Taskforce Meeting Zurich 6./7.09.2004 Summary and Progress Jochen Köhler, ETH Zurich, Switzerland.
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Transcript of Taskforce Meeting Zurich 6./7.09.2004 Summary and Progress Jochen Köhler, ETH Zurich, Switzerland.
Contents
• Stress Strain Relation
• Serviceability
• DOL
• GLULAM
• Connections
• Quantification of model parameters
Stress Strain Relation• According to Glos (1978)
1
2 3 4
0
0
N
N
t
k
k k k
E
,1
1 ,,
,
2
3, ,
14
,
1 1
1
1
1
c a
N c ac c u
c u
c
c u c c u
c a
fk
fN E
f
kE
Nk
f N E
kk
f
Stress Strain Relation• According to Glos (1978)
1
2 3 4
0
0
N
N
t
k
k k k
E
,1
1 ,,
,
2
3, ,
14
,
1 1
1
1
1
c a
N c ac c u
c u
c
c u c c u
c a
fk
fN E
f
kE
Nk
f N E
kk
f
Stress Strain Relation• According to Glos (1978)
1
2 3 4
0
0
N
N
t
k
k k k
E
,1
1 ,,
,
2
3, ,
14
,
1 1
1
1
1
c a
N c ac c u
c u
c
c u c c u
c a
fk
fN E
f
kE
Nk
f N E
kk
f
, ,
,
1
1
c a c u
c uc
c
f f
fN
N E
Conditions:
Stress Strain Relation• According to Glos (1978)
, ,
,
1
1
c a c u
c uc
c
f f
fN
N E
Conditions:
-0.71 0.65 0.34-0.71 -0.28 00.65 -0.28 0.650.34 0 0.65
cE c ,c uf ,c af
cE
c,c uf
,c af
• According to Glos (1978)Discussion:
MOE in tension = MOE compression ?
Quantification of asymptotic compression strength and strain.
Modelling of N ?
Typical values:
, , 1c a c uf f
8.0/, cyc ff
%2.18.0 c
cu 3
Stress Strain Relation
Stress Strain Relation
Actions:
• Quantify asymptotic stress
• Include into the Model Code
Coordination:
Jochen Köhler
Serviceability
• According to Torratti (1992):
The following conditions apply– The deformations are calculated in the grain direction only– The maximum stress bending stress is 20 Mpa– Natural conditions environment conditions apply (temperature
and humidity)– The model has been successfully compared to tests on
European softwoods, both solid wood and glulam of different sizes
(t, u) = e (t,u) + c (t)+ ms (t, u)+ u(u)
ServiceabilityRelative deformation
0
0.5
1
1.5
2
2.5
3
0 1000 2000 3000 4000 5000 6000 7000 8000 9000
Time [hours]
Model
Serviceability
Actions:
• Producing a matrix for different load and climate situations. Therefore the following is needed:
– quantify moisture loads (Lars-Oluf Nielsson (Lund)/study from DTU 2003)
– quantify load sequences
– acquiring data, quantify model parameters
– doing calculations and sensitivity analysis
Coordination:Tomi Toratti
DOL
Limit state function:
Model (Nielsen):
Applied stress:
0, ( ) ( , ( ), , )ult ultg S t S t f z p
1
1
2 2
12
with
81
b
i i i
t dtii i
i
FL SLd
t dt qSL
0
S tSL
f
combined with climate deviations 0
with 1S t
SL t tf
DOL
Limit state function:
Model (Barrett):
Applied stress:
01 ( , ( ), , )loadg X S t f z p
1
with
0
i i i
Bt dti id A SL C SL
t dt SL
0
S tSL
f
combined with climate deviations 1 load load moisture moistureg X X
DOL
Actions:
• Acquire North American data
• Review data, quantify model parameters
• Distribute tasks according ‘Tension perpendicular to the grain’ and ‘Connections’
Coordination:John D. Sorensen
GLULAM
• Glued laminated timber in BENDING
• Load carring capacity depending on the outermost lamination
• Lamination = timber boards with length a; jointed by finger joints
• a is assumed to be Poisson distributed
• The tensile strength and stiffness of each board is assumed to be constant and lognormal distributed.
• The strength of the finger joints is assumed to be lognormal distributed
GLULAM
fm,mean = min {9.3 MPa + 1.15 fl,mean ; 2.7 MPa + 1.15 ffj,mean}
Standard deviations?
Property
Bending f m,,mean = 9.3 + 1.15 f l,mean
Tension parallel to grain f t, 0,k = 6.7 + 0.8 f l,mean
perpendicular to grain f t, 90,k = 0.27 + 0.015 f l,mean
Compression parallel to grain f c, 0,k = 8 f l,mean 0,45
perpendicular to grain f c 0,g,k = 0.75 f l,mean 0,5
Shear shear f v,k = 0.23 f l,mean 0,8
MOE mean E mean = 1.05 E l,mean
Shear modulus G mean = 0.065 E l,mean
Connections
Probabilistic Framework:• Johansen equations• “Splitting Mode parallel”• “Splitting Mode perpendicular”
0 0 :F F
0F
90F
1
2 0 0
3 90 90
ef
g nF R
g n F R
g F R
Connections
Probabilistic Framework:• Johansen equations
h,1 1
h,2 2
yh,1 10
2h,1 1
cal y h,1
(g)
(h)
(j)
(k)
0,5
5 (2 )min 2 (1 )2
21,15 2
1
f t d
f t d
Mf t dFf d t
k M f d
Connections
Probabilistic Framework:• Johansen equations
,0 ,90
, 2 2,0 ,90sin cos
h hh
h h
f ff
f f
2,60.3y uM f d
Connections
Probabilistic Framework:• “Splitting Mode parallel”
00
2cG E d h dF t
h
cG the fracture energy for mixed mode according to Peterson [1995] loading
parallel to the grain [Nmm/mm2]
d diameter of the dowel type fastener mm
0E modulus of elasticity parallel to the grain MPa
h member width mm
t member thickness mm
Connections
Mixed Mode Fracture Energy
2 1
1 1 2
411 1 1
2cG
31
32
2
,90
3 2
,90 90
0
1
IIc
Ic
t
v
t
v
G
G
f
f
f E
f E
2
2
162 1.07
3.5
Ic
IIc Ic
NmGm
NmG Gm
IcG is the fracture energy required for opening mode I
IIcG is the fracture energy required for opening mode II
is the timber density 3kg
m
,90tf is the tension strength perpendicular to the grain
vf is the shear strength
90E is the MOE perpendicular to the grain
0E is the MOE parallel to the grain
Connections
Probabilistic Framework:• “Splitting Mode perpendicular”
c90
0.6(1 )
ec
e
h GGF k b
h
h
where,
b width of the component
eh maximum distance between the stressed edge and a fastener
h height of the component
G shear modulus
cG the fracture energy for mixed mode according to Peterson [1995] loading
parallel to the grain [Nmm/mm2]
ck factor depending on the failure mode of the fastener
Connections
Probabilistic Framework:• Effective number of fasteners
1n n
n
C DB
ef n
a tn A n
d d
, , ,A B C D regression coefficients as random variables
1a spacing or loaded end distance parallel to the grain
n number of fasteners in a row in the grain direction
t member thickness mm
Parameter A B C D
mean 0.42 0.91 0.28 0.19
c.o.v.
Connections
Actions:
• Acquire test data
• Case study – reliability analysis
Coordination: André Jorissen
Topic Task Data required Sources (as mentioned in our meeting)
Grading Describe the stochastic properties of graded timber material
Bending strength, MOE bending, density. Regression with indicators
Stress-strain curve
Quantify model parameters, proposal for perpendicular to the grain
Tension and compression tests Glos, Gehri
Serviceability Quantify model parameters Specify moisture load model
Long term test - deflection Toratti
DOL Quantify model parameters Duration of load test data Foschi, Rosowsky, Hoffmeyer
Glulam Propose a simple model Lamella properties, finger joint properties, properties of glulam components
Gehri, Jorissen, Solli, ‘Austrians’
Connections Quantify model parameters Material properties, properties of conections
Rouger, Jorissen
Bending strength model (Isaksson)
Quantify model parameters for different species Definition of weak section
Longithudinal distribution of weak sections Strength of weak section
Isaksson
Quantification of Model Parameters