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

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}

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

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”

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

Quantification of Model Parameters

Actions:

• Collecting Data for a Data Base

Coordination:

Summary

Topic: Coordination:

Stress Strain Relation, Basic Material Properties- Tension Perpendicular

- Grading

Jochen Köhler??

??

Serviceability Tomi Toratti

GLULAM Hans-J. Larsen

DOL- Connections

John Sorensen??

Connections André Jorissen

Data Base ??

Moisture ??