Steel connections - SCIA Help

Steel connectionsTheoretical background

Chapter 0

Contacts 5Introduction 7Bolted and welded frame connections 8

Introduction 8

List of abbreviations 8

Bolted connections and welded beam-column connections 14

General 14

Bolts 16

Bendingmoment resistance 17

Remarks: 23

Remarks: 23

Remarks: 25

Remarks: 26

Remarks: 26

Remarks: 27

Remarks: 28

Haunch with flange 28

Haunch without flange 29

Column flange in bending 36End plate in bending 36Beam flange in compression 37Column flange in twisting 38Column web in bending 38

Normal force resistance 38

Shear force resistance 40

Weld size calculation 44

Stiffener dimensions 53

Welded splice connections 54

Column base connections 55

Partial safety factor gc 55

The design compression resistance 55

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The designmoment resistance 58

The design tension resistance 60

The design shear resistance 60

The anchorage length 63

The influence of the normal force 66

Rectangular Hollow Sections 67

Column minor axis connections 72

Introduction 72

Strength of columnweb in bending and punching 73

Application to rigid bolted connection 76

Application to rigid welded connections 76

Rotational stiffness and ductility 77

Stiffnesscalculation 77

Stiffnesscoefficients 78

Stiffnessclassification 81

Stiffnesscheck 82

Update stiffness 83

Weakaxis calculation 84

Ductility classification 86

Pinned frame connections 87Introduction 87

List of abbreviations 87

Calculation of VRd and NRd 91

Welded pinned plate 91

Bolted pinned plate 94

Cleat 100

Short end-plate 106

Weld size calculation 109

Grid pinned connections 112Introduction 112

Design shear resistance VRd at notch 113

Notched elements : calculation design block shear resistance VRd 114

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Chapter 0

Long cleat connection VRd : design shear resistance for the connection element 115

Long cleat connection VRd : design shear resistance due to the bolt distribution in the column116

Bolted diagonal connections 118Introduction to the bolted diagonal connection 118

Member resistance 118

Resistance of the grosssection of diagonal 118

Resistance of the net section of diagonal 118

Resistance of the grosssection of gusset plate 122

Resistance of the net section of gusset plate 122

Determination of Anet 122

Connection resistance 124

Shear resistance 124

Bearing resistance 125

Checking the connection resistance 125

Weld size calculation for gusset plate 126

Calculation of weld length 126

Weld symbols 127Bolt symbols 128References 129

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Contacts

Contacts

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Chapter 0

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©Copyright 2016SCIAnv. All rights reserved.

Document created: 27 / 05 / 2016

SCIAEngineer 15.3

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Introduction

Introduction

In thisTheoreticalBackground in depth information isgiven regarding the design of steel connectionswithin Scia Engineer.

While a connection is being defined by a set of connection editable properties, in the graphical windows of Scia Engineer,each connection component is drawn (connected members, endplates, stiffeners, bolts, etc.). In addition, the programchecks detailing requirements specified in the EN code. The allowable resistance forces for the connection are calculatedand compared with the actual forcesacting in the connection. The program also lists the parts that determine the resistanceof the connection, thusenabling the user to take appropriate actions.

After design and calculation, the program can generate overview drawings and detail drawings of the connection and theconnection elements. A full-detailed report on the calculation can be also printed.

The design isbased onEN 1993-1-8.

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Chapter 2

Bolted and welded frame connections

IntroductionFor the calculation of connections, the following characteristicsof connection are introduced in EN 1993-1-8:

l Moment Resistancel Normal forceResistancel Shear forceResistancel RotationalStiffness

This design method allows us to determine a "Moment-rotation characteristic", which in tum allows us to represent the realconnection by a rotational spring connection defined in the center lines of column and connected beam in the point of theirintersection (approximation to the real behaviour of the connection).

By using this method, the design of non-stiffened connections can be considered, which results in a reduction of the totalcost of structural steelwork.

The principles for the connection design are satisfied for a beam-column and beam to beam connections, when the detailedapplication rules given in the EN 1993-1-8, Art 6.7.1 - Design moment resistance of beam-to-column joints and splices, arefollowed. For the design of column bases, the application rules given the EN 1993-1-8, Art 6.7.1 - Design resistance ofcolumn baseswith base plates, are followed.

The following typesof connectionsare supported :

l Beam-to-column connectionsl Beam-to-beamconnectionsl Column bases

The types "Beam-to-beam" and "Column bases" are limited to symmetric and asymmetric I beams (including the elementswith variable height) andRHSsections, both for major-axisbending configurations.

For the type " Beam-to-column", the beam element is limited to symmetric and asymmetric I beams (including the elementswith variable height) and RHS sections, both for major-axis bending configuration ; the column element is limited to sym-metric I beams (including elementswith variable height) in major-axis configuration, and to symmetric I beams inminor-axisbending configuration.

List of abbreviationsβ Transformation parameter

µ Stiffness ratio

µ stiffness ratio = Sj/Sj,iniρ intermediate parameters for minor axis connection

β intermediate parameters for minor axis bending

α intermediate parameters for minor axis bending

θ intermediate parameters for minor axis bending

γc Partial safety factor for resistance of concrete

γfr Partial safety factor for friction

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Bolted andwelded frame connections

βj Joint coefficient

γM0 Partial safety factor for resistance of cross-section to overall yielding

γM1 Partial safety factor for resistance to buckling

γMb Partial safety factor for resistance of bolts

γMs Partial safety factor for slip resistance

γMw Partial safety factor for welds

γMw Partial safety factor for resistance of welds

βW Correlation factor

a Throat thickness of weld

a Factor for anchorage type

A Sectional area of the welds

a intermediate parameters for minor axis connection

a1 Weld size a1a2 Weld size a2a3 Weld size a3Ad Area

Af Area of compressed beam flange

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

ah Weld size of the stiffener

alfa 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 web doubler

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 beamweb

aw Throat thickness of weld at beamweb (fillet weld)

b Width of element

b b=b0+0.9dmb0 Bolt pitch in x direction

beff Effective width

bf Beam flange width

bhf Width of haunch flange

bhi Critical width for haunch flange

bm intermediate parameters for minor axis connection

bs Width of web doubler

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Chapter 2

Bt,Rd Design tension resistance of a bolt

c Additional bearing width

c c=c0+0.9dmc0 Bolt pitch in y direction between extreme bolt in tension zone

d1 Edge distance of circular plate

da Height of angle shaped shear iron

dc 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

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

Fc,ha,Rd,buckling 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 individual bolt 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,Ed Applied tensile force

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Ft,wb,Rd Design resistance of beamweb 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 strength of the column web

fyb Yield strength of the beam

h Height of element

h Distance from bolt row to center 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

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 tension

kc 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 resistance

kwc 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

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Chapter 2

l2 Length for weld size a2l3 Length for weld size a3La 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

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 considered individually

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

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

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

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

Lq Length of I shaped shear iron

ls Length of web doubler

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 elasticmoment 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

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p1 Spacing

p2 Lower part of bolt pitch

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 rotational stiffness

Sj,low lower boundary stiffness

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

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 web doubler

tw Web thickness of cross section

twb Thickness of the beamweb

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

z Lever arm

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Chapter 2

Bolted connections and welded beam-column con-nectionsGeneral

Connection configurationsTheEN 1993-1-8 Art 1.4 Figure 1.2 specifiespossible steel connectionsconfigurations:

The same configurationsare recognizedwithin Scia Engineer:

l Single sidedl Double sidedl Splicel Column base

In a splice connection a geometry check for both top and bottom flange is performed. Thedifference between left and right flange axis positions is being tested. Maximum differencemay be equal to the minimum thickness of the adjacent beam/haunch flanges from bothsides. If the limit isbreached, calculation design endswith an error.

Supported cross-sectionsScia Engineer Steel Connection module supports a limited number of cross-section types that may appear on connectedbeams. Scia Engineer can dealwith the following cross-section types:

l Rolled I beam - (I+H)l Symmetricalwelded I section - (Iw)l Asymmetricalwelded I section - (Iwn)l I sectionwith a haunch - (I var, I + I var, I +Pl var, I + Iw var, I +2I var, I + I var (c))l Rolled hollow section - (RHS)

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The possible combinations of supported cross-sections with relevance to a geometric connection type is indicated in thetablesbelow. Column base connectionssupport all cross-sections.

It is important to mention that in this context, beam is the entity connected to a column. It isperfectlypossible that columnmaybe horizontal and beamvertical.

Structural modelConnection design within Scia Engineer is based on the Structural model. Within the properties of each member the Struc-turalmodel can be defined in three possible modes. It is recommended to use the "Automatic" mode. The 'Manual' mode isnot fully supported for connection design.

Local coordinate systemThe design angle for a connected member is taken from LCS rotation angle of the member. It is to be defined in the prop-ertiesof a connectedmember. The design angle has to be equal to 0, or amultiple of 180 degrees. In all other cases the geo-metryof a connection isnot valid and designwill endwith an error.

It is crucial, that Alpha rotation angle is set to zero. Breaking of this rulemaycause connection design discrepancies.

The direction of z-axis of local coordinate system for both beams in any splice connection has to be the same. Breaking ofthis rulemaycause connection design discrepancies.

In Scia Engineer it is possible to define both top and bottom structural haunch in a connection. The top haunch is placed onthe positive LCS z-axis side of the beam. On the other side the bottom haunch is placed on the negative LCS z-axis side ofthe beam.

Internal forcesThere is a possibility to choose the section fromwhere the design internal forces for the connection design are taken. Thereare two possibilitieswhich can be specified in the connection setup properties by selecting Transformation of internal forcesparameter:

In axisInternal forces in the connection node, intersection of beamand column axis, are used.

In connection faceIn this case, internal forcesat the connection face, whichmeans the sectionwhere the beamends, are used.

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Chapter 2

Bolts

Bolt placementPositioning of bolts isdetermined according to theEN 1993-1-8, Art 3.5, Table 3.3.

In Scia Engineer the possible vertical positions are calculated according to the size of the cross-section and bolt assembly.Maximum number of bolt-rows per connection is 50. The algorithm for calculation of default bolt-row locations displayed inthe boltsdialog is calculated according to the steps indicated below:

l Calculation of available space between flanges, or flange and end of end-plate, based on theminimumdistancesl Calculation ofminimumspacing p1 given asmaximumof average diameter of bolt head (d1+d2)/4 and value based on

borehole diameter d0multipliedwith setup value for minimump1 distancel Determination of themaximumavailable bolt-row locationsper interval defined in the first step abovel Calculation of the final bolt-row locationsbased on the uniformdistribution of bolt-rows in the interval

If there is only space for placement of only one bolt-row in the defined interval, the location of this bolt-row is defined in themiddle of such interval.

The inclinationsof the beamand flangesare taken into account when determining the bolt-row locations.

Within Scia Engineer the limit distances below are being checked in addition to the one above for minimum and maximum,asdefined by the given reference:

End distance e1 - vertical distance between bolt-row and the end of end-plate

Edge distance e2 - horizontal distance between boltsand the left/right edge of end-plate

Spacing p1 - vertical distance between two bolt-rows

Spacing p2 - horizontal distance between bolts in one bolt-row

Distance to the beam or haunch flange - vertical distance from bolt-row to the beam or haunch flange. The minimum isdefined as half of the wrench diameter or as an average diameter of bolt head (d1+d2)/4. This parameters is to be definedin the bolt assemblyproperties.If a bolt row isplacedwithin any restricted distance, awarning in theBoltsdialog isdisplayed.

The flange andwebweld-sizesare not taken into account in the limit distances.

In the splice connections, the side used for bolt activation is used for the calculation of thelimit distances. It is up to the user to manually check the positioning of the bolts on the otherside.

Bolt tension resistanceTension bolt resistance Ft,Rd is calculated according to the EN 1993-1-8, Art 3.6.1, Table 3.4. In Scia Engineer the tensilestressarea of the bolt As isused together with the coefficient k2 equal to 0,9.

With reference to EN 1993-1-8, Art. 3.6.1 (3) it is assumed that the bolt threads do alwayscomply with EN 1090, therefore the relevant resistance values based on formulas given inTable 3.4 should not need to bemultiplied byan additional factor of 0,85.

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Bolt shear resistanceNormal boltsShear bolt resistance for normal bolts per shear plane Fv,Rd and bearing resistance Fb,Rd is calculated according to the EN1993-1-8, Art 3.6.1, Table 3.4. In Scia Engineer it is alwaysassumed that the shear plane passes through the threaded por-tion of the bolt (A is the tensile stressarea of the bolt As, therefore αv is based on the bolt class).

For more info on calculation of joint shear force resistancewith normal bolts see chapter: "Normal bolts" on page 40.

Preloaded boltsSlip resistance of a preloaded bolts is calculated according to EN 1993-1-8 Art 3.9.1 and 3.9.2 in case combined tension andshear effect.

In Scia Engineer it is assumed, that bolts are placed in normal holes. Therefore, based on table 3.6, the coefficient ks isalwaysequal to 1.

For more info on calculation of joint shear force resistancewith preloadedl bolts see chapter: "Preloaded bolts" on page 41.

According to the Note in EN 1993-1-8, Art. 3.4.2 (1): If preload is not explicitly used in thedesign calculations for slip resistancesbut is required for execution purposesor asa qualitymeasure (e.g. for durability) then the level of preload can be specified in the NationalAnnex.

There isa possibility to define this coefficient in theNAsetup dialog for part EN 1993-1-8, tobe used in the calculation of preloading force Fp,C .

Bending moment resistance

Transformation factorThe transformation factor β is calculated according to EN 1993-1-8, Art 5.3 (9), formulas5.4a, 5.4b.

with:

Mj,b1,Ed themoment at the intersection from the right hand beam

Mj,b2,Ed themoment at the intersection from the left hand beam

The value of the transformation factor β is according to the reference limitedwith value of 2.0.

Bolt-row contributionThe EN 1993-1-8, Art 6.2.3 (9) specifies, that: In a bolted connection with more than one bolt-row in tension, as a sim-plification the contribution of any bolt-row may be neglected, provided that the contributions of all other bolt-rows closer tothe center of compression are also neglected.

Within Scia Engineer it is possible to neglect the contribution only for last bolt row. The last bolt-row is the one which is nor-mally located farthest away from the tension flange in a direction to the center of compression.

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Chapter 2

Bolt elongation lengthThe EN 1993-1-8, Art 6.2.4.1 Table 6.2 specifies Lb as the bolt elongation length, taken equal to the grip length (total thick-nessofmaterial andwashers), plushalf the sumof the height of the bolt head and the height of the nut.

Within SCIAEngineer:

Lb = tf+tep+(hh +hn)/2

with:

tf thicknessof the column flange

tep thicknessof the end-plate

hh height of the bolt head

hn height of the nut

If relevant also thicknessof awasher/sand thicknessof a backing plate isadded. In this case:

Lb = tf+tep+(hh +hn)/2 +alt (twh+twn+tbp)

with:

twh thicknessof thewasher at bolt head

twn thicknessof thewasher at nut

tbp thicknessof the backing plate

Similar formulas are being used in case of a splice connection. The thickness of a column flange tf is replaced by the thick-nessof the additional end-plate.

Classification of Bolt-rowsThe EN 1993-1-8 Art. 6.2.6.4 Table 6.4 and 6.5 and Art. 6.2.6.5 Table 6.6 specifies, how the bolt-rows should be classifiedeither for a column, respectively end-plate side. According to this classification effective lengths, both for individual andgroup approach, are calculated.

The classification for both sides has been extended based on publication Joints in Steel Construction - Moment -ResistingJoints to Eurocode 3 (P398) with relation to the possible yield lines and based on HERON vol. 20 publication by P. Zoete-meijer, with relation to the limit distance determining the border of influence of a stiffener or beam flange.

- 18 -


In general, if a space between bolt-row and a stiffener/beam flange is smaller than this "limit" value, the formulas taking intoaccount the presence of obstacle (formulas including α coefficient) should be used. The real distance is measured notexactly to the obstacle, but to the part of the adjacent obstacle weld (similar approach as in calculation of m distance given byEN 1993-1-8 Art. 6.2.6.4 Figure 6.8).

The smaller value of 'n' from left or right side end-plate extensions isused in case of not sym-metricend-plate.

Column sideWithin Scia Engineer, a bolt rowmaybe classified on a column side as:

l Bolt-row adjacent to stiffener - if the bolt row liesnext to a stiffener and iswithin limit distancel Other inner bolt-row - if the bolt-row liesbetween other bolt-rowsl Other end bolt-row - if the bolt-row liesnext to a stiffener, which is farther away to the axisof a connected beam, and is

outside the limit distancel End bolt-row adjacent to stiffener - if the bolt-row is the first or the last bolt-row, liesnext to a stiffener, which is closer

to the axisof a connected beaml Other end bolt-row at end of column - if the bolt-row is the first or the last bolt-row, liesnext to a stiffener, which is

closer to the axisof a connected beam, and isoutside the limit distance or if the bolt-row is the first or the last bolt-row anddoesnot lie next to a stiffener

l Bolt-row between stiffeners - if the bolt row is the onlybolt-row between stiffenersand lieswithin the limit distance ofboth stiffeners

Effective length formulas for column flange classifications :

- 19 -

Chapter 2

End-plate sideWithin Scia Engineer, a bolt rowmaybe classified on an end-plate side as:

l Bolt-row outside of beam - if the bolt-row liesoutside of the connected beamon an ustiffened end-plate extension (noplate haunch ispresent)

l Bolt-row adjacent to beam flange - if the bolt-row liesnext to a beam flange and iswithin limit distancel Other inner bolt-row - if the bolt-row liesbetween other bolt-rowsl Other end bolt-row - if the bolt-row liesnext to a beam flange, which is farther away to the axisof a connected beam,

and isoutside the limit distance or lieson a stiffened end-plate extension, liesnext to a beam flange and isoutside limit dis-tance

l Bolt-row at the end of stiffened extension adjacent to beam flange - if the bolt-row is the first or the last bolt-row, lieson a stiffened end-plate extension, liesnext to a beam flange and iswithin limit distance

l Bolt-row at the end of stiffened extension away from beam flange - if the bolt-row is the first or the last bolt-row,lieson a stiffened end-plate extension, liesnext to a beam flange and isoutside limit distance or if the bolt-row is the first orthe last bolt-row, lieson a stiffened end-plate extension and doesnot lie next to a beam flange

l Bolt-row between flanges - if the bolt row is the onlybolt-row between beam flangesand lieswithin the limit distanceof both flanges

Effective length formulas for end-plate classifications :

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For the calculation of group "start" and "end" partial effective lengths for bolt-rows clas-sified as "Other inner bolt- row", the formulas for "Other end bolt- row" are being used.(See also chapter: "Group of bolt-rows" below)

Group of bolt-rowsTheEN 1993-1-8 Art 6.2.4.2 specifies that each bolt-row should be considered either asan individual bolt-row and also asapart of the group of bolt-rows if possible.

Within Scia Engineer, we can split themaking "group of bolt-rows" approach into two steps:

l Define the borders for a group of bolt-rows. Presence of the beam/haunch flange or a stiffener createssuch a border. Asa result of that, we know towhich group everybolt-row belongs.

l Considering the first bolt-row (the one farthest away from center of compression) in each of the group frompreviousstep, asa starting bolt-row and byadding additional bolt-rowsbelow, the final groupsof bolt-rowsare generated. Thenwe do the same the second, the third and other bolt-rows, untilwe hit the last bolt-row.

Alpha coefficientTheEN 1993-1-8with Figure 6.11 indicates, how the coefficient α isdetermined.

Within Scia Engineer we use similar, but more exact method described in Ref [34], the publication by Ed. Moore D.B. andWald F.: Design of Structural Connections to Eurocode 3 – Frequently Asked Questions (Q&A 6.2 Effective Length ofStiffened T-stub).

The algorithm consist of several steps:

1 - calculate λ1 and λ2with the standard formulas

2 - make a first default estimate input to α

3 - calculate λ1* and λ2*

4 - calculate λ1,calc according to the formulasand conditions

- 21 -

Chapter 2

5 - compare λ1,calc with λ1.

5a - if the valuesmatchwith a certain precision, thenwewill use the estimated α

5b - if the valuesdoesnotmatch,modify the α and repeat the steps1-5 until 5a ishit

Calculated value of α must bewithin range of the interval <4.45;8>.

Numbering of bolt-rowsThe EN 1993-1-8, Art 6.2.7.2 (1) specifies in the that: In a bolted joint with more than one bolt-row in tension, the bolt-rowsare numbered starting from the bolt-row farthest from the center of compression.

Scia Engineer complies this specification with one assumption. The numbering always starts at bolt row farthest from thecenter of compression in the direction to the tension flange. Bolt rows which are located below center of compression areneglected asa start of thisnumbering.

Center of compressionIn accordance with EN 1993-1-8, Art 6.2.7.2 (2) for bolted end-plate connections, the center of compression is assumed tobe in linewith the center of the compression flange of the connectedmember.

Within SCIAEngineer:

l In case of a presence of a haunchwith flange in compression, the center of compression isassumed to be in linewith thecenter of the inclined compression flange of the haunch.

l In case of a presence of a plate haunch in compression, the center of compression isassumed to be in linewith the centerof the compression flange of the connectedmember. In fact in the same location, like if the plate haunch isnot present,therefore it isnot possible to define component "Stiffener at haunch end" in such case.

The inclination of the beam/haunch flange is taken into account in calculation of leverage arm for Mj,Rd determination.

The size of the haunch weld ac has no impact on the location of the center of compression.(See also chapter: "Haunchwith flange" on page 49)

In the splice connections, the positions of center of compression for each side may be loc-ated differently. Maximum difference may be equal to the minimum thickness of the adja-cent beam/haunch flanges from both sides. For any further calculations, the center ofcompression is taken from the side, where the boltshave been activated.

Connection componentsColumn web panel in shearComponent is calculated according to EN 1993-1-8 Art 6.2.6.1.

- 22 -


Remarks:(1) Not implemented.

(2) The calculation within Scia Engineer is valid also for a double-sided joint in which the beam depths are not similar or forstiffened columnweb panel.

(4) To take the additional resistance into account, the "Use stiffeners in column web panel resistance" has to be activated inthe connection setup and both top and bottom stiffenersare present in the connection.

For calculation of plasticmoment resistance of a column flange a separate calculation for each flange isused:

For calculation of plasticmoment resistance of a stiffener awidth of the column isconsidered.

It is assumed that both stiffeners are the same and fulfil the minimum criteria based on the connected beam. Values of tf,stifand fy,stiff are taken equal to the beam tf and fy.

ResistanceVwp,Rd is calculated as:

which has to be smaller than:

(5) When a diagonal stiffener is activated in a connection, the resistance of the component is taken equal to the "Beamflange and web in compression" component ((See also chapter: "Beam flange and web in compression" on page 27). Tri-angular diagonal stiffener isnot recognized asa stiffener, only rectangular diagonal stiffener is taken into account.

(6) The increase of the Avc area due to the presence of web doubler is implemented according to the article asbs*tw also forcase 2web plates.

(8)-(13) Checksnot implemented.

Column web in transverse compressionComponent is calculated according to EN 1993-1-8 Art 6.2.6.2.

Remarks:(1)The beff,c,wc for bolted connections is calculated according to the formula (6.11), where:

with:

sp_top

spread increase due to the dispersion through the end plate at top of the com-pression flange

sp_bot

spread increase due to the dispersion through the end plate at bottomof thecompression flange

- 23 -

Chapter 2

For bolted end-plate connections, normally both sp_top and sp_bot distancesare equal to ep due to the dispersion at 45°, butif:

l in a perpendicular connection, the end-plate bottomextension below the flange doesnot provide enough space for thespread through the end-plate, i.e.: the extension is smaller than (√2)*a +ep), the sp_bot is calculated as:

Effectivewidth beff,c,wc for a bolted perpendicular connection:

with:

ep thicknessof end-plate

a size of the flangeweld

tfb thicknessof a beam flange

tfc thicknessof a column flange

Platebot_ext bottomextension of the end-plate

The same logic will be used in case plate haunch is defined , since the center of the com-pression is located within bottom beam flange (See also chapter: "Center of compression"on page 22).

l in a haunchwith flange connection, end-plate bottomextension below the flange doesnot provide enough space for thespread from the end of the acweld (See also chapter: "Haunchwith flange" on page 49) through the end-plate, i.e.: theextension is smaller than ( ep - ( tfl / sin(α) - ac ) ) in case ac< tfl / sin(α), or than ( ep + ( ac - tfl / sin(α) ) ) in case ac>= tfl /sin(α, the sp_bot is calculated as:

Effectivewidth beff,c,wc for a bolted haunch connection:

- 24 -


with:

ep thicknessof end-plate

tfb thicknessof beam flange

tfc thicknessof a column flange

ac size of theweld between haunch and end-plate / column

α angle between column and the flange (haunch input degree)

Platebot_ext bottomextension of the end-plate

(2)To take the effect of axial force and bending moment in the column on the design resistance of the column web in com-pression into account, user has to activate "Include stress reduction in columnweb" check box in the connection setup. Onlythen the reduction coefficient kwc is printed on the output. Internal forces for the determination of the compressive stressσcom,Ed are taken from the node of the connection. The section for the internal forces is however not from the node directlybut from the section right next to it, in the direction to the center of compression.

(5)When a stiffener at the location of the center of compression is activated on a column side of a connection, the resistanceof the component is taken equal to the "Beam flange andweb in compression" component (See also chapter: "Beam flangeandweb in compression" on page 27).

(6)Column web thickness twc is taken alone, or as 1,5*twc or 2*twc , based on the presence of one or two web doublers.Shear area Avc for determination of ω values is taken from "Column web in shear component" (See also chapter: "Columnweb panel in shear" on page 22).

Column web in transverse tensionComponent is calculated according to EN 1993-1-8 Art 6.2.6.3.

Remarks:(3)The effective width beff,t,wc used in the formula (6.15) for the calculation of the design tension resistance of column webFt,wc,Rd for a bolted connection, are taken equal to the effective length of the "Column flange in transverse bending"

- 25 -

Chapter 2

component, with respect to the failuremode (See also chapter: "Column flange in transverse bending" below.

(6)If a transverseweb stiffener is found in the tension zone of a column, it isassumed, that the component will not fail and theresistance of each bolt-row is taken equal to the "Beam flange andweb in compression" component.

(8)For the calculation of tw,eff in case of a presence of web doubler it is assumed, that longitudinal welds are fillet weldswitha throat thickness satisfying the given condition, therefore the coefficient of 1,4 respectively 1,3, based on the usedmaterial,isused.

Column flange in transverse bendingComponent is calculated according to EN 1993-1-8 Art 6.2.6.4.

There is a distinction in the EN 1993-1-8 between un-stiffened (6.2.6.4.1) and stiffened (6.2.6.4.2) column flange, but sincethe content of article 6.2.6.4.1 can be also found in article 6.2.6.4.2, the remarksbelow are related to that article.

Remarks:(1)+(3)See chapter: "Group of bolt-rows" on page 21.

(2)The alternative method given in Art 6.2.4.1 by Table 6.2 may be used by activating "Use alternative method for Ft,1,Rd"checkbox in the connection setup. (See also chapter: "Bolt elongation length" on page 18)

(5)The effective lengths leff of an equivalent T-stub flange is using the values for each bolt-row given in Table 6.5 with oneexception. This exception concerns calculation of non-circular pattern for bolt-rowsclassified as " End bolt-row adjacent to astiffener ". In addition to the formula "e1+α*m-(2*m + 0,625*e)" an additional criterion of "α*m" is used. The minimum ofthese values is then used as leff,nc . (See also chapters: "Classification of Bolt- rows" on page 18, "Alpha coefficient" onpage 21)

Note: Vertical distance e1

The EN 1993-1-8, Art 3.5 Figure 3.1 specifies e1 as the end distance from the center of a bore hole to the adjacent end ofcolumn flange,measured in the direction of load transfer.

Within Scia Engineer thise1 distance ismeasured from the center of an edge bolt to the appropriate end of a column, wherethe connection isdefined. All internal nodeswith possible beamsand connectionsare neglected.

(6)Not implemented.

End-plate in bendingComponent is calculated according to EN 1993-1-8 Art 6.2.6.5.

Remarks:(1)The alternative method given in Art 6.2.4.1 by Table 6.2 may be used by activating "Use alternative method for Ft,1,Rd"checkbox in the connection setup. (See also chapter: "Bolt elongation length" on page 18)

(2)See chapter: "Group of bolt-rows" on page 21.

(4)Table 6.6 does not provide any formulas for such bolt-rows classified as "Bolt-row outside of beam" for calculation ofeffective lengths leff for bolt-row considered aspart of a group of bolt-rows.Within Scia Engineer thismeans, that for a con-nection design, on tension side of an end-plate it is not allowed to have more than one bolt-row classified as "Outside of a

- 26 -


beam". If more bolt-rows, classified as Outside of Beam, are found on the tension side of the conencted beam, the Errormessage is displayed and connection design proceedure is terminated. (See also chapters: "Classification of Bolt-rows" onpage 18, "Alpha coefficient" on page 21)

If an end-plate extension is found beyond the height of the existing plate haunch and a bolt-row is defined within, or even outside, this haunch, software recognizes this geometry asnot consistent with the yield line patterns and warning is being printed in the output. In thiscase a possible "jump" of yield line patternsmay occur, which is not covered byEN. A platehaunch gap near beam flange isassumed not to influence the yield line patterns.

Beam flange and web in compressionComponent is calculated according to EN 1993-1-8 Art 6.2.6.7.

Remarks:(1)The component resistance Fc,fb,Rd is calculated with equation (6.21), using the design moment resistance of the beamcross-section Mc,Rd calculated with influence of haunch/es if aplicable, If a connected member is inclined the Mc,Rd cal-culation doesnot take this inclination into account. The hauncheswithout flangesare also ignored in theMc,Rd caluclation.

The influence of the inclined section and inclined haunch flange is neglected in calculation of the leverage arm hb-tfb. Dif-ferent thicknessesof beamand haunch flange are however taken into account.

When calculation the sectionwith oneREAL haunchwith flange, the leverage armhb-tfb.is given as:

with:

(hb-tfb) leverage arm

hb height of the beamwithout haunch

tfb thicknessof the beam flange

hfull height of the haunch at the full end

lfull length of the haunch from the start to the full end

tfh thicknessof the haunch flange

lface length of the haunch from the start to the connection face

When calculation the sectionwith plate haunch, the leverage armhb-tfb.is calculated as if the haunch isnot defined.

The inclination of the beam/haunch flange isnot taken into account in calculation of leverage armhb-tfb neither inMc,Rd.

The rule, described by the last sentence of thispart, so-called 20% rule, is fully implemented. The limiting height of 600mm isbeing compared with total height of the section, excluding possible haunches without flange. The calculated limit is cal-culated by the formula below:

with:

- 27 -

Chapter 2

bh width of the haunch flange

th thicknessof the haunch flange

fyb yield strength of the beammaterial

Final component resistance is taken asaminimumof the initial value and the limiting value.

(2)Ahaunchwith flange has to fulfil the criteriamentioned below, given by the article:

– the flangewidth and thickness, and theweb thicknessof the haunch should not be less than that of themember;

– the angle of the haunch flange to the flange of themember should not be greater than 45°

If the criteria are not fulfilled awarning isbeing displayed.

(3)Not implemented.

Beam web in tensionComponent is calculated according to EN 1993-1-8 Art 6.2.6.8.

Remarks:(2)The effective width beff,t,wb used in the formula (6.22) for the calculation of the design tension resistance of beam webF t,wb,Rd for a bolted connection, are taken equal to the effective length of the " End-plate in bending" component, withrespect to the failuremode (See also chapter: "End-plate in bending" on page 26).

Haunch resistanceThe calculation isbased onRef. [3]and [4].

The compression force in the haunch should be transferred by the haunch into the beam. The formula used for the bucklingof the columnweb can also be applied to the check failure of the beamweb due to the vertical component of the force trans-ferred by the haunch. See Ref.[15], Annex 8-B. The influence of the local beam web buckling is taken into account by thefactor ρ.

This design moment resistance Mj,Rd is compared with the moment Mc at the position of haunch end. The moment Mc istaken from the section on the connected beamwith distance from the connection node equal to the∑(h/2; tep; lc).

with:

h height of the column

tep

thicknessof the end-plate

lclength of the haunch, not taking into account theweld size ab (calculated as tan(α)*hc)

If the Mc/Mj,Rd unity check is worse than the moment unity check of the whole connection, then it is used as a final momentunity check together with the resistance.

Haunch with flangeThemoment resistanceMj,Rd is given by:

- 28 -


with:

tf thicknessof the beam flange

tw thicknessof the beamweb

b width of the beam flange

α angle between haunch flange and connected beam

Af area of the beam flange (Af =b*tf)

Methe design elasticmoment resistance of the connected beam (Me =Wely * fy /γM0)

Mc themoment at haunch end position lc (maximum from two adjacent sections)

ρ local beamweb buckling coefficient

beff effectivewidth, beff =ab+5*(tf+r)

ab size of the haunchweld between haunch flange and beam flange

r rounding of the connected beam

dc length of a beamweb, dc =hb-2*(tf+r)

hb height of the connected beam

Ad effective area, Ad =beff*tw

See also chapters: "Haunchwith flange" on page 49.

In case a stiffener at haunch end is present the Mj,Rd resistance is equal to the elastic res-istance of the connected beamMe.

Haunch without flangeThemoment resistanceMj,Rd is not calculated in this case, since the center of compression is considered to be placed in thelower flange of the beam, therefore no force isbeing transferred into the beam.

See also chapters: "Haunchwithout flange" on page 52, "Center of compression" on page 22

- 29 -

Chapter 2

Bolt-rows with 4 boltsCalculation of resistance of a bolt-row containing 4 bolts is based on the publication: Application of Eurocode 3 to Steel con-nectionswith four boltsper horizontal (J.-F. Demonceau, K.Weynand, J.-P. Jaspart andC.Müller) - 2010.

The referencemakesa clear distinction between so-called "Outer bolt-row" and "Inner bolt-row" in order to define T-stubs,either vertical or horizontal.Within Scia Engineer this is related to the classification of bolt-row.

For theOuter bolt-row, the T-stub is vertical, and takes into account two bolts (the T-stubweb is the beam flange). The pres-ence of four bolts within this row only influence the values of the effective lengths. The modification of effective length for-mulas touchesonlyone bolt-row classification:

l Bolt-row outside of beam

For the Inner bolt-row, the T-stub is horizontal, and takes into account four bolts (the T-stub web is the beam web). Thepresence of four bolts within this row is taken into account bymodification of the effective lengths and by used formulas forbolt-row resistance. Themodification of effective length formulas touches these bolt-row classifications:

l Bolt-row adjacent to beam flangel Bolt-row at the end of stiffened extension adjacent to beam flangel Bolt-row between flangesl Bolt-row adjacent to stiffenerl End bolt-row adjacent to stiffenerl Bolt-row between stiffeners

For further info on the classification of bolt-row see the chapter "Classification of Bolt-rows" on page 18.

Effective length formulas for column flange classificationsused for 4 bolt per row:

- 30 -


Effective length formulas for end-plate classificationsused for 4 bolt per row:

The classificationswith white background were not modified in comparison with standard 2bolts per row formulas. These bolt-rowsare neglecting the 2 additional side bolts in the

- 31 -

Chapter 2

calculation of the tension resistance of the bolt-row, and therefore are used in full for shearresistance even if the bolt-row is in tension.

Extract of EN 1993-1-8 Article 6.2.4.1, Table 6.2 Mode 2 formulas to predict the design resistance of T-stubs for each pos-sible failuremode in casePrying forceswill develop.

The parameters used by the formulas are in general defined by EN 1993-1-8 Article 6.2.4.1, Table 6.2 with the exceptionthat for a T-stubwith 4 bolts (bolt row with the blue background in the tablesabove), n =(w2+e) with n≤1,25*m, n1 =w2 andn2 =ewith n2≤1,25*m+n1.

Conversion of the parametersused in the reference andScia Engineer:

Bolt-row picture FT,Rd formulas Scia Engineer

m1 m m

e1 n1 w2

e2 n2 e

Summary:

l Mode 1: All formulas for bothMethod 1 and 2, including backing plate or not, remain unchanged. Onlysome of the para-metersmayvary.

l Mode 2:Modified formulas for FT,2,Rd for bolt-rowswithmodified leff formulas (classificationswith blue background inthe tablesabove).

l Mode 3: Reduction coefficient 0,9 for bolt-rowswithmodified leff formulas (classificationswith blue background in thetablesabove).

If no prying forces will develop, initial formulas are to be used for Mode 1 and 2 resistances. Mode 3 resistance is modifiedwith the coefficient of 0.9.

An additional modification on the level of calculation of FT,Rd of groups of bolt-rows is implemented in the Scia Engineer.The reason for this is, that reference does not specify which FT,Rd formulas should be used for groups of bolt-rows whichcontain bolt-rowswithmodified effective lengths (calculated as4 bolts in a row) and those not modified (calculated as2 boltsin a row) in case prying forces will develop. If a group of bolt-rows containing both types of bolt-rows is found and for thisgroup prying forces would develop, this group is removed from the calculation. The removal is done only for components

- 32 -


"Column flange in bending" and "End-plate in bending". In calculation of another connection components the groups areused normally.

The "Outer bolt-row", as described above, is excluded from this modification, since it can-not be part of a group anyway. Only "Inner bolt-rows", as given by the reference, are pos-sibly removed.

The calculation of shear force resistance VRd, and possible different usage of the inner and outer bolts in a bolt- row isaccounted for. The reduction given byEN 1993-1-8 Art 6.2.2 of the shear resistance of the bolt-row is implemented accord-ing to the diagrambelow:

Inner and outer bolts in this context means the bolts which are closer or more far to thecolumn/beamweb.

For further info on the calculation of shear force resistance see the chapter "Shear force resistance" on page 40.

Rectangular Hollow SectionsTheRectangular hollow section are designed according to theRef.[22] andRef.[23].

The bolts can onlybe positioned outside theRectangular hollow sectionwith internal bolt distance not exceedingwidth of thesection. At least two bolt-rowsmust be present.

Beam-column connectionsThe Rectangular hollow section may be used as a connected beam in bolted column-beam connections. For further infosee also chapter: "Supported cross-sections" on page 14.

The normalprocedure described inRef.[32] is followed for the calculation of the connection characteristics.

The rotational stiffness isnot calculated due to the lackof theoryavailable.

Splice connectionsThe Rectangular hollow section may be used in bolted splice connections. For further info see also chapter: "Supportedcross-sections" on page 14.

For the calculation of the tension resistance of each bolt-row, refer to chapter "The design tension resistance" on page 69.

More info on the calculation of moment resistance may be found in chapter "The design moment resistance" on page 71neglecting the compression component resistance.


- 33 -

Chapter 2

Weak-axis calculation

GeneralThe calculation of out-of-plane moment M j,z,Rd resistance is based on the publications "DESIGN OF STRUCTURALJOINTS CONNECTING H OR I SECTIONS subjected to in-plane and out-of-plane bending" by Neumann N, Nuhic F:,EUROSTEEL, 2011 and publication "Single-sided structural beam-to-column joint of H- or I-profiles with bolted endplateexposed to in-plane and out-of-plane bending" byKristensenSO, Stavanger, 2010.

The study addresses the strong axis beam-to-column joints between H or I section members. The focus is on bolted end-plate joints, with two linesand two or more rowsof bolts symmetrical about both the beam'smajor and itsminor axis.

In Scia Engineer this theoryadoptedwhen needed, will be used for all strong-axis frame bolted beam-column and splice con-nectionswith I or H sections. Themethodwill be used only for 2 bolts / row configuration.

If needed, the complete weak-axis calculation (out-of-plane moment resistance Mj,z,Rd, shear force resistance Vy,Rd andstiffness for weak bending) may be skipped by activating "Neglect weak-axis calculation" check box in the connection setup.If so, the weak-axis calculation is not performed and amessage is displayed on the output in the part dedicated to the weak-axis calculation. The checkbox isdeactivated bydefault.

If the user wants to performweak-axis calculation (the check boxmentioned above is deactivated), but the connection doesnot fulfill the required conditions, weak-axis calculation is not performed and the user is informed about that. It is still possibleto calculate shear force resistance Vy,Rd even if the conditions are not fulfilled, but only in case design bending momentMz,Ed is zero.

The additional weak-axis bending unity check is displayed by the check and also linear interpolations for strong and weak-axis bending moment components are performed and unity checks calculated if weak-axis bending moment resistanceMj,z,Rd is calculated:

And in case of design normal forceNEd>0,05*Npl,Rd also:

For further info see chapter: "Interactionwith bending" on page 39.

ResistanceConnection geometryand design bendingmomentmaybe seen on the picture below:

- 34 -


The strong-axismoment resistanceMj,y,Rd of the joint is determined based on EN 1993-1-8, assuming noweak-axis bend-ing influence. Similarly to this, it is assumed that the strong-axis moment bending will not influence calculation of weak-axismoment resistanceMj,z,Rd of the joint.

Theweak-axismoment resistanceMj,z,Rd of the joint maybe determined by:

with:

yis the design distance from the bolt-line in tension to the center of compression for weak-axisbending. The leveragearm isdependent on the stiffnessof the components.Within Scia Engineer it isassumed, that joint componentsareinfinitely stiff. The additional split is based on the type of the bolts

with:

bb is thewidth of the beam (in case of non-symmetricbeamor splice connection theminimum isused

p2 is the horizontal spacing between the two linesof bolts

- 35 -

Chapter 2

Fta,Rd-is the effective design tension resistance of a bolt-line for theweak-axismoment calculation taken as:

with:

Fta,fc,Rd is the design tension resistance for bolt-line a of the column flange in transverse bending

Fta,ep,Rd is the design tension resistance for bolt-line a of the end-plate in bending

Fcb,fb,Rd is the design compression resistance for bolt-line b of the beam flange in compression

Fta,fct,Rd is the design tension resistance for bolt-line a of the column flange in twisting

Fta,wbc,Rd is the design tension resistance for bolt-line a of the columnweb in bending

For splice connections only Fta,ep,Rd and Fcb,fb,Rd component resistances are calculated for each side and minimum res-istance from the four components is taken asFta,Rd.

Calculation of theweak-axis componentsmaybe seen below:

Column flange in bending

The component resistance Fta,fc,Rd for each bolt-row is already calculated according to EN 1993-1-8 Art.6.2.6.4 in strong-axis moment resistance calculation as resistance Ft,fc,Rd. The final bolt-row resistances for that component are shown inthe appropriate columns in the table of potential tension resistances, where the individual and group approaches areaccounted for.

Since tension of weak-axis bending concerns only one side of the connected member, the final weak-axis component res-istance for each bolt Fta,fc,Rd is calculated asFt,fc,Rd, divided by two.

For further info on the calculation of the strong-axis F t,fc,Rd component resistance see chapter: "Column flange in trans-verse bending" on page 26.

End plate in bending

The component resistance Fta,ep,Rd for each bolt-row isalreadycalculated according to EN 1993-1-8 Art.6.2.6.5 in strong-axis moment resistance calculation as resistance Ft,ep,Rd. The final bolt-row resistances for that component are shown inthe appropriate columns in the table of potential tension resistances, where the individual and group approaches areaccounted for.

Since tension of weak-axis bending concerns only one side of the connected member, the final weak-axis component res-istance for each bolt Fta,ep,Rd is calculated asFt,ep,Rd, divided by two.

Minor modification in calculation of effective length for individual approach is done for bolt-rows classified as "Bolt-row out-side of beam". Compared to the strong-axis calculation, the patterns breaching the z-axis of the connected beam wereremoved.Weak-axis calculation formulas for the given classificationmaybe seen below:

- 36 -

Beam flange in compression

The T-stub resistance of such bolt-row is calculated in a standard way, only using modified effective length. The re-cal-culatedweak-axis component resistance isusedwith full value in the Fta,ep,Rd resistance.

For further info on the calculation of the strong-axis Ft,ep,Rd component resistance see chapter: "End-plate in bending" onpage 26.

Beam flange in compression

The design component resistance Fcb.fb.Rdmay be taken as the design compression resistance of one beam flange. Finalresistance of the component isgiven as:

with:

fy is the yield strength of the beam

tfb is the thicknessof the beam flange

γM0 is the partial safety factor for resistance of cross-sections

beff,wbc is the effectivewidth of the component given as:

but not greater than :

For splice connection the bc,fb,eff is calculated onlyas:

where:

twc is the thicknessof the columnweb

tfc is the thicknessof the column flange

tep is the thicknessof the end-plate

rc is the rounding r1 of the column

bb is thewidth of the beam

k thickness reduction coefficient given as:

- 37 -

Chapter 2

In case of non-symmetricbeam isused, calculation isassuming symmetric sectionwhile using theminimumvalue.

Column flange in twisting

The design resistance of the bolt-line in tension for the column flange in twisting Fta,fct,Rd is taken as :

with:

bc is thewidth of the column


fyc is the yield strength of the column

γM0 is the partial safety factor for resistance of cross-sections

y is the design distance from the bolt-line in tension to the center of compression for weak-axisbending

Column web in bending

For determination of the design resistance of the bolt -line in tension for the column web in bending Fta,wbc,Rd the effectivelength of theweb in bending beff,wbc is proposed to be calculated assuming amaximumspread at 60° from the outer bolts.

with:

twc is theweb thicknessof the columnweb

beff,wbc is the effective length of theweb in bending given as:

with:

∑p1 is the vertical spacing between the first and last bolt-row

p2 is the horizontal spacing between the two bolt-lines

Normal force resistanceNormal force resistanceNj,Rd is based on componentsdefined in EN 1993-1-8 Table 6.1.

- 38 -

Columnweb in bending

Beam-column connectionsIn caseNj,Ed is a tensile force, theNj,Rd is determined byaminimumvalue for the following components:

For bolted connections, based both on the individual and group approach (sum of calculated minimum values of each bolt-row):

l component 3 : Columnweb in transverse tensionl component 4 : Column flange in bendingl component 5 : End-plate in bendingl component 8 : Beamweb in tension

For welded connections :

l component 3 : Columnweb in transverse tension (the value for tfb in formula (6.16) is replaced by the beamheight)

In caseNj,Ed is a compressive force, theNj,Rd is determined by the following components:

For bolted andwelded connections:

l component 2 : Columnweb in transverse compression (the value for tfb in formulas (6.10) and (6.11) is replaced by thebeamheight)

l component 7 : Beam flange andweb in compression (initial component resistance ismultiplied by2 to take the resistanceof the 2nd flange into account)

Splice connectionsIn caseNj,Ed is a tensile force, theNj,Rd is determined byaminimumvalue for the following components:

For bolted connections, based both on the individual and group approach (sum of calculated minimum values of each bolt-row fromboth left and right side):

l component 5 : End-plate in bendingl component 8 : Beamweb in tension

For welded connections :

l Resistance isnot calculated due to the lackof theoryavailable.

In caseNj,Ed is a compressive force, theNj,Rd is determined by the following components:

For bolted andwelded connections:

l component 7 : Beam flange andweb in compression (initial component resistance ismultiplied by2 to take the resistanceof the 2nd flange into account)

In all cases, Nj,Rd£Npl,Rd.

Interaction with bendingTheEN 1993-1-8 Art 6.2.7.1 (3) specifies that: If the axial forceNEd in the connected beamexceeds5% of the design plasticresistance, Npl,Rd , the following conservativemethodmaybe used andM+N unity check isadded in theResultsdialog:

with:

- 39 -

Chapter 2

My,Ed the design bendingmoment in connection

Mj,y,Rd the designmoment resistance of the joint, assuming no axial force

NEd the design normal force in the connection

Nj,Rd the axial design resistance of the joint, assuming no appliedmoment

Shear force resistance

Normal boltsThe design shear resistance of a connection is calculated according to EN 1993-1-8 Art 6.2.2.

As it is described in EN 1993-1-8 Art 6.2.2 (2), the contribution of each bolt is dependent on the fact, whether the bolt shouldresist the tension or not. Each bolt contributeswith:

l the total design shear resistance of the bolt if bolt isnot required to resist any tensionl 0.4/1.4 of the total design shear resistance of the bolt if bolt is required to resist also tension (interaction doesnot apply to

anchor bolts in column base connections)

The design shear force resistance of a joint Vz,Rd is then calculated as:

with:

Fv,Rd

design shear resistance of a bolt calculated according to EN 1993-1-8 Art 3.6.1Table 3.4

nt number of boltswhich are also required to resist tension

nn number of boltswhich are not required to resist tension

The design bearing resistance of a joint Fb,Rd of a bolt is calculated according to EN 1993-1-8 Art 3.6.1 Table 3.4 separatelyfor each relevant component:

l the bearing resistance for endplate Fb,ep,Rdl the bearing resistance for column flange Fb,fc,Rd

with:

ntot total number of bolts

The final design shear force resistance of a joint Vz,Rd is taken asminimum of design shear force resistance and the designbearing resistance of a joint.

For further info on calculation of shear force resistance of a normal bolt see chapter: "Normal bolts" on page 17.

For further info on the calculation of shear force resistance for connection with 4 bolts per row see the chapter: "Bolt-rowswith 4 bolts" on page 30.

- 40 -


Preloaded boltsThe design shear resistance of a connection is calculated according to EN 1993-1-8 Art 6.2.2 assuming the bolt resistanceFs,Rd and all bolt are not sustained to tension due to the preload.

The design shear force resistance of a joint VRd is thuscalculated as:

with:

Fs,Rd

design slip resistance of a bolt calculated according to to EN 1993-1-8 Art 3.9.1or 3.9.2.

ntot total number of bolts

For further info on calculation of shear force resistance of a preloaded bolt see chapter: "Preloaded bolts" on page 17.

Beam resistanceIt is also important to verify that the joint shear resistance of bolts, calculated above, is not limited byshear force resistance ofa connected beam(s). The plastic resistance of the beam in general is calculated according to EN 1993-1-1 Article 6.2.6 (2)as:

with:

fy yield strength of beammaterial

γM0

partial factor for resistance of cross-sections

Avis the shear area of a connected beamcalculated for different cross-sectionsasindicated by the table below distinguished for strong andweak-axis calculations:

with:

- 41 -

Chapter 2

b is the overallwidth

h is the overall height

hw

is the depth of theweb

r is the root radius

tf is the flange thickness

tw

is theweb thickness

η national annexcoefficient defined byEN 1993-1-5 Article 5.1.(2).

A

is the cross-sectional area always taken from the cross-section library in case a"real" haunch isnot defined on a connected beam. If a real haunch isdefined on aconnected beam, the area of cross-sectionwithout haunch iscalculated by formulabelow (distinction between top and bottom flange isused by the formula variables):

The final shear area Av area also include the appropriate area of the defined haunch(es) if defined. The added area of ahaunch iscalculated as:

l the area of the haunchweb for strong-axis shear resistanceVz,Rdl the area of the haunch flange for weak-axis shear resistanceVy,Rd

According to the publication "Design example of a joint with extended end plate" byD.Grotmann, J.P.Jaspart, M.Steenhuis,K.Weynand, 1993, the reduction of the final VRd resistance needs to be done to take into account the fact, that the part ofthe connected beam is already used in tension. The part of a cross-section, recognized to be in tension, is determined inmeansof a vertical distance l1 from the top of the steel section (assuming that the tension ison top of the section) to the pointwhere the tensile yield line pattern from the last bolt row in tensionmaydevelop.

In general thismeans that distance l1 is calculated as sum of distance between top of the beam and the last bolt-row in ten-sion and the distance calculated as 2*m+0,625*e. If the value is negative, reduction coefficient l1 is set to zero and no reduc-tion needs to be done. On the other hand distance l1 is limited by the height of the beam and in such case coefficient l1 is setto 1. See picture below.

The last bolt-row in tension is recognized as such bolt row, which is the closest to the center of compression and is still con-tributing to the final bending moment resistance Mj,y,Rd. This means that the force Ft,r,Rd in the bolt-row is not zero in the"Determination ofMj,y,Rd" table.

The reduced shear force resistance is then calculated by themodified formula:

- 42 -


with:

l1

coefficient calculated as l1/h and representing relative part of a cross-sectionwherethe reduction isneeded

l2

coefficient calculated as1-l1 and representing relative part of a cross-sectionwherethe reduction isnot needed

In case a bolt-row classified as "Outside of beam" is recognized as the last bolt-row in ten-sion, the formula for calculation of the half of the additional yield line pattern, in the cal-culation of distance l1, ismodified to 2*mx+0,625*ex.

Weak axis calculationThe shear resistance calculation is similar to the strong-axis shear resistance calculation, however severalmodificationsareneeded in calculation of:

l The design shear force resistance of a joint Vy,Rd for normal bolt:

For weak-axis shear force resistance Vy,Rd the number of bolts nt ,which are also required to resist tension, andnumber of bolts nn ,not required to resist tension, is set to half of the total number of all bolts each. The aboveapplies to the case when a design bending moment Mz,Ed is present. If the design bending moment Mz,Ed iszero, the number of boltsnt is set to zero and number of boltsnn is set to number of all bolts.

l The design bearing resistance of a joint Fb,Rd

The endplate Fb,ep,Rd and column flange Fb,cf,Rd component resistances are re-used. No resistance recal-culation isdone for weak-axis.

l The reduction of shear force resistanceVpl,Rdof the connected beam:

The shear force resistance Vy,Rd of a beam the formula given by EN 1993-1-1 Article 6.2.6 (2) is used, but thefinal resistance ismultiplied bycoefficient 0,5.

For further info see chapter: "Shear force resistance" on page 40.

The additional weak-axis shear unity check is displayed by the check and also linear interpolations for strong and weak-axisshear force components isperformed and unity checkscalculated if weak-axis shear force resistanceVy,Rd is calculated:

For further info onweak-axis calculation see chapter: "Weak-axis calculation" on page 34.

- 43 -

Chapter 2

Weld size calculation

Calculation of flange weld sizeWithin Scia Engineer there is a possibility to choose from three methods for determination of the flange weld sizes bymodi-fying theWeld size determination parameter in the connection setup.

Minimum for full strengthThe default calculation of flangeweld size isbased on theRef. [35] - ECCSN°126. The final formula isderived as:

with

fy the yield strength of theweaker part

fu the ultimate tensile strength of theweaker part

βW the correlation factor

γM0 the partial safety factor for material

γM2 the partial safety factor for welds

t the thicknessof the beam flange

Calculated from connection resistanceThe weld size af is designed according to the resistance of the joint. The design force in the beam flange can be estimatedas:

with:

FRd the design force in the beam flange

Mj,Rd the designmoment resistance of the connection

h the lever armof the connected beam

The design resistance of the weld Fw should be greater than the flange force FRd, multiplied by a factor α. The value of thefactor α is specified in theRef. [34] - EN 1993-1-8, Art 6.2.3 (5).

α =1.7 for sway frames (braced)

α =1.4 for all other frames (unbraced)

However, in no case should theweld design resistance exceed the design plastic resistance of the beam flangeNt.Rd :

with:

- 44 -


bf thewidth of a beam flange

tfb the thicknessof a beam flange

fyb the yield strength of the beammaterial

Dimensionsof the smaller flange are used in the calculation.

The final design resistance of theweld Fw should be taken assmaller of: α*FRd andNt.Rd.

Theweld size design for af, usingRef.[32] - EN 1993-1-8 Art. 4.5.3 andRef.[35] - ECCSN°126:

with.

Fw the design resistance of theweld

bf thewidth of a beam flange




Calculated using Internal forcesThe weld size af is then designed similarly as in the prevous method (See also chapter: "Calculated from connection res-istance" on the previous page), with the only difference that resistance Fw is taken as minimum of the above and force Fobtained from the internal forcespresent in the connection. The force is calculated as:

Calculation of web weld sizeWithin Scia Engineer there is a possibility to choose from two methods for determination of the flange weld sizes by modi-fying theWeld size determination parameter in the connection setup. (In case of web welds 2nd and 3rdmethod are recog-nized asone - based on connection type)

Minimum for full strengthThe default calculation of flangeweld size isbased on theRef. [35] - ECCSN°126. The final formula isderived as:

with




- 45 -

Chapter 2



t the thicknessof the beamweb

Calculation of aw for welded connectionCalculation of theweld size aw isbased on theRef[14], pp.545.

In the section, the moment M is defined by the critical design moment resistance of the connection. The normal force N istaken as the maximum internal normal force in the node, the shear force V is taken as the maximum internal shear force inthe node.

We can define the following properties:

a1 =afa3 =afa2 =aw (to be calculated)

l1 =bfl2 =h –2 tfb –2r

l3 = (bf – twb – 2r) /2

- 46 -


with:

bf the beam flangewidth

tfb the beam flange thickness

r the radiusof root fillet

twb the beamweb thickness

a1 theweld size a1a2 theweld size a2a3 theweld size a3l1 the length for weld size a1l2 the length for weld size a2l3 the length for weld size a3A the sectional area of thewelds

I themoment of inertia of thewelds

To determine the weld size a2 in a connection, we use a iterative process with a2 as parameter until the Von Mises rules isrespected. SeeRef.[32] - EN 1993-1-8 Art. 4.5.3.

with:




Calculation of aw for bolted connectionCalculation of theweld size aw isbased on theRef. [32] - EN 1993-1-8 Art 4.5.3.

- 47 -

Chapter 2

For all possible bolt bolt-rows and groups of bolt-rows, the maximum tension per unit length is calculated. The tension perunit length is calculated as (Fi +Fi+1)/lw.

with:

Iw taken as the effective length of non-circular pattern (leff,2) for the considered bolt-row or group of bolt-rows.

On the weld 2 x l2 x a2, the normal force N =Fi +Fi+1 and the shear force V is acting. The shear force is taken as that part ofthemaximum internal shear force on the node that isacting on the bolt rows i and i+1. (pure bolt-row ratio- to be checked)

To determine the weld size a2 in a connection, we use a iterative process with a2 as parameter until the Von Mises rules isrespected. SeeRef.[32] - EN 1993-1-8 Art. 4.5.3. The iteration startswith theweld a2 equal to 1mm.

with:




A weld area (2*a2*l2)

In case the option "Calculated using internal forces" is chosen in the connection setup, theT-stub resistances are not calculated and themethod used for welded connections is usedalso for bolted connections.

- 48 -


Calculation of haunch weldsHaunch with flangeThe calculation isbased onRef. [3],Ref. [4]andRef. [35].

Theweld size ab (weld between haunch and beam) isgiven by:

A similar formula isused for theweld size ac (weld between haunch and endplate/column):

where:

with:


tw|thickness of the

- 49 -

Chapter 2

beam web


hc height of the haunch, not taking into account theweld size ac

β angle between column and haunch flanges

lc length of the haunch, not taking into account theweld size ab(calculated as tan(α)*hc)

bc width of the haunch flange


h height of the column

Me the design elasticmoment resistance of the connected beam(Me=Wel,y * fy)

Mc themoment at haunch end position lc

fy the yield tensile strength of theweaker part



γM0 the partial safety factor


For the design, it is assumed thatMc=Me.

The denominator (10*tf+2*tw) represents the designwidth (bd) of the haunch flange. It can-not be bigger than thewidth of the haunch flange bc.

The haunch weld size representation is set to "Length" by default in the connection setup. In this case the direct values aband ac weld sizes are represented in the graphics and connection monodrawings. In case "Fillet" haunch weld size rep-resentation is selected in the connection setup, the represented size of both welds is recalculated using notation and for-mulasbelow.

Weld dimensions for weld ab:

- 50 -


Weld dimensions for weld ac:

with:

ab final haunchweld ab size calculated according to the "Length" approach

ac final haunchweld acsize calculated according to the "Length" approach

α angle between column and haunch flanges (input angle for haunch)

β angle between beamand haunch flanges

γ complementaryhaunch angles (γ=180-α-90; γ=180-β-90) asappropriate

tf thicknessof the haunch flange

- 51 -

Chapter 2

S area of theweld triangle

d outer length of the hanchweld

See also chapters: "Calculation of flangeweld size" on page 44, "Haunchwith flange" on page 28.

Haunch without flange

Theweld size awc isgiven by :

with:




hc height of the haunch, not taking into account theweld size ac

twc

thicknessof the haunch plate (web)

α angle between haunch flange and direction perpendicular to the column

lclength of the haunch, not taking into account theweld size ab (calculated as tan(α)*hc)

Me the design elasticmoment resistance of the connected beam (Me=Wel,y * fy/γM0)

Mc themoment at haunch end position lc

For the design, it is assumed thatMc=Me.

- 52 -


See also chapter: "Haunchwithout flange" on page 29

Stiffener dimensionsThe stiffener thickness th is designed according to the resistance of the joint. The design resistance of the stiffener isequal tothe design resistance of theweld Fw (See also chapter: "Calculated from connection resistance" on page 44)

with:

Fw the design resistance of theweld taken assmaller of: α*FRd andNt.Rd.

bfthe beam flangewidth taken as the smaller flangewidth in case of un-symmetricbeam

fy the yield strength of the stiffener

γM0the partial safety factor

th the thicknessof the stiffener

The final thickness of the stiffener is multiplied by the ratio of fy,beam /fy,stiffener to assure that the stiffener will be strongenough to transverse the force from the beam.

In case conditions for aplying the additional resistance the the "Column web in shear" component (for further info see"Column web panel in shear" on page 22 chapter) are fulfilled, the calculated stiffener thickness is taken equal to the thick-nessof the bottom flange of the beam.

For calculation of weld sizes of stiffeners perpendicular to the column/beam flange, the same method described "Minimumfor full strength" on page 44 in chaper Calculation of flange weld size, is used. The calculation is based on the Ref. [35] -ECCSN°126. The final formula isderived as:

with






t the thicknessof the stiffener

Each stiffener thickessandweld size is calculated separately, based on the usedmaterial.

Thickness of the web doubler is always taken as the inputted thickness of that component. Weld size of a web doubler withrelation to the article EN 1993-1-8, Art 6.2.6.3 (8), isbased on the type of theweb doubler:

- 53 -

Chapter 2

l Smallmeans that fillet weldsare used for the component and theweld size is calculated as:

l Largemeans that butt weldsare used for the component and theweld size is calculated as:

Welded splice connections

Consider the figure above:

Whenwewrite the horizontal equilibrium in point A, we have :

Whenwewrite the vertical equilibrium in point A, we have :

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

b thewidth of the endplate

t the thicknessof the endplate

fy the yield strength

γM0 the partial safety factor for resistance of cross-section to overall yielding

Out of the vertical and horizontal equilibrium, and the value for Fep in the limit state, we can calculate the maximum forceFfl,right and Ffl,left. These valueswill result in the design resistance of endplate in compression Fc,ep,Rd for both sides.

- 54 -


Minimumof the above resistance and resistance of "Beam flange andweb in compression"component is then being used for the calculation of bending moment resistance Mj,Rd forsuch connection.

Column base connectionsIf EN 1993-1-8 is selected, the column base connection isdesigned according toRef.[32] :

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

In all other cases, the following rulesare applied :

"The design compression resistance" below

"The designmoment resistance" on page 58

"The design tension resistance" on page 60

Partial safety factor γcFor a Base plate connection design, the partial safety factor for concrete γc is to be defined, independently of EN 1992setup, in the EN 1993-1-8NAsetup.

The design compression resistanceThe determination of NRd,c is based onRef. [5]

with

A the resulting bearing area (The area in compression under the base plate)

f j the bearing strength of the joint

For the determination of the resulting bearing area the additional bearingwidth c is introduced.

with:

t the thicknessof the steel base plate.

fy the yield strength of the steel base platematerial.

- 55 -

Chapter 2

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

Where the projection of the base plate exceedsc the additional projection should be neglected, see figure.

with

A bearing area

A' area not included in bearing area

The bearing strength of the joint fj is determined from:

with

- 56 -


βj

the joint coefficient, which may be taken as 2/3 (0.667) provided that the char-acteristic strength of the grout is not less than 0.2 times the characteristic strengthof the concrete foundation and the thickness of the grout is not greater than 0.2times the smallest width of the steel base plate.

This value can be set in theConcrete Basicdata.

fcd

is the design value of the concrete cylinder compressive strength of the concrete

given by:

in which fck is the characteristic cylinder compressive strength of the concretedetermined in conformitywith Ref. [6].

This value can be set in theConcrete data.

γc is the partial safety factor for concrete material properties given in Ref. [6]. Thisvalue can be set in the Safety factorsdialog box.

kj

the concentration factor

where

a&b are the dimensionsof the base plate

a1&b1 are the dimensionsof the effective area.

See figures.

For a1 the least of the following should be taken:

l a1=a+2arl a1=5a

l a1=a+h

l a1=5b1 but a1≥a

For b1 the least of the following should be taken:

l b1=b+2brl b1=5b

l b1=b+h

l b1=5a1 but b1≥b

Note 1:Conservatively kj can be taken as1.0, The value can be set in the concrete data.

Bp=Base plate

- 57 -

Chapter 2

Cf=Concrete foundation

The design moment resistanceThe determination ofMRd is based onRef. [1].

The following remarksaremade.

l The resistancemoment of the base plate iselastic, therefore the calculation of FtRd is donewith

l Anew joint component is introduced: The concrete in compression. The design compression resistance for concreteunder the flange.

fj the bearing strength of the joint

Afl the bearing area under the compression flange. See the following figures.

- 58 -


- 59 -

Chapter 2

The design tension resistanceThe determination of NRd,t is based onRef.[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.

The design shear resistanceEN 1993-1-8 Article 6.2.2 (8) specifies how the shear force resistance Fv,Rd should be calculated for base plate con-nections. The design friction resistance Ff,Rd is specified in the same article in part (6) and should be taken into account onlyin case compressive normal force. If normal force is tensile, then the Ff,Rd is equal to zero. In Scia Engineer it is possible toneglect the friction resistance also in case compressive normal force. This can be done by deactivating the "Frictionincluded" checkbox in concrete data of the connection. Bydefault. thisoption isdeactivated.

Nc,Ed the design compressive force

Cf,d the friction coefficient between base plate and grout layer (≅0.20)

Note: In calculation of shear force resistance Fv,Rd , the rule described in EN 1993-1-8Article 3.6 Table 3.4 (28% rule) is not being applied in base plate connections. This inter-action of shear and tensile forces is already taken into account by coefficient αb in F2,vb,Rdformula given in EN 1993-1-8 Article 6.2.2 (7).

The design shear resistance for shear iron.The calculation of the shear resistance for shear irons isbased onRef. [7] pp116-120.

- 60 -


The design shear resistance for I shaped shear iron.

Consider the figure.

The design shear resistance for I shaped shear iron isgiven by theminimumof the following shear resistance :

l VRd,1 : limited by the concrete capacity

l VRd,2 : limited by the stress in the shear iron flange

l VRd,3 : limited by the stress in the columnweb

l VRd,4 : limited by the shear capacityof the shear iron

The following formulasare used :

with

fcd the design value of the concrete cylinder compressive strength of the concrete

Lq the length of shear iron

b thewidth of the shear iron

h the height of the shear iron

t the flange thicknessof the shear iron

hc the height of column

- 61 -

Chapter 2

fyd,s the yield strength of the shear iron

fyd,c the yield strength of the column


tp the thicknessof baseplate

kc 1.4 awcawc theweld size for columnweb/base plate

Av the shear area of shear iron

twc theweb thicknessof the column

∆l 30mm

The design shear resistance for angle shaped shear iron.

Consider the figure.

The design shear resistance for angle shaped shear iron isgiven by theminimumof the following shear resistance :

l VRd,1 : limited by the concrete capacity

l VRd,2 : limited by the stress in the shear iron

l VRd,3 : limited by the shear capacityof the shear iron

The following formulasare used :

with

- 62 -


fcd the design value of the concrete cylinder compressive strength of the concrete

La the length of shear iron

da the height of the shear iron

t the flange thicknessof the shear iron

hc the height of column

fyd the yield strength of the shear iron


tp the thicknessof baseplate

∆l 30mm

The anchorage length

CalculationThe determination of the anchorage length of the holding down bolts isbased onRef. [6].

The required anchorage length lb,net is calculated from:

with

the diameter of the holding down bolt.

fyd

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

fu the ultimate tensile strength of the anchor

γMb

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

f bd

the design value for the ultimate bond stress.

fbd is dependent on the bond condition, which normally is good for a column baseand also dependent of the type of holding down bolts. (plain or high bondbars)The bond condition and the type of bars can be set in the concrete data dia-log box.

lbthe basicanchorage length.

αa is dependent on the anchoragemethod.

- 63 -

Chapter 2

=1 for straight bars.

=0.7 for curved bars.

As,req is the required tensile stressarea of the anchor

with

Ft,bolt themaximum tensile force in the anchors. (due toNRd,t or MRd)

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

fu the ultimate tensile strength of the anchor

As,prov is the provided tensile stressarea of the anchor

lb,min is theminimumanchorage length

lb,min is themaximumof 0.3 lb , 10

Calculation according to internal forcesThe tensile force in the anchor can be calculated using the actual internal forces. This calculation is based on the regulationsgiven in ref.[24], chapter 6.4.1.

This settingmaybe changed in theConnection Setup.

Consider the following configuration :

- 64 -


Moment equilibriumgives :

Ft is the tensile force for each anchor row in the tension zone,Mand N are the actual internal forces.

When Ft<0, all anchorsare in compression. Theminimumanchor length is calculated.

When Ft>0.0, the value for Ft,bolt is calculated.

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

Design of the washer plate.The design of a circular plate isbased onRef. [7]

The allowable tensile forceNj in 1 anchorage isgiven by:

with

- 65 -

Chapter 2

v the smallest of l and d1. See figure.

Bymeansof this formula r, the radiusof the circular plate isdetermined.

The iterative process is started using 2,5 times the anchor diameter asan initial value for r.

The thickness t isgiven by

with

E Modulusof elasticity for anchorage.

The influence of the normal forceWhen the axial forceNSd in the connectedmember exceeds10% of the plastic resistanceNpl,Rd of its cross-section, awarn-ing isprinted out andMj,Rd is decreased.

The value of the designmoment resistanceMj,Rd is decreased by the presence of the axial tensile forceNSd.

with

h the distance between the compression and tension point in the connectedmember

If there isan axial compression forceNSd, we check the following :

- 66 -


with

h the distance between the compression and tension point in the connectedmember

Fc,Base,Rd

Design compression resistance for concrete under the flange

Fc,fb,RdBearingResistance for column flange

Ftot The sumof the tensile forces in the anchor rowsatMj,Rd

Rectangular Hollow SectionsThe Rectangular hollow section may be used in bolted column base connections. For further info see also chapter: "Sup-ported cross-sections" on page 14.

TheRectangular hollow section are designed according to theRef.[22] andRef.[32].

The bolts can onlybe positioned outside theRectangular hollow sectionwith internal bolt distance not exceedingwidth of thesection. At least two bolt-rowsmust be present.


The design compression resistanceThe determination of NRd,c is :

For more information, see chapter "The design compression resistance" on page 55.

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

- 67 -

Chapter 2

Where the projection of the base plate exceedsc the additional projection should be neglected, see the figure,

with

A Bearing area

A' Area not included in bearing area.

- 68 -


The design tension resistanceConsider the following figures :

- 69 -

Chapter 2

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

with

tp plate thickness

fyp yield strength of plate

d’ bolthole diameter

d bolt diameter

ti thicknessof RHSsection

a,b see figures

p

=2e

=w/2

=2e

=w

Ft,Rd design tension resistance of a bolt

The total design tension resistanceNt,Rd is then

- 70 -


The design moment resistance

MRd isgiven by

with

FT ΣFT,Rd,i for the bolts in tension

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

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

with

fj the bearing strength of the joint

Afl the bearing area under the compression flange.

- 71 -

Chapter 2

The design compression resistance for theRHScompression flange, Fc,rhs_flange is :

with

b width of RHSsection

t thicknessof RHSsection

fy yield strength of RHSsection

γM0 partial safety factor

Column minor axis connectionsIntroductionIn Ref.[21], some extensions are proposed to design the behavior if the beam is attached to the column web through someelement asangle, plate…etc. The implementation isbased on thisproposals, and are described in the following chapters.

The new components are the column web submitted to punching shear and bending. Different failure mechanisms ofcolumnweb have been analysed and are essentiallybased on the yield line theory.

- 72 -


The moment resistance and the rotational capacity of a minor-axis joint is calculated based on the methods as proposed inRef.[1].

The following elementsare taken into account in the design procedure:

l Columnweb in bending and punchingl Bolts in tensionl End plate in bendingl Beamweb in tensionl Beam flange andweb in compression

The figure shows some common types of minor-axis connections where beams are assembled with column web withoutstiffeners.

Strength of column web in bending and punching

GeneralThe plastic resistance of the web results from its yielding and from a progressive apparition of plastic yields line mechanism.The failure modemechanism is divide into twomain groups: the local and the globalmechanism similarly to those proposedin Ref.[1] J.3.6.2 (5) & (6). A local mechanism means that the yield line is localized only in the compressive zone or in thetensile zone of the joint while global failuremode design the yields line pattern involvesboth in compressive and tensile zone. In the design model, it is assumed that prying action between end plate or the angle cleat doesn’t occur. This assumption isconflicting 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 in transverse compression ortension is finallydefined as: FRd=min(Flocal,Fglobal).

- 73 -

Chapter 2

Definition and design of local and global failure modeThe moment carried out by the beam to the column web may be decomposed in a couple of forces F acting in the com-pressive and the tensile zone. It is assumed that these forces act on an area (compressive and tensile zone) defined in theplane of the columnweb. The design value of themoment resistance can be calculated as follows:

with

z the lever arm in the joint

FRd the resistance of theweakest axis component in theminor axis joint

Basic failuremechanismsare obtained byyields linemethod.. In the flexuralmechanism, it is assumed that plasticmoment isnot reduced by the presence of shear forcesperpendicular to the plane web. The plasticmoment per unit length of yield lineisgiven by:

where fy is the yield stressand tw the thicknessof the columnweb.

Local failure mechanismIn the local failuremode different localmechanismsof the columnweb are considered. The force F actson a rigid rectangle.This rectangle is defined by the dimensions bxc (see figure). The weld perimeter rectangle around the beam flange or theloaded area around the bolt pattern defined the rigid rectangle. The yield pattern is localised in the compression or the ten-sion zone. As result from this definition, the resistance force is evaluated in each rigid rectangle: one in the compressionzone and one in the tension zone. Thismechanism is associated to the smallest force FRd,local between the punching shearresistance and the combination of punching shear and bending resistance in the compression and the tension zone. Someadaptationsand interpretationsare needed to design a pinned connection.

The resistance to punching dependson the loading case. For the loading case 1 the punching function of the punching peri-meter 2(b+c). For the loading case 2, the punching perimeter of the columnweb dependson the diameter of the bolt heads(or nuts) and the number n of bolts respectively in the tension/compression zone. The resistance isgiven by:

- 74 -


: loading case 1

: loading case 2

with

twc the thicknessof the columnweb

fy the yield strength of the columnweb

γM0 the partial safety factor of steel

dm average diameter of the bolt head (see further)

Combined flexural and punching shear mechanism takes also into account that the plastic moment per unit length of yieldline is reduced by the presence of shear force.

- 75 -

Chapter 2

Application to rigid bolted connectionFor each zone (respectively tension/compression), the local punching shear resistance following loading case 1&2 isdeterm-ined. The tension rigid rectangle is defined by the perimeter around the bolts placed respectively in the tension zone 2(b+c) .The rigid rectangle of the compression zone through which the punching is transmitted to the column web corresponds tothe beam flange thicknessand the beam flangewidth .

In the sameway, the local combined punching and bending is calculated both for the tension and the compression followingthe sameperimeter valuesb&c.

Application to rigid welded connectionsFor each zone (respectively tension/compression), the local punching shear resistance following loading case 1&2 isdeterm-ined. For welded connections, the tension, respectively the compression rectangle is the beam flange thickness and thebeam flange width. In the same way, the local combined punching and bending is calculated both for the tension and thecompression following the sameperimeter valuesb&c.

Global mechanismIn the global failure mechanism, the force F is transmitted to the column web by one or more rows of bolts. In this case, thedefinition of the loaded area depends on the distance between bolts and the diameter of bolt heads (or nuts), or the weldaround the beam flanges. The yields line pattern involvesboth compression and tension zones.

The combined flexural and punchingmechanism isevaluated as:

where FComb,Rd: combined punching and flexural local resistance

Global failure mechanism involves both compression and tensile zones. If the dimensions bxc of the compression zone aredifferent from those of the tensile zone, the FGlobal,Rd expression will be applied twice, once for the compression zone andonce for the tension zone separately.

- 76 -


Rotational stiffness and ductilityStiffness calculationThe rotational stiffness is calculated with the component method according to EN 1993-1-8 Article 6.3, considering bolt-rows located above center of compression (See also chapter: "Center of compression" on page 22). Bolt-rowsused only forshear are not used for stiffnesscalculation.

Stiffnessmodel for strong-axisbending:

For bolted end-plate connections, the basic components related to each single bolt row, are represented by a single effect-ive stiffness coefficient keff,r as given by EN 1993-1-8 Article 6.3.3.1 (2). These effective stiffness coefficients for each bolt-row are, based onEN 1993-1-8 Article 6.3.3.1 (1), transformed to the equivalent stiffnesscoefficient keq, to be used finally inthe final stiffness formula specified byEN 1993-1-8 Article 6.3.3.1 (4). The leverage arm zeq is given byEN 1993-1-8 Article6.3.3.1 (3).

The basic formula for calculation of rotational stiffness specified in EN 1993-1-8, Article 6.3.1 (4) is used, independently ofthe 5%Npl,Rd limit defined by the samearticle.

The programmakesa distinction between three stiffness types:

l Sj,ini- the initial rotational stiffness

l Sj- the rotational stiffness, related to the actualmomentMy,Ed

l Sj,MRd- the rotational stiffness, related toMj,Rd (without the influence of the normal force)

As specified µ is the stiffness ratio Sj,ini/Sj. Determination of this stiffness ratio is specified byEN 1993-1-8, Article 6.3.1 (6).The value of coefficient ψ isgiven byTable 6.8.

Themoment-rotation diagram isbased on the valuesof Sj,ini andSj,MRd.

- 77 -

Chapter 2

Stiffness coefficientsThe stiffnesscoefficientsand their usage in the steel connectionsare defined by theEN 1993-1-8 Article 6.3.1 Table 6.9 and6.10.:

Coefficient Basic component Formula

k1 column web panel in shear

2 column web in compression

k3 column web in tension, single bolt row in tension

k4 column flange, single bolt row in tension

k5 endplate, single bolt row in tension

K10 bolts, single bolt row in tension

with

Avc

the shear area of the column

- 78 -


z the lever arm

β the transformation parameter

beff

the effectivewidth of the columnweb

dc the clear depth of the columnweb

leffthe smallest effective length for the bolt (minimum of individual and relevant partialeffective lengths)

m the distance bolt to beam/columnweb

As the tensile stressarea of the bolt

Lbthe elongation length of the bolt

In Scia Engineer the usage of the stiffnesscoefficients is related to a connection type:

For a bolted beam-to-column connection, the following coefficientsare used :

Coefficient Present keqk1 x

k2 x

k3 x x

k4 x x

k5 x x

K10 x x

For awelded beam-to-column connection, the following coefficientsare used :

Coefficient Present keqk1 x

k2 x

k3

k4 x

k5

K10

When a columnminor axis configuration isused, the values for k1 and k2 are replaced byki, the stiffnesscoefficient in the ten-sion or the compression zone of the columnweb in bending and punching. The value for ki is given by (seeRef.[21]) :

with

c1 1.50

- 79 -

Chapter 2

c2 1.63

10≤u≤50

0.08≤β≤0.75

0.05≤α≤0.2

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

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

Coefficient Present keqk1

k2

k3

k4

k5 Left side

k5 Right side

x

x

x

x

K10 x x

Awelded plate-to-plate connection is considered as rigid.

For a column base, the following coefficientsare used :

Coefficient Present keqk1

k2

k3

k4

k5 x x

K10 x x

kc x

The value of Lb in coefficient k7 is taken as the free length of the anchor boltsplus the free length of embedded part. The freelength of the anchor bolts is equal to the base plate thickness plus the head height of the anchor bolt. The free length of theembedded part isequal to 8-times the anchor diameter.

The stiffnesskc is the stiffnesscoefficient for the compression zone in the concrete block.

- 80 -


with

Afl the bearing area under the compression flange

Ec

the Emodulusof concrete

(Ec in Gpa, fck inMpa)

E the Youngmodulus (of steel)

heq

the equivalent height

where aeff and beff are based on the rectangle for determining AflAfl=aeff xbeff

Stiffness classificationThe connection is classified as rigid, pinned or semi-rigid according to its stiffness by using the initial rotational stiffness Sj,iniand comparing it with classification boundariesgiven inRef.[1] Figure J.8.

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

If Sj,ini <=Sj,pinned, the connection is classified aspinned.

If Sj,ini<Sj,rigid andSj,ini>Sj,pinned, the connection is classified assemi-rigid.

Braced frame connections:

Unbraced frame connections

Column base connectionsBased onRef.[17].

- 81 -

Chapter 2

with:

Ib the secondmoment of area of the beam

Lb the span of the beam

Ic the secondmoment of area of the column

Lc the storeyheight of the column

E the Youngmodulus

Stiffness checkThe actual stiffnessof the connections is comparedwith the required stiffness, based on the approximate joint stiffnessusedin the analysismodel. See alsoRef.[15] Part 6.1.2, Ref.[18] andRef.[19].

A lower boundaryand an upper boundarydefine the required stiffness :

FrameLower boundary

Sj,low

Upper boundary

Sj,upper

Braced

Unbraced

with

Ib the secondmoment of area of the beam

Lb the span of the beam

Ic the secondmoment of area of the column

Lc the storeyheight of the column

E the Youngmodulus

Sj,app the approximate joint stiffness

Sj,ini the actual initial joint stiffness

Sj,low the lower boundarystiffness

Sj,upper the upper boundarystiffness

Sj the actual joint stiffness

When a linear spring isused in the analysismodel, we check the following :

WhenSj,ini >=Sj,low andSj,ini<=Sj,upper, the actual joint stiffness is conformwith the applied Sj,app in the analysismodel.

- 82 -


The value of Sj,app is taken as the linear spring value introduced for <fiy> (in the hinge dialog), multiplied by the stiffnessmodification coefficientη.

Type of connection η

bolted beam-to-column 2

welded beam-to-column 2

bolted plate-to-plate 3

column base 3

When a non-linear function isused during the analysismodel, we check the following :

WhenSj >=Sj,low andSj<=Sj,upper, the actual joint stiffness is conformwith the applied Sj,app in the analysismodel.

The value of Sj,app is taken as the analysis stiffnessdefined by the non-linear function.

For column base connections, the stiffnesschecks in not performed and a note isdisplayed.

Update stiffnessThe actual connection stiffnessmay be transferred to the analysismodel. The linear spring value for <fi y> (in the hinge dia-log) is taken asSj,ini divided by the stiffnessmodification coefficientη. Other stiffnessparameters remain unchanged.

For asymmetric connectionswhich are loaded in both directions (i.e. tension on top and tension in bottom), the linear springvalue for <fi y> (in the hinge dialog) is taken as the smallest Sj,ini (from both directions) divided by the stiffnessmodificationcoefficientη.

If the user hasactivated functionality "Beam local nonlinearity" in the project dialog, a non-linear function isalso generated. Itrepresents the moment-rotation diagram for both tension top and bottom sides. The function may be used as a replace-ment of the linear spring value <fi y> for the created hinge. The advantage of using the nonlinear function is, that a correctstiffness isavailable for all setsof internal forces. This is crucial for example for column base connection design.

In order to be able to use a nonlinear function three conditionshas to be fulfilled:

- 83 -

Chapter 2

l functionality "Beam local nonlinearity" isactivated in the project dialogl the nonlinear function is selected for <fi y> in the relevant hinge dialogl a nonlinear combination isused for the connection design

For column base connections, the update stiffness feature isnot available.

Weak axis calculationStiffnessmodel for weak-axis bending showing weak-axis bolt-line components given by the general weak-axis reference.For further info onweak-axis calculation see chapter: "Weak-axis calculation" on page 34.

Asgiven by the reference, theweak-axis stiffnessshould be calculated in a similar wayas in-plane stiffness.We do not recog-nize any difference in the stiffness between component 4a and 4b in Scia Engineer. Stiffness coefficients k4, k5,k10 for allbolt-rowsare calculated according EN 1993-1-8 Article 6.3.2 Table 6.11 as for the strong-axis calculation. The final value ishowever divided by 2 for usage in weak-axis calculation. In weak-axis calculation all bolt-rows are used compared to thestrong-axis stiffnesscalculation, where onlybolt-rowsabove center of compression are used.

The additional stiffness bolt-line coefficients for components Column flange in twisting k17 and for Column web in bendingk18 are defined by the reference as:

Column flange in twisting:

with:

bc is thewidth of the column


ν Poisson's ratio of a columnmaterial

∑p1 is the spacing between the first and last bolt-row

y is the design distance from the bolt-line in tension to the centre of compressionfor weak-axisbending

leff,fct

effective length of column in twisting calculated assuming amaximumspread at60° from the boltsacross thewidth of the column flange, given as:

- 84 -


Column web in bending:

with:

twc is theweb thicknessof the columnweb

p2 is the spacing between the two bolt-lines

hc is the height of the column

beff,wbc

is the effective length of theweb in bending, considered simplysupported inboth ends, given as:

Based on the different bending stiffnessmodel severalmodification, to the strong-axis calculation, are introduced both for:

Beam-column connections:

l the keff,r stiffnessgiven byEN 1993-1-8 Article 6.3.3.1 (1) isnot required, since onlyone bolt-line needs to be calculated.The stiffness for each of the components in the bolt-line is calculated asa sumof the component stiffnesscoefficientsof allbolts in the bolt-line

l the keq stiffnessgiven byEN 1993-1-8 Article 6.3.3.1 (2) isnot required to be used, since it isnot used by the stiffnessmodel

l the leverage arm zeq given byEN 1993-1-8 Article 6.3.3.1 (3) is set equal to "y"

l rotational stiffnessSj formula given byEN 1993-1-8 Article 6.3.1 (4) is changed to the formula below, while coefficient k4,k5,k10 are taken as: ki =∑(ki,r), where "r" represent the number of all bolt-rows. Coefficient k7 is taken as infinity.

Splice connections:

l the keff,r stiffnessgiven byEN 1993-1-8 Article 6.3.3.1 (1) isnot required, since onlyone bolt-line needs to be calculated.The stiffness for each of the components in the bolt-line is calculated asa sumof the component stiffnesscoefficientsof allbolts in the bolt-line

l the keq stiffnessgiven byEN 1993-1-8 Article 6.3.3.1 (2) isnot required to be used, since it isnot used by the stiffnessmodel

l the leverage arm zeq given byEN 1993-1-8 Article 6.3.3.1 (3) is set equal to "y"

l rotational stiffnessSj formula given byEN 1993-1-8 Article 6.3.1 (4) is changed to the formula below, while coefficient k5,l,k5,r,k10 are taken as: ki =∑(ki,r), where "r" represent the number of all bolt-rows. Coefficient k7 is taken as infinity.

- 85 -

Chapter 2

The stiffness classification and check are not done for the weak-axis stiffness calculation, since the classification and checkboardersare not available.

Ductility classificationAccording toRef.[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 forceswithin the joints and a sufficiently good rota-tion capacity isavailable to allow a plastic frame analysisand design.

Class 2 joint : Mj,Rd is reached by full plastic redistribution of the internal forceswithin the joints but the rotational capacity islimited. An elastic frame analysis possibly combined with a plastic verification of the joints has to be performed. A plasticframe analysis is also allowed as long as it does not result in a too high required rotation capacity of the joints where theplastichingesare likely to occur.

Class 3 joint : brittle failure (or instability) limits the moment resistance and does not allow a full redistribution of the internalforces in the joints. It is compulsory to perform an elastic verification of the joints unless it is shown that no hinge occurs in thejoint locations.

Bolted jointsIf the failuremode of the joint is the situated in the shear zone of the columnweb, the joint is classified asa ductile, i.e. a class1 joint.

If the failuremode isnot in the shear zone, the classification isbased on the following :

Classification by ductility Class

Ductile 1

Intermediaire 2

Non-ductile 3

with

t the thicknessof 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

Welded jointsIf the failuremode of the joint is the situated in the shear zone of the columnweb, the joint is classified asa ductile, i.e. a class1 joint. If the failuremode isnot in the shear zone, the joint is classified as intermediate for ductility, i.e. a class2 joint.

- 86 -

Pinned frame connections


IntroductionIn this appendix, we give information about the calculation rules for the Frame Pinned connections. Four types of con-nectionsare 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 VRd (taking into account the present normal force N ) and the design com-pression/tension resistanceNRd are calculated.

The design shear resistance iscalculated for the following failuremodes :

l design shear resistance for the connection elementl design shear resistance of the beaml design blockshear resistance l design shear resistance due to the bolt distribution in the beamwebl design shear resistance due to the bolt distribution in the column

The design compression/tension resistance iscalculated for the following failuremodes :

l design compression/tension resistance for the connection elementl design compression/tension resistance of the beaml design tension resistance due to the bolt distribution in the column

In the following chapter, we give an overview of the abbreviations, which are used in the dialogsand the output.

In the next chapters, the theoretical background is given for the calculation of the various design shear resistance anddesign compression/tension resistance, according to EC3-ENV (Ref.[2]).

List of abbreviationsτ Shear stress

µSlip factor

Weld size parameter

δ Weld size parameter

β Transformation parameter

ρ Reduction factor

Γ Weld size parameter

σ1 Normal stress in weld part

τ1 Shear stress in weld part

τ2 Shear stress in weld part

- 87 -

Chapter 3

σD Stress around point d in calculation of design shear resistance for bolts in column

σf,Ed the longitudinal stress in the flange

σM Normal stress generated bymomentM


σN Normal stress generated by normal force N

βw Correlation factor in weld size calculation

AArea of beam

Area of element

A Parameter in design shear resistance for bolts in column

aLever arm - Bolt center - Weld size

Position of bolt center with regard to underside of the plate (dir. x)

a distance to the nearer end of the member

a1 length in block shear resistance



alfa,bw Alfa value for beamweb

alfa,el Alfa value for element

AnetReduced area of the beam

Reduced area of the element

As Tensile area for the bolt

Av Shear area of the beam

Av.net Reduced shear area of the beam element

B Parameter in design shear resistance for bolts in column

bWidth

Position of bolt center with regard to underside of the plate (dir. y)

bd Length in calculation of design shear resistance for bolts in column

bf the column flange width

c Maximum horizontal distance between bolts and bolt center

D Shear force on the plate

dBolt diameter

Maximum horizontal distance between bolts and bolt center

d the column web depth

d0 Hole diameter

do Hole diameter

e Diagonal diameter of bolt head

e1 Edge distance

Fb,bw,Rd Bearing Resistance for beamweb

Fb,el,Rd Bearing Resistance for element

Fp,Cd Design preloading force

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

Ft,Sd Applied tensile force

- 88 -


fu Ultimate tensile strength of the element

fub Tensile strength of the bolt

Fv,Rd Shear resistance per shear plane

fy Yield strength of the element

g weld size parameter

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

Gamma M1 Partial safety factor for resistance to buckling

Gamma Mb Partial safety factor for resistance of bolts

Gamma Ms Partial safety factor for slip resistance

Gamma Mw Partial safety factor for resistance of welds

h Height

h the column height

hd Height in calculation of design shear resistance for bolts in column

Ip : Polar moment of inertia of the bolts with regard to the boltcenter

IpD Polar moment of inertia of the bolts around point d in calculation of design shear resistance for bolts in column

K Parameter in calculation of design shear resistance for bolts in column

ks Value for slip resistance

l length of the weld part

L parameter in weld size

l1 length of the weld part

L1 Length for block shear resistance

l2 length of the weld part



leff equivalent length in T-Stub model

Lv Length for block shear resistance

Lveff Length for block shear resistance

M Presentmoment

m factor in T-Stub model

Mpl,1,Rd Design plasticmoment resistance for MODE 1 in T-Stub model

Mpl,2,Rd Design plasticmoment resistance for MODE 2 in T-Stub model

My Actual bending moment

N Present normal force

nNumber of friction interfaces

Number of plates of number of bolt

NRd Design tension/compression resistance

NSd Internal tension/Compression force

p1 Bolt pitch

Pl Gap between column’s flange and beam’s web

QResulting forces acting on the extreme bolt of a plate:

- 89 -

Chapter 3

Qhk Horizontal force acting on the bolts in bolt-row k

Qhn

QhM

Horizontal force acting on the extreme bolt of a plate

Qvj Vertical force acting on the bolts in bolt column j

QvM Vertical force acting on the extreme bolt of a plate

Qvr Vertical force acting on the extreme bolt of a plate

R Shear force

r Radius

S Width across flats, diameter of bolt head

ss the plate height

t Element thickness

t Thickness

tf Flange thickness

tf the column flange thickness

tw Web thickness

tw the column web thickness

VRd Design shear resistance

VSd Internal shear force

Vz Actual shear force

W Elastic section modulus of beam

x1 Edge distance for bolts in connection element

x2 Edge distance for bolts in connection element

xj Maximum horizontal distance between bolts and d point

y1 Edge distance for bolts in connection element

y2 Edge distance for bolts in connection element

zk Maximum vertical distance between bolts and d point in design shear resistance of column

- 90 -


Calculation of VRd and NRdWelded pinned plate

Calculation design shear resistance VRd for connection elementThe design shear resistanceVRd is given by

with

fy the yield strength of the element


A h t n

W n t h² / 6

- 91 -

Chapter 3

N the present normal force

a b/2

σN the normal stressgenerated bynormal forceN

nthe number of plates

Calculation design shear resistance VRd for beamThe design shear resistanceVRd is given by

with

fy the yield strength of the beam


r the radiusof root fillet

Avthe shear area of the beam

Calculation design compression/tension resistance NRd for connection elementThe design compression/tension resistanceNRd is given by

with



A the area of the element (n h t)


Calculation design compression/tension resistance NRd for beamThe design compression/tension resistanceNRd is given by

with

- 92 -


fy the yield strength of the beamelement


Athe area of the beam

Calculation design compression resistance NRd for column webThe design compression resistance NRd is given by the minimum of the crushing resistance Ry,Rd, the crippling resistanceRa,Rd and the buckling resistanceRb,Rd of the columnweb (seeRef.[2], 5.7.3., 5.7.4., 5.7.5)

Rb,Rd is obtained by considering the web as a virtual compression member with an effective breadth beff and bucklinglength d.

with

fy the yield strength of the beamelement


tw the columnweb thickness

ss the plate height

bf the column flangewidth

σf,Ed the longitudinal stress in the flange

tf the column flange thickness

d the columnweb depth

a distance to the nearer end of themember

h the column height

- 93 -

Chapter 3

Bolted pinned plate

Calculation design shear resistance VRd for connection elementThe design shear resistanceVRd is given by

The bolt holesare not taken into account when

WhenAv.net is less than this limit, an effective shear area of Av= (fu/fy) Av.netmaybe assumed, else Av=A.

with



- 94 -


A h t n

W n t h² / 6


a x1



Av.netthe reduced shear area

Calculation design shear resistance VRd for beamThe design shear resistanceVRd is given by :

The bolt holesare not taken into account when

WhenAv.net is less than this limit, an effective shear area of Av1=(fu/fy) Av.netmaybe assumed, else Av1=Av.

with



n the number of bolt in a section

Avthe shear area of the beam

Av.netthe reduced shear area of the beamelement

fu the ultimate tensile strength of the element

Calculation design shear resistance VRd for bolts in beamThe extreme bolt of the plate is submitted to the following forces (seeRef.[12] IWE1 andRef. [13] p162-207):

Vertical forces :

- 95 -

Chapter 3

Horizontal forces :

The resulting forcesacting on thisbolt is conditioning byFv,Rd (See 11.3.1) and Fb,RD,Plate and Beam:

Considering that, in the limit state, VRd is acting, we get the following equation in VRd:

with

a the position (xdirection) of bolt center with regard to underside of the plate

bthe position (ydirection) of the bolt center with regard to underside of the plate

d themaximumvertical distance between boltsand bolt center

- 96 -


c themaximumhorizontal distance between boltsand bolt center

e1 the end distance

p the pitch

Ip : the polar moment of inertia of the boltswith regard to the bolt center

n the number of bolts

R the shear force

N the normal force

Mthemoment: R a

Calculation design block shear resistance for beam element VRdThe design value of effective resistance to block shear is determined by using the following expression given byEN 1993-1-8 Article 3.10.2 (2):

with:

Ant - the net area subjected to tension calculated as:

for a single vertical line of bolts:

for two vertical linesof bolts:

Anv - the net area subjected to shear calculated as:

tw - thicknessof the beamweb

e2 - horizontal distance from the side bolt to the edge of beam

d0 - borehole diameter

p2 - horizontal space between the bolts

hb - height of the beam

e1 - vertical distance from the bottomof the beam to the bolt

- 97 -

Chapter 3

n1 - number of bolt-rows

Calculation design block shear resistance VRd in connection element (beam side)The design value of effective resistance to block shear is determined by using the following expression given byEN 1993-1-8 Article 3.10.2 (2):

with:





tp - thicknessof the element

e2 - horizontal distance from the side bolt to the element edge



hp - height of the element

e1 - vertical distance from the bottomof the element to the bolt


- 98 -


Calculation design compression/tension resistance NRd for connection elementThe design compressionNRd is given by (seeRef.[2], 5.4.4.(1))

The design tensionNRd is given by (seeRef.[2], 5.4.3.(1))

with


futhe ultimate tensile strength of the element


A the area of the element (n h t)

Anet the reduced area of the element


Calculation design compression/tension resistance NRd for beamThe design compression resistanceNRd is given by (seeRef.[2], 5.4.4.(1))

The design tensionNRd is given by (seeRef.[2], 5.4.3.(1))

with


fu the ultimate tensile strength of the beam


A the area of the beam

Anetthe reduced area of the beam

- 99 -

Chapter 3

Calculation design compression resistance NRd for column webSee chapter '"Calculation design compression resistanceNRd for columnweb" on page 93'

Cleat

Calculation design shear resistance VRd for connection elementSee chapter ""Calculation design shear resistanceVRd for connection element" on page 94".

Calculation design shear resistance VRd for beamSee chapter ""Calculation design shear resistanceVRd for beam" on page 95".

Calculation design shear resistance VRd for bolts in beamSee chapter ""Calculation design shear resistanceVRd for bolts in beam" on page 95".

Calculation design block shear resistance for beam element VRdSee chapter ""Calculation design blockshear resistance for beamelement VRd " on page 97"

Calculation design block shear resistance VRd in connection element (beam side)See chapter ""Calculation design blockshear resistanceVRd in connection element (beamside) " on page 98"

Calculation design block shear resistance VRd in connection element (column side)The design value of effective resistance to block shear is determined by using the following expression given byEN 1993-1-8 Article 3.10.2 (2):

- 100 -


with:





tp - thicknessof the cleat

e2 - horizontal distance from the side bolt to the cleat edge



hp - height of the cleat

e1 - vertical distance from the bottomof the cleate to the bolt


Calculation design shear resistance VRd for bolts in column

The acting shear force C/2 is divided in a shear force V0 acting in the bolt center and a moment M0 rotating around point don a distance hd/2 from the upper side (Ref. [13] p194-197).

: Vertical force acting on the bolts in bolt-column j

: Horizontal force acting on the bolts in bolt-row k

- 101 -

Chapter 3

Byequilibrium, we find:

In the example represented in the figure , we have :

Supposing that :

- 102 -


we find :

In the limit state, the shear force VRd is acting in the connection :

The resulting force Q acting on the bolts is conditioning by Fv,Rd (See "Welded pinned plate" on page 91) and Fb,Rd,Angleand Beam . If a normal forceN isacting, the following condition is valid:

thismeans that:

with

with

n the umber of bolts

IpD the polar moment of inertia of the boltsaround point d

Calculation design compression/tension resistance NRd for connection elementSee chapter ""Calculation design compression/tension resistanceNRd for connection element" on page 99".

Calculation design compression/tension resistance NRd for beamSee chapter ""Calculation design compression/tension resistanceNRd for beam" on page 99".


- 103 -

Chapter 3

Calculation design resistance NRdCalculation design tension resistance NRdAsdescribed inRef. [1], Ref.[23], we can substitute a bolt joint byan equivalent T-Stub tomodel the resistance of the columnflange. The length of the considered T-stub is note leff. The problem consists first to calculate the equivalent length and thandetermine the failuremode.

To calculate the equivalent length in the corner for the equivalent T-stubmodel, we consider the bolt individually or as a partof a group of bolt-rows. Each of this case we’ll be calculate for circular pattern (note cp) and for non-circular pattern (notenc).We define in the following table p as the pitch of the holesand parametersmand e as represented in the figure.

Remark: if the playPl≤0.4 tcor thenmcor=a-tcor-0.8r, else see figure

Bolt-row location

Bolt –row considered individually

Circular Pattern leff,cp Non-circular Pattern leff,nc

Inner bolt-row

End bolt-row

the smaller of: the smaller of:

Mode 1 leff,1=min(leff,nc,leff,cp)

Mode 2 leff,2=leff,nc

Bolt-row location

Bolt –row considered as part of a group of bolt-rows

Circular Pattern leff,cp Non-circular Pattern leff,nc

Inner bolt-row p

End bolt-row

the smaller of: the smaller of:

Mode 1 Σleff,1=min(Σleff,nc,Σleff,cp)

Mode 2 Σleff,2=Σleff,nc

- 104 -


Remark: e1 hasno sense for column

Aswe’ve determined the equivalent T-stubmodel, we can determine the design tension resistance of the connection bycal-culating themaximum resistance of each group (element and column) and for each bolt-row.

Bolt-group Each bolt individually

Mpl,1,Rd

Mpl,2,RD

Bt,Rd

FailureMode 1

FailureMode 2

FailureMode 3

Remark: n=min(eElement,eColumn,1.25m)

From thisabove tablewe determine:

The previous relation lead to the determination of the design resistance tension for the column flange, the column web andthe connected element:

- 105 -

Chapter 3

When a column minor axis configuration is used, the value for NRd,Comumn,Web is calculated based on the rules given inRef.[21]. The normal force will carried by the bolts through the column web. In this particular case, the systemwill calculatethe punching and the combined punching and bending resistance for each bolt row and for the complete bolt pattern. Onlythe most critical design resistance is taken into account. The global failure is not taken into account because no moment istransmitted.

Calculation design compression resistance NRdWhen a column minor axis configuration is used, the value for NRd,Comumn,Web is calculated based on the rules given inRef.[21]. The beam subjected to compression will transfer the forces to the column web through the complete connectionelement (angle or end plate). The total perimeter of the connection element determines the parameter b and c. The globalfailure isnot taken into account because nomoment is transmitted.

Short end-plate

Calculation design local shear resistance VRd for beamIn section AA, the following stressesare present :

with

A hEndplate.tbeamweb


a the bolt center


τ the shear stress

In the limit state, we allow the following :

- 106 -


with



The design shear resistanceVRd is the solution of the following equation :

Calculation design shear resistance VRd for bolts in columnThe calculation of the design shear resistance for bolt in the column isbased on the following expression :

whereQ is limited byFv,Rd and Fb,Rd if the connection ismade of normal bolt, and byFs,Rd if the connection ismade of pre-loaded bolt.

If a normal forceN isacting, the following condition is valid :

Thismeans that we have :

with

VRd the limit shear force

n the number of bolts

- 107 -

Chapter 3

N the normal force

Fv,Rd the design shear resistance for normal bolt

Fb,Rd the bearing resistance for bolt

Fs,Rd the design slip resistance for preloaded bolts

Calculation design block shear resistance VRd in endplateThe design value of effective resistance to block shear is determined by using the following expression given byEN 1993-1-8 Article 3.10.2 (2):

with:





tp - thicknessof the end-plate

e2 - horizontal distance from the side bolt to the end-plate edge



hp - height of the end-plate

e1 - vertical distance from the bottomof the end-plate to the bolt


Calculation design compression/tension resistance NRd for beam webSee chapter "Calculation design shear resistanceVRd for bolts in column" on page 101.

Remark: in this caseA=twbeam hEndplate

- 108 -



Calculation design tension resistance NRdThe calculation of the design tension resistance ismade in the sameway than for connection type 3 but wemust replace thefigure.

Weld size calculationTo determine the weld size a in a connection, we use a iterative process with a as parameter until the Von Mises rules isrespected (AnnexeM/EC3) :

- 109 -

Chapter 3

First, we calculate the following parameter (Ref. [14] p529-532) :

As thisparametersare known, we can calculate the stressdistribution in eachweld part :

Between Element and beam :

WeldCheck1: and

- 110 -


WeldCheck2: and

BetweenElement andColumn :

with

D the shear force on the plate

N the normal force

M themoment: L.D

Wthe flexionmodule:

- 111 -

Chapter 4

Grid pinned connections

IntroductionThe grid pinned connectionsare checked for critical shear force and normal force.

The following critical situationsare considered :

l (1) VRd : design shear resistance for the connection element

l (2) VRd : design shear resistance of the beam

l (3a) VRd : design blockshear resistance for beamweb

l (3b) VRd : design blockshear resistance for connection element (beamside)

l (3c) VRd : design blockshear resistance for connection element (column side)

l (3d) VRd : design blockshear resistance for endplate (beamside)

l (4) VRd : design shear resistance due to the bolt distribution in the beamweb

l (5) VRd : design shear resistance due to the bolt distribution in the column

l (6) VRd : design shear resistance at the notch

l (7) NRd : design compression/tension resistance for the connection element

l (8) NRd : design compression/tension resistance of the beam

l (9) NRd : design tension resistance due to the bolt distribution in the column

l (10) NRd : design compression resistance for columnweb

In the next chapters, the theoretical background is given for the calculation of the various design shear resistance anddesign compression/tension resistance, according to EC3-ENV (Ref.[2]).

The critical situations (1) (2) (3a) (3b) (3c) (3d) (4) (5) (7) (8) (9) (10) are described in publication.

For grid pinned connections, these critical situations remain valid, taking into account the followingmodifications :

l critical situation (6) isadded for notched elements– seeChapter "Design shear resistanceVRd at notch" on the facingpage"

l critical situation (3a) ismodified for notched elements– seeChapter "Notched elements : calculation design blockshearresistanceVRd " on page 114

l critical situation (10) isnot valid for grid pinnedl critical situation (1) ismodified for long cleat connections - seeChapter "Long cleat connection VRd : design shear res-

istance for the connection element" on page 115l critical situation (5) ismodified for long cleat connections– seeChapter "Long cleat connection VRd : design shear res-

istance due to the bolt distribution in the column" on page 116

- 112 -


Design shear resistance VRd at notch

At the position of the notch ( at a distance a1), the geometrical propertiesof the reduced section are calculated.

At the section, the normal forceN isacting. (N positive is for compression). The design shear VRd resistance isgiven by :

- 113 -

Chapter 4


with




with

fy the yield strength of the element –member


A the reduced section at notch

az,ad the positionsof center of gravity in notch

Iy1 moment of inertia in notch

Av

shear area

=h1 *twFor BScode, Av=h1*tw*0.9

Notched elements : calculation design block shear res-istance VRdThe design value of effective resistance to block shear is determined by using the following expression given byEN 1993-1-8 Article 3.10.2 (2):

- 114 -


with:





tp - thicknessof the notch

e2 - horizontal distance from the side bolt to the notch edge



hp - height of the notch

e1 - vertical distance from the bottomof the notch to the bolt


Long cleat connection VRd : design shear resistancefor the connection elementSeeRef.[30].

When only1 bolt ispresent at each cleat in the columnweb, the shear stress isadapted as follows :

The normal stress remainsvalid as follows :

with

- 115 -

Chapter 4

A h t n

W n t h² / 6


M the presentmoment : VRd a

a


σM the normal stressgenerated bymomentM

τ the shear stress

n the number of plates

eu see figure


with




Long cleat connection VRd : design shear resistancedue to the bolt distribution in the columnSeeRef.[30].

The design shear resistance isgiven by :

- 116 -


with

with

n the number of bolts in 1 cleat

eu, h see figure

N normal force

Fb,Rd the bolt bearing resistance

Fv,Rd the bolt shear resistance

- 117 -

Chapter 5

Bolted diagonal connections

Introduction to the bolted diagonal connectionThe design and check of a bolted connection, where the member is subjected to normal force, are considered. The con-nection ismade bybolts on a gusset plate, or bybolting themember directly to the columnmember. The checksare accord-ing to EC3 Ref.[32]

The following checksare performed to establish the unity checkof the connection :

l "Member resistance" belowl "Connection resistance" on page 124l "Weld size calculation for gusset plate" on page 126

Member resistanceResistance of the gross section of diagonalThe design plastic resistance of the grosssection isgiven by :

with

A the area of the diagonal element

fy the yield strength of the diagonal element

Npl,Rd the design plastic resistance


Resistance of the net section of diagonalThe design ultimate resistance of the net section isgiven by :

with

Anetthe net area of the diagonal element

See also chapter ""Determination of Anet" on page 122"

fu the ultimate tensile strength of the diagonal element

Nu,Rd the design ultimate resistance

γM2 the partial safety factor for resistance of net section

- 118 -


In the case of unsymmetrical connected diagonals (such as angles by one leg), the eccentricity of the fasteners in end con-nectionsshall be taken into account.

Angle diagonal with 1 bolt

with

e2 the edge distance




t thematerial thickness

d0 the bore hole

Angle diagonal with 2 bolts on 1 line

- 119 -

Chapter 5

with

Anet

the net area of the diagonal element :

for unequal- leg angle connected by its smaller leg, Anet should be taken asequal to the net section area of an equivalent equal-leg angle of leg size to thatof the smaller leg.


Nu,Rd

the design ultimate resistance


β2 reduction factor (see table)

d0 the bore hole

Pitch p1 <= 2.5 d0 >5.0 d02 bolts :β2 0.4 0.7

3 bolts or more :β3 0.5 0.7

Angle diagonal with 3 bolts on 1 line

with

Anet

the net area of the diagonal element :

for unequal- leg angle connected by its smaller leg, Anet should be taken asequal to the net section area of an equivalent equal-leg angle of leg size to that ofthe smaller leg.

- 120 -



Nu,Rd

the design ultimate resistance


β3reduction factor (see table in chapter ""Resistance of the net section of diagonal"on page 118")

d0 the bore hole

Angle diagonal with Double Leg connection

with


A the area of the diagonal element

Anet the net area of the diagonal element




d0 the bore hole

Other sections and configurationsSeeRef.[31] pp.4.9

with

A1the net area of the connected flange

See also chapter ""Determination of Anet" on the next page"

A2 the area of the free flanges / webs




- 121 -

Chapter 5

Resistance of the gross section of gusset plateThe design plastic resistance of the grosssection isgiven by :

with

A the area of the gusset plate

fy the yield strength of the gusset plate



In case of a double leg connection, the calculated resistance ismultiplied by2.

Resistance of the net section of gusset plateThe design ultimate resistance of the net section isgiven by :

with

Anetthe net area of the gusset plate

See also chapter "Determination of Anet" below

fu the ultimate tensile strength of the gusset plate



In case of a double leg connection, the calculated resistance ismultiplied by2.

Determination of AnetFor 2 rowsof bolts in a non-staggered configuration, the Anet is given by :

with

Anet the net area



p2 the spacing

d0 the bore hole

- 122 -


For 2 rowsof bolts in a staggered configuration , the Anet is given by :

with

Anet the net area



p2 the spacing

d0 the bore hole

s the staggered pitch

- 123 -

Chapter 5

Connection resistanceShear resistance

Normal boltsThe shear resistance per shear plane and per bolt isgiven by :

for bolt grade 4.6, 5.6 and 8.8 :

for bolt grade 4.8, 5.8 and 10.9 :

with

As the tensile stressarea of bolt

fub the ultimate tensile strength of bolt

γM2 the partial safety factor for resistance of bolts

βLf the reduction factor for long joints

Fv.Rd the shear resistance

with

d the bolt diameter

Lj the connection length

- 124 -


Shear resistance for preloaded boltsThe design preloading force Fp,Cd is given by

with

fub the tensile strength of the bolt

As the tensile stressarea of the bolt

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

with

n the number of friction interfaces

ks the value for slip resistance(=1.0 for holeswith standard nominal clearances)

μ the slip factor

γM3 the partial safety factor for slip resistance

Bearing resistanceThe bearing resistance for each part of the connection and per bolt, Fb.Rd is given byRef.[32] Table 3.4.

The bearing resistance of single lap jointswith 1 bolt is limited by

If the edge distance e2 is smaller than 1.5 d 0 or the spacing p2 is smaller than 3.0 d0, the bearing resistance should bereduced. This reduction is2/3 when e2=1.2 d0 or p2=2.4 d0. For intermediate values (1.2 d0 <e2≤1.5 d0 and/or 2.4 d0 <p2≤3.0 d0) the value of Fb.Rd is determined by linear interpolation.

Checking the connection resistanceIf no preloading isused, the connection is considered ascategoryAbolted connections :

If preloading isused, the connection is considered ascategoryC bolted connections :

with

Fv.Sd the design shear force per bolt for the ultimate limit state

- 125 -

Chapter 5

Weld size calculation for gusset plateCalculation of weld lengthThe length of theweld size La iscalculated according toRef.[32] part 4.5.3.3..

The default throat thicknessa isequal to plate thickness/2.

with

a the throat thickness

La theweld size length

t the plate thickness

Fw;Rd theweld design resistance per unit length

fvw.d the design shear strength of theweld

fu the ultimate tensile strength of theweld

βw the correlation factor

γM3 the partial safety factor for resistance of welds

NRd the design resistance



Steel gradeUltimate tensile strength

(N/mm²)βW

Fe 360 360 0.80

Fe 430 430 0.85

Fe 510 510 0.90

- 126 -

Weld symbols

Weld symbols

The followingweld symbolsare used ( seeRef. [8] andRef.[9]) :

Number Description

1 fillet weld

2 double fillet weld

3 bevel (HV) weld

4 square weld

5 plug weld

6 weld length at haunch

Remark : the weld symbol (6) is not defined in the codes. This symbol is used to represent the weld length which is cal-culated according to chapter "Haunch with flange" on page 49. On the graphical representation, the symbol (6) or the sym-bol (3) can be used for representing theweld size at the haunches. This can be set in the basicdata.

The location of the weld is defined by the above welding symbol. The X stands for the weld size, and Y stands for the weldsymbol. The circle symbol in (2) is theweld-all-around symbol.

The example given in (3) means : fillet weldwith 6mmweld size.

- 127 -

Chapter 7

Bolt symbols

For somemetricbolt diameters (M10,M12,M16,M20,M22,M24), the following symbolsare used (SeeRef.[9]) :

The symbol for M20, isused as the default symbolic representation for all other diameters.

- 128 -

References

References

[1]

Eurocode 3 : Part 1.1.

Revised annexJ : Joints in building frames

ENV1993-1-1/pr A2

[2]

Eurocode 3

Design of steel structures

Part 1 - 1 : General rulesand rules for buildings

ENV1993-1-1:1992, 1992

[3]

P. Zoetemeijer

Bolted beam to column knee connectionswith haunched beams

Testsand computations

Report 6-81-23

Delft Universityof Technology, Stevin Laboratory, December 1981

[4]

P. Zoetemeijer

Een rekenmethode voor het ontwerpen van geboute hoekverbindingenmet eenkolomschot in de trekzone van de verbinding en een niet boven de ligger uit-stekende kopplaat.

Rapport 6-81-4

StaalcentrumNederland, StaalbouwkundigGenootschap, Juni 1982

[5]

Eurocode 3 : Part 1.1.

AnnexL: Design of column bases

ENV1993-1-1:1992

[6]

Eurocode 2

Design of concrete structures

Part 1: General rulesand rules for buildings

ENV1992-1-1:1991

[7] Y. Lescouarc’h

- 129 -

Chapter 8

Lespiedsde poteauxarticulésen acier

CTICM, 1982

[8]

Manual of SteelConstruction

Load&Resistance Factor Design

Volume II : Connections

Part 8 : Bolts,Welds, andConnectedElements

AISC 1995

[9]

U. Portmann

Symbole und Sinnbilder in Bauzeichnungen nach Normen, Richtlinien undRegeln

Wiesbaden, Berlin : Bauverlag, 1979

[10]

Sprint Contract RA351

SteelMoment Connectionsaccording to Eurocode 3

SimpleDesign aids for rigid and semi-rigid joints

1992-1996

[11]

DIN18800 Teil 1

Stahlbauten : Bemessung undKonstruktion

November 1990

[12]

J. Rudnitzky

Typisierte Verbindungen imStahlhochbau. 2. Auflage

Stahlbau-Verlags-GmbH-Köln 1979

[13]

H. BuchenauA.Tiele

Stahlhochbau 1

B.G. Teubner

Stuttgart 1981

[14]

F.Mortelmans

Berekening van konstructiesDeel 2

StaalAcco

- 130 -

References

Leuven, 1980

[15]

FrameDesign Including Joint Behaviour

Volume 1

ECSCContractsn°7210-SA/212 and 7210-SA/320

January1997

[16]

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

Application of the componentmethod to column bases

Proceedingsof theCOST C1Conference

Liège, Sept.17-19, 1998

[17]

F.C.T. Gomes, U. Kuhlmann, G. DeMatteis, A.Mandara

Recent developmentson 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 C1Workshop

Prague, October 1994

[19]

M.Steenhuis, N. Gresnigt, K.Weynand

Flexibele verbindingen in raamwerken

Bouwenmet Staal 126

September/Oktober 1995

[20]

O.Oberegge, H.-P. Hockelmann, L. Dorsch

Bemessungshilfen für profilorientiertesKonstruieren

3. Auflage 1997

Stahlbau-Verlagsgesellschaft mbHKöln

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

Application of the componentmethod to steel joints

- 131 -

Chapter 8


Liège, Sept.17-19, 1998

[22]

J.A. Packer, J.Wardenier, Y. Kurobane, X.-L. Zhao, G.J. van der Vegte

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

CIDECT

2009

[23]

Eurocode 3

Part 1.1. RevisedAnnexJ

Joints in building frames, edited

Approved draft : january1997

[24]

Rekenregels voor het ontwerpen van kolomvoetplaten en experimentele veri-ficatie

TNO report N°BI-81-51

[25]

Typisierte Anschlüsse imStahlhochbau

Band 1

DSTV - 2000

[26]

Typisierte Anschlüsse imStahlhochbau

Band 2

DSTV - 2000

[27]

Joints in SteelConstruction

Moment Connections

BCSA - 1997

[28]

Joints in SimpleConstruction

Volume 1 : Designmethods

BCSA - 1994

[29] BS5950

- 132 -

References

Structural use of steelwork in building

Part 1 : Code of practice for design - Rolled andwelded sections

2000

[30]

HotzR.

Oberkantenbündige Deckenträger- Unterzug- Anschlüsse mit verbesserterWirtschaftlichkeit (II)

Stahlbau 64 (1995) Heft 2

[31]

MaquoiR.

Elementsde constructionsmétalliques

Université de Liège, 1988

[32]

EN 1993-1-8:2005

Eurocode 3 : Design of steel structures

Part 1-8 : Design of Joints

2005

[33]

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

Corrigendum toEN 1993-1-8:2005

Eurocode 3 : Design of steel structures

Part 1-8 : Design of Joints

CEN, 2005

[34]

Design of StructuralConnections to Eurocode 3 – FrequentlyAskedQuestions

Ed.MooreD.B. andWald F.

2003

[35]

ECCSTechnical committee 10 - Structural connections. No 126

J.P.jaspart, J.F.Demonceau, S.Renkin,M.L. Guillaume

2009

[36] Joints in SteelConstruction - Moment -Resisting Joints to Eurocode 3 (P398)

TheSteelConstruction Institute &TheBritishConstructionalSteelwork

Association

- 133 -

Chapter 8

2013

[37]HERON vol. 20 - A design method for the tension side of statically loaded, boltedbeam to columnconnections

P. Zoetemeijer,

1974

- 134 -

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