Timber Design Using Eurocode
Short Description
Timber Design...
Description
Seminar on Sustainable Future through Timber Design UITM, Dec. 16.12.2014
Design Timber Structures using Eurocode 5
Simon Aicher Page 1 of 119
Contents of lecture Basics 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) Aicher
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Aicher
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100 years old glulam beams, train repair hall, Bellinzona, Italy
Olympic Ice rink Hammar, Norway, 1994 glulam truss beams, span:97m
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Manufacture of timber parasols for Expo 2000, Hannover
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HESS – Limitless –Verbindung (22)
Aicher
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HESS – Limitless –Verbindung (23)
Aicher
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7-storey timber Page 10 of 119
building, Berlin, 2011
10-storey timber building, Melbourne, Page 11 of 119
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 Page 12 of 119
Permissible stress concept σact = σ95
acting loads, hence resulting section forces E and stresses σ represent in general 95% quantiles of the distributions
Design verification σact ≤ σpermissible where in case of structural timber (roughly)
σpermissible = f50 /3 f50 Aicher
mean value of strength
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Semiprobabilistic design concept with partial factors
σact = σ95
as in permissible stress concept the loads / section forces/ stress distributions represent 95% quantiles of the distributions
Design verification σd design stress
σd ≤ fd
fd design strength
σd = σact · γL γL partial factor for load (1,5 for live load; 1,35 for perm. load) f d = fk · kmod / γM fk
characteristic strength property (5% quantile)
kmod modification factor (time, climate) γM partial factor for strength (material dependant; 1,1 to 1,3) Aicher
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Semiprobabilistic vs. permissible stress design concept f05 = f50 (1 - 1,64 · COV) assuming COV = 0,12 f05 = f50 (1 – 0,2) = f50 / 1,25 f05 · kmod γM
=
γL = 1,5 partial factor for load
f50 · kmod 1,25 γM
with γM = 1,3 and kmod = 0,8 f05 · kmod γM
=
f50 · 0,8 1,25 · 1,3
≈
f50 2
f05 · kmod f50 = σd = σact · γL = σact · 1,5 ≤ fd = γM 2 f50 σact ≤ f50 2 · 1,5 = 3 = σpermissible Aicher
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Graphical illustration of semiprobabilistic design concept Probability density
ms fs
β · σz = mz = kmod · mR - ms fz
ms 95 pf = 10 -6 Aicher
ms 95· γs
kmod · mR 05
=
kmod · mR fR
R, s
kmod · mR 05 / γR
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Eurocode 5: Design of Timber Structures – Part 1-1
Aicher
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Structural Eurocode Program comprises
Aicher
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Scope of EN 1995
Aicher
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Structure of Eurocode 5 ( = EN 1995)
Aicher
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Subjects / Topics of EN 1995-1-1
Aicher
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Normative References
Aicher
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Normative References (continued)
Aicher
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Normative References (continued)
Aicher
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Aicher
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Section 2 of EC 5: Basis of design
Aicher
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Section 2.2 of EC 5: Principles of limit state design
Aicher
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2.2.2 Ultimate limit states
Aicher
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2.2.3 Serviceability limit states
Aicher
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2.2.3 Serviceability limit states
Aicher
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2.3 Basic variables
Aicher
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2.3.1.2 Load-duration classes
Aicher
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2.3.1.2 Load-duration classes
Aicher
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2.3.1.3 Service classes
Aicher
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2.3.2 Materials and product properties
Aicher
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2.3.2 Materials and product properties
Aicher
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2.4 Verification by the partial factor method
5%- quantile value (lognormal dist.)
Aicher
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Recommended partial factors γM for material properties EC 5 – Table 2.3
Aicher
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2.4.2 Design values of geometrical data
Aicher
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2.4.2 Design value of a resistance
Example: Rk = Xk · relevant cross-sectional quantity
Aicher
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EC 5 –Section 3 – Materials properties
Aicher
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3.1.3/4 Strength and deformation modification factors
Aicher
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EC 5 – Table 3.1 Strength modification values kmod
Aicher
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EC 5 – Table 3.1 Strength modification values kmod (continued)
Aicher
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Strength modification values kmod = f( time; moisture) short 1 min
Strength modification factor
1.2 kmod
10Jahre years50 Jahre 10 1 1 week Woche 66months Monate 10 years
Madison-Kurve
Service class 11/2 and2 Nutzungsklasse
1
0.8
Service class 3
Nutzungsklasse 3
0.6
0.4
very short
short kurz
sehr kurz
medium mittel
permanent ständig
long lang
0.2
0
0 0 .0
1
1 0 . 0
0 .1
1
10
10
0
0 10
0 1
0 00
0 10
0 00
Accumulated duration of load [hours] Aicher
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0 10
0
0 00
0
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EC 5 – Table 3.2 Deformation modification values kdef
Aicher
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EC 5 – Table 3.2 Deformation modification values kdef (continued)
Aicher
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EC 5 – 3.2: Solid timber
EN 15497 Aicher
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EC 5 – 3.3: Glued laminated timber
Aicher
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EC 5 – 3.3: Glued laminated timber
Now large finger joints are directly regulated in the harmonized product standard for glulam,
Aicher
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EN 14080
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Example of large finger joint (single joint line)
Aicher
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Example of large finger joint (two joint lines)
Aicher
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Example of large finger joint (two joint lines)
Aicher
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EC 5 – 3.3: Glued laminated timber
Aicher
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EC 5 – 3.4: Laminated veneer lumber (LVL)
Aicher
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EC 5 – 3.4: Laminated veneer lumber (LVL)
Aicher
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EC 5 – 3.5: Wood-based panels
Aicher
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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
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EC 5 – 3.7: Metal fasteners
Aicher
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EC 5 – Section 4: Durability
Aicher
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EC 5 – Section 4: Durability
Aicher
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EC 5 – Section 4: Durability
Aicher
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EC 5 – Table 4.1 Corrosion protection of fasteners
Aicher
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EC 5 - Section 5: Basis of structural analysis
Aicher
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5.2 Members
Aicher
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5.4 Assemblies
Aicher
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5.4 Assemblies
Aicher
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5.4.2 Frame structures
Aicher
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5.4.4 Plane frames and arches
Aicher
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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
Aicher
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EC 5 - Section 6: Ultimate limit states
Aicher
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Tension 6.1.2 Tension parallel to the grain
6.1.2 Tension perpendicular to the grain
Aicher
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Compression 6.1.4 Compression parallel to the grain
Aicher
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Compression
6.1.4 Compression perpendicular to the grain
where
σc,90,d
is the design compressive stress in the effective contact area perpendicular to the grain;
Fc,90,d
is the design compressive load perpendicular to the grain;
Aef
is the effective contact area in compression perpendicular to the grain;
Fc,90,d
is the design compressive strength perpendicular to the grain;
kc,90
is a factor taking into account the load configuration, the possibility of splitting and the degree of compressive deformation.
Aicher
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Compression
6.1.4 Compression perpendicular to the grain
The effective contact area perpendicular to the grain, Aef, 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 ℓ1/2, see Figure 6.2. 2. The value of kc,90 should be taken as 1,0 unless the conditions in the following paragraphs apply. In these cases the higher value of kc,90 specified may be taken, with a limiting value of kc,90 = 1,75. 3. For members on continuous supports, provided that ℓ1 ≥ 2h, see Figure 6.2a, the value of kc,90 should be taken as: – kc,90 = 1,25 for solid softwood timber – kc,90 = 1,5 for glued laminated softwood timber where h is the depth of the member and ℓ is the contact length.
Aicher
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Compression
6.1.4 Compression perpendicular to the grain
4. For members on discrete supports, provided that ℓ1 ≥ 2h, see Figure 6.2b, the value of kc,90 should be taken as: – kc,90 = 1,5 for solid softwood timber – kc,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.
Aicher
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6.1.6 Bending
Aicher
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6.1.6 Bending
Aicher
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6.1.7 Shear
Aicher
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6.1.7 Shear (crack factor issue) 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: bef = kcr b where b is the width of the relevant section of the member. NOTE: The recommended value for kcr is given as kcr = 0,67
for solid timber
kcr = 0,67
for glued laminated timber
kcr = 1,0
for other wood-based products in accordance with EN 13986 and EN 14374.
Aicher
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6.1.7 Shear
Aicher
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6.1.8 Torsion
Aicher
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6.2.2 Compression stresses at an angle to grain
Aicher
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6.2.3 Combined bending and axial tension
Aicher
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6.2.3 Combined bending and axial compression
Aicher
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6.4 Members with varying cross-section or curved shape
Aicher
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6.4 Members with varying cross-section or curved shape
Figure 6.8 Single tapered beam
Aicher
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6.4 Members with varying cross-section or curved shape
Aicher
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6.4 Members with varying cross-section or curved shape
Aicher
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6.4 Members with varying cross-section or curved shape
Aicher
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6.4 Members with varying cross-section or curved shape
(a)
Note: In curved beams the apex zone extends over the curved parts of the beam
Figure 6.9 – Double tapered (a) and curved (b) beams with the fibre direction parallel to the lower edge of the beam Aicher
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6.4 Members with varying cross-section or curved shape Note: In pitched cambered beams the apex zone extends over the curved parts of the beam
Figure 6.9 – Pitched cambered beam (c) beam with the fibre direction parallel to the lower edge of the beam Aicher
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6.4 Members with varying cross-section or curved shape
Aicher
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6.4 Members with varying cross-section or curved shape
Aicher
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6.4 Members with varying cross-section or curved shape
Aicher
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6.4 Members with varying cross-section or curved shape
Aicher
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6.4 Members with varying cross-section or curved shape
or Aicher
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6.4 Members with varying cross-section or curved shape
Aicher
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Design examples
Design of straight glulam member - comparison of Eurocode 5 vs. DIN 1052
Aicher
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Straight beam design comparison – EC 5 vs. perm. stress concept
16x80 cm
q = 9 kN/m, g = 6 kN/m
GL 24 / BS 11 10 m
Geometry: l = 10 m b = 160 mm h = 800 mm S = b h²/6 = 17 ⋅ 10-6 mm³ I = b h³/12 = 6.8 ⋅ 10-9 mm4
Aicher
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Design comparison – EC 5 vs. perm. stress concept Property
permissible concept
semi-probabilistic concept
Bending strength
σm,perm = 11 N/mm²
fm,k = 24 N/mm²
Shear strength
τv,perm = 1.2 N/mm²
fv,k = 3.5 N/mm²
MOE
Em = 11000 N/mm²
Em,mean = 11000 N/mm²
crack factor
-
kcr = 0.67
modification factor for duration of load and moisture content
kmod = 0.6 (Service Class I/II, medium-term)
Partial factor for material properties
γM = 1.25
(glulam, EC 5)
Deformation factor
kdef = 0.8 (Service Class I)
Partial factor for permanent actions
γG = 1.35
Partial factor for variable actions
γG = 1.5
Factor for quasi-permanent value of a variable action
ψ2,1 = 0.3
Aicher
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Design comparison – EC 5 vs. perm. stress concept
Result
permissible concept
semi-probabilistic concept
distributed load
F = g + q = 15 kN/m
Fd = γG g + γQ q = 21.6 kN/m
bending moment M
M = F l² / 8 = 188 kNm
Md = Fd ⋅ l² / 8 = 270 kNm
bending stress
σm = M/S = 11 N/mm²
σm = Md/S = 15.8 N/mm²
utilization (bending)
11 / 11 = 1.00
fm,d = fm,k ⋅kmod /γM = 15.4 N/mm² 15.8 / fm,d = 1.03
shear force V
V = F l/2 = 75 kN
Vd = Fd l/2 = 108 kN
shear stress τv
1.5 V / (b h) = 0.88 N/mm²
1.5 Vd / (b h) = 1.89 N/mm²
1.2 / 0.88 = 0.73
fv,d = fv,k ⋅kmod /γM = 2.24 N/mm² 1.89 / fv,d = 0.84
utilization (shear)
Aicher
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Design comparison – EC 5 vs. perm. stress concept
deflection
utilitization (deflection)
Aicher
5 𝐹 𝑙4 𝑢= = 26𝑚𝑚 384𝐸𝐸
𝑢 = 0.78 𝑙/300
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𝑢𝑖𝑖𝑖𝑖 = 𝑢𝑖𝑖𝑖𝑖,𝑔 + 𝑢𝑖𝑖𝑖𝑖,𝑞= 5𝑔𝑙 4 5𝑞𝑙 4 + = 10.4 + 15.6 384𝐸𝐸 384𝐸𝐸 = 26𝑚𝑚 𝑢𝑓𝑓𝑓 = 𝑢𝑖𝑖𝑖𝑖,𝑔 (1 + 𝑘𝑑𝑑𝑑 ) + 𝑢𝑖𝑖𝑖𝑖,𝑞 (1 +ψ2,1 𝑘𝑑𝑑𝑑 )= 16.7 + 18.4 = 35.1mm 𝑢𝑖𝑖𝑖𝑖 = 0.78 𝑙/300 𝑢𝑓𝑓𝑓 = 0.53 𝑙/150
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Design examples
Design of curved glulam beam - comparison of Eurocode 5 vs. DIN 1052
Aicher
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HESS – Limitless –Verbindung (7)
Aicher
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Stress distributions in curved beams with const. moment
H
R
H
R
R1 < R2
R1 < R2
H/R2 = 0,09
= 0,09 RH/R 2 / H2 = 11
+
RH/R =2,5 0,4 1 / H1 =
bending stresses parallel to grain
tension stresses perpendicular to grain
σ ⊥ ,max Aicher
H/R1 = 0,4
2 H H M σ II = 1+ 0,35 + 0,6 R R W
H M = 0,25 R W Page 107 of 119
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Stress σt,90 of curved and tapered beams with line loads
stress perp. to grain h
-
+
stress perp. to grain
h
Aicher
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+
108
Aicher
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Aicher
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Curved beam design comparison – EC 5 vs. perm. stress concept
DIN 1052 BS 14: σm,permissible = 14 N/mm2 EN 14080 GL 28: fm,k = 28 N/mm2 Geometry, dimensions and quality /strength class of example beam Aicher
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Curved beam design comparison – EC 5 vs. perm. stress concept
EC5
F = 23,31 kN
Design for bending:
rin/t = 200, kr = 0,96
hap / r = 0,118 k1 = 1; k2 = 0,35, k3 = 0,6 kl = 1,05 Aicher
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Curved beam design comparison – EC 5 vs. perm. stress concept
F = 23,31 kN
EC5
Design for bending:
GL28: fm,k = 28 N/mm2
load duration: „medium“, kmod = 0,8
fm,d = fm,k × kmod /γm
kr = 0,96
fm,d =
glulam: γm = 1,25
17,92 N/mm2
ratio = 0,38 kl = 1,05
Map,d = γf × Map
σm,d = 6,85 N/mm2
combined loading: γf = 1,4
Aicher
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curved beam design comparison – EC 5 vs. perm. stress concept
EC5
Design for tension perp.:
glulam: V0 = 0,01 m3 kdis = 1,4
V = 0,691 m3
kVol = (V0/V)0,2 = 0,43
hap / r = 0,118 k5 = 0; k6 = 0,25, k7 = 0 kp = 0,0294 Aicher
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Example: Curved Beam with pure moment loading F = 23,31 kN
EC5
Design for tension perp.:
glulam: ft,90,k = 0,5 N/mm2
kdis = 1,4 , kVol = 0,43,
load duration: „medium“, kmod = 0,8
ft,90,d = ft,90,k × kmod /γm
glulam: γm = 1,25
ft,90,d = 0,32 N/mm2
1,4 x 0,43 x 0,32 = 0,19 N/mm2 kp = 0,0294
Map,d = γf × Map
σt,90,d = 0,19 N/mm2
ratio = 1,0
combined loading: γf = 1,4
Aicher
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Curved beam design comparison – EC 5 vs. perm. stress concept
DIN 1052
F = 23,31 kN
Design for bending: σm ≤ σm,permissible
σm,permissible = 14 N/mm2
ratio = 0,33 σm = kl × 6 Map/b h2 hap / r = 0,118, kl = 1,05 Aicher
σm = 4,66 N/mm2
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curved beam design comparison – EC 5 vs. perm. stress concept
DIN 1052
F = 23,31 kN
Design für tension perp.: σt,90 ≤ σt,90,permissible
σt,90,permissible = 0,2 N/mm2
ratio = 0,69
σt,90 = kp× 6 Map/b h2 hap / r = 0,118, kp = 0,0294
Aicher
Page 117 of 119
Eurocode 5 Timber Structures
σt,90 = 0,14 N/mm2
UITM 2014, Malaysia
117
curved beam design comparison – EC 5 vs. perm. stress concept
F = 23,31 kN
bending
tension perp.
EC5
0,40
1,00
DIN 1052
0,33
0,69
no pre-stress effect Aicher
Page 118 of 119
Eurocode 5 Timber Structures
no size effect UITM 2014, Malaysia
118
Now ist time to finish!
Thank you very much for your patient listening!
Aicher
Page 119 of 119
Eurocode 5 Timber Structures
UITM 2014, Malaysia
119
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