03 1 Weynand Moment Resistant Joints
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Transcript of 03 1 Weynand Moment Resistant Joints
Design of Joints in Steel Design of Joints in Steel StructuresStructures
International SeminarInternational Seminar
Norwegian Structural Steel AssociationNorwegian Structural Steel Association
Oslo Oslo –– 20 April 200520 April 2005
Design Procedures of Welded Design Procedures of Welded and Moment Resistant Jointsand Moment Resistant Joints
Dr.Dr.--Ing. Klaus WeynandIng. Klaus Weynand
PSP PSP -- Prof. Sedlacek & PartnerProf. Sedlacek & PartnerTechnologien im Bauwesen GmbH, AachenTechnologien im Bauwesen GmbH, Aachen
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Joints in Steel StructuresJoints in Steel Structures
B AA
C
D
A
A
A
D
C
A
D
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Joints in Steel StructuresJoints in Steel Structures
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5
Joints in Steel StructuresJoints in Steel Structures
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Joints in Steel StructuresJoints in Steel Structures
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Joints in Steel StructuresJoints in Steel Structures
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Joints in Steel StructuresJoints in Steel Structures
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Joints in Steel StructuresJoints in Steel Structures
16 x M 24, 10.9M = 660 kNm
12 x M 30, 10.9
M = 648 kNm
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ContentsContents
Basics and BackgroundBasics and BackgroundConcepts, methods, proceduresConcepts, methods, procedures
Determination of joint propertiesDetermination of joint propertiesWorked ExampleWorked Example
BeamBeam--toto--column joints with flush end platecolumn joints with flush end plate
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Joints in FramesJoints in Frames
M
MM
Single sidedSingle sided Double sidedDouble sidedjoint configurationjoint configuration joint configurationjoint configuration
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Design of JointsDesign of Joints
Old subject of discussionOld subject of discussionSeparate design for members and jointsSeparate design for members and jointsIntensive research activities for more Intensive research activities for more than 20 yearsthan 20 yearsObjective:Objective:
JOINTS MEMBERSJOINTS MEMBERS
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Joints as Joints as ““Structural ElementStructural Element””
φ/2 φ/2
φ
joint
Mj,Rd Mb.Rd
member, e.g. beam
φ Sj,ini
φ
EI/L
Members and jointsMembers and jointsResistanceResistanceDuctilityDuctilityStiffnessStiffnessEnergy dissipationEnergy dissipation
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Joints as Joints as ““Structural ElementStructural Element””
Joint properties Joint properties
M
Sj
Mj,Rd
φcd
(simplified) designcurve
actual behaviour
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Joints in FramesJoints in Frames
CharacterisationCharacterisationM
φ?
? ?
M
φ
12 3
ClassificationClassification
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Joints in Frames Joints in Frames
ModellingModelling
IdealisationIdealisation
M
φ
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ContentsContents
Basics and BackgroundBasics and BackgroundConcepts, methods, proceduresConcepts, methods, procedures
Determination of joint propertiesDetermination of joint propertiesWorked ExampleWorked Example
BeamBeam--toto--column joints with flush end platecolumn joints with flush end plate
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CharacterisationCharacterisation
Determination of joint properties:Determination of joint properties:Experiments (test results)Experiments (test results)„„Curve fittingCurve fitting““FEM calculationsFEM calculationsMechanical modelsMechanical modelsSimplified analytical modelsSimplified analytical models
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Characterisation Characterisation
ExperimentalExperimentalJoint properties for one joints onlyJoint properties for one joints onlyTime / money consumingTime / money consumingDatabasesDatabases
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Characterisation Characterisation
„„Curve fittingCurve fitting““Data bases of test resultsData bases of test resultsLimited field of applicationLimited field of applicationno extrapolation possibleno extrapolation possible
M
φ
M a b c( )φ φ φ φ= + +2 3
M a b( ) lnφ φ= ??
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Characterisation Characterisation
Finite Element MethodFinite Element MethodO.K. for welded joints (open and hollow sections)O.K. for welded joints (open and hollow sections)very complex for bolted jointsvery complex for bolted joints
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Characterisation Characterisation
Mechanical modelsMechanical modelsComplex models (nonComplex models (non--linearitieslinearities))Research orientatedResearch orientated
Simplified analytical modelsSimplified analytical modelsSuitable for practical design Suitable for practical design
NM
zγ
ϕM
N
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Characterisation Characterisation
ENV Annex J of ENV 1993ENV Annex J of ENV 1993BeamBeam--toto--column jointscolumn jointsBeamBeam--toto--beam jointsbeam joints
EN 1993 Part 1.8EN 1993 Part 1.8Column basesColumn basesBeam haunchesBeam haunchesMM--N interactionN interaction
EN 1994EN 1994Composite jointsComposite joints
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Characterisation Characterisation
h
boltstensionzone Ft1,Rd
Ft2,Rd
h2h1
shear panel
M
compressionzone end plate
welded connection bolted connection
Component method
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Component Method Component Method
Step 1:Step 1:Identification of Identification of componentscomponents
Step 2:Step 2:Determination of Determination of component component propertiesproperties
Step 3:Step 3:Assembly of Assembly of componentscomponents
F F F
E k1 E k2 E k3
F1,RdF2,Rd
F3,Rd
δ δ δ
column webin shear
M
Sj,ini
Mj,Rd
φcd
column webin compression
column webin tension
( )M min F zj,Rd i,Rd= ⋅
SE z
kj,ini
2
i
=⋅
∑ 1
27
Component Method Component Method
Determination of component propertiesDetermination of component propertiesComponent testsComponent testsFEM calculationsFEM calculationsAnalytical or mechanical modelsAnalytical or mechanical models(complex or simplified)(complex or simplified)
AssemblyAssemblyAlso different levels of complexityAlso different levels of complexity
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Basic Joint ComponentsBasic Joint Components
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Basic Joint ComponentsBasic Joint Components
Concrete incompression
Normal forces andbending moments
Anchor boltsin tension / shear
Column bases
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Component PropertiesComponent Properties
F /4t
Ft
F /4t
F /4t
F /4t
m e
leff
T-stub
ResistanceStiffness
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TT--Stub ResistanceStub Resistance
3 failure modes of T3 failure modes of T--stubstub
Mode1:Mode1:Flange yieldingFlange yielding
Mode 2:Mode 2:Combined mechanismCombined mechanism
Mode 3:Mode 3:Bolt failureBolt failure
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TT--Stub StiffnessStub Stiffness
mm
m m
A A
n
1,25m 1,25m
n
2B2B
Actual behaviourQ Q
F
F F
0,13F0,13F
0,63F
0,63F 0,63F
0,63F
Deformation of T-Stub Deformation of bolts
Separation of Separation of TT--stubstub
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TT--Stub StiffnessStub Stiffness
TT--stub in bendingstub in bending
A 1,25 m
0,3235 Fm
0,1765 Fm
m
'1'δ
F2
iii δEkF ⋅⋅=
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Assembly of ComponentsAssembly of Components
Based on the internal distribution of Based on the internal distribution of forcesforcesRespecting the following criteriaRespecting the following criteria
Equilibrium of internal and external forcesEquilibrium of internal and external forcesRespect criterion of plasticityRespect criterion of plasticityRespect criterion of maximum deformationRespect criterion of maximum deformationCompatibility of displacements between Compatibility of displacements between components
ththééororèèmemestatiquestatique
components
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Assembly of ComponentsAssembly of Components
Application to a member sectionApplication to a member section
H y
M
IyM .
=σ
full elastic distributionfull elastic distribution
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Assembly of ComponentsAssembly of Components
Application to a member sectionApplication to a member section
fy
mγ
max. elastic moment (class 3 section)max. elastic moment (class 3 section)
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Assembly of ComponentsAssembly of Components
Application to a member sectionApplication to a member section
fy
mγ
max. plastic moment (class 1 or 2 section)max. plastic moment (class 1 or 2 section)
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Assembly of ComponentsAssembly of Components
Joints with one bolt row onlyJoints with one bolt row only
M
FRd h
.zFM RdRdj, =
elastic distribution = plastic distributionelastic distribution = plastic distribution
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Assembly of ComponentsAssembly of Components
Joints with more than one bolt rowJoints with more than one bolt row
h1
h2
hi
FRd
Fc
M
∑= 2i
1
RdRdj, h
hFM
thick end platesthick end plates
full elastic distributionfull elastic distributionmax. moment = elastic momentmax. moment = elastic moment
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Assembly of ComponentsAssembly of Components
Joints with more than one bolt rowJoints with more than one bolt row
M
h1
h2
hi
thin end platesthin end plates
elastic distribution, butelastic distribution, butnot linear for all bolt rowsnot linear for all bolt rows
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Assembly of ComponentsAssembly of Components
Joints with more than one bolt rowJoints with more than one bolt row
M
h1
hi
FRd
FRd,i
∑=i
iiRd,Rdj, hFMRdt,iRd, B1,9F ≤
thin end platesthin end plates
plastic distributionplastic distributionplastic moment resistanceplastic moment resistance
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Assembly of ComponentsAssembly of Components
Joints with more than one bolt rowJoints with more than one bolt row
M
h1
hk
hj
FRd,1
FRd,k
∑ ∑= +=
+=k1,i n1,kj
2j
k
kRd,iiRd,Rdj, h
hF
hFMRdt,kRd, B1,9F >
thin end platesthin end plates
elasticelastic--plastic distributionplastic distributionductile and nonductile and non--ductile bolt rowsductile bolt rows
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Assembly of ComponentsAssembly of Components
Joint stiffnessJoint stiffnesswelded, one bolt rowwelded, one bolt row
iii δEkF ⋅⋅=
φ M
k 2
k3
k1
z
zFM j ⋅=z
δδδ 321 ++=φ
j
jinij,
MS
φ=
...=
∑⋅
=
i
2
inij,
k1zES
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Assembly of ComponentsAssembly of Components
Joint stiffnessJoint stiffnesstwo or more bolt rowstwo or more bolt rows
φ
φ φ
M
M M
k3,1
keff,1
k1
k1 k1
k2
k2 k2
keq
k3,2
keff,2
k4,1
k4,2
k5,1
k5,2
k10,1
k10,2
z
h1 h2
a)
b) c)
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Stiffness ModelStiffness Model
M
φ
M j,Sd
2/3 Mj,Rd
Mj,Rd
Sj*
*
Sj
Sj,ini
1 2 3
φcdφ ' µ φ '
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ContentsContents
Basics and BackgroundBasics and BackgroundConcepts, methods, proceduresConcepts, methods, procedures
Determination of joint propertiesDetermination of joint propertiesWorked ExampleWorked Example
BeamBeam--toto--column joints with flush end platecolumn joints with flush end plate
47
Worked ExampleWorked Example
Beam-to-column joint with flush end plate
+ +
+ +
M
V15
3
IPE220 HEB140
120
60 10
8030 30
240
4 M16 8.8
140
u=10p=60
5
w=
Determination of - Design moment resistance- Stiffness
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CoefficientsCoefficients
Column
h h t r mmwc c fc c= − − = − × − × =2 2 140 2 12 2 12 92
( ) ( )A A b t t r mmvc c c fc wc c= − + + = − × × + + × × =2 2 4295 6 2 140 12 7 2 12 12 1307 6 2, ,
mw t
r mmfcc=
−− =
−− × =
20 8
80 72
0 8 12 26 9, , ,
eb w
mmc=−
=−
=2
140 802
30
mt f
Nmm mmpl fcfc yc
M, , ,
,/= =
×=0 25 0 25
12 23511
76912
0
2
γ
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CoefficientsCoefficients
Beam
Lever arm:
z h ut
p mmbfb= + − − = + − − =2
220 109 22
60 165 4,
,
MW f
kNmc Rdpl yb yb
M,
,
,, (Klasse 1 Querschnitt) = =
× ×=
−
γ 0
6285406 235 1011
60 97
+ +
+ +
15
3
IPE220 120
60 10
8030 30
240
4 M16 8.8
140
u=10p=60
5
w=
z
( class 1 section )
50
CoefficientsCoefficients
mp
mp2End plate
mw t
a mmpwb
w=−
− =−
− × × =2
0 8 280 5 9
20 8 2 3 33 66,
,, ,
m p u t a mmp fb f2 0 8 2 60 10 9 2 0 8 2 5 3514= − − − = − − − × =, , , ,
eb w
mmpp=
−=
−=
2140 80
230
mt f
Nmm mmpl pp yp
M, , ,
,/= =
×=0 25 0 25
15 23511
120172
0
2
γ
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CoefficientsCoefficients
λ1
33 6633 66 30
0 529=+
=+
=m
m ep
p p
,,
,
λ22 3514
33 66 300 552=
+=
+=
mm e
p
p p
,,
,
Coefficients for the determinationof the effective length
α = 514,
End plate
52
CoefficientsCoefficients
Bolts
Ff A
kNt Rdub s
Mb,
, ,,
,= =× × ×
=−0 9 0 9 800 157 10
1 2590 4
3
γ
Ff A
kNv Rdub s
Mb,
, ,.
, (Abscherfläche im Gewinde) = =× × ×
=−0 6 0 6 800 157 10
12560 3
3
γ
( ) ( )L t t h h mmb fc p bolt nut= + + + = + + + =0 5 12 1512
10 13 38 5, ,
( shear plane in the thread )
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ComponentsComponents
1. Column web in shear
Resistance
VA f
kNwc Rdvc y cw
M,
,, , ,,
,= =× × ×
×=
−0 93
0 9 1307 6 235 103 11
145 20
3
γ
Transformation parameter β Annahme: β = 1
FV
kNRdwc Rd
,, ,
,1
145 21
145 2= = =β
Stiffness
kA
hmmvc
1
0 385 0 385 1307 61 165 4
3 044= =×
×=
, , ,,
,β
Vwp
Vwp
γ
F
M
z
F
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ComponentsComponents
2. Column web in compressionResistance
( ) ( )[ ]( ) ( )[ ]
b min t a t t s t a t u t s
min mm
eff c wc fb f p fc fb f p fc, , ;
, ; , ,
= + + + + + + + + +
= + × × + × + × + + × + + + + =
2 2 2 5 2 5
9 2 2 5 2 2 15 5 12 12 9 2 5 2 15 10 5 12 12 161 27
Reduction factors to consider normal stresses and buckling in the column web panel:
Annahme k minfwccom Ed
y wc: , ; , , ,,
,= −
⎡
⎣⎢⎢
⎤
⎦⎥⎥
=1 0 1 25 0 5 1 0σ
λ ρpeff c wc c y wc
wc
b d fE t
= =× ×
× ×= ≤ → =0 932 0 932
161 27 92 235210000 7 7
0 543 0 673 1 02, ,,
, , ,, , ,
( ) ( )ω ω= =
+=
+ ×=1 2 2
1
1 1 3
1
1 1 3 161 27 7 1307 60 713
, / , , ,,
, ,b t Aeff c wc wc vc
F k b t f kNRd wc eff c wc wc y wc M, , , , / , , , ,2 1
31 0 713 1 161 27 7 235 10 11 171 9= = × × × × × × =−ω ρ γ
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ComponentsComponents
2. Column web in compression
Stiffness
kb t
hmmeff c wc wc
wc2
0 7 0 7 161 27 792
8 589= =× ×
=, , ,
,, ,
F
δF k Ei i i= δ
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ComponentsComponents
2. Column web in tension
Resistance
[ ] ( )b min m m e min mmeff t wc, , ; , , ; , , ,= + = × × + × =2 4 1 25 2 26 9 4 26 9 1 25 30 14510π π
( ) ( )ω1 2 2
1
1 1 3
1
1 1 3 1451 7 1307 60 749=
+=
+ ×=
, / , , ,,
, ,b t Aeff t wc wc vc
F b t f kNRd eff t wc wc y wc M, , , , / , , , ,3 0
30 749 1451 7 235 10 11 162 4= = × × × × =−ω γ
Stiffness
kb t
hmmeff t wc wc
wc3
0 7 0 7 1451 792
7 728= =× ×
=, , ,
,, ,
57
ComponentsComponents
4. Column flange in bending
5. End plate in bending
Equivalent T-Stub
58
ComponentsComponents
Equivalent T-Stub
F /4t
Ft
F /4t
F /4t
F /4t
m e
leff
59
ComponentsComponents
4. Column flange in bending
Resistance l b mm vgl Stützensteg auf Zugeff t fc eff t wc, , , , , ( . )= = 131 35
( )[ ] ( )n min e m b w min mmp= − = × =; , ; / ; , , ;1 25 2 30 1 25 26 9 30 30
Reduction factor to consider normal stresses in column web:
[ ]Annahme k min f ffc y fc com Ed y fc: , ; ) / ( ) ,, , ,= − − − =1 0 2 180 2 360 1 0σ
60
ComponentsComponents
4. Column flange in bending
Mode 1 – Flange yielding
Fl k m
mkNfc Rd t
eff t fc fc pl fc, ,
, , , ,,
,13
4 4 1451 1 769126 9
10 165 9= =× × ×
× =−
Mode 2 – Combined failure
Fl k m B n
m nfc Rd teff t fc fc pl fc t Rd
, ,, , , ,
2
2 2=
+
+
=× × × + × × ×
+× =−2 1451 1 7691 2 90 4 10 30
26 9 3010 134 6
33, ,
,, kN
Mode 3 – Bolt failure
F B kNfc Rd t t Rd, , , , ,3 2 2 90 4 180 8= = × =
61
ComponentsComponents
Resistance
[ ]F min F F kNRd fc Rd t fc Rd t, , , , ,; ,4 1 2 134 6= =
Stiffness
kl tm
mmeff fc t fc4
3
3
3
3
0 85 0 85 1451 1226 9
10 95= =× ×
=, , ,
,,, ,
4. Column flange in bending
62
ComponentsComponents
Resistance
[ ] ( )l min m m min mmeff t p p p, , ; , ; , , ,= = × × =2 2 33 66 514 33 66 173 0π α π
[ ] ( )n min e m e min mmp p p= = × =; , ; ; , , ;1 25 30 1 25 33 66 30 30
Fl m
mkNep Rd
eff t p pl p
p, ,
, , , ,,
,13
4 4 173 0 1201733 66
10 247 1= =× ×
× =−
Fl m B n
m nkNep Rd
eff p t pl p t Rd p
p p, ,
, , , , , ,,
,2
33
2 2 2 173 0 12017 2 90 4 10 3033 66 30
10 150 5=+
+=
× × + × × ×+
× =−
[ ]F min F F kNRd ep Rd ep Rd, , , , ,; ,5 1 2 150 5= =
5. End plate in bending
63
ComponentsComponents
5. End plate in bending
Stiffness
kl tm
mmeff t p p
p5
3
3
3
3
0 85 0 85 173 0 1533 66
13 014= =× ×
=, , ,
,,, ,
64
ComponentsComponents
7. Beam flange and web in compression
Resistance
( )F M h t kNRd c Rd b fb, , /,
,,7 3
60 97210 8 10
289 2= − =×
=−
Stiffness k7 = ∞
65
ComponentsComponents
8. Bean web in tension
Resistance b l mmeff t wb eff t p, , , , ,= = 173 0
F b t f kNRd eff t wb wb yb M, , , / , , , ,8 0
3173 0 5 9 235 10 11 218 1= = × × × =−γ
Stiffness k8 = ∞
66
ComponentsComponents
10. Bolts in tension
Resistance F B kNRd t Rd, , , ,10 2 2 90 4 180 8= = × = T-stub mode 3 for components: „Column flange in bending“ and „End plate in bending“ Stiffness
kAL
mms
b10 1 6 1 6
15738 5
6 525= = × =, ,,
,
67
Step 3 Step 3 -- AssemblyAssembly
Design moment resistance
Relevant component:
[ ]F min F kNRd Rd i= =. ,134 6 (Stützenflansch auf Biegung) Design plastic moment resistance : M F z kNmj Rd Rd, , , ,= = × × =−134 6 165 4 10 22 263
Design elastic moment resistcane :
M M kNmj el Rd j Rd, , , ,= =23
14 84
Mj,Rd
( column flange in bending )
68
Step 3 Step 3 -- AssemblyAssembly
Stiffnessφ
S j,ini
Initial stiffness:
S E h kj ini ii
, /= =∑2 1
=× ×
+ + + + +=
−210000 165 4 101
3 0441
8 5891
6 5251
7 7281
10 951
13 01
64132 6,
, , , , , ,
/kNm rad
Idealised stiffness : S S kNm radj j ini= =, / /2 3207
69
Joints PropertiesJoints Properties
Design moment-rotations curve
φ
M
Sj,ini
S j,ini
SjS j = /ηErsatzsteifigkeit:
M j,Rd
2/3Mj,Rd
Idealised stiffness
70
Further ApplicationsFurther Applications
Component method:Component method:Joints in Joints in „„slenderslender““ sectionssectionsWeak axis moment resistant joints Weak axis moment resistant joints Joints in hollow sectionsJoints in hollow sections
StandardisationStandardisationEN 1993 part 1.8 EN 1993 part 1.8 „„Design of jointsDesign of joints““
Future research:Future research:Fire resistanceFire resistanceFatigue resistance, earth quake resistanceFatigue resistance, earth quake resistance
71
Further ApplicationsFurther Applications
Haunches without flanges
Girders with slender webs (instability, buckling)
intermediate stiffeners
72
Further ApplicationsFurther Applications
Additional stiffeners in extended end plates