Transcript Slide 1
T3. DESIGN OF TIMBER BEAM
Floor plan
Timber framed structure
Beam: linear member subjected to bending and shear (N=0).
Example: Check of beam G1, design secondary girder spacing.
page 1.
T3. Design of timber beam
I. Design of beam G1
I.1. Geometry, model, loads
I.1.1. Model, Geometry:
Cross-sectional Data:
b
h
leff =
I.1.2. Loads: floor
Dead load: self-weight
kN
gK 2
m
g ,sup 1.35
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
g Kföd
Σ
page 2.
T3. Design of timber beam
kN
m2
- Load of partition walls (see T1 practical):
q 1.5
- Live load (variable load): q Kfloor
(balcony: qKbalc
floor
pEd
g gK q qKfloor
Load on the beam G1:
Self-weight and floor load (approximately):
beam
Self-weigth of the beam: g Ed
1 floor 4.8
beam
beam
pEd
pEd
g Ed
2
2
I. 2. Calculation of internal forces
VEd
5 pEd leff
8
M Ed
p Ed l eff2
8
I. 3. Ultimate limit state: Strength analysis:
I.3.0. Material properties
Timber: homogenous, anizotropic,
linear-elastic material model
Idealized - diagram
page 3.
T3. Design of timber beam
kN
)
m2
Study Aid for Timber Structures (ST)
For all strength values:
f
f d kmod k
design value modification factor
M
caracteristic value
safetyfactor
Here:
Grade of material: GL28h
(ST)
medium term load, service class 1. kmod=
(ST)
glued laminated timber M=
Design value of bending strength:
f m,d kmod
f m, k
M
Design value of shear strength:
f v,d kmod
f v ,k
M
page 4.
T3. Design of timber beam
I.3.1. Bending
Always elastic!
Force equilibrium :
N 0
Moment equilibrium: at limit state
M M Rd
M Rd Wel , y f m,d
elastic section modulus :
bh3
Iy
bh2
Wel , y
12
h
ymax
6
2
M Rd
M Rd
M Ed
I.3.2. Shear
bh2
VS y
8 1.5V
I b V 3
bh
bh b
y
12
VRd f vd
Vc,Rd
2
bh
Sy
8
bh
1.5
VEd
page 5.
T3. gyakorlat: Fa gerenda méretezése
I.4. Buckling analysis:
- Lateral-torsional buckling
I.5. Serviceability limit state: Deflection
Creep has to be taken into account!
(ST)
w fin, g winst , g (1 k def )
w fin,q
k def
winst ,q (1 2 k def )
2
wfin wfin, g wfin,q wfin, p
p fin gk 1 kdef qk 1 2kdef
E0.mean
(ST) I y
4
5 p fin l
w fin
384 E0,mean I y
allowed deflection:
page 6.
T3. Design of timber beam
II. Design of secondary girder F1
Design spacing of secondary girders considering the size of OSB-board! t=?
Possible spacing:
II.1 Loads, Geometry, model
Cross-sectional data: board
Model: simple supported beam
b
leff =
h
Floor load transferred to the secondary girder:
floor
pEd
II.2. Internal forces
V Ed
1m
pEd leff
2
M Ed
1m
2
pEd leff
8
page 7.
T3. Design of timber beam
II.3. Ultimate limit state: Strength analysis
II.3.0. Material properties
Grade of material:
f m,d
C24
(ST)
0.8
f m,k
1.3
M 1.3
f v ,d
kmod 0.8
0 .8
f v ,k
1 .3
II.3.1. Bending design: (elastic analysis)
M Rd Wel , y f m,d
M Rd M Ed
t max
II.3.2. Shear
bh
1 .5
VRd VEd
VRd f v ,d
t
max
talk
II.4. Stability analysis
-lateral-torsional buckling:
II.5. Serviceability limit state: Deformation analysis
page 8.
T3. Design of timber beam