[Eng]Advanced Training Steel Connections 2008.0.1

Advanced Training Steel Connections

Steel Connections

2

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Table of contents

3

Contents

Introduction ...................................... ............................................................................................. 1

Frame Connect : column-beam joints ................ ........................................................................ 2

Scope ............................................. ..................................................................................................... 2

The Moment-Rotation characteristic ................ ............................................................................... 3

The resistance properties.......................... ....................................................................................... 9

The component strength ................................................................................................................ 9

The strength assembly ................................................................................................................. 12

The influence of the normal force................................................................................................. 14

The design shear resistance ........................................................................................................ 16

The stiffness properties........................... ....................................................................................... 18

The component stiffness .............................................................................................................. 18

The stiffness assembly ................................................................................................................. 19

The classification on stiffness ...................................................................................................... 20

The required stiffness ................................................................................................................... 21

Transferring the joint stiffness to the analysis model .................................................................. 22

Ductility classes ................................. ............................................................................................. 23

Ductility classification for bolted joints .......................................................................................... 23

Ductility classification for welded joints ........................................................................................ 24

Examples .......................................... ................................................................................................ 25

Calculation of bolted connection .................................................................................................. 25

Calculation of welded connection................................................................................................. 26

Calculation of connections in 3D Frame ...................................................................................... 30

Special features .................................. ............................................................................................. 31

Use of haunches .......................................................................................................................... 31

Column in minor axis configuration .............................................................................................. 33

Base plate connections : shear iron, flange wideners ................................................................. 34

The use of 4 bolts / row ................................................................................................................ 35

RHS beam .................................................................................................................................... 38

Frame Connect : pinned joint ...................... .............................................................................. 39

Examples .......................................... ................................................................................................ 39

Welded fin plate connection ......................................................................................................... 39

Bolted fin plate connection ........................................................................................................... 43

Bolted cleat connection ................................................................................................................ 45

Flexible end plate connection....................................................................................................... 48

References and literature ......................... ................................................................................. 49

Introduction

The design methods for connection design are explained. More details and references to the applied articles can be found in (Ref.[30])

Scia EngineerTheoretical BackgroundRelease : Revision :

The explained rules are valid for Scia Engineer 2008.0 and higher. The examples are marked by ‘The following examples are available :

Project Subject

CON_001.esa 2D Frame with pinned connections

CON_002.esa 2D Frame with semi

CON_003.esa 2D Frame with rigid connections

CON_004.esa Bolted connection

CON_005.esa welded connection

RHS connection

Base plate connection

CON_006.esa Connection with haunch

CON_007.esa Connection with column i

CON_008.esa Connections in 3D Frame

CON_009.esa Welded fin plate

CON_010.esa Bolted fin plate

CON_011.esa Cleat connection

CON_012.esa Flexible end plate connection

The design methods for connection design are explained. More details and references to the applied articles can be found in (Ref.[30])

Scia Engineer Connect Frame & Grid Theoretical Background

: 5.2 : 05/2008

The explained rules are valid for Scia Engineer 2008.0 and higher.

The examples are marked by ‘ Example’ The following examples are available :

2D Frame with pinned connections

2D Frame with semi-rigid connections

2D Frame with rigid connections

Bolted connection

welded connection

RHS connection

Base plate connection

Connection with haunch

Connection with column in minor axis bending

Connections in 3D Frame

Welded fin plate

Bolted fin plate

Cleat connection

Flexible end plate connection

1

The design methods for connection design are explained. More details and references to the applied

Steel Connections

2

Frame Connect : column-beam joints

Scope The design methods for the column-beam joints are taken from EC3 – Revised Annex J and EN 1933-1-8. More detailed information about the applied rules and specific implementations are found in Ref.[1]. The following chapters are valid for the bolted and welded column-beam joints. The design methods for the beam-column joints are principally for moment-resisting joints between I or H sections in which the beams are connected to the flanges of the column.

Figure 1 : Typical configurations

3

The difference between joint and connection is given in Figure 2. In the text, the name ‘joint’ will be used.

Figure 2 : Connection vs. Joint

The Moment-Rotation characteristic The joint is defined by the moment rotation characteristic that describes the relationship between the bending moment Mj,Sd applied to a joint by the connected beam and the corresponding rotation φEd between the connected members.

Figure 3 : Joint and Model

This moment-rotation characteristic defines three main properties :

- the moment resistance Mj,Rd - the rotational stiffness Sj - the rotation capacity φCd

Steel Connections

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Figure 4 : Moment-rotation characteristic (1 = limit for Sj)

The general analytical procedure which is used for determining the resistance and stiffness properties of a joint, is the so-called component method. The component method considers any joint as a set of individual basic components. Each of these basic components possesses its own strength and stiffness. The application of the component method requires the following steps :

- identification of the active components in the joint being considered

- evaluation of the stiffness and/or resistance characteristics for each individual basic component

- assembly of all the constituent components and evaluation of the stiffness and/or resistance characteristics of the whole joint

5

Figure 5 : Basic components according to EN 1993-1-8 (1)

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Figure 6 : Basic components according to EN 1993-1-8 (2)

7

Figure 7 : Basic components EN 1993-1-8 (3)

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8

Figure 8 : Components in bolted beam-column joint

Zone Ref

Tension a bolts in tension

b end plate bending

c column flange bending

d beam web tension

e column web tension

[f] flange to end plate weld

[g] web to end plate weld

Horizontal shear h column web panel shear

Compression j beam flange compression

[k] beam flange weld

l, m column web in compression

Vertical shear [n] web to end plate weld

p bolt shear

q bolt bearing

9

Figure 9 : Application of the component method to a welded joint

The resistance properties

The component strength

In EC – Revised Annex J and Eurocode 3 – EN 1993-1-8, evaluation formulae are provided for each of the basic components.

The equivalent T stub

The endplate bending and the column flange bending or bolt yielding, are analysed, using an equivalent T-stub. The three possible modes of failure of the flange of the T stub are :

- complete flange yielding

- bolt failure with flange yielding

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10

- bolt failure

Figure 10 : Complete flange yielding

Figure 11: Bolt failure with flange yielding

Figure 12 : Bolt failure

The plastic moment capacity of the equivalent T-stub is related to the effective length of the yield line. The effective length is a notional length. The values of the effective length for the different bolt locations are defined in EN 1993-1-8.

11

Figure 7 : Effective length for unstiffened column flange

The use of national code

The capacities of the underlying steel parts are calculated by the formulas given in the respective national codes (EC3, DIN18800 T1 or BS 5950-1:2000), depending on the national code set-up. For other codes (NEN, CM, ONORM, CSN, …), the default EC3 capacities are used. Remark : the frame bolted, frame welded and frame pinned joint types are affected. The concrete parts (for base plate joints) are not affected. The concrete parts are designed according the EC definitions. Examples : Column web panel in shear

EC3

0M

vcwc,yRd,wp

3

Af9.0V

γ=

DIN

M

vcwc,k,yRd,wp

3

1.1Af9.0V

γ=

BS

ccycRd,wpv Dtp6.0VP ==

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12

Bolts in tension

EC3

Mb

subRd,t

Af9.0B

γ=

DIN

( )

M

k,b,uRd,2

M

k,b,yRd,1

Rd,2sRd,1RdRd,t

25.1

f

1.1

f

A,AminNB

γ=σ

γ=σ

σσ==

BS

tt't ApP =

The strength assembly

The design model is based on a plastic distribution of bolt forces. Suppose the following joint :

Figure 84 : Plate-to-plate joint

The failure may occur in 3 different ways :

1. The plastic redistribution of the internal forces extends to all bolt-rows when they have sufficient deformation capacity. The resulting distribution is called ‘plastic’.

Figure 15 : Plastic distribution

2. The plastic redistribution of forces is interrupted because of the lack of deformation capacity of a given bolt row. In the bolt-rows located lower than this bolt row, the forces are linearly distributed. The resulting distribution is called ‘elasto-plastic’.

13

Figure 16 : Elasto-plastic distribution

3. The plastic or elasto-plastic distribution of internal forces is interrupted because the compression force Fc attains the design resistance.

Figure 9 : Reduced distribution

The concept of individual and group yield mechanisms is explained in EC3 –EN 1993-1-8. When adjacent bolt-rows are subjected to tension forces, various yield mechanisms are likely to form in the connected plates (end-plate or column flange). Individual mechanism develops when the distance between the bolt-rows are sufficiently large. Group mechanism includes more than one adjacent bolt row. To each of these mechanisms are associated specific design resistances.

Steel Connections

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Figure 10 : Individual vs. group yield mechanism

The influence of the normal force

Default Interaction check according to EC – Revised Annex J

When the axial force NSd in the connected member exceeds 10 % of the plastic resistance Npl,Rd of its cross-section, a warning is printed out and the value of the design moment resistance Mj,Rd is decreased.

� For bolted joints

The value of the design moment resistance Mj,Rd is decreased by the presence of the axial tensile force NSd.

2

h.NMM SdRd,jRd,j −=

with

h the distance between the compression and tension point in the connected member

15

If there is an axial compression force NSd, we check the following :

hNMM

))FFc(2

N,0max(N

)F,F,Vmin(F

Rd,jRd,j

totSd

Rd,fb,cRd,wc,cRd,wpc

⋅−=

−−=

=

with


Fc,wc,Rd Design compression resistance for column web

Fc,fb,Rd Design compression resistance for beam web and flange

Vwp,Rd Design shear resistance of column web Ftot The sum of the tensile forces in the bolt

rows at Mj,Rd

� For welded joints

)F,F,F,F,Vmin(F Rdwc,t,Rdfc,t,Rdfb,c,Rdwc,c,Rdwp,tot =

When an axial tensile force NSd is present :

hNMM

))FFc(2

N,0max(N

)F,Fmin(F

Rd,jRd,j

totSd

Rdwc,t,Rdfc,t,c

⋅−=

−−=

=

When an axial compressive force NSd is present :

hNMM

))FFc(2

N,0max(N

)F,F,Vmin(F

Rd,jRd,j

totSd

Rdfb,c,Rdwc,c,Rdwp,c

⋅−=

−−=

=

with


Fc,wc,Rd Design compression resistance for column web

Fc,fb,Rd Design compression resistance for beam web and flange

Vwp,Rd Design shear resistance of column web

Ft,wc,Rd Design resistance of column web in tension

Ft,fc,Rd Design resistance of column flange in tension

Steel Connections

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Interaction Check according to EN 1993-1-8 (Ref.[32 ])

If the axial force NEd in the connected beam exceeds 5% of the design resistance, Npl,Rd ,

the following unity check is added :

Mj.Rd is the design moment resistance of the joint, assuming no axial force Nj.Rd is the axial design resistance of the joint, assuming no applied moment Nj,Ed is the actual normal force in the connection Mj,Ed is the actual bending moment in connection The value for Nj,Rd is calculated as follows : If Nj,Ed is a tensile force, the Nj,Rd is determined by critical value for the following components (Ref.[32], table 6.1.):

- For bolted connection, as a combination for all bolt rows : - component 3 : column web in transverse tension - component 4 : column flange in bending - component 5 : end plate in bending - component 8 : beam web in tension - component 10 : bolts in tension

- For welded connection :

- component 3 : column web in transverse tension, where the value for tfb in formulas (6.10) and

- (6.11) is replaced by the beam height. - component 4 : column flange in bending, by considering the sum of formula (6.20) at the top

and - bottom flange of the beam. - If Nj,Ed is a compressive force, the Nj,Rd is determined by the following components (Ref.[32],

table 6.1.): - component 2 : column web in transverse compression, where the value for tfb in formulas

(6.16) is - replaced by the beam height. - component 4 : column flange in bending, by considering the sum of formula (6.20) at the top

and - bottom flange of the beam.

In all cases, Nj,Rd ≤ Npl,Rd.

The design shear resistance

The design shear resistance for normal bolts

17

EC3

nn*Fnt28.0FV Rd,vRd,vRd +⋅⋅=

Mb

subRd,v

Af6.0F

γ⋅⋅

= for grade 4.6, 5.6, 8.8

Mb

subRd,v

Af5.0F

γ⋅⋅

= for other grades

DIN


M

sk,b,uad,R,aRd,v

AfVF

γ⋅⋅α

==

for grade 4.6 , αa=0.60




for other grades, αa=0.55

BS


sssRd,v A.pPF ==

for grade 4.6 , ps=160 N/mm²



for other grades, ps=0.4 fub

with nt number of bolts in tension nn number of bolts not in tension

Remark : For anchors, the shear (Fv,Rd, Va,R,d and Ps) are reduced by multiplying them with a factor 0.85

The design shear resistance for preloaded bolts

Suppose we have ntot number of bolts.

EC3

subCd,p Af7.0F ⋅⋅=

( )Ms

Sd,tCd,psRd,s

F8.0FnkF

γ⋅−⋅µ⋅⋅

=

BS

)F(Pk9.0P

Af7.0P

Rd,sossL

subo

=⋅µ⋅⋅=⋅⋅=

Steel Connections

18

with fub the tensile strength of the bolt As the tensile stress area of the bolt n the number of friction interfaces (=1) ks the value for slip resistance

(=1.0 for holes with standard nominal clearances) µ the slip factor Ft,Sd the applied tensile force (=NSd/ntot) γMs the partial safety factor for slip resistance

The design shear force VRd is :

totRd,sRd nFV ⋅=

The stiffness properties

The component stiffness

In EN 1993-1-8 and Eurocode 3 – Revised Annex J, evaluation formulae are provided for each of the basic components.

The following stiffness coefficients are used :

Coefficient Basic component Formula

k1 column web panel in shear

z

A38.0 vc

β⋅

k2 column web in compression

c

wceff

d

tb7.0 ⋅

k3 column flange, single bolt row in tension

3

3fceff

m

tl85.0 ⋅

k4 column web in tension, single bolt row in tension

c

wceff

d

tb7.0 ⋅

k5 endplate, single bolt row in tension

3

3peff

m

tl85.0 ⋅

k7 bolts, single bolt row in tension

b

s

L

A6.1

with Avc

the shear area of the column

z the lever arm β the transformation parameter beff the effective width of the column web dc the clear depth of the column web leff the smallest effective length for the

bolt m the distance bolt to beam/column

web As the tensile stress area of the bolt

19

Lb

the elongation length of the bolt

For a column base, we also consider the stiffness coefficient kc for the compression zone on the concrete block.

eq

cflc Eh

EAk =

with Afl the bearing area under the compression flange

Ec the E modulus of concrete

( ) 3/1ck 8f5.9 +=

(Ec in Gpa, fck in Mpa) E the Young modulus (of steel) heq the equivalent height

( )2

ba effeff +=

where aeff and beff are based on the rectangle for determining Afl Afl=aeff x beff

The stiffness assembly

The initial stiffness Sj,ini is derived from the elastic stiffness of the components. The elastic behaviour of each component is represented by an extensional spring. The spring components are combined into a spring model.

Figure 11 : Spring model for beam-to-column bolted joint

The program calculates 3 stiff nesses :

Sj,ini the initial rotational stiffness Sj the rotational stiffness, related to the actual moment Mj,Sd Sj,MRd the rotational stiffness, related to Mj,Rd (without the influence of

the normal force) The moment-rotation diagram is based on the values of Sj,ini and Sj,MRd.

Steel Connections

20

Sj,MRd

Sj,ini

M

fi

MRd

0.66 MRd

Figure 20 :Simplified Moment-rotation characteristic

The classification on stiffness

The joint is classified as rigid, pinned or semi-rigid according to its stiffness by using the initial rotational stiffness Sj,ini and comparing this with classification boundaries given in EN 1993-1-8 or EC3 – Revised Annex J. If Sj,ini >= Sj,rigid, the joint is rigid. If Sj,ini <= Sj,pinned, the joint is classified as pinned. If Sj,ini<Sj,rigid and Sj,ini>Sj,pinned, the joint is classified as semi-rigid. For braced frames :

b

b

b

b

L

EI5.0pinned,Sj

L

EI8rigid,Sj

=

=

For unbraced frames :

b

b

b

b

L

EI5.0pinned,Sj

L

EI25rigid,Sj

=

=

For column base joints, we use :

c

c

c

c

L

EI5.0pinned,Sj

L

EI15rigid,Sj

=

=

with Ib the second moment of area of the beam

Lb the span of the beam Ic the second moment of area of the

column Lc the storey height of the column

21

E the Young modulus

Figure 21 : Stiffness classification boundaries

Figure 22 : Beam length for stiffness classification

The required stiffness

The actual stiffness of the joints is compared with the required stiffness, based on the approximate joint stiffness used in the analysis model. A lower boundary and an upper boundary define the required stiffness.

Figure 23 : Check of stiffness requirement

When a linear spring is used in the analysis model, we check the following :

Steel Connections

22

When Sj,ini >= Sj,low and Sj,ini<=Sj,upper, the actual joint stiffness is conform with the applied Sj,app in the analysis model. The value of Sj,app is taken as the linear spring value introduced for <fi y> (in the hinge dialog), multiplied by the stiffness modification coefficient η.

Type of joint η

bolted beam-to-column 2

welded beam-to-column 2

welded plate-to-plate 3

column base 3

When a non-linear function is used during the analy sis model, we check the following :

When Sj >= Sj,low and Sj<=Sj,upper, the actual joint stiffness is conform with the applied Sj,app in the analysis model. The value of Sj,app is taken as the analysis stiffness defined by the non-linear function.

Transferring the joint stiffness to the analysis m odel

When requested, the actual stiffness of the joint can be transferred to the analysis model. The linear spring value for <fi y> (in the hinge dialog) is taken as Sj,ini divided by the stiffness modification coefficient η.

Figure 24 : Linear stiffness

For asymmetric joint s which are loaded in both directions (i.e. tension on top and tension in bottom), the linear spring value for <fi y> (in the hinge dialog) is taken as the smallest Sj,ini (from both directions) divided by the stiffness modification coefficient η. At the same time, a non-linear function is generated, representing the moment-rotation diagram.

23

Figure 25 : Non-linear function

Ductility classes The following classification is valid for joints : Class 1 joint : Mj,Rd is reached by full plastic redistribution of the internal forces within the joints and a sufficiently good rotation capacity is available to allow a plastic frame analysis and design. Class 2 joint : Mj,Rd is reached by full plastic redistribution of the internal forces within the joints but the rotational capacity is limited. An elastic frame analysis possibly combined with a plastic verification of the joints has to be performed. A plastic frame analysis is also allowed as long as it does not result in a too high required rotation capacity of the joints where the plastic hinges are likely to occur. Class 3 joint : brittle failure (or instability) limits the moment resistance and does not allow a full redistribution of the internal forces in the joints. It is compulsory to perform an elastic verification of the joints unless it is shown that no hinge occurs in the joint locations.

Ductility classification for bolted joints

If the failure mode of the joint is the situated in the shear zone of the column web, the joint is classified as a ductile, i.e. a class 1 joint . If the failure mode is not in the shear zone, the classification is based on the following :

Classification by ductility Class

df

f36.0t

y

ub≤ Ductile

1

df

f53.0td

f

f36.0

y

ub

y

ub ≤<

Intermediary

2

df

f53.0t

y

ub> Non-ductile

3

Steel Connections

24

with t the thickness of either the column

flange or the endplate d the nominal diameter of the bolts fub the ultimate tensile strength of the

bolt fy the yield strength of the proper basic

component

Figure 26 : Ductility classification for bolted joint

Ductility classification for welded joints

If the failure mode of the joint is the situated in the shear zone of the column web, the joint is classified as a ductile, i.e. a class 1 joint . If the failure mode is not in the shear zone, the joint is classified as intermediary for ductility, i.e. a class 2 joint .

Examples

Calculation of bolted connection

Example

CON_004.esa – Node N1

- See text ‘Design example of a joint with extended end

Figure 27 : Example CON_004.ESA

Calculation of bolted connection

See text ‘Design example of a joint with extended end plate’

: Example CON_004.ESA – NodeN1

25

Steel Connections

26

Calculation of welded connection

Example

CON_005.esa – Node N3 Calculation V wp,Rd : Column web panel in shear

0M

vcyRd,wp

3

'Af9.0V

γ=

When a web doubler is used :

13

2350.9RdVwp,

101724113'A

²mm4113A

280213140A

t(bt2AA

tbA'A

vc

vc

vc

wfvc

ssvcvc

⋅⋅=

⋅+==

⋅−=+−=

+=

Calculation F c,wc,Rd : Column web in compression

.1

1525279.0F

'A

tb3.11

1

9222.17b

5a22tb

105.1t5.1t

ftbF

Rd,wc,c

vc

wceff

1

1

eff

fbeff

wwc

0M

ywceffRd,wc,c

⋅⋅=

+

=ρ

ρ=ρ⋅+=

++=

⋅==γ

ρ=

Calculation F c,fb,Rd : Beam flange in compression

2.17550

595F

1.1

655MM

th

MF

Rd,fb,c

0M

Rd,plRd,c

fbb

Rd,cRd,fb,c

=−

=

=γ

=

−=

Calculation F t,fc,Rd : Column flange in bending

2425.10(F

r2t(F

Rd,fc,c

cwcRd,fc,c

⋅+=

++=

Calculation F t,wc,Rd : Column web in tensio

Calculation of welded connection

Column web panel in shear

When a web doubler is used :

kN6571.1

5919235

²mm59195.10

18)2425.10(18280

t)r2 fw

=⋅=

⋅++⋅+

: Column web in compression

( )

kN6741.

23575.15

79.0

mm252)2418(5

rt5

mm75.155.10

2

wc

fc

=⋅

=

=++

+

=

: Beam flange in compression

kN1116

kNm5951

655

=

=

: Column flange in bending

kN6771.1

23520.17)181724

ft)kt7

0M

ywcfc

=⋅⋅⋅+

γ

: Column web in tensio n

27

( )

kN6441.1

2357.1425281.0F

81.0

'A

tb3.11

1

mm252)2418(59222.17b

rt5a22tb

mm7.145.104.1t4.1t

ftbF

Rd,wc,t

2

vc

wceff

1

1

eff

fcfbeff

wwc

0M

ywceffRd,wc,t

=⋅⋅⋅=

=

+

=ρ

ρ=ρ=++⋅+=

+++=

=⋅==γ

ρ=

Calculation MRd : Design moment resistance 644 kN x 0.532 m = 343 kNm Calculation af The weld size af is designed according to the resistance of the joint. The design force in the beam flange can be estimated as:

kN644532.0

343F

h

MF

Rd

RdRd

==

=

The design resistance of the weld Fw shall be greater than the flange force FRd, multiplied by a factor γ. The value of the factor γ is :

γ = 1.7 for sway frames γ = 1.4 for non sway frames

However, in no case shall the weld design resistance be required to exceed the design plastic resistance of the beam flange Nt.Rd :

kN7711.1

2352.17210N

ftbN

Rd,t

M

ybfbfRd,t

0

=⋅⋅=

γ⋅⋅

=

Fw = min ( Nt.Rd, γ FRd) = min (771, 1.4 x 645)= 771 kN The weld size design for af, using Annex M of EC3

mm23.72210360

8.025.1771000a

2bf

Fa

f

fu

WMwwf

=⋅⋅

⋅⋅≥

⋅⋅β⋅γ⋅

≥

We take af=9 mm. Calculation of a w

Steel Connections

28

Figure 12 : Weld size calculation

The section is sollicitated by the moment M, the normal force N and the shear force D. The moment M is defined by the critical design moment resistance of the connection. The normal force N is taken as the maximum internal normal force on the node, the shear force D is taken as the maximum internal shear force on the node. M = 343 kNm N = 148 kN D = 84 kN To determine the weld size a2 in a connection, we use a iterative process with a2 as parameter until the Von Mises rules is respected (Annex M/EC3).

Figure 13 : Weld size calculation

29

Figure 14 : Example CON_005.ESA – Node N3

Steel Connections

30

Calculation of connections in 3D Frame

Example

CON_008.esa (WSS_002d.esa ��

- copy of connections

- expert system

- wizard for monodrawings

- multiple check of connections


Calculation of connections in 3D Frame

�� CON_008.esa)

wizard for monodrawings

multiple check of connections

: Example CON_008.ESA - Multiple connection check

31

Special features

Use of haunches

lc

ab

tc

hc

alfa

bc

b

tw

tf

h

r

Figure 16 : Haunches

The compression force in the haunch should be transferred by the haunch into the beam. The formula used for the buckling of the column web can also be applied to the check failure of the beam web due to the vertical component of the force transferred by the haunch. This design moment resistance Mj,Rd is compared with the moment Mc at the position where haunch and beam are meeting. For more info about this topic, we refer to Ref.[30].

Steel Connections

32

Example


Figure 17 : Additional check at haunches


: Additional check at haunches

: Example CON_006.ESA – Node N7

Column in minor axis configuration

In beam-to-column minor-axis jointscausing bending about the minorcolumn web in bending and punching, the following failure mechanisms are considered :

- Local mechanism : the yield pattern is localised in the compression zone or in the tension zone

- Global mechanism : the yield line pattern involves both compression and tension zone. For more info about this topic, we refer to Ref.[30].

Figure 19 : Local and global mechanism

Example



Column in minor axis configuration

axis joints, the beam is directly connected to the web of an Icausing bending about the minor-axis of the column section. In order to determine the strength of a column web in bending and punching, the following failure mechanisms are considered :

cal mechanism : the yield pattern is localised in the compression zone or in the tension zone

Global mechanism : the yield line pattern involves both compression and tension zone.

For more info about this topic, we refer to Ref.[30].

: Local and global mechanism

: Example CON_007.ESA

33

, the beam is directly connected to the web of an I-section column, axis of the column section. In order to determine the strength of a

column web in bending and punching, the following failure mechanisms are considered :

cal mechanism : the yield pattern is localised in the compression zone or in the tension zone

Global mechanism : the yield line pattern involves both compression and tension zone.

Steel Connections

34

Base plate connections : shear iron, flange widener s

In a column base, 2 connection deformabilities need to be disti

- the deformability of the connection between the column and the concrete foundation

- the deformability of the connection between the concrete foundation and the soil. In the Frame Connect base plate design, the column

Figure 21 : Base plate connection

For more info about base plate design (shear irons, etc…), we refer to Ref.[30].

Example


Base plate connections : shear iron, flange widener s

In a column base, 2 connection deformabilities need to be distinguished :

the deformability of the connection between the column and the concrete foundation

the deformability of the connection between the concrete foundation and the soil.

In the Frame Connect base plate design, the column-to-concrete “connection’ is

: Base plate connection


the deformability of the connection between the column and the concrete foundation

the deformability of the connection between the concrete foundation and the soil.

concrete “connection’ is considered.


35

Figure 22 : Example CON_005.ESA –Node N9

The use of 4 bolts / row

Figure 23 : Four bolts/row

Steel Connections

36

When 4 bolts/row are used, additional capacity Fcolumn flange and/or the endplate. F

- the capacity of the inner two bolts is equal to the bolt tension resistance (failure mode 3) or is defined by a circular pattern

- the bolt row / group is stiffened- the bolt group contains only 1 bolt row

For more info about this topic, we refe

Example


Figure 24 : Additonal capacity for 4 bolts/row

When 4 bolts/row are used, additional capacity Fadd is added to the bolt row/group capacity of the column flange and/or the endplate. Fadd is defined for the following conditions :

the capacity of the inner two bolts is equal to the bolt tension resistance (failure mode 3) or is defined by a circular pattern the bolt row / group is stiffened the bolt group contains only 1 bolt row


: Additonal capacity for 4 bolts/row

is added to the bolt row/group capacity of the conditions :

the capacity of the inner two bolts is equal to the bolt tension resistance (failure mode 3) or is

37

Figure 25 : Example CON_005.ESA - Node N8

Steel Connections

38

RHS beam

For more info about this topic, we refer to Ref.[30]

Example




: Example CON_005.ESA - Node N7

Frame Connect : pinned joint

Four types of joints are supported :

Type 1 welded plate in beam, welded to column

Type 2 bolted plate in beam, we

Type 3 bolted angle in beam and column

Type 4 short endplate welded to beam, bolted in column

For each type, the design shear resistance Vthe design compression/tension resistance The design shear resistance is calculated for the following failure modes :

- design shear resistance for the connection element- design shear resistance of the beam- design block shear resistance - design shear resistance due to the bolt- design shear resistance due to the bolt distribution in the column

The design compression/tension resistance is calculated for the following failure modes :

- design compression/tension resistance for the connection element- design compression/tension resistance of the beam- design tension resistance due to the bolt distribution in the column

In Ref.[30], more info on the used formulas is given.

Examples

Welded fin plate connection

Example

CON_009.esa – Node N7 Calculat ion Design Shear Resistance VRd for Connection Elem entTransversal section of the plate :

Normal stress : N A=σ

Flexion module : plW =

Design Shear Resistance :

W

a2

Vpl

N

Rd

+⋅σ⋅

−

=

Calculation Design Shear Resistance VRd for BeamShear Area : v AA −=

Frame Connect : pinned joint

Four types of joints are supported :

welded plate in beam, welded to column

bolted plate in beam, welded to column

bolted angle in beam and column

short endplate welded to beam, bolted in column

For each type, the design shear resistance VRd (taking into account the present normal force N ) and the design compression/tension resistance NRd are calculated. The design shear resistance is calculated for the following failure modes :

design shear resistance for the connection element design shear resistance of the beam design block shear resistance design shear resistance due to the bolt distribution in the beam web design shear resistance due to the bolt distribution in the column


design compression/tension resistance for the connection element sign compression/tension resistance of the beam

design tension resistance due to the bolt distribution in the column

In Ref.[30], more info on the used formulas is given.

Welded fin plate connection

ion Design Shear Resistance VRd for Connection Elem entTransversal section of the plate : 2

plplpl m003912.0th2A =⋅⋅= (2 plates)

2pl m

N667.67099003912.0

4939.262

A

N ==

32

pl m000106276.06

ht2

pl

=⋅

⋅=

Design Shear Resistance : a= 0.082 m is the centre

240087

A

3

W

a2

f

N

a4

W

a2

2pl

2

2

2M

2y2

N2

22

pl

N

pl

0 =

+⋅

γ−σ⋅

⋅−

⋅σ⋅

Calculation Design Shear Resistance VRd for Beam ( ) 2

fwf m00191276.0tr2ttb2 =⋅⋅++⋅⋅−

39

(taking into account the present normal force N ) and


ion Design Shear Resistance VRd for Connection Elem ent (2 plates)

kN240N66.240087 =

Steel Connections

40

Shear Resistance : kN236N57.2359253

fAVRd

0M

yv ==γ⋅

⋅=

Calculation Design Tension Resistance NRd for Conne ction Element Area of the element : 2

plplpl m003912.0th2A =⋅⋅=

Tension Resistance : kN835N45.835745fA

N0M

yplRd ==

γ⋅

=

Calculation Design Tension Resistance NRd for Beam Area of the Beam : 2m003910.0A =

Tension Resistance : kN835N18.835318fA

N0M

yRd ==

γ⋅

=

Weld size Calculation for Plate, Beam and Column To determine the weld size a for the plate on the beam and on the column, we must use a iterative process with a as parameter until the Von Mises rules is respected (Annex M/EC3) :

( )ww

211M

u1

Mw

u222 f and

f3

γ≤σ

γ⋅β≤τ+τ⋅+σ

We’ll only check the weld size for the final value of a. For the weld between plate and beam we find a=4mm and for weld between plate and column, the weld size is a=10mm. Weld size Plate/Beam We define the play as the effective distance between the end of the beam and the flange of the column. In this case, the play is 10mm. By using EC3 and the Chapter 11 of the manual, we compute the following parameters : Weld size : a=0.004 Weld Length : m139.012.02163.0t2hl plpl1 =⋅−=⋅−=

m13.0t2Playbl plpl2 =⋅−−=

m154.001.0164.0Playll pl =−=−=

By EC3 : fuw=360000000N/m2 and βw=0.8 The parameters are :

( )10.104

la414.1la577.0

lla577.0la707.0g

21

11 =⋅⋅+⋅⋅

⋅⋅⋅+⋅⋅=

30377.0la414.1la577.0

la577.0

21

1 =⋅⋅+⋅⋅

⋅⋅=δ

15603.0hla577.0la117.0

la117.0

pl221

21 =

⋅⋅⋅+⋅⋅

⋅⋅=µ

3987.0la14.1la707.0

la707.0

21

1 =⋅⋅+⋅⋅

⋅⋅=Γ

g10L +=

Shear force on one plate : N789.1179622

VD Rd == (for one plate)

Normal force on one plate : N24.1312

NN ==

Moment on the plate : Nm781.13459LDM =⋅=

Weld Check 1: 21

211 mN74.115363040

la2

N

la2

M6

1

==⋅⋅

⋅Γ+⋅⋅

⋅µ⋅=σ=τ

41

21

2 mN72.64449431

la

D =⋅⋅δ=τ

Unity Check : ( )

14.0f

and 1316.0f

3

ww

211

M

u

1

Mw

u

222

≤=

γ

σ≤=

γ⋅β

τ+τ⋅+σ

Weld Check 2 : ( )

22

11 mN8731.55840293

la22

D1 =⋅⋅⋅

⋅δ−=τ=σ

( ) ( )2

222 m

N161.134095932la2

N1

lah

M1 =

⋅⋅⋅Γ−+

⋅⋅⋅µ−=τ

Unity Check : ( )

1193.0f

and 1715.0f

3

ww

211

M

u

1

Mw

u

222

≤=

γ

σ≤=

γ⋅β

τ+τ⋅+σ

Weld size Plate/Column Weld size : a=0.01 m Normal Force : N=262.4939N Moment : Nm89674.19345082.057.235925LDM =⋅=⋅= Stress Calculation :

22pl

11 mN96.154518316

6

ha22

LD

la22

N

W

M

la22

N =

⋅⋅⋅

⋅+⋅⋅⋅

=+⋅⋅⋅

=τ−=σ

22 mN7485.72369806

la2

D =⋅⋅

=τ

Unity Check : ( )

192.0f

3

w

211

Mw

u

222

≤=

γ⋅β

τ+τ⋅+σ

153.0f

wM

u

1 ≤=

γ

σ

Steel Connections

42

Figure 27 : Example CON_009.ESA - Node N2

Bolted fin plate connection

Example

CON_010.esa – Node N7 Calculation Design Shear Resistance VRd for Connect ion Element Transversal section of the plate :

Normal Stress : N =σ

Flexion Module : W =

Bolt Centre : a=0.0995mDesign Shear Resistance :

W

a2

V

N

Rd

+⋅σ⋅

−

=

Calculation Design Shear Resistance VRd for BeamShear Area : v AA −=

Net Area : AA vnet =

For the calculation of VRd in the beam,

Shear Resistance: VRd

Calculation Design Tension Resistance NRd for Conne ction ElementArea : 004512.0ht2A =⋅⋅=Net Area : net 2AA −=Tension Resistance :

⋅

γ⋅

=0M

yRd

9.0,

fAminN

Calculation Design Tension Resistance NRd for Beam

Area : 003910.0A =Net Area : net AA −=

Tension Resistance :

( 1085930,18.835318min=Calculation Design Shear Resistance VRd for Bolt in BeamThe calculation of the shear resistance for bolt in beam is based on the following equation to be solve

I

ca

n

1V

2p

22

22

Rd

+⋅+⋅

Where : 0.0995ma =

4

1i

2ip 66.95rI ∑ ∑==

=

( Rd,vF2minQ ⋅=

Calculation Design Shear Resistance VRd for Connect ion Element Transversal section of the plate : m004512.0012.0188.02th2A =⋅⋅=⋅⋅=

2mN8395.58176

004512.0

4939.262

A

N ==

32

m000141376.06

ht2 =⋅⋅

Bolt Centre : a=0.0995m Design Shear Resistance :

266422

A

3

W

a2

f

N

a4

W

a2

22

2

2M

2y2

N2

22

N

0 =

+⋅

γ−σ⋅

⋅−

⋅σ⋅+

Calculation Design Shear Resistance VRd for Beam ( ) 2

fwf m00191276.0tr2ttb2 =⋅⋅++⋅⋅−

m56.001689.0dt2 0w =⋅⋅−

For the calculation of VRd in the beam, we use Av because vu

ynet A

f

fA ⋅≥

kN236N57.2359253

fAVRd

0M

yv ==γ⋅

⋅=

Calculation Design Tension Resistance NRd for Conne ction Element2m004512

20 m003648.0d2t2 =⋅⋅⋅

γ

⋅⋅

1

net

M

ufA ( ) 96392781.1074501,27.963927min ==

Calculation Design Tension Resistance NRd for Beam 2m003910

20 m0036868.0dt2 =⋅⋅−

γ

⋅⋅

γ⋅

=1

net

0 M

u

M

yRd

fA9.0,

fAminN

) kN836N18.83531818.1085930 == Calculation Design Shear Resistance VRd for Bolt in Beam The calculation of the shear resistance for bolt in beam is based on the following equation to

0Qn

N

nI

dNa2V

I

da 22

2

pRd2

p

22

=−+

⋅⋅⋅⋅⋅+

⋅+

0.0995m 0.094mb = 0.0655mc = 0.07md = 2

2 m036761.066 =

( ))beam,Rd,bplate,Rd,bRd F;Fmin, =31740.8256N for two plates, where

43

Calculation Design Shear Resistance VRd for Connect ion Element 2m (2 plates)

kN266N015.266422 =

2v m00124860.0=

Calculation Design Tension Resistance NRd for Conne ction Element

kN963N27.963927 =

The calculation of the shear resistance for bolt in beam is based on the following equation to

for two plates, where

Steel Connections

44

• kN1.30N30144Af6.0

FMb

subV dR

==γ

⋅⋅=

• kN7.31N8256.31740tdf5.2

FMb

upBeam,Rd,b ==

γ⋅⋅⋅α⋅

=

444.01;f

f;

4

1

d3

p;

d3

eminwith

u

ub

0

1

0

1p =

−=α

• N712.122867tdf5.2

FMb

plupplate,Rd,b =

γ⋅⋅⋅α⋅

=

444.01;f

f;

4

1

d3

p;

d3

eminwith

u

ub

0

1

0

1p =

−=α

By solving the second-degree equation, we find kN9.67N89.67907VRd == Calculation Design Block Shear Resistance The design value of the effective resistance to block shear is determined by the following expression :

eff,veffv,

M

eff,vyRd,eff LtA with

3

AfV

0

⋅=γ⋅

⋅=

We determined the effective shear area Av,eff as follows : m049.0a1 = m155.0a2 = m051.0a3 =

m14.0aahL 21v =−−=

( )

( ) m24.02849.0;24.0min

f

fdnaaL;aaLminL

y

u031v31v3

==

⋅⋅−++++=

( ) m049.0d5;aminL 011 =⋅=

( )

bolt rows 2for 2.5k with

m1685.0f

fdkaL

y

u022

=

=⋅⋅−=

( ) m24.0L;LLLminL 321veff,v =++= 2

eff,v m001488.0A =

kN185N40.1835343

AfV

0M

eff,vyRd,eff ==

γ⋅⋅

=


Bolted cleat connection

Example

CON_011.esa – Node N2 To determine the design shear resistance for bolts in the flange of the column, we use a iterative process with h

We’ll only consider the check for the final value of hm008.0r =


To determine the design shear resistance for bolts in the flange of the column, we cess with hD as parameter until we reach a equilibrium :

γγ=σ

00 M

cor,y

M

beam,yD

f,

fmin

We’ll only consider the check for the final value of hD. We have the following data :m03.0a = m006.0s =

45

To determine the design shear resistance for bolts in the flange of the column, we as parameter until we reach a equilibrium :

. We have the following data :

Steel Connections

46

m0128436.0s577.1r4227.0b =⋅+⋅= m0028436.0Playbbs =−=

m011.0hD = 22ipD m029194.0rID

==∑

We compute : 0951.1anI

aK

2pD

=⋅−

=

We define xj=0.03m and zj=0.165m respectively as the maximum horizontal distance between bolts and d and the maximum vertical distance between the bolts and d. Its corresponds to the further bolts how is submitted to the higher force.

( ) 5.0xaKn

1A j =−⋅+= 18069.0zKB j =⋅=

N16224Fn4.1

N1F,FminQ

Rd,tRd,vRd,b =

⋅⋅−⋅= where:

• N16224Af6.0

FMb

subcor,V dR

=γ

⋅⋅= and N24336

Af9.0F

Mb

subRd,t =

γ⋅⋅

=

• N2.22187tdf5.2

FMb

corupcor,Rd,b =

γ⋅⋅⋅α⋅

=

428.01;f

f;

4

1

d3

p;

d3

eminwith

u

ub

0

1

0

1p =

−=α

• kN8.77tdf5.2

FMb

flangeupflange,Rd,b =

γ⋅⋅⋅α⋅

=

0.11;f

f;

4

1

d3

p;

d3

eminwith

u

ub

0

1

0

1p =

−=α

With this values, we have :

N94.61032BA

Q2V

22ColFlange,Rd =

+

⋅= ∑ ∑ =⋅⋅= N64.5948zKVQ jRdh

2DD

hD m

N89.209194259bh

Q=

⋅=σ ∑

View A-

47

Figure 29 : Example CON_011.ESA -Node N2

Steel Connections

48


Example





49

References and literature

[1] Eurocode 3 : Part 1.1.

Revised annex J : Joints in building frames

ENV 1993-1-1/pr A2

[2] Eurocode 3

Design of steel structures

Part 1 - 1 : General rules and rules for buildings

ENV 1993-1-1:1992, 1992

[3] P. Zoetemeijer

Bolted beam to column knee connections with haunched beams

Tests and computations

Report 6-81-23

Delft University of Technology, Stevin Laboratory, December 1981

[4] P. Zoetemeijer

Een rekenmethode voor het ontwerpen van geboute hoekverbindingen met een kolomschot in de trekzone van de verbinding en een niet boven de ligger uitstekende kopplaat.

Rapport 6-81-4

Staalcentrum Nederland, Staalbouwkundig Genootschap, Juni 1982

[5] Eurocode 3 : Part 1.1.

Annex L: Design of column bases

ENV 1993-1-1:1992

[6] Eurocode 2

Design of concrete structures

Part 1: General rules and rules for buildings

ENV 1992-1-1:1991

[7] Y. Lescouarc’h

Les pieds de poteaux articulés en acier

CTICM, 1982

[8] Manual of Steel Construction

Load & Resistance Factor Design

Volume II : Connections

Part 8 : Bolts, Welds, and Connected Elements

AISC 1995

[9] U. Portmann

Symbole und Sinnbilder in Bauzeichnungen nach Normen, Richtlinien und Regeln

Wiesbaden, Berlin : Bauverlag, 1979

[10] Sprint Contract RA351

Steel Moment Connections according to Eurocode 3

Simple Design aids for rigid and semi-rigid joints

1992-1996

[11] DIN18800 Teil 1

Stahlbauten : Bemessung und Konstruktion

November 1990

Steel Connections

50

[12] J. Rudnitzky

Typisierte Verbindungen im Stahlhochbau. 2. Auflage

Stahlbau-Verlags-GmbH-Köln 1979

[13] H. Buchenau A.Tiele

Stahlhochbau 1

B.G. Teubner

Stuttgart 1981

[14] F. Mortelmans

Berekening van konstructies Deel 2

Staal Acco

Leuven, 1980

[15] Frame Design Including Joint Behaviour

Volume 1

ECSC Contracts n° 7210-SA/212 and 7210-SA/320

January 1997

[16] F. Wald, A.M. Gresnigt, K. Weynand, J.P. Jaspart

Application of the component method to column bases

Proceedings of the COST C1 Conference

Liège, Sept.17-19, 1998

[17] F.C.T. Gomes, U. Kuhlmann, G. De Matteis, A. Mandara

Recent developments on classification of joints


Liège, Sept.17-19, 1998

[18] M. Steenhuis, N. Gresnigt, K. Weynand

Pre-design of semi-rigid joints in steel frames

COST C1 Workshop

Prague, October 1994

[19] M. Steenhuis, N. Gresnigt, K. Weynand

Flexibele verbindingen in raamwerken

Bouwen met Staal 126

September/Oktober 1995

[20] O. Oberegge, H.-P. Hockelmann, L. Dorsch

Bemessungshilfen für profilorientiertes Konstruieren

3. Auflage 1997

Stahlbau-Verlagsgesellschaft mbH Köln

[21] M. Steenhuis, JP Jaspart, F. Gomes, T. Leino

Application of the component method to steel joints


Liège, Sept.17-19, 1998

[22] J.A. Packer, J. Wardenier, Y. Kurobane, D. Dutta, N. Yeomans

Design Guide for rectangular hollow sections (RHS) joints under predominantly static loading

CIDECT

Köln, 1992, Verlag TUV Rheinland

51

[23] Eurocode 3

Part 1.1. Revised Annex J

Joints in building frames, edited

Approved draft : january 1997

[24] Rekenregels voor het ontwerpen van kolomvoetplaten en experimentele verificatie

TNO report N° BI-81-51

[25] Typisierte Anschlüsse im Stahlhochbau

Band 1

DSTV - 2000

[26] Typisierte Anschlüsse im Stahlhochbau

Band 2

DSTV - 2000

[27] Joints in Steel Construction

Moment Connections

BCSA - 1997

[28] Joints in Simple Construction

Volume 1 : Design methods

BCSA - 1994

[29] BS 5950

Structural use of steelwork in building

Part 1 : Code of practice for design - Rolled and welded sections

2000

[30] Scia Engineer Connect Frame & Grid

Theoretical Background

Release : 8.0

Revision : 05/2008

[Eng]Advanced Training Steel Connections 2008.0.1

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