design timber structures using eurocode 5
DESCRIPTION
Eurocode 5TRANSCRIPT
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
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)
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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
Manufacture of timber parasols for Expo 2000, Hannover
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HESS – Limitless –Verbindung (22)
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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
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 mean value of strength
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Semiprobabilistic design concept with partial factors
14
σact = σ95 as in permissible stress concept the loads / section forces/ stress distributions represent 95% quantiles of the distributions
Design verification σd ≤ fd
σd design stress 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)
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Semiprobabilistic vs. permissible stress design concept
15
σact ≤
σd = σact · γL = σact · 1,5 ≤ fd =
γL = 1,5 partial factor for load f05 = f50 (1 - 1,64 · COV) assuming COV = 0,12 f05 = f50 (1 – 0,2) = f50 / 1,25
f05 · kmod f50 · kmod
γM 1,25 γM
with γM = 1,3 and kmod = 0,8
f05 · kmod f50 · 0,8
γM 1,25 · 1,3
=
= ≈ f50
2 f05 · kmod f50
γM =
f50 2 · 1,5 = f50
3 = σpermissible
2
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Graphical illustration of semiprobabilistic design concept
Probability density
ms
fs
ms 95
ms 95· γs kmod · mR 05 / γR
kmod · mR 05
kmod · mR
fR
R, s
=
β · σz = mz = kmod · mR - ms
fz
pf = 10 -6
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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 γM for 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: Rk = Xk · 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
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EC 5 – Table 3.1 Strength modification values kmod
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EC 5 – Table 3.1 Strength modification values kmod
(continued)
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Accumulated duration of load [hours]
Stre
ngth
mod
ifica
tion
fact
or
kmod
0
0.2
0.4
0.6
0.8
1
1.2
0.0010.01 0.1 1 10 100
100010000
100000
1000000
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 kmod = 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
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EC 5 – Table 3.2 Deformation modification values kdef
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EC 5 – Table 3.2 Deformation modification values kdef
(continued)
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EC 5 – 3.2: Solid timber
EN 15497
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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.
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EC 5 – 3.7: Metal fasteners
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EC 5 – Section 4: Durability
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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
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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
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Compression 6.1.4 Compression perpendicular to the grain
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.
where
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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.
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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.
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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)
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.
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
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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
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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
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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
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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
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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
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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
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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
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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
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GL 24 / BS 11
q = 9 kN/m, g = 6 kN/m
10 m
16x8
0 cm
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
Straight beam design comparison – EC 5 vs. perm. stress concept
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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
Design comparison – EC 5 vs. perm. stress concept
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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
utilization (shear)
1.2 / 0.88 = 0.73
fv,d = fv,k ⋅kmod /γM = 2.24 N/mm² 1.89 / fv,d = 0.84
Design comparison – EC 5 vs. perm. stress concept
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deflection 𝑢 =
5 𝐹 𝑙4
384𝐸𝐸 = 26𝑚𝑚 𝑢𝑖𝑖𝑖𝑖 = 𝑢𝑖𝑖𝑖𝑖,𝑔 + 𝑢𝑖𝑖𝑖𝑖,𝑞=
5𝑔𝑙4
384𝐸𝐸 +5𝑞𝑙4
384𝐸𝐸 = 10.4 + 15.6= 26𝑚𝑚
𝑢𝑓𝑖𝑖 = 𝑢𝑖𝑖𝑖𝑖,𝑔(1 + 𝑘𝑑𝑑𝑓) +𝑢𝑖𝑖𝑖𝑖,𝑞(1 +ψ2,1 𝑘𝑑𝑑𝑓)= 16.7 + 18.4 = 35.1mm
utilitization (deflection) 𝑢𝑙/300 = 0.78
𝑢𝑖𝑖𝑖𝑖𝑙/300 = 0.78 𝑢𝑓𝑖𝑖𝑙/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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WM
RH,max, 250=σ⊥
R H
R2 / H = 11
R1 / H = 2,5
R H
H/R2 = 0,09
H/R1 = 0,4
WM
RH,
RH,II
++=σ
2
603501
+
-
H/R2 = 0,09
H/R1 = 0,4
tension stresses perpendicular to grain
Stress distributions in curved beams with const. moment
bending stresses parallel to grain
R1 < R2
R1 < R2
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h
stress perp. to grain
- +
h
- +
Stress σt,90 of 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: fm,k = 28 N/mm2
DIN 1052 BS 14: σm,permissible = 14 N/mm2
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Design for bending:
kr = 0,96
hap / r = 0,118
EC5 F = 23,31 kN
Curved beam design comparison – EC 5 vs. perm. stress concept
rin/t = 200,
kl = 1,05
k1 = 1; k2 = 0,35, k3 = 0,6
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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 kN
Curved 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
k5 = 0; k6 = 0,25, k7 = 0
hap / r = 0,118
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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/mm2
Design for tension perp.:
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Design for bending:
hap / r = 0,118, kl = 1,05
DIN 1052
F = 23,31 kN
σm ≤ σm,permissible
σm = kl × 6 Map/b h2
σm,permissible = 14 N/mm2
σm = 4,66 N/mm2
ratio = 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 kN
σt,90 ≤ σt,90,permissible
σt,90 = kp× 6 Map/b h2
σt,90,permissible = 0,2 N/mm2
σt,90 = 0,14 N/mm2
ratio = 0,69
hap / r = 0,118, kp = 0,0294
curved beam design comparison – EC 5 vs. perm. stress concept
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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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Now ist time to finish!
Thank you very much for your patient listening!