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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..