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

3

Joints in Steel StructuresJoints in Steel Structures

B AA

C

D

A

A

A

D

C

A

D

4


7

5


6


7


8


9


16 x M 24, 10.9M = 660 kNm

12 x M 30, 10.9

M = 648 kNm

11

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

12

Joints in FramesJoints in Frames

M

MM

Single sidedSingle sided Double sidedDouble sidedjoint configurationjoint configuration joint configurationjoint configuration

13

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

14

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

15

Joints as Joints as ““Structural ElementStructural Element””

Joint properties Joint properties

M

Sj

Mj,Rd

φcd

(simplified) designcurve

actual behaviour

16

Joints in FramesJoints in Frames

CharacterisationCharacterisationM

φ?

? ?

M

φ

12 3

ClassificationClassification

17

Joints in Frames Joints in Frames

ModellingModelling

IdealisationIdealisation

M

φ

18

ContentsContents




19

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

20

Characterisation Characterisation

ExperimentalExperimentalJoint properties for one joints onlyJoint properties for one joints onlyTime / money consumingTime / money consumingDatabasesDatabases

21


„„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= ??

22


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

23


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

24


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

25


h

boltstensionzone Ft1,Rd

Ft2,Rd

h2h1

shear panel

M

compressionzone end plate

welded connection bolted connection

Component method

26

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

28

Basic Joint ComponentsBasic Joint Components

29

Basic Joint ComponentsBasic Joint Components

Concrete incompression

Normal forces andbending moments

Anchor boltsin tension / shear

Column bases

30

Component PropertiesComponent Properties

F /4t

Ft

F /4t

F /4t

F /4t

m e

leff

T-stub

ResistanceStiffness

31

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

32

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

33

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 ⋅⋅=

34

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

35


Application to a member sectionApplication to a member section

H y

M

IyM .

=σ

full elastic distributionfull elastic distribution

36



fy

mγ

max. elastic moment (class 3 section)max. elastic moment (class 3 section)

37



fy

mγ

max. plastic moment (class 1 or 2 section)max. plastic moment (class 1 or 2 section)

38


Joints with one bolt row onlyJoints with one bolt row only

M

FRd h

.zFM RdRdj, =

elastic distribution = plastic distributionelastic distribution = plastic distribution

39


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

40



M

h1

h2

hi

thin end platesthin end plates

elastic distribution, butelastic distribution, butnot linear for all bolt rowsnot linear for all bolt rows

41



M

h1

hi

FRd

FRd,i

∑=i

iiRd,Rdj, hFMRdt,iRd, B1,9F ≤


plastic distributionplastic distributionplastic moment resistanceplastic moment resistance

42



M

h1

hk

hj

FRd,1

FRd,k

∑ ∑= +=

+=k1,i n1,kj

2j

k

kRd,iiRd,Rdj, h

hF

hFMRdt,kRd, B1,9F >


elasticelastic--plastic distributionplastic distributionductile and nonductile and non--ductile bolt rowsductile bolt rows

43


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

44


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)

45

Stiffness ModelStiffness Model

M

φ

M j,Sd

2/3 Mj,Rd

Mj,Rd

Sj*

*

Sj

Sj,ini

1 2 3

φcdφ ' µ φ '

46

ContentsContents




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

48

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

49


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


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

51


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


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 )

53

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

54


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

55


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

56


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


4. Column flange in bending

5. End plate in bending

Equivalent T-Stub

58


Equivalent T-Stub

F /4t

Ft

F /4t

F /4t

F /4t

m e

leff

59



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



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


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= =× ×

=, , ,

,,, ,


62


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= =


63



Stiffness

kl tm

mmeff t p p

p5

3

3

3

3

0 85 0 85 173 0 1533 66

13 014= =× ×

=, , ,

,,, ,

64


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


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


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


Haunches without flanges

Girders with slender webs (instability, buckling)

intermediate stiffeners

72


Additional stiffeners in extended end plates

03 1 weynand moment resistant joints

Documents

joints members

bolted joints

aachen joints

composite joints

column joints beam

beam joints en

rd frd

moment resistant joints