T3. DESIGN OF TIMBER BEAM

Timber framed structure

T3. Design of timber beam

page 1.

Beam: linear member subjected to bending and shear (N=0).

Example: Check of beam G1, design secondary girder spacing.

Floor plan

I. Design of beam G1

I.1. Geometry, model, loads

I.1.1. Model, Geometry:

leff =

I.1.2. Loads: floor

Dead load: self-weight

Floor layers:

2 cm glued ceramic

6 cm reinforced concrete subbase

1 layer PE foil

2 cm TDP sound insulating layer

2.2 cm OSB deck

50 150 secondary girder (spacing: 0.8m)

5 cm floating layer

1.9 cm boarding

1 layer plasterboard

Σ

2m

kNKg 35.1sup, g

födKg

page 2.

Cross-sectional Data:

h

b

T3. Design of timber beam

- Live load (variable load): 2m

kNfloor

Kq 5.1q (balcony: 2m

kNbalc

Kq )

- Load of partition walls (see T1 practical):

floorKqKg

floorEd qgp

Load on the beam G1:

8

2effEd

Ed

lpM

8

5 effEdEd

lpV

page 3.

I. 3. Ultimate limit state: Strength analysis:

I.3.0. Material properties

Timber: homogenous, anizotropic,

linear-elastic material model

Idealized - diagram

T3. Design of timber beam

Self-weight and floor load (approximately): Self-weigth of the beam: beam

Edg

beam

Edfloor

EdbeamEd gpp

2

8.4

2

1

I. 2. Calculation of internal forces

page 4.

Study Aid for Timber Structures (ST)

T3. Design of timber beam

M

kd

fkf

mod

M

kmdm

fkf

,

mod,

M

kvdv

fkf

,

mod,

(ST)

For all strength values:

Here:

Grade of material: GL28h (ST)

medium term load, service class 1. kmod=

glued laminated timber M=

Design value of bending strength:

Design value of shear strength:

factorsafety

valueticcaracterisfactor on modificatiuedesign val

Force equilibrium : 0N

Moment equilibrium: at limit state RdMM

dmyelRd fWM ,,

elastic section modulus :

62

122

3

max,

bhh

bh

y

IW y

yel

EdRd

Rd

MM

M

T3. gyakorlat: Fa gerenda méretezése

page 5.

I.3.2. Shear

8

5.1

12

8 2

3

2

bhSbh

V

bbh

bhV

bI

VSy

y

y

5.1

bhfV vdRd

EdRdc VV ,

I.3.1. Bending

Always elastic!

I.4. Buckling analysis:

- Lateral-torsional buckling

page 6.

22,,

,,

)1(

)1(def

defqinstqfin

defginstgfin k

kww

kww

ymean ISTE )(.0

ymean

finfin IE

lpw

,0

4

384

5

defkdefkfin kqkgp 211

pfinqfingfinfin wwww ,,,

allowed deflection:

I.5. Serviceability limit state: Deflection

Creep has to be taken into account!

(ST)

T3. Design of timber beam

II.1 Loads, Geometry, model Model: simple supported beam

leff = Floor load transferred to the secondary girder:

floorEdp

II.2. Internal forces

T3. Design of timber beam

2

m1 effEd lpV

Ed

8

2m1 effEd lp

MEd

Cross-sectional data: board

h

b

II. Design of secondary girder F1

Design spacing of secondary girders considering the size of OSB-board! t=?

Possible spacing:

page 7.

page 8.

T3. Design of timber beam

max

,,

t

MM

fWM

EdRd

dmyelRd

max

, 5.1

t

VV

bhfV

EdRd

dvRd

II.3.2. Shear

alkt

II.4. Stability analysis

-lateral-torsional buckling:

II.5. Serviceability limit state: Deformation analysis

II.3. Ultimate limit state: Strength analysis

II.3.0. Material properties

Grade of material: C24 )(ST 3.1M 8.0mod k

kmdm ff ,, 3.1

8.0 kvdv ff ,, 3.1

8.0

II.3.1. Bending design: (elastic analysis)