Transcript Slide 1

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)
   k1 N

      k2  k3  k4 N

Et 

k1 
  0
  0
f c ,a
f c ,a
 N 1 
N

1
E

1


 c c,u 
f c ,u

k2 
1
Ec
k3 
1
N

f c ,u  N  1 Ec c ,u
k4 
k1
f c ,a



Stress Strain Relation
•
According to Glos (1978)
   k1 N

      k2  k3  k4 N

Et 

k1 
  0
  0
f c ,a
f c ,a
 N 1 
N

1
E

1


 c c,u 
f c ,u

k2 
1
Ec
k3 
1
N

f c ,u  N  1 Ec c ,u
k4 
k1
f c ,a



Stress Strain Relation
•
According to Glos (1978)
   k1 N

      k2  k3  k4 N

Et 

k1 
Conditions:
f c , a  f c ,u  1
c 
f c ,u
N
 N  1 Ec
  0
  0
f c ,a
f c ,a
 N 1 
N

1
E

1


 c c,u 
f c ,u

k2 
1
Ec
k3 
1
N

f c ,u  N  1 Ec c ,u
k4 
k1
f c ,a



Stress Strain Relation
•
According to Glos (1978)
Ec
Ec
c
f c ,u
f c ,a
Conditions:
f c , a  f c ,u  1
c 
f c ,u
N
 N  1 Ec
-0.71
0.65
0.34
c
-0.71
-0.28
0
f c ,u
0.65
-0.28
0.65
f c ,a
0.34
0
0.65
Stress Strain Relation
•
According to Glos (1978)
Discussion:
MOE in tension = MOE compression ?
Quantification of asymptotic compression
strength and strain.
fc,a  fc,u 1
Modelling of N ?
Typical values:
f c, y / f c  0.8
 c  0.8  1.2%
 u  3 c
Stress Strain Relation
Actions:
• Quantify asymptotic stress
• Include into the Model Code
Coordination:
Jochen Köhler
Serviceability
• According to Torratti (1992):
(t, u) = e (t,u) + c (t)+ ms (t, u)+ u(u)
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
Serviceability
Relative deformation
3
2.5
2
1.5
Model
1
0.5
0
0
1000
2000
3000
4000
5000
Time [hours]
6000
7000
8000
9000
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):
g ult ,   ult  S (t )    (p, S (t ), f 0 , z)
 i 1   i   i
with
 i
t
Applied stress:
combined with
climate deviations
 i  SL 
d i  FL 


1
b

1
dt
8q 
2

 1
  i  SL 


S t 
SL  0
f
t  dt
2
2


S t  
SL     t  0  with   t   1
f 


DOL
Limit state function:
Model (Barrett):
g    1  X load (p, S (t ), f 0 , z)
 i 1   i   i
with
 i
t
Applied stress:
combined with
climate deviations
t  dt

SL 
B
d i 
 A  SL     C

dt

0
S t 
f0
g    1 X loadload X moisturemoisture


SL  
SL  
DOL
Gaps:
• DOL - Tension perpendicular to the grain
• DOL - Connections
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}
Property
Bending
Tension
f m,,mean = 9.3 + 1.15 f l,mean
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
parallel to grain
f c, 0,k = 8 f l,mean
perpendicular to grain
f c 0,g,k = 0.75 f l,mean
Shear
shear
MOE
mean
f v,k = 0.23 f l,mean 0,8
E mean = 1.05 E l,mean
Compression
Shear modulus
Standard deviations?
0,45
0,5
G mean = 0.065 E l,mean
GLULAM
Actions:
• Proposal of a simple model
• Test data acquisition
Coordination:
Hans-J. Larsen
Connections
Probabilistic Framework:
• Johansen equations
• “Splitting Mode parallel”
• “Splitting Mode perpendicular”
 F
 F0
  0: F0 
 F90
g1  nF  R
g 2  nef F0  R0
g 3  F90  R90
Connections
Probabilistic Framework:
• Johansen equations
 f h,1 t1 d

0,5 f h,2 t2 d



 f h,1 t1 d 
5

(2


)
M
y
F0  min 

 2  (1   ) 
2
f h,1d t1
 2   



1,15 kcal 2
2 M y f h,1 d

1 
(g)
(h)
(j)
(k)
Connections
Probabilistic Framework:
• Johansen equations
f h, 
f h,0 f h,90
f h,0 sin 2    f h,90 cos2  
M y  0.3 fu d 2,6
Connections
Probabilistic Framework:
• “Splitting Mode parallel”
F0  t
Gc
Gc E0 d  2h  d 
h
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
E0
modulus of elasticity parallel to the grain  MPa 
h
member width mm
t
member thickness mm
Connections
Mixed Mode Fracture Energy
2 
4
1
Gc  1 
1 1 1

1  21 
2

 

1 
2 
1  3
GIIc
3
GIc
2
GIc  162  1.07 
GIIc  3.5GIc
 f t ,90 


f
 v 
3 
2
 f t ,90 
E90



f
E0
 v 
 Nm 
m 2 

 Nm 

m 2 
ft ,90
is the tension strength perpendicular to the grain
GIc
is the fracture energy required for opening mode I
fv
is the shear strength
GIIc
is the fracture energy required for opening mode II
E90
is the MOE perpendicular to the grain

is the timber density  kg m3 
E0
is the MOE parallel to the grain
Connections
Probabilistic Framework:
• “Splitting Mode perpendicular”
F90  kcb
heGGc
h
0.6(1  e )
h
where,
b
width of the component
he
maximum distance between the stressed edge and a fastener
h
height of the component
G
shear modulus
Gc
the fracture energy for mixed mode according to Peterson [1995] loading
parallel to the grain [Nmm/mm2]
kc
factor depending on the failure mode of the fastener
Connections
Probabilistic Framework:
• Effective number of fasteners
C
n
 a1   t 
nef  An n    
 d  d 
Dn
Bn
A, B, C , D
regression coefficients as random variables
a1
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
mean
c.o.v.
A
B
C
D
0.42
0.91
0.28
0.19
Connections
Actions:
• Acquire test data
• Case study – reliability analysis
Coordination:
André Jorissen
Quantification of Model Parameters
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
Tension and compression tests
Glos,
Gehri
Long term test - deflection
Toratti
DOL
Quantify model parameters,
proposal for perpendicular to the
grain
Quantify model parameters
Specify moisture load model
Quantify model parameters
Duration of load test data
Glulam
Propose a simple model
Lamella properties, finger joint properties,
properties of glulam components
Connections
Quantify model parameters
Bending
strength model
(Isaksson)
Quantify model parameters for
different species
Definition of weak section
Material
properties,
properties
of
conections
Longithudinal distribution of weak
sections
Strength of weak section
Foschi,
Rosowsky,
Hoffmeyer
Gehri,
Jorissen,
Solli,
‘Austrians’
Rouger,
Jorissen
Isaksson
Serviceability
Quantification of Model Parameters
Actions:
• Collecting Data for a Data Base
Coordination:
Summary
Topic:
Coordination:
Stress Strain Relation, Basic Material Properties Jochen Köhler
- Tension Perpendicular
- Grading
??
??
Serviceability
Tomi Toratti
GLULAM
Hans-J. Larsen
DOL
John Sorensen
- Connections
??
Connections
André Jorissen
Data Base
??
Moisture
??