steel connections theory enu

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Theory

Steel Connections


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Introduction

Welcome to the Steel ConnectionsTheoretical Background.

This document provides background information on the connection checks according todifferent national and international regulations.

Version info

Documentation Title Steel ConnectionsTheoretical Background

Release 2011.0

Revision 09/2010


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Scia Engineer Connections Frame & Grid Theoretical Background

Scia Group NV 3

Table of Contents

Introduction .............................................................................................................................................. i

Version info ............................................................................................................ iTable of Contents .......................................................................................................... 3

Bolted and welded frame connections ................................................................................................. 7

Introduction ................................................................................................................... 7List of abbreviations ..................................................................................................... 8

The influence of the normal force ............................................................................ 15

Default Interaction Check......................................................................................... 15

For bolted connections ....................................................................................... 15

For welded connections ...................................................................................... 16

Interaction Check according to EN 1993-1-8 ........................................................... 17

The effective width beff .............................................................................................. 17The calculation of weld sizes ..................................................................................... 18

Default ...................................................................................................................... 18

Calculation of af........................................................................................................ 18

Calculation of aw for welded connection ................................................................... 20

Calculation of aw for bolted connection .................................................................... 21The calculation of stiffener dimensions ................................................................... 22The transformation factor .......................................................................................... 23

Center of compression ............................................................................................... 23

Default ...................................................................................................................... 23

Center of compression according to EN 1993-1-8 .................................................. 23

The use of 4 bolts / row .............................................................................................. 24

The use of haunches .................................................................................................. 26

Weld sizes for haunches .......................................................................................... 26

Haunch with flange ............................................................................................. 26

Haunch without flange ....................................................................................... 27

Column web in transverse compression .................................................................. 28

Resistance for haunches ......................................................................................... 29

Compression resistance for haunch without flange ................................................. 30

The design moment resistance for haunches at beam ............................................ 30

Mj,Rd for haunches with flange ............................................................................. 30

Mj,Rd for haunches without flange ..................................................................... 31

The design shear resistance ...................................................................................... 32

The design shear resistance for normal bolts ......................................................... 32

The design shear resistance for preloaded bolts ..................................................... 32The welded plate-to-plate connection ....................................................................... 33The column base connection .................................................................................... 34

The design compression resistance ........................................................................ 34

The design moment resistance ................................................................................ 38

The design tension resistance ................................................................................. 40

The design shear resistance .................................................................................... 40

Default ................................................................................................................. 40

Friction resistance according to EN 1993-1-8 .................................................... 41


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Scia Group NV 4

The design shear resistance for shear iron. ............................................................ 41

The design shear resistance for I shaped shear iron. ........................................ 41

The design shear resistance for angle shaped shear iron. ................................ 43

The anchorage length .............................................................................................. 44

Calculation of tensile force in anchors Ft,boltaccording to internal forces. ............... 45

Design of the washer plate. ..................................................................................... 46

The influence of the normal force ............................................................................ 47

The use of RHS beam ................................................................................................. 48

The use of RHS beam in bolted beam-to-column connection ................................. 48

The use of RHS beam in column base connection ................................................. 48

The design compression resistance ................................................................... 48

The design tension resistance ............................................................................ 50

The design moment resistance ........................................................................... 52

The influence of the normal force ....................................................................... 54

The use of RHS beam in bolted plate-to-plate connection ...................................... 54Connections with column minor axis ....................................................................... 56

Introduction .............................................................................................................. 56

Strength of column web in bending and punching ................................................... 57

Generalities ......................................................................................................... 57

Definition and design of local and global failure mode ....................................... 57

Local failure mechanism ..................................................................................... 58

Global mechanism .............................................................................................. 60Rotational stiffness and ductility .............................................................................. 61

Stiffness coefficients ................................................................................................ 61

Calculation of stiffness ............................................................................................. 65Stiffness classification .............................................................................................. 66

Check of required stiffness ...................................................................................... 67

Transferring the connection stiffness to the analysis model .................................... 68

Ductility classes ....................................................................................................... 69

Ductility classification for bolted joints ..................................................................... 70

Ductility classification for welded joints .................................................................... 70

Theoretical background for frame pinned connections ................................................................... 71

Introduction ................................................................................................................. 71

List of abbreviations ................................................................................................... 72Calculation of VRd and NRd ...................................................................................... 75

Calculation VRd and NRd for connection type 1 ..................................................... 75

Calculation design shear resistance VRd for connection element ..................... 76

Calculation design shear resistance VRd for beam............................................ 76

Calculation design compression/tension resistance NRd for connection element............................................................................................................................ 77

Calculation design compression/tension resistance NRd for beam ................... 77

Calculation design compression resistance NRd for column web ...................... 77





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Scia Group NV 5

Calculation design shear resistance VRd for bolts in beam ............................... 81

Calculation design block shear resistance for beam element VRd .................... 83

Calculation design block shear resistance VRd in connection element (beam

side) .................................................................................................................... 84







Calculation design shear resistance VRd for bolts in beam ............................... 86

Calculation design block shear resistance for beam element VRd .................... 86

Calculation design block shear resistance VRd in connection element (beam

side) .................................................................................................................... 87

Calculation design block shear resistance VRd in connection element (columnside) .................................................................................................................... 87

Calculation design shear resistance VRd for bolts in column ............................ 87




Calculation design resistance NRd ..................................................................... 90


Calculation design local shear resistance VRd for beam ................................... 93

Calculation design shear resistance VRd for bolts in column ............................ 94Calculation design block shear resistance VRd in endplate ............................... 95

Calculation design compression/tension resistance NRd for beam web ........... 96


Calculation design tension resistance NRd ........................................................ 96Calculation of weld sizes ........................................................................................... 97

Theoretical background for GRID pinned connections .................................................................... 99

Introduction ................................................................................................................. 99

VRd : Design shear resistance at notch ................................................................. 100Notched elements : calculation design block shear resistance VRd .................. 102Long cleat connection VRd: design shear resistance for the connection element.................................................................................................................................... 104

Long cleat connection VRd: design shear resistance due to the bolt distributionin the column ............................................................................................................. 105

Connection analysis according to Different Codes ........................................................................ 106

Introduction ............................................................................................................... 106Column web panel in shear ..................................................................................... 107Column web in compression ................................................................................... 107Column web in tension ............................................................................................. 108Beam flange and web in compression .................................................................. 108

Beam web in tension ................................................................................................ 109Bolts in tension ......................................................................................................... 109Plastic moment capacity of T stub .......................................................................... 110Resistance to shear force / bolts in shear .............................................................. 110


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Scia Group NV 6

Bearing resistance for bolts/elements .................................................................... 111The design shear resistance for preloaded bolts .................................................. 113Column flange in bending ........................................................................................ 113

Calculation design shear resistance VRd for beam / Connection Element ........ 115Block shear resistance ............................................................................................. 116

Design compression/tension resistance NRd for connection element ............... 117Bolt interaction Shear/Tension ................................................................................ 118

Column web in compression ................................................................................... 119Weld size .................................................................................................................... 120List of abbreviations ................................................................................................. 121

Theoretical background for bolted diagonal connections ............................................................. 125

Introduction to the bolted diagonal connection .................................................... 125

Member resistance.................................................................................................... 125

Resistance of the gross section of diagonal .......................................................... 125

Resistance of the net section of diagonal .............................................................. 125

Angle diagonal with 1 bolt ................................................................................. 126

Angle diagonal with 2 bolts on 1 line ................................................................ 127

Angle diagonal with 3 bolts on 1 line ................................................................ 128

Angle diagonal with Double Leg connection ..................................................... 128

Other sections and configurations .................................................................... 129

Resistance of the gross section of gusset plate .................................................... 129

Resistance of the net section of gusset plate ........................................................ 130

Determination of Anet ............................................................................................ 130

Connection resistance ............................................................................................. 132

Shear resistance .................................................................................................... 132

Shear resistance for preloaded bolts ................................................................ 133

Bearing resistance ................................................................................................. 134

Checking the connection resistance ...................................................................... 134Weld size calculation for gusset plate .................................................................... 135

Calculation of weld length ...................................................................................... 135Basic Weld symbols ........................................................................................................................... 136

Weld symbols ............................................................................................................ 136Bolt symbols ........................................................................................................................................ 137

Bolt symbols .............................................................................................................. 137References ........................................................................................................................................... 138

List of references ...................................................................................................... 138


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Scia Group NV 7

Bolted and welded frame connections

Introduction

In this document additional information is given about the used theory.

For the beam-to-column moment-resisting joints, we refer to Ref. 1, [23] and [32].For the other code regulations, we refer to chapter Connection analysis according toDifferent Codes.

In the following parts, a list of the used abbreviations is given. In next parts, some moretheoretical background is given for particular items, or items which are not covered by Ref.

1, Ref. [23], [32].

The influence of the normal force

The effective width beff

The calculation of weld sizes

The calculation of stiffener dimensions

The transformation factor

Center of compression

The use of 4 bolts / row

The use of haunches

The design shear resistance

The welded plate-to-plate connection

The column base connection

The use of RHS beam

Connections with column minor axis

Rotational stiffness and ductility

For EN 1993-1-8 the calculation is done according to the following code regulationsRef.[32],[33]:

EN 1993-1-8:2005

Eurocode 3 : Design of steel structures

Part 1-8 : Design of Joints

Corrigendum

EN 1993-1-8:2005/AC:2009


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Scia Group NV 8

List of abbreviations

Transformation parameter

Stiffness ratio

stiffness ratio = Sj/Sj,ini

intermediate parameters for minor axis connection

intermediate parameters for minor axis bending



c Partial safety factor for resistance of concrete

fr Partial safety factor for friction

jJoint coefficient

M0 Partial safety factor for resistance of cross-section to overall yielding

M1 Partial safety factor for resistance to buckling

Mb Partial safety factor for resistance of bolts

Ms Partial safety factor for slip resistance

Mw Partial safety factor for welds

Mw Partial safety factor for resistance of welds

W Correlation factor

a Throat thickness of weld

a Factor for anchorage typeA Sectional area of the welds

a intermediate parameters for minor axis connection

a1 Weld size a1

a2 Weld size a2

a3 Weld size a3

Ad Area

Af Area of compressed beam flange

af Throat thickness of weld at beam flange (fillet weld)

ah Weld size of the stiffeneralfa Ratio for bolts stiffened column flange and endplate

alfa Angle between haunch and beam

alfa left Angle between endplate and left beam

alfa right Angle between endplate and right beam

alfa,ep Alfa value for endplate

alfa,fc Alfa value for column flange

As Tensile stress area of bolt

as Weld size for webdoubler


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Scia Group NV 9

As,prov Provided tensile stress area of the anchor

As,req Required tensile stress area of the anchor

Av Shear area for shear iron

Avc Shear area

aw Throat thickness of weld at beam web

aw Throat thickness of weld at beam web (fillet weld)

b Width of element

b b=b0+0.9dm

b0 Bolt pitch in x direction

beff Effective width

bf Beam flange width

bhf Width of haunch flangebhi Critical width for haunch flange

bm intermediate parameters for minor axis connection

bs Width of webdoubler

Bt,Rd Design tension resistance of a bolt

c Additional bearing width

c c=c0+0.9dm

c0 Bolt pitch in y direction between extreme bolt in tension zone

d1 Edge distance of circular plate

da Height of angle shaped shear irondc Clear depth of the column web

dm mean diameter of bolt head (nut)

do Hole diameter

e Diagonal diameter of bolt head

e Edge distance

E Modulus of elasticity

e1 Edge distance

e1,cf Edge distance for column flange

e1,ep Edge distance for endplate

Ec Modulus of elasticity for concrete

emin Minimum edge distance

F Design resistance

Fb,ep,Rd Bearing Resistance for endplate

Fb,fc,Rd Bearing Resistance for column flange

Fc,base,Rd Design compression resistance for concrete under the flange

Fc,ep,Rd Design resistance of endplate in compression

Fc,fb,Rd Design resistance of beam flange and web in compression


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Scia Group NV 10

Fc,h,Rd Design resistance of haunch flange in compression

Fc,ha,Rd,buck

ling

Design resistance of haunch web in buckling mode

Fc,ha,Rd,yielding

Design resistance of haunch web in yielding mode

Fc,wc,Rd Design resistance of column web in compression

fcd Design value of the concrete cylinder compressive strength

fck_c Characteristic cylinder compressive strength of the concrete

FCom,Rd Punching and bending (for tension or compression zone, for individualbolt row or bolt group)

FGlobal,Rd Global failure force (for tension and compression zone)

fj Bearing strength of the joint

Fp,Cd Design preloading force

FPunch,Rd,L1 Punching resistance loading case 1. (for tension or compression zone,for individual bolt row or bolt group)

FPunch,Rd,L2 Punching resistance loading case 2. (for tension or compression zone,for individual bolt row or bolt group)

FRd Design force in the beam flange

Fs,Rd Design slip resistance of preloaded high-strength bolt

Ft Effective design tension resistance of bolt row

Ft,anchor,max The maximum tensile force in the anchor

Ft,ep,Rd Design tension resistance of endplate in bending

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

Ft,Sd Applied tensile force

Ft,wb,Rd Design resistance of beam web in tension

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

fu Tensile strength

fu Ultimate tensile strength of the weaker part

Fv,Rd Shear resistance per shear plane

Fw Design resistance of the weld

fy Yield strength

fy yield strengh of the column web

fyb Yield strenght of the beam

h Height of element

h Distance from bolt row to centre of compression

h Lever arm of the connection

h head Height of bolt head

h nut Height of nut

h1 Effective height for haunch without flange


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Scia Group NV 11

hb Height of beam

hc Height of haunch

hd Effective height for haunch without flange

I Moment of inertia of the welds

Ib Moment of inertia for beam

k intermediate parameters for minor axis connection

k1 Stiffness coefficient for web panel in shear

k2 Stiffness coefficient for column web in compression

k3 Stiffness coefficient for column flange

k4 Stiffness coefficient for column web in tension

k5 Stiffness coefficient for endplate in tension

k7 Stiffness coefficient for bolt in tensionkc Stiffness coefficient for concrete block in compression

keff Effective stiffness coefficient for bolt row

keq Equivalent stiffness coefficient

kfc Reduction factor

kfr Friction factor

kI stiffness factors

kj Concentration factor

krot rotational stiffness factor

ks Value for slip resistancekwc Reduction factor

l Depth of circular plate in concrete

L intermediate parameters for minor axis connection

l,anchor Anchor length

l1 Buckling Length for haunch without flange

l1 Length for weld size a1



La Length of angle shaped shear iron

lambda_rel

Web slenderness ratio

Lb Beam length

lb Basic anchorage length

lb,min Minimum anchorage length

lb,net Required anchorage length

lc Length of haunch

leff Effective length


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Scia Group NV 12

leff,1 Effective length for mode 1

leff,2 Effective length for mode 2

leff,cp,g Effective length for circular patterns and inner bolt-row as part of group

leff,cp,g1 Effective length for circular patterns and end bolt-row as end of group

leff,cp,g2 Effective length for circular patterns and end bolt-row as start of group

leff,cp,i Effective length for circular patterns and bolt-row consideredindividually

leff,nc,g Effective length for non-circular patterns and inner bolt-row as part ofgroup

leff,nc,g1 Effective length for non-circular patterns and end bolt-row as end ofgroup

leff,nc,g2 Effective length for non-circular patterns and end bolt-row as start of

groupleff,nc,i Effective length for non-circular patterns and bolt-row considered

individually

Lq Length of I shaped shear iron

ls Length of webdoubler

M Actual moment

m Distance bolt to beam/column web

m1 Distance bolt to beam/column web

m2 Distance bolt to beam flange/stiffener

Mc,Rd Design moment resistance of the beam cross-section

Me Design elastic moment resistance

Mj,Rd Design moment resistance

MRd Design moment resistance

MRd Design moment resistance of the connection

MSd Design value for moment

My Actual moment around y axis

N Actual normal force

n minimum of 1.25m and emin

n Number of friction interfaces

Npl,Rd Design plastic resistance of cross section

NRd,c Design compression resistance for concrete

NRd,t Design tension resistance

NSd Design value for normal force

p Bolt pitch

p1 Upper part of bolt pitch

p1 Spacing

p2 Lower part of bolt pitch


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Scia Group NV 13

pos Position of stiffener

r Root radius

r Radius of root fillet

ro Reduction factor

ro1 Reduction factor 1

ro2 Reduction factor 2

S Width across flats, diameter of bolt head

Sj Rotational stiffness

Sj,app Approximate joint stiffness

Sj,ini Rotational stiffness when the moment is zero, then initial rotationalstiffness

Sj,low lower boundary stiffness

Sj,MRd Rotational stiffness when the moment is equal to the design momentresistance

Sj,rigid Classification boundary for rigid classification

Sj,upper upper boundary stiffness

Sl,pinned Classification boundary for pinned classification

t Thickness of element

tf Flange thickness of cross section

tfb Thickness of the beam flange

th Thickness of the stiffener

ts Thickness webdoubler

tw Web thickness of cross section

twb Thickness of the beam web

twc Effective thickness of the web

twc column web thickness

u intermediate parameters for minor axis bending

VRd Design shear resistance

VRd,f Friction resistance between steel base plate and concrete

VRd,i Design shear resistance for shear iron

VSd Design value for shear force

Vwp,Rd Design shear resistance of column web

Vz Actual shear force in z direction

weld ab Weld size between beam and haunch

weld ac Weld size between column/endplate and haunch

weld awc Weld size for haunch without flange

x intermediate parameters for minor axis connection

x0 intermediate parameters for minor axis connection

y Position of bolt row in relation to endplate bottom


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Scia Group NV 14

z Lever arm

p

p1

p2

e1

e

emin

m

0.8 a 1.41

e

emin

m

0.8 r


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Scia Group NV 15


Default Interaction CheckWhen the axial force NSdin 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 connections

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 andtension point in the connected member

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

tot

Sd

Rd,fb,cRd,wc,cRd,wpc


Fc,wc,Rd Design compression resistance for columnweb

Fc,fb,Rd Design compression resistance for beam weband flange


Ftot The sum of the tensile forces in the bolt rowsat Mj,Rd


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Scia Group NV 16

For welded connections

)F,F,F,F,Vmin(FRdwc,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

tot

Sd

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

tot

Sd

Rdfb,c,Rdwc,c,Rdwp,c


Fc,wc,Rd Design compression resistance for column web

Fc,fb,Rd Design compression resistance for beam web andflange


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

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


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Scia Group NV 17

Interaction Check according to EN 1993-1-8

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

the following unity check is added :

0.1N

N

M

M

Rd,j

Ed,j

Rd,j

Ed,j

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,Edis the actual normal force in the connectionMj,Edis the actual bending moment in connection

The value for Nj,Rdis calculated as follows :

If Nj,Edis a tensile force, the Nj,Rdis determined by critical value for the followingcomponents (Ref.[32], table 6.1.):

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

o component 10 : bolts in tension

- For welded connection :

o component 3 : column web in transverse tension, where the value for tfbinformulas (6.10) and (6.11) is replaced by the beam height.

o 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,Edis a compressive force, the Nj,Rdis determined by the following components(Ref.[32], table 6.1.):

o component 2 : column web in transverse compression, where the value for tfbinformulas (6.16) is replaced by the beam height.

o 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,RdNpl,Rd.

The effective width beff

The effective width beffused in the formulas for the calculation of the design tensionresistance of beam web (F t,wb,Rd) and the design tension resistance of column web(Ft,wc,Rd) for a bolted connection, are taken equal to the effective length of the non-circularpattern (in the output these values can be found under the heading leff).


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Scia Group NV 18

The calculation of weld sizes

Default

The default values for the double fillet welds to the beam flange afand for the double filletwelds to the beam web aw, are as follows (see Ref. [10] and Ref. [11](Element (833))

fyd Weld size

240 N/mm af 0.5 tfb

aw 0.5 twb

> 240 N/mm af 0.7 tfb

aw 0.7 t

wb

with af the throat thickness of weld at beam flange(fillet weld)

aw the throat thickness of weld at beam web (filletweld)

tfb the thickness of the beam flange

twb the thickness of the beam web

In case the setting is activated in the Connection Setup , the weld sizes are calculated.

Calculation of af

The weld size afis designed according to the resistance of the joint. The design force inthe beam flange can be estimated as:

h

MF RdRd

with FRd the design force in the beam flange

MRd the design moment resistance of theconnection

h the lever arm of the connection

The design resistance of the weld Fwshall be greater than the flange force FRd, multiplied

by a factor . The value of the factor is (ref[1], J.3.1.3.) :

= 1.7 for sway frames= 1.4 for non sway frames


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Scia Group NV 19

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

0M

ybfbf

Rd,t

ftbN

with bf the beam flange width

tfb the beam flange thickness

fyb the yield strenght of the beam

So, we have

Fw= min ( Nt.Rd, FRd)The weld size design for a f, using Annex M of EC3 (ref[2])

2bf

Fa

fu

WMwwf

with Fw the design resistance of the weld

bf the beam flange width

fu the ultimate tensile strength of the weaker part

W the correlation factor

Mw the partial safety factor for welds


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Scia Group NV 20

Calculation of aw for welded connection

l1,a1

l3,a3

l2,a2

Consider the figure. (See also Ref[14], pp.545)

In the section, the moment M, the normal force N and the shear force D are present.The moment M is defined by the critical design moment resistance of the connection. Thenormal force N is taken as the maximum internal normal force on the node, the shearforce D is taken as the maximum internal shear force on the node.

We can define the following properties :

a1= af(see above)a3= af(see above)a2= aw(to be calculated)l1= bfl2= h3 tfb2rl3= (bftwb2r) /2.0

)t.2h(la6la

2hlaI fb33

3

2211

332211 la4la2la2A

with bf the beam flange width

tfb the beam flange thickness

r the radius of root fillet

twb the beam web thickness

a1 the weld size a1

a2 the weld size a2


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Scia Group NV 21

a3 the weld size a3

l1 the length for weld size a1

l2 the length for weld size a2l3 the length for weld size a3

A the sectional area of the welds

I the moment of inertia of the welds

To determine the weldsize a2in a connection, we use a iterative process with a2as

parameter until the Von Mises rules is respected (Ref[2],Annex M/EC3, Ref.[32], 4.5.3.) :

ww

211

M

u

1

Mw

u222 fandf

3

2

1

I2

lM

A

N 221

22

1la2

D

with fu the ultimate tensile strength of the weaker part



Calculation of aw for bolted connection

Consider the figure.

For all possible bolt groups, the maximum tension pro unit length is calculated.The tension pro unit length is (Fi+ Fi+1)/l2.l2 is taken as the effective length of non-circular pattern for the considered bolt group.


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Scia Group NV 22

On the weld 2 x l2 x a2, the normal force N (=Fi+ Fi+1) and the shear force D is acting.The shear force D is taken as that part of the maximum internal shear force on the nodethat is acting on the bolt rows i and i+1.

To determine the weld size a2in a connection, we use a iterative process with a2asparameter until the Von Mises rules is respected (Ref[2],Annex M/EC3, Ref.[32] 4.5.3.) :

ww

211

M

u

1

Mw

u222 fandf

3

2

1

A

N21

22

1la2

D

with fu the ultimate tensile strength of the weaker part



A 2 a2l2

The calculation of stiffener dimensions

The stiffener thickness this designed according to the resistance of the joint. The designresistance of the stiffener is equal to the design resistance of the weld Fw(see chapter"The calculation of weld sizes").

fy

Mwh

bf

Ft

0

with Fw the design resistance of the weld

bf the beam flange width

fy the yield strength

M0 the partial safety factor

th the thickness of the stiffener

The weld size ahfor the stiffener is:

2

ta hh


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Scia Group NV 23

The transformation factor

The transformator factor is calculated according to Ref.[23], formula (J.2a) and (J.2b)and Ref.[32], formula (5.4a, 5.4b).

Sd,1b,j

Sd,2b,j

M

M1

with Mj,b2,Sd the moment at the intersection from the lefthand beam

Mj,b1,Sd the moment at the intersection from the righthand beam

The value of the factor is limited to 2.0.

Center of compression

Default

For calculating the design moment resistance of bolted end-plate connections the centerof compression is assumed to be at the exterior of the compression flange of theconnected member.

Center of compression according to EN 1993-1-8

In accordance with EN 1993-1-8 (Ref.[32]) article 6.2.7.2(2) for bolted end-plateconnections, the centre of compression is assumed to be in line with the centre of thecompression flange of the connected member.


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Scia Group NV 24

The use of 4 bolts / row

Consider the figure. See alse Ref.[4], parts 1.2.1,1.2.2 and table 3.

When 4 bolts/row are used, additional capacity Faddis added to the bolt row/groupcapacity of the column flange and/or the endplate.

Faddis defined as the minimum of Fadd,1, Fadd,2, Fadd,3, Fadd,4, Fadd,5for the followingconditions :

- The capacity of the inner two bolts is equal to the bolt tension resistance (failure mode3) or is defined by a circular pattern

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

If these conditions are not fulfilled, Fadd= 0.0.


27/143


Scia Group NV 25

y9

yB10ftb

F

y4

f)tt(bF

B2F

m9

mB10ftb

F

m4

ftb2F

m2wbb

)m,mmin(m

Rd.t

0M

y

2

dm

5,add

0M

y

2

d

2

fm

4,add

Rd.t3,add

2

2Rd.t

0M

y

2

fm

2,add

0M2

y2fm

1,add

122m

2112

with fy the yield strength


td the thickness of the stiffener

tf the flange / plate thicknessBt.Rd the design tension resistance of the bolt


28/143


Scia Group NV 26

The use of haunches

Weld sizes for haunches

The calculations of the weld size for the haunch elements, are taken from Ref. 3and 4.

Haunch with flange

lc

ab

tc

hc

alfa

bc

b

tw

tf

h

r


29/143


Scia Group NV 27

The weld size ab is given by :

2

wf

f

e

c

tan3t2t10

A7.0

M

Mab

with Af b tf

Me the design elastic moment resistance

Mc the moment at position lc

For the limit state, we suppose Mc=Me.

A similar formula is used for the weld size ac (between haunch and endplate/column) :

2

wf

f

e

c tan31t2t10

A7.0

M

Mac

Haunch without flange

lc

hc

b

tw

tf

twc

alfa

h1

hd


30/143


Scia Group NV 28

The weld size awc is given by :

c

f

e

c

L65.1

A

M

Mawc

with Af b tf


Mc the moment at position lc

Lc 0.75 lc

For the limit state, we suppose Mc=Me.

Column web in transverse compression

The effective width beff,c,wcof the column web in compression for a bolted end-plateconnection is calculated as follows in case of a haunch with flange is applied to theconnected member:

beff,c,wc= ac + 5(tfc + s) + sp

With: ac Weldsize ac between haunch and endplate/column

tfc, s, sp As defined in Ref.[32]


31/143


Scia Group NV 29

Resistance for haunches

The design resistance of beam flange and web in compression Fc,fb,Rd is given by :

fbb

Rd,c

Rd,fb,cth

MF

with Mc,Rd the design moment resistance of the beamcross section

hb the overall depth of the beam

tfb the thickness of the beam flange

The values for Mc,Rd, hband tfbcan be taken from section (1) i.e. the beam or section (2)i.e. the beam with haunch (see figure). This choice is made in the Connections Setup.

As an alternative, when the haunch flange is compressed, the design resistance Fc,h,Rdforthe compressed haunch flange can be calculated by the method given by ( Ref.[15],

Annex 8-B)

0M

ych

Rd,h,c

)cos(ftb

F

with bh min(bhf,bhi)

tc, see figure

bhiyc f/t 23542

bhf bc, width of haunch flange

This choice is made in the Connections Setup.


32/143


Scia Group NV 30

Compression resistance for haunch without flange

See figure in chapter "Haunch without flange".

The design resistance of haunch web in yielding mode Fc,ha,Rd,yieldingis given by :

0M

ywc1

Yielding,Rd,ha,c

fthF

with hd 0.5 hc

The design resistance of haunch web in buckling mode Fc,ha,Rd,buckling is calculated as

follows :

For the rectangular cross-section (h1* twc), the buckling reduction factor is calculatedaround the weak axis with buckling curve d. The buckling length l1is taken equal to l*0.5.

1M

y

bu ckl in g,Rd,ha,c

fAF

with A h1* twc

The design moment resistance for haunches at beam

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 checkfailure of the beam web due to the vertical component of the force transferred by thehaunch. See Ref.[15], Annex 8-B. The influence of the local beam web buckling is taken

into account by the factor .

The calculation of this design moment resistance Mj,Rd , are taken from Ref. 3and 4.This design moment resistance Mj,Rd is compared with the moment Mcat the positionwhere haunch and beam are meeting.

Mj,Rd for haunches with flange

Consider the figure in chapter "Haunch with flange"

d

fe

d

feRd,j

A

A

cotM

cot5.0A

A

cot25.1MM


33/143


Scia Group NV 31

with Af b tf


Ad {tc+ 5 (tf+r)}twr rounding in beam

67.0if0.1

67.0if22.0

11

r

r

rr

r

2

w

ydceff

Et

fdb93.0

beff {tc+ 5 (tf+r)}

dc h-2 (tf+r)

Mj,Rd for haunches without flange

f

2

dwceRd,j

A

coshtMM

Consider the figure in chapter "Haunch without flange".

with Af b tf


hd 0.5 hc


34/143


Scia Group NV 32


The design shear resistance for normal bolts

The shear resistance per shear plane Fv,Rd is given by the respective code.

The design shear force is given by (see Ref.1J.3.1.2.)

the total design shear resistance of the bolts in those bolt-rows that are not required toresist tension.

0.4/1.4 (28%) of the total design shear resistance of the bolts in those bolt-rows that arealso required to resist tension

Suppose we have nt number of bolts in tension and nn number of bolts not in tension. Thedesign shear force VRdis :

nn*Fnt28.0FV Rd,vRd,vRd

The bearing resistance for endplate (Fb,ep,Rd) and the bearing resistance for column flange(Fb,fc,Rd) is given by the respective code.

Suppose we have ntotnumber of bolts. The design shear force VRdis :

totRd,bRd nFV

The design shear resistance for preloaded bolts

Suppose we have ntotnumber of bolts.

The design preloading force Fp,Cd is given by the resepctive code.

The design slip resistance of preloaded high-strength bolt Fs,Rd is given by the respectivecode.

The design shear force VRdis :

totRd,sRd nFV


35/143


Scia Group NV 33

The welded plate-to-plate connection

Consider the figure :

When we write the horizontal equilibrium in point A, we have :

)left_alfacos(Fright_alfacosF left,flright,fl

When we write the vertical equilibrium in point A, we have :

epleft,flright,fl F)left_alfasin(Fright_alfasinF

In the limit state, the value Fep is limited by the capacity of the endplate :

0M

y

ep

ftbF

with b the width of the endplate

t the thickness of the endplate

fy the yield strength

M0 the partial safety factor for resistance of cross-section to overall yielding

Out of the vertical and horizontal equilibrium, and the value for Fepin the limit state, wecan calculate the maximum force Ffl,right and Ffl,left. These values will result in the designresistance of endplate in compression Fc,ep,Rd for both sides.


36/143


Scia Group NV 34

The column base connection

If EN 1993-1-8 is selected, the column base connection is designed according to Ref.[32] :

- art. 6.2.5.- art. 6.2.6.9- art. 6.2.6.10- art. 6.2.6.11- art. 6.2.6.12- art. 6.2.8

In all other cases, the following rules are applied :-The design compression resistance-The design moment resistance-The design tension resistance

The design compression resistance

The determination of NRd,c is based on Ref. [5]

jfc,RdAN

with A the resulting bearing area (The area incompression under the base plate)

fj the bearing strength of the joint

For the determination of the resulting bearing area the additional bearing width c isintroduced.

0Mj

y

f3

ftc

with t the thickness of the steel base plate.

fy the yield strength of the steel base platematerial.

Where the projection of the base plate is less than c the effective bearing area should beassumed to be as indicated in the figure.


37/143


Scia Group NV 35

Where the projection of the base plate exceeds c the additional projection should beneglected, see figure.

with A bearing area

A' area not included in bearing area

The bearing strength of the joint fjis determined from:

cdjjj fkf

with j the joint coefficient, which may be taken as 2/3 (0.667) provided


38/143


Scia Group NV 36

that the characteristic strength of the grout is not less than 0.2times the characteristic strength of the concrete foundation andthe thickness of the grout is not greater than 0.2 times the

smallest width of the steel base plate.This value can be set in the Concrete Basic data.

fcd is the design value of the concrete cylinder compressive strength

of the concrete given by:c

ckcd

ff

in which fckis the characteristic cylinder compressive strength ofthe concrete determined in conformity with Ref. [6].

This value can be set in the Concrete data.

cis the partial safety factor for concrete material properties

given in Ref. [6]. This value can be set in the Safety factorsdialog box.

kj the concentration factor

ab

bak 11j

where

a & b are the dimensions of the base plate

a1& b1are the dimensions of the effective area.

See figures.

For a1the least of the following should be taken:

a1=a+2ar

a1=5a

a1=a+h

a1=5b1but a1a

For b1the least of the following should be taken:

b1=b+2br

b1=5b

b1=b+h b1=5a1but b1b

Note 1:Conservatively kjcan be taken as 1.0, The value can be set in the concretedata.

Bp = Base plateCf = Concrete foundation


39/143


Scia Group NV 37

a1

aar

h

b1b

br

Bp

Cf


40/143


Scia Group NV 38

The design moment resistance

The determination of MRdis based on Ref. [1].

The following remarks are made.

The resistance moment of the base plate is elastic, therefore the calculation of FtRd is done

with

0M

y

2

eff

Rd,el6

ftlM

A new joint component is introduced: The concrete in compression. The design compressionresistance for concrete under the flange.

jflRd,base,c fAF

with fj the bearing strength of the joint

Afl the bearing area under the compressionflange. See the following figures.


41/143


Scia Group NV 39


42/143


Scia Group NV 40

The design tension resistance

The determination of NRd,t is based on Ref.[1].It is the design tension resistance for the group of all bolt-rows. (No compression limits)NRd,t is the resistance against tension due to uplift.


Default

The determination of VRdis described in chapter "The design shear resistance".

The following feature is added:It is possible to increase the shear resistance with the value of the friction resistancebetween the base plate and the concrete. (This option is controlled in concrete datadialog box.)

The friction resistance between the steel base plate and the concrete.

fr

frckNf,VRd

with Nc= Nsd,c the design compressive force

kfr the friction coefficient between steel and

concrete. (0.25)

fr the safety factor for friction. (2)

Note: kfcand frcan be set in the concrete data dialog box.


43/143


Scia Group NV 41

Friction resistance according to EN 1993-1-8

For EN 1993-1-8 Ref.[32] the design friction resistance is defined as follows:

EdcdfRdf NCF ,,,

with Nc,Ed the design compressive force

Cf,d the friction coefficient between base

plate and grout layer (0.20)

The design shear resistance for shear iron.

The calculation of the shear resistance for shear irons is based on Ref. [7] pp116-120.

The design shear resistance for I shaped shear iron.


The design shear resistance for I shaped shear iron is given by the minimum of the followingshear resistance :

- VRd,1 : limited by the concrete capacity- VRd,2 : limited by the stress in the shear iron flange- VRd,3 : limited by the stress in the column web- VRd,4 : limited by the shear capacity of the shear iron


44/143


Scia Group NV 42

The following formulas are used :

0M

s,ydv

4,Rd

0Mcq

c,ydcwccp

3,Rd

0Mcq

s,ydc

,Rd

cdq1,Rd

3

fAV

)hh(L

fhht)k5t2t(3V

)hh(L

fhhtb32V

f)lL(bV

with fcd the design value of the concrete cylindercompressive strength of the concrete

Lq the length of shear iron

b the width of the shear iron

h the height of the shear iron

t the flange thickness of the shear iron

hc the height of column

fyd,s the yield strength of the shear iron

fyd,c the yield strength of the column


tp the thickness of baseplate

kc 1.4 awc

awc the weld size for column web/base plate

Av the shear area of shear iron

twc the web thickness of the column

l 30 mm


45/143


Scia Group NV 43

The design shear resistance for angle shaped shear iron.


The design shear resistance for angle shaped shear iron is given by the minimum of thefollowing shear resistance :

- VRd,1 : limited by the concrete capacity- VRd,2 : limited by the stress in the shear iron- VRd,3 : limited by the shear capacity of the shear iron

The following formulas are used :

0M

yda

3,Rd

0M2

c

2

a

yda

2,Rd

cdaa1,Rd

3

ftLV

)3h9

d4(

fLtV

f)lL(dV

with fcd the design value of the concrete cylindercompressive strength of the concrete

La the length of shear iron

da the height of the shear iron


46/143


Scia Group NV 44

t the flange thickness of the shear iron

hc the height of column

fyd the yield strength of the shear ironM0 the partial safety factor

tp the thickness of baseplate

l 30 mm

The anchorage length

The determination of the anchorage length of the holding down bolts is based on Ref. [6].The required anchorage length lb,netis calculated from:

min,b

prov,s

req,sbanet,b l

A

All

bd

yd

4bf

fl

with the diameter of the holding down bolt.

fyd the design yield strength of the holding down bolt. This isdetermined as follows :

Mb

uf9.0

fu the ultimate tensile strength of the anchor

Mb the partial safety factor for a bolted connection. (= 1.25)

fbd the design value for the ultimate bond stress.

fbdis dependent on the bond condition, which normally is goodfor a column base and also dependent of the type of holdingdown bolts. (plain or high bond bars)The bond condition and thetype of bars can be set in the concrete data dialog box.

lb the basic anchorage length.

ais dependent on the anchorage method.= 1 for straight bars.= 0.7 for curved bars.

As,req is the required tensile stress area of the anchor

u

Mbbolt,t

req,sf9.0

FA


47/143


Scia Group NV 45

with Ft,bolt the maximum tensile force in the anchors. (dueto NRd,tor MRd)

Mbthe partial safety factor for a bolted connection.(= 1.25)

fu the ultimate tensile strength of the anchor

As,prov is the provided tensile stress area of the anchor

lb,min is the minimum anchorage length

lb,min is the maximum of 0.3 lb, 10

Calculation of tensile force in anchors Ft,boltaccording to internal forces.

The tensile force in the anchor can be calculated using the actual internal forces. Thiscalculation is based on the regulations given in ref.[24], chapter 6.4.1.

This choice can be made in the Connection Setup.

Consider the following configuration :

N

M

Nb

Ft Ft

h/2

h1

h2


48/143


Scia Group NV 46

Moment equilibrium gives :

21

2t1t

hh

2

hNM

Ft

hFhF2

h

NM

Ftis the tensile force for each anchor row in the tension zone, M and N are the actualinternal forces.When Ft0.0, the value for Ft,boltis calculated.

The anchor rows in the tensile zone, are those anchor rows where h i> h/2 is valid.

Design of the washer plate.

The design of a circular plate is based on Ref. [7]

The allowable tensile force Njin 1 anchorage is given by:

v

r1

4rf3N

22

cdj

with v the smallest of l and d1. See figure.

By means of this formula r, the radius of the circular plate is determined.The iterative process is started using 2,5 times the anchor diameter as an initial value forr.

The thickness t is given by33.0

cd

E

fr8t

with E Modulus of elasticity for anchorage.


49/143


Scia Group NV 47


When the axial force NSdin the connected member exceeds 10 % of the plastic resistanceNpl,Rd of its cross-section, a warning is printed out and Mj,Rdis decreased.The value of the design moment resistance Mj,Rd is decreased by the presence of the axialtensile force NSd.

2

h.NMM SdRd,jRd,j


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

hNMM

))FFc(2

N,0max(N

)F,Fmin(F

Rd,jRd,j

tot

Sd

Rd,fb,cRd,base,cc

with h the distance between the compression and tension pointin the connected member

Fc,Base,Rd Design compression resistance for concrete under theflange

Fc,fb,Rd Bearing Resistance for column flange

Ftot The sum of the tensile forces in the anchor rows at Mj,Rd


50/143


Scia Group NV 48

The use of RHS beam

The use of RHS beam in bolted beam-to-column connection

The bolts can only be positioned outside the beam flange. The normal proceduredescribed in Ref.[1] is followed for the calculation of the connection characterisrtics.

The use of RHS beam in column base connection

The bolts can only be positioned outside the beam flange. However, 3 bolts/row arepossible.The rotational stiffness is not calculated.

The design compression resistance

The determination of NRd,c is :

jc,Rd AfN

For more information, see chapter "The design compression resistance".

Where the projection of the base plate is less than c the effective bearing area should beassumed to be as indicated in the following figures.

Where the projection of the base plate exceeds c the additional projection should beneglected, see the figure,


51/143


Scia Group NV 49

with A Bearingarea

A' Area not included in bearing area.


52/143


Scia Group NV 50

The design tension resistance

The determination of NRd,t is based on Ref.[22].

Consider the following figures :


53/143


Scia Group NV 51

The allowable tension force for each bolt FT,Rd,iis given by

i

ip

r

yp

Rd,t

p

i,Rd,T

t)2/d(b'b

b25.1a

tba2

da

1t

KT

p

'd1

pf9.0

'b4K

B,K

)1(tminF

with tp plate thickness

fyp yield strength of plate

d bolthole diameter

d bolt diameter

ti thickness of RHS section

a,b see figures

p = 2e

= w/2

= 2e

= w

Bt,Rd design tension resistance of a bolt

The total design tension resistance Nt,Rd is then

i,Rd,TRd,t FN


54/143


Scia Group NV 52

The design moment resistance

The determination of MRdis based on Ref. [1] and Ref.[22].

MRd is given by

h)F,Fmin(M cTRd

with FT FT,RD,Ifor the bolts in tension

Fc min( Fc,base,Rd, Fc,rhs_flange)

The design compression resistance for concrete under the flange, Fc,base,Rdis :

jflRd,base,c fAF

with fj the bearing strength of the joint

Afl the bearing area under the compressionflange.


55/143


Scia Group NV 53

The design compression resistance for the RHS compression flange, Fc,rhs_flangeis :

0M

y

flange_rhs,c

btfF

with b width of RHS section

t thickness of RHS section

fy yield strength of RHS section

M0 partial safety factor


56/143


57/143


Scia Group NV 55

The design tension resistance".

The rotational stiffness is not calculated.


58/143


Scia Group NV 56

Connections with column minor axis

Introduction

In Ref.[21], some extensions are proposed to design the behaviour if the beam is attachedto the column web through some element as angle, plate etc. The implementation isbased on this proposals, and are described in the following chapters.The new components are the column web submitted to punching shear and bending.Different failure mechanisms of column web have been analysed and are essentiallybased on the yield line theory.

The moment resistance and the rotational capacity of a minor-axis joint is calculatedbased on the methods as proposed in Ref.[1].The following elements are taken into account in the design procedure:

Column web in bending and punching Bolts in tension End plate in bending Beam web in tension Beam flange and web in compression

The figure some common types of minor-axis connections where beams are assembled

with column web without stiffeners.

b)flushendplate

c)flange


59/143


Scia Group NV 57

Strength of column web in bending and punching

Generalities

The plastic resistance of the web results from its yielding and from a progressive apparition ofplastic yields line mechanism. The failure mode mechanism is divide into two main groups: thelocal and the global mechanism similarly to those proposed in Ref.[1] J.3.6.2 (5) & (6). A localmechanism means that the yield line is localized only in the compressive zone or in the tensilezone of the joint while global failure mode design the yields line pattern involves both incompressive and tensile zone. In the design model, it is assumed that prying action betweenend plate or the angle cleat doesnt occur. This assumption is conflicting with assumptionsmade in Ref.[1]. This point is still under investigation but in most practical cases, it is reasonableto assume that no prying develops between components. The design resistance of the web intransverse compression or tension is finally defined as: FRd=min(Flocal,Fglobal).

Definition and design of local and global failure mode

The moment carried out by the beam to the column web may be decomposed in a coupleof forces F acting in the compressive and the tensile zone. It is assumed that these forcesact on an area (compressive and tensile zone) defined in the plane of the column web.The design value of the moment resistance can be calculated as follows:

RdRd,j FzM

with z the lever arm in the joint

FRd the resistance of the weakest axis component in the minor axis joint


60/143


Scia Group NV 58

Basic failure mechanisms are obtained by yields line method.. In the flexural mechanism,it is assumed that plastic moment is not reduced by the presence of shear forces

perpendicular to the plane web. The plastic moment per unit length of yield line is givenby:

0M

y

2

w

pl

ft25.0m

where fy is the yield stress and twthe thickness of the column web.

Local failure mechanism

In the local failure mode different local mechanisms of the column web are considered.The force F acts on a rigid rectangle. This rectangle is defined by the dimensions bxc (seefigure). The weld perimeter rectangle around the beam flange or the loaded area aroundthe bolt pattern defined the rigid rectangle. The yield pattern is localised in thecompression or the tension zone. As result from this definition, the resistance force isevaluated in each rigid rectangle: one in the compression zone and one in the tensionzone. This mechanism is associated to the smallest force FRd,localbetween the punchingshear resistance and the combination of punching shear and bending resistance in thecompression and the tension zone. Some adaptations and interpretations are needed todesign a pinned connection.

The resistance to punching depends on the loading case. For the loading case 1thepunching function of the punching perimeter 2(b+c). For the loading case 2, the punching

perimeter of the column web depends on the diameter of the bolt heads (or nuts) and thenumber n of bolts respectively in the tension/compression zone. The resistance is givenby:

0M

ywc

Rd,Punching3

ftcb2F

: loading case 1

0M

ywcm

Rd,Punching3

ftdn

F

: loading case 2

with twc the thickness of the column web

fy the yield strength of the column web

M0 the partial safety factor of steel

dm average diameter of the bolt head (see further)


61/143


Scia Group NV 59

Combined flexural and punching shear mechanism takes also into account that the plasticmoment per unit length of yield line is reduced by the presence of shear force.

0Mwc

2

y

2

wcRd,Comb

1

xat3

xxc5.1

xa

c2xaLftkF

bbifc4xaL2

t3ca5.1aa

bbif0

x

m0

wc2

m

m

m3

1

c3

2

c0

bL

bb

L

t

L

c23.0

L

tLx

0bbutLt

c8.211

c

t82.01Lb m

2

wc

2

2

2

wc

m

5.0L

cbifL

cb6.07.0

5.0L

cbif1k

bLa

2

ddd

d9.0cc

d9.0bb

21m

m0

m0

d2

d1


62/143


Scia Group NV 60

Appl icat ion to r ig id bol ted c onnect ion

For each zone (respectively tension/compression), the local punching shear resistancefollowing loading case 1&2 is determined. The tension rigid rectangle is defined by theperimeter around the bolts placed respectively in the tension zone 2(b+c) . The rigidrectangle of the compression zone through which the punching is transmitted to thecolumn web corresponds to the beam flange thickness and the beam flange width .In the same way, the local combined punching and bending is calculated both for thetension and the compression following the same perimeter values b & c.

Appl icat ion to r ig id w elded conn ect ions

For each zone (respectively tension/compression), the local punching shear resistancefollowing loading case 1&2 is determined. For welded connections, the tension,

respectively the compression rectangle is the beam flange thickness and the beam flangewidth.In the same way, the local combined punching and bending is calculated both forthe tension and the compression following the same perimeter values b & c.

Global mechanism

In the global failure mechanism, the force F is transmitted to the column web by one ormore rows of bolts. In this case, the definition of the loaded area depends on the distancebetween bolts and the diameter of bolt heads (or nuts), or the weld around the beamflanges. The yields line pattern involves both compression and tension zones.

The combined flexural and punching mechanism is evaluated as:

0M

pl

Rd,Com

Rd,Global

12

z

b2m

2

FF

where FComb,Rd: combined punching and flexural local resistance

10

b-L

zif

bL

z

1b-L

zif1

Global failure mechanism involves both compression and tensile zones. If the dimensionsbxc of the compression zone are different from those of the tensile zone, the FGlobal,Rdexpression will be applied twice, once for the compression zone and once for the tensionzone separately.


63/143


Scia Group NV 61

Rotational stiffness and ductility

Stiffness coefficients

The rotational stiffness is calculated with the component method, which is described inRef.[1] Part J.4.

The following stiffness coefficients are used :

Coefficient Basic component Formula

k1 column web panel inshear

z

A38.0 vc

k2 column web in

compressionc

wceffd

tb7.0

k3 column flange, singlebolt row in tension

3

3fceff

m

tl85.0

k4 column web in tension,single bolt row intension c

wceff

d

tb7.0

k5 endplate, single bolt

row in tension 3

3peff

m

tl85.0

k7 bolts, single bolt row intension

b

s

L

A6.1

with Avc the shear area of the column

z the lever arm

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

Lb the elongation length of the bolt

For the proper values of these variables, we refer to Ref.[1].


64/143


65/143


Scia Group NV 63

When a column minor axis configuration is used, the values for k1 and k2 are replaced byki, the stiffness coefficient in the tension or the compression zone of the column web inbending and punching.

The value for kiis given by (see Ref.[21]) :

rot

2

2132

3

wci k

u

cc4.101

tan116

L

tk

with c1 1.50

c2 1.63

wct

Lu

10u50

L

b 0.080.75

L

c

0.050.2

1035

The factor krotis equal to 1 if the rotation of the column flanges restrained

HEM600-HEB500-HEA400toequalorsmallersectionsHEfor1

sectionsIPEforandHEM600-HEB500-400HEAangreater thsectionsHEfor4.052.0krot

For a bolted plate-to-plate connection, the following coefficients are used :

Coefficient Present keq

k1

k2

k3

k4

k5 Left side

k5 Right side

x

x

x

x

k7 x x

A welded plate-to-plate connection is considered as rigid.

For a column base, the following coefficients are used :

Coefficient Present keq

k1


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k2

k3

k4

k5 x x

k7 x x

kc x

See also Ref.[16].

The value of Lbin coefficient k7 is taken as the free length of the anchor bolts plus the freelength of embedded part. The free length of the anchor bolts is equal to the base platethickness plus the head height of the anchor bolt. The free length of the embedded part isequal to 8 x the anchor diameter.

The stiffness kcis the stiffness coefficient for the compression zone in the concrete block.

eq

cflcEh

EAk

with Afl the bearing area under the compressionflange

Ec the E modulus of concrete

3/1ck 8f5.9

(Ecin Gpa, fckin Mpa)E the Young modulus (of steel)

heq the equivalent height

2

ba effeff

where aeffand beffare based on therectangle for determining Afl

Afl=aeffx beff


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Calculation of stiffness

The program calculates 3 stiffnesses :

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 thenormal force)

The values for Sj,ini and Sj can be found on the numerical output.The moment-rotation diagram is based on the values of Sj,ini and Sj,MRd.

Sj,MRd

Sj,ini

M

fi

MRd

0.66 MRd


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Stiffness classification

The connection is classified as rigid, pinned or semi-rigid according to its stiffness byusing the initial rotational stiffness Sj,ini and comparing this with classification boundariesgiven in Ref.[1] Figure J.8.

If Sj,ini >= Sj,rigid, the connection is rigid.If Sj,ini


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Check of required stiffness

The actual stiffness of the connections is compared with the required stiffness, based on

the approximate joint stiffness used in the analysis model. See also Ref.[15] Part 6.1.2,Ref.[18] and Ref.[19].A lower boundary and an upper boundary define the required stiffness :

Frame Lower boundary

Sj,low

Upper boundary

Sj,upper

Braced

bb

b

Lapp,SjIE10

IEapp,Sj8

b

b

L

IE8app,Sj

bb

b

Lapp,SjIE8

IEapp,Sj10

b

b

L

IE8app,Sj

Unbraced

bb

b

Lapp,SjIE30

IEapp,Sj24

b

b

L

IE24app,Sj

bb

b

Lapp,SjIE24

IEapp,Sj30

b

b

L

IE24app,Sj

For column base connection , we use the following extrapolation :

Lower boundary Upper boundary

cc

c

Lapp,SjIE20

IEapp,Sj16

c

c

L

IE16app,Sj

cc

c

Lapp,SjIE16

IEapp,Sj20

c

c

L

IE16app,Sj

with Ib the second moment of area of the beam

Lb the span of the beam

Ic the second moment of area of thecolumn

Lc the storey height of the column

E the Young modulus

Sj,app the approximate joint stiffness

Sj,ini the actual initial joint stiffness

Sj,low the lower boundary stiffness

Sj,upper the upper boundary stiffness

Sj the actual joint stiffness


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

When Sj,ini >= Sj,low and Sj,ini= Sj,low and Sj


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Sj,ini+

M

fi

MRd+

0.66 MRd+

0.66 MRd-

MRd-

Fi+ 3Fi+

Fi-3Fi-Sj,ini-

Ductility classes

According to Ref.[15] part 4.7, the following classification is valid for connections :

Class 1 joint : Mj,Rd is reached by full plastic redistribution of the internal forces within thejoints and a sufficiently good rotation capacity is available to allow a plastic frame analysisand design.

Class 2 joint : Mj,Rd is reached by full plastic redistribution of the internal forces within thejoints but the rotational capacity is limited. An elastic frame analysis possibly combinedwith a plastic verification of the joints has to be performed. A plastic frame analysis is alsoallowed as long as it does not result in a too high required rotation capacity of the jointswhere the plastic hinges are likely to occur.

Class 3 joint : brittle failure (or instability) limits the moment resistance and does not allowa full redistribution of the internal forces in the joints. It is compulsory to perform an elasticverification of the joints unless it is shown that no hinge occurs in the joint locations.


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Ductility classification for bolted joints

If the failure mode of the joint is the situated in the shear zone of the column web, the jointis 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 byductility

Class

df

f36.0t

y

ub Ductile 1

df

f53.0td

f

f36.0

y

ub

y

ub

Intermediaire 2

df

f53.0t

y

ub Non-ductile 3

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 basiccomponent

Ductility classification for welded joints

If the failure mode of the joint is the situated in the shear zone of the column web, the jointis 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 intermediaire for ductility, i.e. a class 2 joint.


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Theoretical background for frame pinned connections

Introduction

In this appendix, we give information about the calculation rules for the Frame Pinnedconnections. Four types of connections are supported :

Type 1 welded plate in beam, welded to column

Type 2 bolted plate in beam, welded to column

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 VR

steel connections theory enu

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