Seminar on
Sustainable Future through
Timber Design
UITM, Dec. 16.12.2014
Simon Aicher
Design Timber Structures
using
Eurocode 5
Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia
Contents of lecture
2
B
asics of permissible stress and
semi-probabilistic partial factor concept
Interrelationship of
- Eurocodes,
- harmonized (timber) product standards,
- classification standards, calculation standards and
- test test standards
Basics of Eurocode 5 structure and contents
Design example: straight glulam beam (EC 5 vs. permissible concept)
Design example: curved glulam beam (EC 5 vs. permissible concept)
100 years old
glulam beams,
train repair hall,
Bellinzona, Italy
Olympic Ice rink
Hammar, Norway,
1994
glulam truss beams,
span:97m
Manufacture of timber parasols for Expo 2000, Hannover
Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 8
HESS – Limitless –Verbindung (22)
Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 9
HESS – Limitless –Verbindung (23)
7-storey timber
building, Berlin, 2011
10-storey timber
building, Melbourne,
Australia 2013
Eurocodes and supporting product and test standards
Eurocodes regulate design of timber, steel, concrete structures
in conjunction with national application documents but give
no provisions on material properties
Harmonized product standards regulate material properties of
harmonized building products (e.g. not adhesives) such as
EN 14080 glulam
EN 14081-1 solid timber in conjunction with national grading rules
and classification standard EN 1912 and strength class standard
EN 338
EN 15497 finger jointed lumber
EN 16351 cross laminated timber
EN 14374 LVL
EN 13986 panel products in conjunction with product / production standards, e.g.
EN 300 for OSB
Test standards, e.g. EN 408, EN 789,…..
Calculation standards, e.g. EN 14358 on characteristic values
Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia
Permissible stress concept
13
σ
act
= σ
95
acting loads, hence resulting section forces E and stresses σ
represent in general 95% quantiles of the distributions
Design verification
σ
act
≤ σ
permissible
where in case of structural timber (roughly)
σ
permissible
= f
50
/3
f
50
mean value of strength
Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia
Semiprobabilistic design concept with partial factors
14
σ
act
= σ
95
as in permissible stress concept the loads / section forces/ stress
distributions represent 95% quantiles of the distributions
Design verification
σ
d
≤ f
d
σ
ddesign stress
f
ddesign strength
σ
d= σ
act· γ
Lγ
Lpartial factor for load (1,5 for live load; 1,35 for perm. load)
f
d= f
k· k
mod/ γ
Mf
kcharacteristic strength property (5% quantile)
k
modmodification factor (time, climate)
γ
Mpartial factor for strength (material dependant; 1,1 to 1,3)
Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia
Semiprobabilistic vs. permissible stress design concept
15
σ
act
≤
σ
d= σ
act· γ
L= σ
act· 1,5 ≤ f
d=
γ
L= 1,5 partial factor for load
f
05= f
50(1 - 1,64 · COV)
assuming COV = 0,12
f
05= f
50(1 – 0,2) = f
50/ 1,25
f
05· k
modf
50· k
modγ
M1,25 γ
Mwith γ
M= 1,3 and k
mod= 0,8
f
05· k
modf
50· 0,8
γ
M1,25 · 1,3
=
=
≈ f
502
f
05· k
modf
50γ
M=
f
502 · 1,5 =
3 =
f
50σ
permissible
2
Page 15 of 119Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 16
Graphical illustration of semiprobabilistic design concept
Probability
density
m
sf
sm
s 95m
s 95· γ
sk
mod· m
R 05/ γ
Rk
mod· m
R 05k
mod· m
Rf
RR, s
=
β · σ
z= m
z= k
mod· m
R- m
sf
zp
f= 10
-6 Page 16 of 119Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 17
Eurocode 5: Design of Timber Structures – Part 1-1
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Structural Eurocode Program comprises
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Scope of EN 1995
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Structure of Eurocode 5 ( = EN 1995)
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Subjects / Topics of EN 1995-1-1
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Normative References
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Normative References (continued)
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Normative References (continued)
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Section 2 of EC 5: Basis of design
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Section 2.2 of EC 5: Principles of limit state design
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2.2.2 Ultimate limit states
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2.2.3 Serviceability limit states
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2.2.3 Serviceability limit states
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2.3 Basic variables
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2.3.1.2 Load-duration classes
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2.3.1.2 Load-duration classes
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2.3.1.3 Service classes
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2.3.2 Materials and product properties
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2.3.2 Materials and product properties
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2.4 Verification by the partial factor method
5%- quantile value (lognormal dist.)
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Recommended partial factors
γ
Mfor material properties
EC 5 – Table 2.3
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2.4.2 Design values of geometrical data
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2.4.2 Design value of a resistance
Example: R
k= X
k· relevant cross-sectional quantity
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EC 5 –Section 3 – Materials properties
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3.1.3/4 Strength and deformation modification factors
Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 43
EC 5 – Table 3.1 Strength modification values k
modAicher Eurocode 5 Timber Structures UITM 2014, Malaysia 44
EC 5 – Table 3.1 Strength modification values k
mod(continued)
Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 45
Accumulated duration of load [hours]
Str
eng
th
mo
dif
ica
tio
n
fa
ct
or
k
mod 0 0.2 0.4 0.6 0.8 1 1.20.
001
0.
01
0.
1
1
10
100
10
00
10
000
10
0000
10
0000
0
1 min 1 Woche 6 Monate 10 Jahre 50 Jahre
sehr kurz kurz mittel lang ständig
Nutzungsklasse 1/2
Nutzungsklasse 3
Madison-Kurve
Strength modification values k
mod= f( time; moisture)
Service class 1 and2
Service class 3
short
very
short
medium
long
permanent
short
1 week
6 months
10 years
10
years
Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 46
EC 5 – Table 3.2 Deformation modification values k
defAicher Eurocode 5 Timber Structures UITM 2014, Malaysia 47
EC 5 – Table 3.2 Deformation modification values k
def(continued)
Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 48
EC 5 – 3.2: Solid timber
EN 15497
Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 49
EC 5 – 3.3: Glued laminated timber
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EC 5 – 3.3: Glued laminated timber
EN 14080
Now large finger joints are directly regulated in the
harmonized product standard for glulam,
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Example of large finger joint (single joint line)
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Example of large finger joint (two joint lines)
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Example of large finger joint (two joint lines)
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EC 5 – 3.3: Glued laminated timber
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EC 5 – 3.4: Laminated veneer lumber (LVL)
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EC 5 – 3.4: Laminated veneer lumber (LVL)
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EC 5 – 3.5: Wood-based panels
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EC 5 – 3.6: Adhesives
Note: As permissible structural adhesive families and respective classifications have
been profoundly changed in conjunction with introduction of one-component
Polyurethane (1K-PU) and polymer isocyanate (EPI) adhesives according to EN 15425
and EN 16351 principle P (2) is no more throughout valid because of EPI definitions.
Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 59
EC 5 – 3.7: Metal fasteners
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EC 5 – Section 4: Durability
Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 61
EC 5 – Section 4: Durability
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EC 5 – Section 4: Durability
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EC 5 – Table 4.1 Corrosion protection of fasteners
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EC 5 - Section 5: Basis of structural analysis
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5.2 Members
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5.4 Assemblies
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5.4 Assemblies
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5.4.2 Frame structures
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5.4.4 Plane frames and arches
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Examples of assumed initial geometry deviations
geometry of
frames
initial geometry
deviation corresponding
to symmetrical load
initial geometry
deviation corresponding
to non-symmetrical load
Page 70 of 119Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 71
EC 5 - Section 6: Ultimate limit states
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Tension
6.1.2 Tension parallel to the grain
6.1.2 Tension perpendicular to the grain
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Compression
6.1.4 Compression parallel to the grain
Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 74
Compression
6.1.4 Compression perpendicular to the grain
σ
c,90,dis the design compressive stress in the effective contact area
perpendicular to the grain;
F
c,90,dis the design compressive load perpendicular to the grain;
A
efis the effective contact area in compression perpendicular to
the grain;
F
c,90,dis the design compressive strength perpendicular to the
grain;
k
c,90is a factor taking into account the load configuration, the
possibility of splitting and the degree of compressive
deformation.
where
Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 75
Compression
6.1.4 Compression perpendicular to the grain
The effective contact area perpendicular to the grain, A
ef, should be determined taking into
account an effective contact length parallel to the grain, where the actual contact length, ℓ, at
each side is increased by 30 mm, but not more than a, ℓ or ℓ
1/2, see Figure 6.2.
2. The value of k
c,90should be taken as 1,0 unless the conditions in the following paragraphs
apply. In these cases the higher value of k
c,90specified may be taken, with a limiting value
of k
c,90= 1,75.
3. For members on continuous supports, provided that ℓ
1≥ 2h, see Figure 6.2a, the value
of k
c,90should be taken as:
– k
c,90= 1,25 for solid softwood timber
– k
c,90= 1,5 for glued laminated softwood timber
where h is the depth of the member and ℓ is the contact length.
Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 76
Compression
6.1.4 Compression perpendicular to the grain
4. For members on discrete supports, provided that ℓ
1≥ 2h, see Figure 6.2b, the value of k
c,90should be taken as:
– k
c,90= 1,5 for solid softwood timber
– k
c,90= 1,75 for glued laminated softwood timber provided that I ℓ ≤ 400 mm
where h is the depth of the member and ℓ is the contact length.
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6.1.6 Bending
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6.1.6 Bending
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6.1.7 Shear
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6.1.7 Shear (crack factor issue)
k
cr= 0,67
for solid timber
k
cr= 0,67
for glued laminated timber
k
cr= 1,0
for other wood-based products in
accordance with EN 13986 and EN
14374.
2. For the verification of shear resistance of members in bending, the influence
of cracks should be taken into account using an effective width of the member
given as:
b
ef= k
crb
where b is the width of the relevant section of the member.
NOTE: The recommended value for k
cris given as
Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 81
6.1.7 Shear
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6.1.8 Torsion
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6.2.2 Compression stresses at an angle to grain
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6.2.3 Combined bending and axial tension
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6.2.3 Combined bending and axial compression
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6.4 Members with varying cross-section or curved shape
Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 87
6.4 Members with varying cross-section or curved shape
Figure 6.8 Single tapered beam
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6.4 Members with varying cross-section or curved shape
Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 89
6.4 Members with varying cross-section or curved shape
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6.4 Members with varying cross-section or curved shape
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6.4 Members with varying cross-section or curved shape
(a)
Figure 6.9 – Double tapered (a) and curved (b) beams with the fibre direction parallel
to the lower edge of the beam
Note: In curved beams
the apex zone extends
over the curved parts
of the beam
Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 92
Figure 6.9 – Pitched cambered beam (c) beam with the fibre direction parallel
to the lower edge of the beam
Note: In pitched cambered
beams the apex zone
extends over the curved
parts of the beam
6.4 Members with varying cross-section or curved shape
Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 93
6.4 Members with varying cross-section or curved shape
Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 94
6.4 Members with varying cross-section or curved shape
Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 95
6.4 Members with varying cross-section or curved shape
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6.4 Members with varying cross-section or curved shape
Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 97
6.4 Members with varying cross-section or curved shape
or
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6.4 Members with varying cross-section or curved shape
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Design of straight glulam member
- comparison of
Eurocode 5 vs. DIN 1052
Design examples
Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 100
GL 24 / BS 11
q = 9 kN/m, g = 6 kN/m
10 m
16x80 c
m
Geometry:
l = 10 m
b = 160 mm
h = 800 mm
S = b h²/6 = 17 ⋅ 10
-6mm³
I = b h³/12 = 6.8 ⋅ 10
-9mm
4Straight beam design comparison – EC 5 vs. perm. stress concept
Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 101
Property
permissible concept
semi-probabilistic concept
Bending strength
σ
m,perm= 11 N/mm²
f
m,k= 24 N/mm²
Shear strength
τ
v,perm= 1.2 N/mm²
f
v,k= 3.5 N/mm²
MOE
E
m= 11000 N/mm²
E
m,mean= 11000 N/mm²
crack factor
-
k
cr= 0.67
modification factor for duration
of load and moisture content
k
medium-term)
mod= 0.6 (Service Class I/II,
Partial factor for material
properties
γ
(glulam, EC 5)
M= 1.25
Deformation factor
k
def= 0.8 (Service Class I)
Partial factor for permanent
actions
γ
G= 1.35
Partial factor for variable
actions
γ
G= 1.5
Factor for quasi-permanent
value of a variable action
ψ
2,1= 0.3
Design comparison – EC 5 vs. perm. stress concept
Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 102
Result
permissible concept
semi-probabilistic concept
distributed load
F = g + q = 15 kN/m
F
d=
γ
Gg +
γ
Qq = 21.6 kN/m
bending moment M
M = F l² / 8 = 188 kNm
M
d= F
d⋅ l² / 8 = 270 kNm
bending stress
σ
m= M/S = 11 N/mm²
σ
m= M
d/S = 15.8 N/mm²
utilization (bending)
11 / 11 = 1.00
f
15.8 / f
m,d= f
m,k m,d⋅
= 1.03
k
mod/
γ
M= 15.4 N/mm²
shear force V
V = F l/2 = 75 kN
V
d= F
dl/2 = 108 kN
shear stress
τ
v1.5 V / (b h) = 0.88 N/mm²
1.5 V
d/ (b h) = 1.89 N/mm²
utilization (shear)
1.2 / 0.88 = 0.73
f
1.89 / f
v,d= f
v,k v,d⋅
k
= 0.84
mod/
γ
M= 2.24 N/mm²
Design comparison – EC 5 vs. perm. stress concept
Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 103
deflection
𝑢 =
384𝐸𝐸 = 26𝑚𝑚
5 𝐹 𝑙
45𝑔𝑙
𝑢
𝑖𝑖𝑖𝑖4= 𝑢
𝑖𝑖𝑖𝑖,𝑔+ 𝑢
𝑖𝑖𝑖𝑖,𝑞=384𝐸𝐸 +
5𝑞𝑙
4384𝐸𝐸 = 10.4 + 15.6
= 26𝑚𝑚
𝑢
𝑓𝑖𝑖= 𝑢
𝑖𝑖𝑖𝑖,𝑔(1 + 𝑘
𝑑𝑑𝑓) +
𝑢
𝑖𝑖𝑖𝑖,𝑞(1 +
ψ
2,1𝑘
𝑑𝑑𝑓)=
16.7 + 18.4 = 35.1mm
utilitization (deflection)
𝑢
𝑙/300 = 0.78
𝑢
𝑖𝑖𝑖𝑖𝑙/300 = 0.78
𝑢
𝑓𝑖𝑖𝑙/150 = 0.53
Design comparison – EC 5 vs. perm. stress concept
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Design of curved glulam beam
- comparison of
Eurocode 5 vs. DIN 1052
Design examples
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HESS – Limitless –Verbindung (7)
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W
M
R
H
,
max ,=
0
25
σ
⊥ R H R2 / H = 11 R1 / H = 2,5 R H H/R2 = 0,09 H/R1 = 0,4W
M
R
H
,
R
H
,
II
+
+
=
σ
26
0
35
0
1
+ - H/R2 = 0,09 H/R1 = 0,4tension stresses
perpendicular to grain
Stress distributions in curved beams with const. moment
bending stresses
parallel to grain
R
1< R
2R
1< R
2Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 108 h stress perp. to grain
-
+ h-
+Stress
σ
t,90of curved and tapered beams with line loads
stress perp. to grain
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Curved beam design comparison – EC 5 vs. perm. stress concept
Geometry, dimensions and quality /strength class
of example beam
EN 14080 GL 28: f
m,k= 28 N/mm
2DIN 1052 BS 14: σ
m,permissible= 14 N/mm
2Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 112
Design for bending:
kr = 0,96
h
ap/ r = 0,118
EC5
F = 23,31 kNCurved beam design comparison – EC 5 vs. perm. stress concept
r
in/t = 200,
k
l= 1,05
k
1= 1; k
2= 0,35, k
3= 0,6
Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 113
Design for bending:
kr = 0,96 kl = 1,05
EC5
fm,d = fm,k × kmod /γm GL28: fm,k = 28 N/mm2 load duration:„medium“, kmod = 0,8 glulam: γm = 1,25
σm,d = 6,85 N/mm2 Map,d = γf × Map combined loading: γf = 1,4 fm,d = 17,92 N/mm2
ratio = 0,38
F = 23,31 kNCurved beam design comparison – EC 5 vs. perm. stress concept
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Design for tension perp.:
kdis = 1,4 kVol = (V0/V)0,2 = 0,43
EC5
glulam: V0 = 0,01 m3 V = 0,691 m3
curved beam design comparison – EC 5 vs. perm. stress concept
kp = 0,0294
k
5= 0; k
6= 0,25, k
7= 0
h
ap/ r = 0,118
Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 115
Example: Curved Beam with pure moment loading
kp = 0,0294
EC5
ft,90,d = ft,90,k × kmod /γm glulam: ft,90,k = 0,5 N/mm2 load duration:„medium“, kmod = 0,8 glulam: γm = 1,25
σt,90,d = 0,19 N/mm2 Map,d = γf × Map combined loading: γf = 1,4 ft,90,d = 0,32 N/mm2
ratio
= 1,0
F = 23,31 kN kdis = 1,4 , kVol = 0,43, 1,4 x 0,43 x 0,32 = 0,19 N/mm2Design for tension perp.:
Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 116
Design for bending:
hap / r = 0,118, kl = 1,05
DIN
1052
F = 23,31 kNσ
m≤ σ
m,permissibleσ
m= k
l× 6 M
ap/b h
2 σm,permissible = 14 N/mm2 σm = 4,66 N/mm2ratio = 0,33
Curved beam design comparison – EC 5 vs. perm. stress concept
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Design für tension perp.:
DIN
1052
F = 23,31 kNσ
t,90≤ σ
t,90,permissibleσ
t,90= k
p× 6 M
ap/b h
2 σt,90,permissible = 0,2 N/mm2 σt,90 = 0,14 N/mm2ratio = 0,69
hap / r = 0,118, kp = 0,0294curved beam design comparison – EC 5 vs. perm. stress concept
Aicher Eurocode 5 Timber Structures UITM 2014, Malaysia 118
DIN 1052
F = 23,31 kN
EC5
bending
tension perp.
1,00
0,69
0,40
0,33
no pre-stress effect
no size effect
curved beam design comparison – EC 5 vs. perm. stress concept
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