Timber Design according to EC5

Timber Design according to EC5EN 1995-1-1:2004

Summary of the AxisVM implementation

• sturctural timber materials, partial factors

• load duration classes, service classes

• material properties for global analysis

• cross-sections, design elements

• design strength of timber materials (modification factors)

• checks of timber elements

• design in seismic enviroment

Timber Design according to EC5

Sturctural timber materials EN 338, EN 1194

• Solid timber /softwood(C), hardwood(D)/

• Glued-laminated timber (Glulam)

• Laminated veneer lumber (LVL)

Characteristic strength Notation

Bending strength fm,k

Tensile strength parallel to grain ft,0,k

Tensile strength perpendicular to grain ft,90,k

Compression strength parallel to grain fc,0,k

Compression strength perependicular to grain

fc,90,k

Shear strength perpendicular to the grain in y direction

fv,k,y

Shear strength perpendicular to the grain in z direction

fv,k,z

Modulus of elasticity Notation

Mean value parallel to grain E0,mean

Mean value perpendicular to grain E90,mean

5% value of modulus parallel to grain

E0,05

Mean value of shear modulus Gmean

Density Notation

Characteristic value of density ρk

Mean value of density ρmean

Timber Design according to EC5

Partial factor (γM )

Timber type Fundamental combination

Accidental combination

Solid timber 1,30 1,0

Glued laminated timber (Glulam) 1,25 1,0

Laminated veneer lumber (LVL) 1,20 1,0

Timber Design according to EC5

Load duration classes and service classes

Load duration class Order of accumulated duration of characteristic

load

Examples of loading

Permanent more than 10 years self-weight

Long-term 6 months – 10 years storage

Medium-term 1 week – 6 months imposed floor load, snow

Short-term less than one week snow, wind

Instantaneous wind, accidental load

Service class Environmental condition

1 the relative humidity in the surrounding air only exceeding 65% for a few weeks per year*

2 the relative humidity in the surrounding air only exceeding 85% for a few weeks per year*

3 The climatic condition leading to higher moisture contents than Service Class 2

(*) the moisture content in the materials corresponding to a temperature of 20 Co

Timber Design according to EC5

Material properties for global analysis

Analysis type ModulusSLS

ModulusULS

First-order linear elastic analysis(*)

(*)

Second-order linear elastic analysis

Vibration analysis

M

meand

EEγ

=

)1( 2,

def

meanfinmean k

EE⋅+

=ψ

)1( 2,

def

meanfinmean k

GG⋅+

=ψ

)1(,def

meanfinmean k

EE+

=

)1(,def

meanfinmean k

GG+

=

M

meand

GGγ

=

M

meand

EEγ

=

M

meand

GGγ

=

meanE meanG meanE meanG

(*) conservative way ψ2 = 1,0 is used

Material type kdef

Service class 1 Service class 2 Service class 3

Solid timber 0,60 0,80 2,0

Glued laminated timber (Glulam) 0,60 0,80 2,0

Laminated veneer lumber (LVL) 0,60 0,80 2,0

Timber Design according to EC5

Cross-sections, design elements

Design assumptions:

• the grain parallel with the member x axis

• there is no hole or other weaking in the members

• the dominant bending plane is the x-z plane of the member (moment about y axis)

• Iy >= Iz

• in case of Glued-laminated timber (Glulam) the laminates are parallel with the y axis

• in case of Laminated veneer lumber (LVL) the laminates are parallel with the z axis

x

y

z

y

Timber Design according to EC5

Cross-sections, design elements

Solid timber (softwood, hardwood)

Glued-laminated timber (Glulam)

Laminated veneer lumber (LVL)

Timber Design according to EC5

Design strength of timber materials

Strength modification factors

• kmod factor depending on the duration of load and the moisture content

• kh factor depending on the cross-section size and the reference depth size

• kl factor depending on the member length and the reference length

• kvol factor depending on the apex zone volume and the reference volume

Timber Design according to EC5

Design strength of timber materials

• kmod modification factor

Material type Service class

kmod

Permanent Longterm

Mediumterm

Shortterm

Instant.

Solid timber 123

0,600,600,50

0,700,700,55

0,800,800,65

0,900,900,70

1,101,100,90

Glued laminated timber (Glulam)

123

0,600,600,50

0,700,700,55

0,800,800,65

0,900,900,70

1,101,100,90

Laminated veneer lumber (LVL)

123

0,600,600,50

0,700,700,55

0,800,800,65

0,900,900,70

1,101,100,90

Timber Design according to EC5

Design strength of timber materials

• kh modification factor

Material type kh

Solid timber(if h < 150 mm)

Glued laminated timber (Glulam)(if h < 600 mm)

Laminated veneer lumber (LVL)

⎪⎩

⎪⎨⎧

⎟⎠⎞

⎜⎝⎛= 3,1 150min

2,0

orh

kh

⎪⎩

⎪⎨⎧

⎟⎠⎞

⎜⎝⎛= 1,1 600min

1,0

orh

kh

⎪⎩

⎪⎨⎧

⎟⎠⎞

⎜⎝⎛= 2,1 300min or

hk

S

h

Timber Design according to EC5

Design strength of timber materials

• kl modification factor

Material type kl

Laminated veneer lumber (LVL) ⎪⎩

⎪⎨⎧

⎟⎠⎞

⎜⎝⎛= 1,1 3000min

2/

orl

kS

l

Timber Design according to EC5

Design strength of timber materials

• kvol modification factor

Material type kvol

Solid timber 1,0

Glued laminated timber (Glulam)

Laminated veneer lumber (LVL)

2,00 ⎟⎠⎞

⎜⎝⎛=

VVkvol

where,

V0 is the reference volume (0,01 m3)

V is the stressed volume of the apex zone, and V < 0,67Vb (total volume of the beam)

Timber Design according to EC5

Design strength of timber materials

• Design strength calculation

Material type fm,k ft,0,k ft,90,k , fc,0,k

fc,90,k , fv,k

Solid timber

Glued laminated timber (Glulam)

Laminated veneer lumber (LVL)

M

kd

fkfγ⋅

= mod

M

kmhdm

fkkf

γ,mod

,

⋅⋅=

M

kthdt

fkkf

γ,0,mod

,0,

⋅⋅=

M

ktldt

fkkf

γ,0,mod

,0,

⋅⋅=

Timber Design according to EC5

Checks of timber elements (interaction formulas for different design situation)

• Normal force, Moments (stress check parallel to the grain)

• Compression force, Moments (in plane buckling check)

• Moment (y), Normal force (lateral torsional buckling check)

• Shear (y), Torsion (shear check)

• Shear (z), Torsion (shear check)

• Moment (y), (tension stress perpendicular to the grain check)

Timber Design according to EC5

Checks of timber elements (interaction formulas for different design situation)

Normal force, Moments (stress check)

Tension and moment Compression and moment

1,,

,,

,,

,,

,0,

,0, ≤++dzm

dzmm

dym

dym

dt

dt

fk

ffσσσ

1,,

,,

,,

,,

,0,

,0, ≤++dzm

dzm

dym

dymm

dt

dt

ffk

fσσσ

1,,

,,

,,

,,

2

,0,

,0, ≤++⎟⎟⎠

⎞⎜⎜⎝

⎛

dzm

dzmm

dym

dym

dc

dc

fk

ffσσσ

1,,

,,

,,

,,

2

,0,

,0, ≤++⎟⎟⎠

⎞⎜⎜⎝

⎛

dzm

dzm

dym

dymm

dc

dc

ffk

fσσσ

where, km = 0,7 for rectangular sectionskm = 1,0 for other cross-sections

Timber Design according to EC5

Checks of timber elements (interaction formulas for different design situation)

Compression force, Moments (in plane buckling check)

Compression and moment

where, km = 0,7 for rectangular sectionskm = 1,0 for other cross-sectionskc,y = buckling reduction factor kc,z = buckling reduction factor

1,,

,,

,,

,,

,0,,

,0, ≤++⋅ dzm

dzmm

dym

dym

dcyc

dc

fk

ffkσσσ

1,,

,,

,,

,,

,0,,

,0, ≤++⋅ dzm

dzm

dym

dymm

dczc

dc

ffk

fkσσσ

Timber Design according to EC5

Checks of timber elements (interaction formulas for different design situation)

Moment (y), Normal force (lateral torsional buckling check)

Moment and compression Moment and small tension

where, kc,z is the buckling reduction factorkcrit is the lateral torsional buckling reduction factor:

where,

1,0,,

,

2

,

, ≤⋅

+⎟⎟⎠

⎞⎜⎜⎝

⎛

⋅ dczc

dc

dmcrit

dm

fkfkσσ

1,

, ≤⋅ dmcrit

dmc

fkσ

0, <+=AN

WM d

y

ddmcσ

λrel,m

≤

0,75 kcrit

= 1,0

0,75 < λrel,m

≤

1,4 kcrit

= 1,56-0,75

λrel,mλrel,m

≤

0,75 kcrit = 1/ l2rel,m

Timber Design according to EC5

Checks of timber elements (interaction formulas for different design situation)

Shear (y), Torsion (shear check) SIA 265:2003

Shear(y) and Torsion

where,

kshape is the cross-section shape factor:

kshape = 1,2 for circular cross-section

for rectangular cross-sections

12

,

,,

,

, ≤⎟⎟⎠

⎞⎜⎜⎝

⎛+

⋅ dv

dyv

dvshape

dtor

ffkττ

{ }0,2; /15,01min bhkshape +=

Timber Design according to EC5

Checks of timber elements (interaction formulas for different design situation)

Shear (z), Torsion (shear check) SIA 265:2003

Shear(y) and Torsion

where,

kshape is the cross-section shape factor:

kshape = 1,2 for circular cross-section

for rectangular cross-sections

12

,

,,

,

, ≤⎟⎟⎠

⎞⎜⎜⎝

⎛+

⋅ dv

dzv

dvshape

dtor

ffkττ

{ }0,2; /15,01min bhkshape +=

Timber Design according to EC5

Checks of timber elements (interaction formulas for different design situation)

Moment (y), (tension stress perpendicular to the grain check)

Moment(y)

where,

kdis is the stress distribution factor in apex zone factor (kdis =1,4)

kvol is the volume modifiction factor in the apex zone

1,90,

,90, ≤⋅⋅ dtvoldis

dt

fkkσ

Timber Design according to EC5

Timber structure design in seismic enviroment

(Response-spectrum analysis)

Ductility class Criteria γM

Low (DCL) q =< 1,5Solid timber: γM = 1,30

Glulam: γM = 1,25

LVL: γM = 1,20

Medium (DCM) 1,5 < q =< 2,5 γM = 1,0

High (DCH) 2,5 < q γM = 1,0

- The dissapitive zones have to be concentrated into the joints- The timber elements works in elastic assuption