EN 1995-1-1
Transcript of EN 1995-1-1
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EN 1995-1-1Design of timber structures
EN 1995-1-1 Design of Timber Structures
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Design of Timber StructuresEN 1995-1-1
Storage building in Japan 4 Jh. v. Ch.
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Design of Timber StructuresEN 1995-1-1
Stave church in Norway 13th century
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Design of Timber StructuresEN 1995-1-1
Bridge across river Sinne (Switzerland)
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Design of Timber StructuresEN 1995-1-1
Faculty of architecture (Lyon)
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EN 1995-1-1 Design of Timber Structures
EN1995-1-1 Scope and structure
• Section 1: General definitions, terminology• Section 2: Basis of design: Timber specific supplement to EN1990• Section 3: Material properties to be used for design• Section 4: Durability concept• Section 5: Basis of structural analysis• Section 6: Ultimate limit state design principles• Section 7: Serviceability limit states• Section 8: Fasteners• Section 9: Design of components and assemblies• Section 10: Workmanship, structural detailing and control
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EN 1995-1-1 Design of Timber Structures
EN1995-1-1 - Definition of axes
EN1995
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EN 1995-1-1 Design of Timber Structures
Link of EN 1995-1-1 to EN1990 and EN1991
EN 1990EN 1990
EN 1991EN 1991
EN 1992EN 1992 EN 1993EN 1993 EN 1994EN 1994
EN 1995EN 1995 EN 1996EN 1996 EN 1999EN 1999
Structural Structural safetysafety,,serviceability serviceability andanddurabilitydurability
Actions onActions onstructuresstructures
Design andDesign anddetailingdetailing
EN 1997EN 1997 EN 1998EN 1998 GeotechnicalGeotechnicaland and seismicseismicdesigndesign
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EN 1995-1-1 Design of Timber Structures
National Annex• Contains nationally determined
parameters• These override EN1995-1-1 values• Take account of national conditions,
such as geographical or workmanship differences
• Are yet not published in all countries
How to spot NDPs!
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EN 1995-1-1 Design of Timber Structures
National choices overview
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EN 1995-1-1 Design of Timber Structures
General General conceptconcept
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12
Ed
Effect of Actions:Self-LoadWindSnowVariable loadsTemperatureFire....
Rd
Resistance:StructureStructural ElementsMaterials, E-Modulus etc.cross sections, Area, Moment of Inertia
Semi-probalistic safety concept
≤
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Safetyfre
quen
cyfre
quen
cy
EffectEffect of of actionaction LoadLoad carryingcarryingcapacitycapacity RR
95% 95% quantilequantile 5% 5% quantilequantile
EEkk RRkk
γγFF γγMMEEdd RRdd
SafetySafety
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EN 1995-1-1 Design of Timber Structures
Design Design situationssituations
•• Permanent Permanent situationsituation((afterafter erectionerection of of thethestructurestructure))
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EN 1995-1-1 Design of Timber Structures
•• temporarytemporary situationsituation((duringduring erectionerection))
Design Design situationssituations
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EN 1995-1-1 Design of Timber Structures
•• AccidentialAccidential situationsituation((impactimpact, , firefire))
Design Design situationssituations
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EN 1995-1-1 Design of Timber Structures
Limit Limit statesstates
•• UltimateUltimate limitlimit statesstates•• ServiceabilityServiceability limitlimit statesstates
For all For all designdesign situationssituations thethe limitlimit statesstates shallshallnotnot bebe exceededexceeded. .
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EN 1995-1-1 Design of Timber Structures
Limit state design
• Limit states are functional levels beyond which the structure no longer satisfies the performance criterias.
• Ultimate limit state:
– Safety level– Concerns safety of people– Integrity of structure
• Serviceability limit state
– Comfort of building user– No excessive deflection, vibration,
cracks– Negotiable from project to project
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EN 1995-1-1 Design of Timber Structures
•• CharacteristicCharacteristic ActionsActions accordingaccordingto EN 1991to EN 1991
GGkk e.ge.g. . selfself--weightweightQQkk e.ge.g. wind, . wind, snowsnow, , traffictrafficAAkk e.ge.g. . impactimpact
ActionsActions
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EN 1995-1-1 Design of Timber Structures
UltimateUltimate limitlimit statestate
Design Design valuesvalues of of actionsactionsBasic Basic combinationcombination::
ΣγΣγG,j G,j ⋅⋅ GGkk,j,j + + γγQ,1 Q,1 ⋅⋅ QQkk,1,1 + + ΣγΣγQ,i Q,i ⋅⋅ ψψ0,i 0,i ⋅⋅ QQkk,i,i
e.g. e.g. 1,351,35 ⋅⋅ GGkk + + 1,51,5 ⋅⋅ WWkk + + 1,51,5 ⋅⋅ 0,50,5 ⋅⋅ SSkk
simplified:simplified:Most Most unfavourableunfavourable variable variable actionaction: :
ΣγΣγG,j G,j ⋅⋅ GGk,jk,j + + γγQ1 Q1 ⋅⋅ QQk,1k,1 1,351,35 ⋅⋅ GGkk + + 1,51,5 ⋅⋅ WWkk
All All unfavourableunfavourable variable variable actionsactions::ΣγΣγG,j G,j ⋅⋅ GGk,jk,j + 1,35 + 1,35 ⋅⋅ ΣΣ QQk,ik,i 1,351,35 ⋅⋅ ((GGkk + + WWkk + + SSkk))
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EN 1995-1-1 Design of Timber Structures Design and calculation principles
From a statistic point of view it´s unlikely that all actions/loads act at the sametime with their fully values.
ψ0 combination coefficient (in fundamental design situations)ψ1 frequent coefficient (in accidential design situations and servicability
calculations)ψ2 quasi-permanent coefficient (in servicability calculations)
Principle rule:
G K Q,1 K ,1 0,i Q,i K ,ii 2
G Q Qγ γ ψ γ≥∑⋅ + ⋅ + ⋅ ⋅
⇒ Coefficient for represantative values of actions ψ(for exact national data see: National Annexes)
Use of ψ0 from the second variable action/load.
Design values of actions; coefficient for representativevalues of actions:
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EN 1995-1-1 Design of Timber Structures
CombinationCombination factorsfactors
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EN 1995-1-1 Design of Timber Structures
CombinationCombination factorsfactors
ActionAction ψψ00 ψψ11 ψψ22
DomesticDomestic residentialresidential areasareas 0,70,7 0,50,5 0,30,3CongregationCongregation areasareas 0,70,7 0,70,7 0,60,6StorageStorage areasareas 1,01,0 0,90,9 0,80,8WindWind 0,60,6 0,50,5 0,00,0SnowSnow ((≤≤ 1000 m)1000 m) 0,50,5 0,20,2 0,00,0
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EN 1995-1-1 Design of Timber Structures
Partial Partial safetysafety factorsfactors forfor actionsactions(EN 1990)(EN 1990)
ActionAction permanentpermanent variablevariable
favourablefavourable γγGG = 1,0= 1,0 γγQQ = 0= 0unfavourableunfavourable γγGG = 1,35= 1,35 γγQQ = 1,5= 1,5
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25
Partial Safety Factors γ F (γ G ,γQ ) , γ M
Gk × γ G + Qk × γQ ≤ kmod × Rk / γ M (timber: γ M = 1,3)
Safety factors in case of fire or other accidentialsituations: γ = 1,0
Safety Concept - simplified
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EN 1995-1-1 Design of Timber Structures
ServiceabilityServiceability limitlimit statesstates
CalculationCalculation of of •• deformationsdeformations•• vibrationsvibrations
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EN 1995-1-1 Design of Timber Structures Design and calculation principles
III.1 Eurocode 5 in basic; loads/actions on structures
. the combination of actionsunder consideration
d Q kQ Qγ= ⋅
d G kG Gγ= ⋅
Increase the actions/load by partial safety factors γ (gamma factors)
less safety risks
Design situation γG γQ
Structural design calculation
favourable effect 1,0 -unfavourable effect 1,35 1,5
Check at servicabilitylimit state 1,0 1,0
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EN 1995-1-1 Design of Timber Structures
Design Design valuesvalues of of actionsactionscharacteristiccharacteristic (rare) (rare) combinationcombination: : ΣΣGGkk,j,j + + QQkk,1,1 + + ΣψΣψ0,i 0,i ⋅⋅ QQkk,i,i
GGkk + + WWkk + + 0,50,5 ⋅⋅ SSkk
quasiquasi--permanent permanent combinationcombination::ΣΣGGkk,j,j + + ΣψΣψ2,i 2,i ⋅⋅ QQkk,i,i
GGkk + + 0,00,0 ⋅⋅ WWkk + + 0,00,0 ⋅⋅ SSkk
ServiceabilityServiceability limitlimit statesstates
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EN 1995-1-1 Design of Timber Structures
ComparisonComparison of of safetysafety conceptsconcepts
TakingTaking intointo accountaccount SemiSemi--probalisticprobalisticmethodmethod
ConceptConcept of of permissiblepermissible
stressesstresses
combinationscombinations CombinationCombination factorfactorψψ
SafetySafety factorfactor
LoadLoad durationduration -- and and serviceservice--classclass
SafetySafety factorfactor
timbertimber
ActionAction
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EN 1995-1-1 Design of Timber Structures
ComparisonComparison of of safetysafety conceptsconcepts
TakingTaking intointo accountaccount SemiSemi--probalisticprobalisticmethodmethod
ConceptConcept of of permissiblepermissible
stressesstresses
combinationscombinations CombinationCombination factorfactorψψ
w+s/2 w+s/2 oror s+w/2s+w/2
SafetySafety factorfactor
LoadLoad durationduration -- and and serviceservice--classclass
SafetySafety factorfactor
timbertimber
ActionAction
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EN 1995-1-1 Design of Timber Structures
ComparisonComparison of of safetysafety conceptsconcepts
TakingTaking intointo accountaccount SemiSemi--probalisticprobalisticmethodmethod
ConceptConcept of of permissiblepermissible
stressesstresses
combinationscombinations CombinationCombination factorfactorψψ
w+s/2 w+s/2 oror s+w/2s+w/2
SafetySafety factorfactor γγ = 1,35 (G)= 1,35 (G)γγ = 1,50 (Q)= 1,50 (Q)
LoadLoad durationduration -- and and serviceservice--classclass
SafetySafety factorfactor
timbertimber
ActionAction
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EN 1995-1-1 Design of Timber Structures
ComparisonComparison of of safetysafety conceptsconcepts
TakingTaking intointo accountaccount SemiSemi--probalisticprobalisticmethodmethod
ConceptConcept of of permissiblepermissible
stressesstresses
combinationscombinations CombinationCombination factorfactorψψ
w+s/2 w+s/2 oror s+w/2s+w/2
SafetySafety factorfactor γγ = 1,35 (G)= 1,35 (G)γγ = 1,50 (Q)= 1,50 (Q)
γγ = ?= ?((permissiblepermissible stress)stress)
LoadLoad durationduration -- and and serviceservice--classclass
SafetySafety factorfactor
timbertimber
ActionAction
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EN 1995-1-1 Design of Timber Structures
ComparisonComparison of of safetysafety conceptsconceptsTakingTaking intointo accountaccount SemiSemi--probalisticprobalistic
methodmethod
ConceptConcept of of permissiblepermissible
stressesstresses
combinationscombinations CombinationCombination factorfactorψψ
w+s/2 w+s/2 oror s+w/2s+w/2
SafetySafety factorfactor γγ = 1,35 (G)= 1,35 (G)γγ = 1,50 (Q)= 1,50 (Q)
γγ = ?= ?((permissiblepermissible stress)stress)
LoadLoad durationduration -- and and serviceservice--classclass
kkmodmod
0,6 0,6 permanent,SCpermanent,SC 110,9 0,9 shortshort, SC 1, SC 10,5 0,5 permanent, SC 3permanent, SC 30,7 0,7 shortshort, SC 3, SC 3
SafetySafety factorfactor
timbertimber
ActionAction
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ComparisonComparison of of safetysafety conceptsconcepts
TakingTaking intointo accountaccount SemiSemi--probalisticprobalisticmethodmethod
ConceptConcept of of permissiblepermissible
stressesstresses
combinationscombinations CombinationCombination factorfactorψψ
w+s/2 w+s/2 oror s+w/2s+w/2
SafetySafety factorfactor γγ = 1,35 (G)= 1,35 (G)γγ = 1,50 (Q)= 1,50 (Q)
γγ = ?= ?((permissiblepermissible stress)stress)
LoadLoad durationduration -- and and serviceservice--classclass
kkmodmod
0,6 0,6 permanent,SCpermanent,SC 110,9 0,9 shortshort, SC 1, SC 10,5 0,5 permanent, SC 30,7 0,7 shortshort, SC 3, SC 3
??((permissiblepermissible stress) stress)
ReductionReduction of 1/6 of 1/6 (SC 3)(SC 3)
SafetySafety factorfactor
timbertimber
ActionAction
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ComparisonComparison of of safetysafety conceptsconcepts
TakingTaking intointo accountaccount SemiSemi--probalisticprobalisticmethodmethod
ConceptConcept of of permissiblepermissible
stressesstresses
combinationscombinations CombinationCombination factorfactorψψ
w+s/2 w+s/2 oror s+w/2s+w/2
SafetySafety factorfactor γγ = 1,35 (G)= 1,35 (G)γγ = 1,50 (Q)= 1,50 (Q)
γγ = ?= ?((permissiblepermissible stress)stress)
LoadLoad durationduration -- and and serviceservice--classclass
kkmodmod
0,6 0,6 permanent,SCpermanent,SC 110,9 0,9 shortshort, SC 1, SC 10,5 0,5 permanent, SC 30,7 0,7 shortshort, SC 3, SC 3
??((permissiblepermissible stress) stress)
ReductionReduction of 1/6 of 1/6 (SC 3)(SC 3)
SafetySafety factorfactor γγ = 1,3 (5%= 1,3 (5%--Quantil)Quantil)
timbertimber
ActionAction
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ComparisonComparison of of safetysafety conceptsconcepts
TakingTaking intointo accountaccount SemiSemi--probalisticprobalisticmethodmethod
ConceptConcept of of permissiblepermissible
stressesstresses
combinationscombinations CombinationCombination factorfactorψψ
w+s/2 w+s/2 oror s+w/2s+w/2
SafetySafety factorfactor γγ = 1,35 (G)= 1,35 (G)γγ = 1,50 (Q)= 1,50 (Q)
γγ = ?= ?((permissiblepermissible stress)stress)
LoadLoad durationduration -- and and serviceservice--classclass
kkmodmod
0,6 0,6 permanent,SCpermanent,SC 110,9 0,9 shortshort, SC 1, SC 10,5 0,5 permanent, SC 30,7 0,7 shortshort, SC 3, SC 3
??((permissiblepermissible stress) stress)
ReductionReduction of 1/6 of 1/6 (SC 3)(SC 3)
SafetySafety factorfactor γγ = 1,3 (5%= 1,3 (5%--Quantil)Quantil)
γγ = ?= ?((permissiblepermissible stress)stress)
timbertimber
ActionAction
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Design of Timber StructuresEN 1995-1-1
Materials and service classes
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EN 1995-1-1 Design of Timber Structures
Steps for the designer
• Identify material strength and stiffness properties in supporting standard
• Establish modification factors– Material– Load– Service class
• Determine material resistance for calculation
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Design of Timber StructuresEN 1995-1-1
Design value of material propertiesXd
Xk - characteristic value of a strength propertyγM – partial factor for a material propertykmod – modification factor, taking into account duration of load and moisture content
Xd =kmod • Xk
γM
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EN 1995-1-1 Design of Timber Structures Design and calculation principles
σd fd≤
loading resistance
freq
uenc
y
÷ γMEk
design values
5%-quantiles
fkx γGγQ
Edx kmod
Structural design calculation
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EC 5-1-1 Design of Timber Structures
CharacteristicCharacteristic valuesvalues of material of material propertiesproperties
•• 5%5%--Quantil of Quantil of strengthstrength propertiesproperties, , e.ge.g. . Bending Bending strengthstrengthTension Tension strengthstrengthCapacityCapacity of a of a connectionconnection
•• MeanMean valuevalue of of stiffnessstiffness propertiesproperties, , e.ge.g..ModulusModulus of of ElasticityElasticity((exceptionsexceptions: : TheoryTheory of second order, of second order, bucklingbuckling))
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Design of Timber StructuresEN 1995-1-1
Partial safety factor γM
Recommended material safety factor γM = 1,3
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EN 1995-1-1 Design of Timber Structures Timber Structures
Mechanical properties in general• Different in growth directions
• Modulus of elasticity
• Mechanical properties are related to the density
0100020003000400050006000700080009000
1000011000
0 10 20 30 40 50 60 70 80 90
α in [°]
Eα in
[N/m
m²]
3
110011000
sin370
Eαα
=
⋅ 3 3
11000 37011000 sin s370
Eco
α
α α
⋅=
⋅ +
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EN 1995-1-1 Design of Timber Structures Timber Structures
Hygroscopisc isotherms for fir timber by W.K. Loughborough, R. Keylwerth
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Design of Timber StructuresEN 1995-1-1
Effect of moisture content
The mechanical properties of timber aremoisture dependend!
- ExampleChange of moisture content from12% to 20%leads to a significant reduction
68 N/mm²
92 N/mm²= 0,7391
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Design of Timber StructuresEN 1995-1-1
Moisture dependend strength properties are leading to
Service Classes
Service Class Average moisturecontent um
Environmental conditions
1 u ≤ 12% 20°C und 65% rel. humidity2 u ≤ 20% 20°C und 85% rel. humidity3 u > 20% Higher humidity compared to SC 2
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EC 5-1-1 Design of Timber Structures
ActionsActions on a on a floorfloor
00 1010 2020 3030 4040 50500,00,0
1,01,0
2,02,0
00 1010 2020 3030 4040 50500,00,0
1,01,0
2,02,0
pp[[ kk
NN //mm
]]22
LoadLoad durationduration[a][a]
QQGG
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EC 5-1-1 Design of Timber Structures
LoadLoad durationduration classesclasses
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EN 1995-1-1 Design of Timber Structures Design and calculation principles
kmod · fk kmod for the action/load with shortest design situation
Ultimate limit state:
Serviceability limit state:
separate for each action/load
wel · (1+ kdef)
def
E1 k+
Influence of service classes and duration of load
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EN 1995-1-1 Design of Timber Structures Design and calculation principles
Festigkeitsklasse (Sortierklasse nach DIN 4074-1)
C16 C24 C30 C35 C40
Festigkeitskennwerte in N/mm2
Biegung fm,k 2) 16 24 30 35 40
Zug parallel ft,0,k 2)
rechtwinklig ft,90,k
10 0,4
14 0,4
18 0,4
21 0,4
24 0,4
Druck parallel fc,0,k rechtwinklig fc,90,k
17 2,2
21 2,5
23 2,7
25 2,8
26 2,9
Schub und Torsion fv,k 3) 6) 2,7 2,7 2,7 2,7 2,7
Steifigkeitskennwerte in N/mm2
Elastizitätsmodul parallel E0,mean 4)
rechtwinklig E90,mean 4) 8000 270
11000 370
12000 400
13000 430
14000 470
Schubmodul Gmean 4) 5) 500 690 750 810 880
Rohdichtekennwerte in kg/m3
Rohdichte ρk 310 350 380 400 420 1) Nur maschinen sortiert 2) Nadelrundholz geschält ohne angeschnittene Faser: +20% 3) Beim Nachweis von Querschnitten die mindestens 1,50 m vom Hirnholz entfernt liegen, darf fv,k um 30 %
erhöht werden. 4) Für die charakteristischen Steifigkeitskennwerte E0,05, E90,05 und G05 gelten die Rechenwerte:
E0,05 = 2/3·E0,mean E90,05 = 2/3·E90,mean G05 = 2/3·Gmean 5) Der zur Rollschubbeanspruchung gehörende Schubmodul darf mit GR,mean = 0,10·Gmean angenommen
werden. 6) Als Rechenwert für die charakteristische Rollschubfestigkeit des Holzes darf für alle Festigkeitsklassen mit
fR,k = 1,0 N/mm2 angenommen werden.
Strength properties for timber (Tab. F. 5 DIN 1052)(for exact national data see: National Annexes)
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EN 1995-1-1 Design of Timber Structures Design and calculation principles
Festigkeitsklasse des Brettschichtholzes GL 24 GL 28 GL 32 GL 36
h = homogen c = kombiniert h c h c h c h c
Festigkeitskennwerte in N/mm2
Biegung fm,y,k 1) 24 24 28 28 32 32 36 36
fm,z,k 2) 28,8 24 33,6 28 38,4 32 43,2 36
Zug parallel ft,0,k
rechtwinklig ft,90,k
16,5 0,5
14 0,5
19,5 0,5
16,5 0,5
22,5 0,5
19,5 0,5
26 0,5
22,5 0,5
Druck parallel fc,0,k rechtwinklig fc,90,k
24 2,7
21 2,4
26,5 3,0
24 2,7
29 3,3
26,5 3,0
31 3,6
29 3,3
Schub und Torsion fv,k 3) 3,5 3,5 3,5 3,5 3,5 3,5 3,5 3,5
Steifigkeitskennwerte in N/mm2
Elastizitätsmodul parallel E0,mean 4)
rechtwinklig E90,mean 4) 11600390
11600320
12600420
12600390
13700460
13700420
14700490
14700460
Schubmodul Gmean 4) 5) 720 590 780 720 850 780 910 850
Rohdichtekennwerte in kg/m3
Rohdichte ρk 380 350 410 380 430 410 450 430 1) Bei Brettschichtholz mit liegenden Lamellen und einer Querschnitthöhe H ≤ 600 mm darf fm,y,k mit folgendem Faktor
multipliziert werden: (600 / H)0,14 ≤ 1,1 2) Brettschichtholz mit mindestens 4 hochkant stehenden Lamellen 3) Als Rechenwert für die charakteristische Rollschubfestigkeit des Holzes darf für alle Festigkeitsklassen fR,k = 1,0
N/mm2 angenommen werden. 4) Für die charakteristischen Steifigkeitskennwerte E0,05, E90,05 und G05 gelten die Rechenwerte:
E0,05 = 5/6·E0,mean E90,05 = 5/6·E90,mean G05 = 5/6·Gmean 5) Der zur Rollschubbeanspruchung gehörende Schubmodul darf mit GR,mean = 0,10·Gmean angenommen werden.
Strength properties for glulam (Tab. F. 9 DIN 1052)(for exact national data see: National Annexes)
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Design of Timber StructuresEN 1995-1-1
kmod- und kdef-values
Modification value kmod und deformation value kdeftaking into account service class and load duration
kmod Modification value for ultimate limit state design
kdefDeformation value for serviceability limit state design
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Design of Timber StructuresEN 1995-1-1
kmod- values
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Design of Timber StructuresEN 1995-1-1
kdef-values
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Design of Timber StructuresEN 1995-1-1
Size factors
Size factors taking into account volume effects
kh is a variable factor in correlation with the referencedepth in bending
Solid timber Glulam LVL
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Design of Timber StructuresEN 1995-1-1
Strength Classes – solid timber
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Visual grading:
Criteria: Knots, cracks, discoloration, bark etc. Reliability ??
Mechanically grading:
Radiation:Empfänger Sender
Bending principe:
Laufrichtung F
w
EmpfängerMeasurement of naturalfrequency:
Strength Classes – solid timber
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Grading
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Design of Timber StructuresEN 1995-1-1
Strength Classes – solid timber (EN 338)
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Design of Timber StructuresEN 1995-1-1
Strength Classes – glulam (EN 1194)
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Design of Timber StructuresEN 1995-1-1
Strength Classes – glulam (EN 1194)
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Design of Timber StructuresEN 1995-1-1
Strength Classes – glulam (DIN 1052)
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Design of Timber StructuresEN 1995-1-1
Strength Classes – glulam (EN 1995-1-1)
Warning Letter !!
Solid timber: fv.k = 2,0 N/mm²
Glulam: fv.k = 2,5 N/mm²
will be taken into account by a factor kcr
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Design of Timber StructuresEN 1995-1-1
kcrack-value
M
kvcrackdv
kfkf
γmod,
,
⋅⋅=
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Design of Timber StructuresEN 1995-1-1
Wood based panels
Wood based panels covered by EN 1995-1-1
Missing materials: Cement bonded particle board,
gypsum based panels,
X – lam (cross laminated glulam) ….
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Design of Timber StructuresEC 5-1-1 Holzbau Grundlagen
Plywood (EN 636)
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Design of Timber StructuresEC 5-1-1 Holzbau Grundlagen
LVL (EN 14374)
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Design of Timber StructuresEC 5-1-1 Holzbau Grundlagen
OSB (EN 300)
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Design of Timber StructuresEC 5-1-1 Holzbau Grundlagen
Particleboard (EN 312)
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Design of Timber StructuresEC 5-1-1 Holzbau Grundlagen
Fibreboard, hard (EN 622-2)
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Design of Timber StructuresEC 5-1-1 Holzbau Grundlagen
Fibreboard medium (EN 622-3)
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Design of Timber StructuresEC 5-1-1 Holzbau Grundlagen
Fibreboard MDF (EN 622-5)
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Design of Timber StructuresEN 1995-1-1
Beams and columns
yIM
z
z ⋅
( )z,yσ
+
=
yM
zMy
z
zIM
y
y ⋅
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EN 1995-1-1 Design of Timber Structures Design and calculation principles
z
z
yy
σ+
-
max σm
min σm= Vd 6
5
Design resistance for cross-sections
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EN 1995-1-1 Design of Timber Structures Design and calculation principles
Ultimate limit state: 05d mod
M
XX kγ
= ⋅
Bending strength:m,k
m,d modM
ff k
γ= ⋅
t ,0 ,kt ,0,d mod
M
ff k
γ= ⋅
Servicability limit state: d mX X=
Modulus of elasticity: d 0,meanE E=
Design value of material properties:
Tensile strength:
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EN 1995-1-1 Design of Timber Structures Design and calculation principles
Vd = design value of the shear force S = static moment (section modulus)
= b·h2/8 (rectangle cross-section)I = second moment of area (moment of inertia)
= b·h3/12 (rectangle cross-section)b = widthfv,d = design shear strength for the actual condition
dd v,d
V1,5 fA
τ = ⋅ ≤ d
v,d
1,5 V A 1f⋅
≤
dd v,d
V S fI b
τ ⋅= ≤
⋅
d
v,d1
fτ
≤
Shear
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EN 1995-1-1 Design of Timber Structures Design and calculation principles
[ ][ ][ ]
⎧⎪
≥ ⋅ ⎨⎪⎩
dd
v ,dv ,d
A in cm²V
erf A 15 with V in kNf
f in N/mm²dimensioning
τ = ⋅ ≤dd v ,d
V15 f
A⋅ ≤d
v,d
V A15 1
f
τd in [N/mm²]Vd in [kN]A in [cm²]fv,d in [N/mm²]
[ ][ ]
⎧ ⎫⎪ ⎪≥ ⋅ ⎨ ⎬⎪ ⎪⎩ ⎭
dd
A in cm²erf A 9 V with
V in kN
For sawn timber C 24, service class 2 and medium term action:
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EN 1995-1-1 Design of Timber Structures Design and calculation principles
uniaxial bending
Roof construction
Pfette
Sparren
static systems
dm,d m,d
n
M fW
σ = ≤ d n
m,d
M / W 1f
≤
σm,d = design value of bending stressMd = design value of bending momentWn = netto moment of resistance considering the cross section weaksfm,d = design value of bending strength
rafter
purlin
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EN 1995-1-1 Design of Timber Structures Design and calculation principles
600 mm ≤ h fm,y,k
250 mm < h <600 mm
h ≤ 250 mm fm,y,k · 1,1
h ⎛ ⎞⋅ ⎜ ⎟⎝ ⎠
0,1
m,y ,k600f
h
dm,d m,d
n
M1000 fW
σ = ⋅ ≤ d n
m,d
M / W1000 1f
⋅ ≤
σm,d in [N/mm²]Md in [kNm]Wn in [cm³]fm,d in [N/mm²]
Influence of height of of glulam
Ultimate limit state
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EN 1995-1-1 Design of Timber Structures Design and calculation principles
[ ][ ][ ]
nd
n dm,d
m,d
W in cm³Merf W 1000 mit M in kNmf
f in N/mm²
⎧⎪
≥ ⋅ ⎨⎪⎩
Dimensioning
For sawn timber C 24, service class 2 and medium term action:
[ ][ ]
⎧ ⎫⎪ ⎪≥ ⋅ ⎨ ⎬⎪ ⎪⎩ ⎭
nn d
d
W in cm³erf W 68 M with
M in kNm
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EN 1995-1-1 Design of Timber Structures Design and calculation principles
4,3
m
w
y y
100 100 mm
yy wz
qz
yy wz
Fc
Fc
Stability of Members
β=1
lef
2
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EN 1995-1-1 Design of Timber Structures Design and calculation principles
imperfections additional bending moment
c,0,dc,0,d c c,0,d
n
Fk f
Aσ = ≤ ⋅ c,0,d n
c c,0,d
F A1
k f≤
⋅
An: local cross section weakenings might be neglected at the stress verification if they are not situated in the middle third of the buckling length.
kc: local cross section weakenings might be neglected at the calculationof the buckling coefficient.
Compression members endangered by buckling
Structural design calculation using compressive stress values and reducedcompressive strength:
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EN 1995-1-1 Design of Timber Structures Design and calculation principles
c 2 2rel ,c
1k 1k k λ
= ≤+ −
Buckling coefficient
k = ( ) 2c rel ,c rel ,c0,5 1 0,3β λ λ⎡ ⎤⋅ + ⋅ − +⎣ ⎦
βc = 0,2 for solid timber 0,1 for glued laminated timber and LVL
λrel,c = Relative Slendernessc,0,k c,0,kef
0,05 0,05
f fi E E
λπ π
= ⋅ = ⋅⋅
λ = efi = Slenderness
ef = β · s = effective lenght β = buckling length coefficient i I A=
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EN 1995-1-1 Design of Timber Structures Design and calculation principles
β=1
lef
2
Buckling length coefficient β
β=0,5
lef
4
β=2
lefs
1
β=0,7
lef
3
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EN 1995-1-1 Design of Timber Structures Design and calculation principles
Compression member with intermediate lateral support:
buckling length = distance of lateral support
different buckling lengths ef,y and ef,z :
2
1y z
Scheibe
hho
hu3
z y
h
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EN 1995-1-1 Design of Timber Structures Design and calculation principles
Design calculation
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EN 1995-1-1 Design of Timber Structures Design and calculation principles
Design calculation
1. determination of buckling lengths ef for buckling around the principal axis
2. calculation of the slenderness ratio λy and λz
3. determination of instability factors kc,y und kc,z
ef iλ = with i = 0,289 · h resp. = 0,289 · w at rectangular cross sections
4. verification of buckling resistance
c,0,dc,0,d c c,0,d
n
F10 k f
Aσ = ⋅ ≤ ⋅ c,0,d n
c c,0,d
F A10 1
k f⋅ ≤
⋅
σc,0,d in [N/mm²]Fc,0,d in [kN]An in [cm²]fc,0,d in [N/mm²]
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EN 1995-1-1 Design of Timber Structures Design and calculation principles
a A Nd, max in kN for a buckling length of lef in m
mm mm² 2,00 2,50 3,00 3,50 4,00 4,50 5,00 5,50 6,00 6,50 7,00
100 10000 72 50,4 36,4 27,4 21,3 17 13,9 11,5 9,7 8,3 7,2
120 14400 130 97,6 72,5 55,2 43,2 34,6 28,3 23,6 20 17,1 14,8
140 19600 202 164 127 98,7 78 62,9 51,6 43,1 36,6 31,4 27,2
160 25600 284 247 202 161 129 105 86,5 72,5 61,5 52,9 45,9
180 32400 375 340 293 243 199 163 136 114 97,1 83,6 72,7
200 40000 476 444 399 343 288 240 201 170 146 126 109
220 48400 587 557 514 459 397 337 286 244 209 181 158
240 57600 709 679 639 586 522 454 391 336 290 252 221
260 67600 841 812 773 723 660 588 515 448 390 340 299
for axial compression
Design resistance of squared columns C 24 in Service class 2 for medium action load
a
a
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EN 1995-1-1 Design of Timber Structures
ThankThank youyou veryvery muchmuchforfor youryour attentionattention!!