (b.) Slip modulus (KKserser) of the staples:) of the staples:

FPB:FPB:

mm/N215.29580

53.112.656

80

dK

m/kg12.6564101050

8.05.1

8.05.1m)FPB(

ser

3tbm

WBB:WBB:

mm/N827.14580

53.1410

80

dK

m/kg410410410

8.05.1

8.05.1m)WBB(

ser

3tbm

c.) Stiffness coefficient c.) Stiffness coefficient γγyiyi before any cracks before any cracks

appearing in the boards (Composite model):appearing in the boards (Composite model):

934.7458.12)5.2542(

5.710009

K2L

sEAk

920.3952.22)5.2542(

5.710009

K2L

sEAk

2

22

)WBB(ser

2eff

t1t2

)WBB(yi

2

22

)FPB(ser

2eff

t1t2

)FPB(yi

112.0934.71

1

k1

1

203.0920.31

1

k1

1

)WBB(yi

)WBB(yi

)FPB(yi

)FPB(yi

d.) Effective bending stiffness (d.) Effective bending stiffness (EIEIyy))effeff of the un- of the un-

cracked cross-section (Composite model):cracked cross-section (Composite model):

28234

3)(

28234

3)(

10114.5112.05899212

94.4

12

921000

12

12550.12920)(

10584.2203.05899212

94.4

12

921000

12

12550.12300)(

kNcm

EI

kNcm

EI

WBBeffy

FPBeffy

e.) He.) Horizontal force (orizontal force (FFH,crH,cr) forming the first tensile ) forming the first tensile

crack in boardcrack in board (Composite model): (Composite model):

)FPB(cr,H

)WBB(cr,H

8)WBB(

cr,H

8)FPB(

cr,H

FF

kN42.525.254125920

10114.55.12F

kN53.135.254125300

10583.225.02F

f.) Cf.) Characteristic horizontal load-carrying capacity (haracteristic horizontal load-carrying capacity (FFH,kH,k))::

FPBFPB (Composite model, timber condition):(Composite model, timber condition):

FPB FPB (Shear model, fastener(Shear model, fastener‘‘s yielding criterias yielding criteria))

WBBWBB (Shear model, fastener (Shear model, fastener‘‘s yielding criterias yielding criteria))

kN58.39

5.2632

9862.77150.01000

10575.13.1F

8)FPB(

k,H

kN99.210.15.7

125660.02c

s

bFF i

iRk,fk,v

kN22.170.15.7

125517.02c

s

bFF i

iRk,fk,v

FH

[kN]

F1(FPB)

[N]

F1(WBB)

[N]

ΔFPB

[mm]

ΔWBB

[mm]

5.0 69.289 19.279 0.235 0.132

10.0 138.579 38.558 0.469 0.264

13.53 = F(FPB)

H,cr

187.497 < Nal

52.170 0.635 0.358

15.0 198.189 57.838 0.671 0.397

20.0 258.064 77.117 0.922 0.529

25.0 306.057 96.396 1.224 0.661

30.0 352.426 115.674 1.532 0.792

35.0 394.036 134.953 1.859 0.924

39.58 = F(FPB)

H,k

437.011 < Ff,Rd

152.613 2.138 1.045

52.42 =F(WBB)

H,cr/ 202.12 ≈ Nal / 1.384

ConclusionsConclusions

FPBFPB

Shear model (EC5) is not recommended!Shear model (EC5) is not recommended!

Practical usePractical use

Reinforcing of FPB by multi-storey buildings Reinforcing of FPB by multi-storey buildings (steel diagonals, CFRP diagonals)(steel diagonals, CFRP diagonals)

!!99.2153.13 )(,

)(, kNFkNF FPB

kvFPBcrH

Experimental results for FPBExperimental results for FPB

P. Dobrila, M. Premrov, P. Dobrila, M. Premrov, Reinforcing Methods for Reinforcing Methods for Composite Timber Frame – Fibreboard Wall Composite Timber Frame – Fibreboard Wall Panels. Panels. Engineering StructuresEngineering Structures, Vol., Vol.25, No.11, 25, No.11, 2003, pp. 1369-1376.2003, pp. 1369-1376.

M. Premrov, P. Dobrila, B.S. Bedenik, Analysis of M. Premrov, P. Dobrila, B.S. Bedenik, Analysis of timber-framed walls coated with CFRP strips timber-framed walls coated with CFRP strips strengthened fibre-plaster boards, strengthened fibre-plaster boards, International International Journal of Solids and StructuresJournal of Solids and Structures, Vol.41, No. 24/25, , Vol.41, No. 24/25, 2004, pp. 7035–7048.2004, pp. 7035–7048.

WBBWBB

Shear model (EC5) is reShear model (EC5) is reccoommmmended!ended!

Practical usePractical use

No need of any board´s reinforcing, No need of any board´s reinforcing, decreasing of fastener´s spacingdecreasing of fastener´s spacing

!!42.5222.17 )(,

)(, kNFF WBB

crHWBBkv

6. Numerical Example for G1 CFRP 6. Numerical Example for G1 CFRP Test SampleTest Sample

Fasteners slip modulus (Fasteners slip modulus (KserKser) can be ) can be computed using Eurocode 5: computed using Eurocode 5:

mm/N215.29580

53.112.656

80

dK

;m/kg12.6564101050

8.05.18.05.1mean

ser

3tbmean

mm/N579.65537.360215.295KKK

mm/N37.36050.24cos3646.91622

2.1300000231cos

nL2

AEK

CFRPser*

0

CFRP

d,1CFRPCFRP

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

;765.1556.62)5.5.2542(

5.710009

K2L

sEAk

2

22

*2eff

t1t2

yi

362.0765.11

1

k1

1

yiyi

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

measured: measured: FH,cr,meas = 24.28 kNFH,cr,meas = 24.28 kN

kN386.235.254125300

10468.425.02F

8

cr,H

The The crushing crushing horizontal force (FH,horizontal force (FH,uu))::

Numerical: FH,u = 42.68 kNNumerical: FH,u = 42.68 kN

measured: measured: FH,u = 40.33 kNFH,u = 40.33 kN

7. Conclusions7. Conclusions

WBB WBB → Shear (EC 5 ) model→ Shear (EC 5 ) model

Fasteners yielding appear before cracks Fasteners yielding appear before cracks forming in the tensile area of boards.forming in the tensile area of boards.

FBP → Composite modelFBP → Composite model

It It was was presented thatpresented that by forming first tensile by forming first tensile craks in boardscraks in boards stresses in stresses in fasteners fasteners are are tolerably under the yield pointstolerably under the yield points..