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