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Advanced Training Steel Connections
Steel Connections
2
All information in this document is subject to modification without prior notice. No part or this manual may be reproduced, stored in a database or retrieval system or published, in any form or in any way, electronically, mechanically, by print, photo print, microfilm or any other means without prior written permission from the publisher. SCIA is not responsible for any direct or indirect damage because of imperfections in the documentation and/or the software. © Copyright 2008 SCIA. All rights reserved.
Table of contents
3
Contents
Introduction ...................................... ............................................................................................. 1
Frame Connect : column-beam joints ................ ........................................................................ 2
Scope ............................................. ..................................................................................................... 2
The Moment-Rotation characteristic ................ ............................................................................... 3
The resistance properties.......................... ....................................................................................... 9
The component strength ................................................................................................................ 9
The strength assembly ................................................................................................................. 12
The influence of the normal force................................................................................................. 14
The design shear resistance ........................................................................................................ 16
The stiffness properties........................... ....................................................................................... 18
The component stiffness .............................................................................................................. 18
The stiffness assembly ................................................................................................................. 19
The classification on stiffness ...................................................................................................... 20
The required stiffness ................................................................................................................... 21
Transferring the joint stiffness to the analysis model .................................................................. 22
Ductility classes ................................. ............................................................................................. 23
Ductility classification for bolted joints .......................................................................................... 23
Ductility classification for welded joints ........................................................................................ 24
Examples .......................................... ................................................................................................ 25
Calculation of bolted connection .................................................................................................. 25
Calculation of welded connection................................................................................................. 26
Calculation of connections in 3D Frame ...................................................................................... 30
Special features .................................. ............................................................................................. 31
Use of haunches .......................................................................................................................... 31
Column in minor axis configuration .............................................................................................. 33
Base plate connections : shear iron, flange wideners ................................................................. 34
The use of 4 bolts / row ................................................................................................................ 35
RHS beam .................................................................................................................................... 38
Frame Connect : pinned joint ...................... .............................................................................. 39
Examples .......................................... ................................................................................................ 39
Welded fin plate connection ......................................................................................................... 39
Bolted fin plate connection ........................................................................................................... 43
Bolted cleat connection ................................................................................................................ 45
Flexible end plate connection....................................................................................................... 48
References and literature ......................... ................................................................................. 49
Introduction
The design methods for connection design are explained. More details and references to the applied articles can be found in (Ref.[30])
Scia EngineerTheoretical BackgroundRelease : Revision :
The explained rules are valid for Scia Engineer 2008.0 and higher. The examples are marked by ‘The following examples are available :
Project Subject
CON_001.esa 2D Frame with pinned connections
CON_002.esa 2D Frame with semi
CON_003.esa 2D Frame with rigid connections
CON_004.esa Bolted connection
CON_005.esa welded connection
RHS connection
Base plate connection
CON_006.esa Connection with haunch
CON_007.esa Connection with column i
CON_008.esa Connections in 3D Frame
CON_009.esa Welded fin plate
CON_010.esa Bolted fin plate
CON_011.esa Cleat connection
CON_012.esa Flexible end plate connection
The design methods for connection design are explained. More details and references to the applied articles can be found in (Ref.[30])
Scia Engineer Connect Frame & Grid Theoretical Background
: 5.2 : 05/2008
The explained rules are valid for Scia Engineer 2008.0 and higher.
The examples are marked by ‘ Example’ The following examples are available :
2D Frame with pinned connections
2D Frame with semi-rigid connections
2D Frame with rigid connections
Bolted connection
welded connection
RHS connection
Base plate connection
Connection with haunch
Connection with column in minor axis bending
Connections in 3D Frame
Welded fin plate
Bolted fin plate
Cleat connection
Flexible end plate connection
1
The design methods for connection design are explained. More details and references to the applied
Steel Connections
2
Frame Connect : column-beam joints
Scope The design methods for the column-beam joints are taken from EC3 – Revised Annex J and EN 1933-1-8. More detailed information about the applied rules and specific implementations are found in Ref.[1]. The following chapters are valid for the bolted and welded column-beam joints. The design methods for the beam-column joints are principally for moment-resisting joints between I or H sections in which the beams are connected to the flanges of the column.
Figure 1 : Typical configurations
3
The difference between joint and connection is given in Figure 2. In the text, the name ‘joint’ will be used.
Figure 2 : Connection vs. Joint
The Moment-Rotation characteristic The joint is defined by the moment rotation characteristic that describes the relationship between the bending moment Mj,Sd applied to a joint by the connected beam and the corresponding rotation φEd between the connected members.
Figure 3 : Joint and Model
This moment-rotation characteristic defines three main properties :
- the moment resistance Mj,Rd - the rotational stiffness Sj - the rotation capacity φCd
Steel Connections
4
Figure 4 : Moment-rotation characteristic (1 = limit for Sj)
The general analytical procedure which is used for determining the resistance and stiffness properties of a joint, is the so-called component method. The component method considers any joint as a set of individual basic components. Each of these basic components possesses its own strength and stiffness. The application of the component method requires the following steps :
- identification of the active components in the joint being considered
- evaluation of the stiffness and/or resistance characteristics for each individual basic component
- assembly of all the constituent components and evaluation of the stiffness and/or resistance characteristics of the whole joint
5
Figure 5 : Basic components according to EN 1993-1-8 (1)
Steel Connections
6
Figure 6 : Basic components according to EN 1993-1-8 (2)
7
Figure 7 : Basic components EN 1993-1-8 (3)
Steel Connections
8
Figure 8 : Components in bolted beam-column joint
Zone Ref
Tension a bolts in tension
b end plate bending
c column flange bending
d beam web tension
e column web tension
[f] flange to end plate weld
[g] web to end plate weld
Horizontal shear h column web panel shear
Compression j beam flange compression
[k] beam flange weld
l, m column web in compression
Vertical shear [n] web to end plate weld
p bolt shear
q bolt bearing
9
Figure 9 : Application of the component method to a welded joint
The resistance properties
The component strength
In EC – Revised Annex J and Eurocode 3 – EN 1993-1-8, evaluation formulae are provided for each of the basic components.
The equivalent T stub
The endplate bending and the column flange bending or bolt yielding, are analysed, using an equivalent T-stub. The three possible modes of failure of the flange of the T stub are :
- complete flange yielding
- bolt failure with flange yielding
Steel Connections
10
- bolt failure
Figure 10 : Complete flange yielding
Figure 11: Bolt failure with flange yielding
Figure 12 : Bolt failure
The plastic moment capacity of the equivalent T-stub is related to the effective length of the yield line. The effective length is a notional length. The values of the effective length for the different bolt locations are defined in EN 1993-1-8.
11
Figure 7 : Effective length for unstiffened column flange
The use of national code
The capacities of the underlying steel parts are calculated by the formulas given in the respective national codes (EC3, DIN18800 T1 or BS 5950-1:2000), depending on the national code set-up. For other codes (NEN, CM, ONORM, CSN, …), the default EC3 capacities are used. Remark : the frame bolted, frame welded and frame pinned joint types are affected. The concrete parts (for base plate joints) are not affected. The concrete parts are designed according the EC definitions. Examples : Column web panel in shear
EC3
0M
vcwc,yRd,wp
3
Af9.0V
γ=
DIN
M
vcwc,k,yRd,wp
3
1.1Af9.0V
γ=
BS
ccycRd,wpv Dtp6.0VP ==
Steel Connections
12
Bolts in tension
EC3
Mb
subRd,t
Af9.0B
γ=
DIN
( )
M
k,b,uRd,2
M
k,b,yRd,1
Rd,2sRd,1RdRd,t
25.1
f
1.1
f
A,AminNB
γ=σ
γ=σ
σσ==
BS
tt't ApP =
The strength assembly
The design model is based on a plastic distribution of bolt forces. Suppose the following joint :
Figure 84 : Plate-to-plate joint
The failure may occur in 3 different ways :
1. The plastic redistribution of the internal forces extends to all bolt-rows when they have sufficient deformation capacity. The resulting distribution is called ‘plastic’.
Figure 15 : Plastic distribution
2. The plastic redistribution of forces is interrupted because of the lack of deformation capacity of a given bolt row. In the bolt-rows located lower than this bolt row, the forces are linearly distributed. The resulting distribution is called ‘elasto-plastic’.
13
Figure 16 : Elasto-plastic distribution
3. The plastic or elasto-plastic distribution of internal forces is interrupted because the compression force Fc attains the design resistance.
Figure 9 : Reduced distribution
The concept of individual and group yield mechanisms is explained in EC3 –EN 1993-1-8. When adjacent bolt-rows are subjected to tension forces, various yield mechanisms are likely to form in the connected plates (end-plate or column flange). Individual mechanism develops when the distance between the bolt-rows are sufficiently large. Group mechanism includes more than one adjacent bolt row. To each of these mechanisms are associated specific design resistances.
Steel Connections
14
Figure 10 : Individual vs. group yield mechanism
The influence of the normal force
Default Interaction check according to EC – Revised Annex J
When the axial force NSd in the connected member exceeds 10 % of the plastic resistance Npl,Rd of its cross-section, a warning is printed out and the value of the design moment resistance Mj,Rd is decreased.
� For bolted joints
The value of the design moment resistance Mj,Rd is decreased by the presence of the axial tensile force NSd.
2
h.NMM SdRd,jRd,j −=
with
h the distance between the compression and tension point in the connected member
15
If there is an axial compression force NSd, we check the following :
hNMM
))FFc(2
N,0max(N
)F,F,Vmin(F
Rd,jRd,j
totSd
Rd,fb,cRd,wc,cRd,wpc
⋅−=
−−=
=
with
h the distance between the compression and tension point in the connected member
Fc,wc,Rd Design compression resistance for column web
Fc,fb,Rd Design compression resistance for beam web and flange
Vwp,Rd Design shear resistance of column web Ftot The sum of the tensile forces in the bolt
rows at Mj,Rd
� For welded joints
)F,F,F,F,Vmin(F Rdwc,t,Rdfc,t,Rdfb,c,Rdwc,c,Rdwp,tot =
When an axial tensile force NSd is present :
hNMM
))FFc(2
N,0max(N
)F,Fmin(F
Rd,jRd,j
totSd
Rdwc,t,Rdfc,t,c
⋅−=
−−=
=
When an axial compressive force NSd is present :
hNMM
))FFc(2
N,0max(N
)F,F,Vmin(F
Rd,jRd,j
totSd
Rdfb,c,Rdwc,c,Rdwp,c
⋅−=
−−=
=
with
h the distance between the compression and tension point in the connected member
Fc,wc,Rd Design compression resistance for column web
Fc,fb,Rd Design compression resistance for beam web and flange
Vwp,Rd Design shear resistance of column web
Ft,wc,Rd Design resistance of column web in tension
Ft,fc,Rd Design resistance of column flange in tension
Steel Connections
16
Interaction Check according to EN 1993-1-8 (Ref.[32 ])
If the axial force NEd in the connected beam exceeds 5% of the design resistance, Npl,Rd ,
the following unity check is added :
Mj.Rd is the design moment resistance of the joint, assuming no axial force Nj.Rd is the axial design resistance of the joint, assuming no applied moment Nj,Ed is the actual normal force in the connection Mj,Ed is the actual bending moment in connection The value for Nj,Rd is calculated as follows : If Nj,Ed is a tensile force, the Nj,Rd is determined by critical value for the following components (Ref.[32], table 6.1.):
- For bolted connection, as a combination for all bolt rows : - component 3 : column web in transverse tension - component 4 : column flange in bending - component 5 : end plate in bending - component 8 : beam web in tension - component 10 : bolts in tension
- For welded connection :
- component 3 : column web in transverse tension, where the value for tfb in formulas (6.10) and
- (6.11) is replaced by the beam height. - component 4 : column flange in bending, by considering the sum of formula (6.20) at the top
and - bottom flange of the beam. - If Nj,Ed is a compressive force, the Nj,Rd is determined by the following components (Ref.[32],
table 6.1.): - component 2 : column web in transverse compression, where the value for tfb in formulas
(6.16) is - replaced by the beam height. - component 4 : column flange in bending, by considering the sum of formula (6.20) at the top
and - bottom flange of the beam.
In all cases, Nj,Rd ≤ Npl,Rd.
The design shear resistance
The design shear resistance for normal bolts
17
EC3
nn*Fnt28.0FV Rd,vRd,vRd +⋅⋅=
Mb
subRd,v
Af6.0F
γ⋅⋅
= for grade 4.6, 5.6, 8.8
Mb
subRd,v
Af5.0F
γ⋅⋅
= for other grades
DIN
nn*Fnt25.0FV Rd,vRd,vRd +⋅⋅=
M
sk,b,uad,R,aRd,v
AfVF
γ⋅⋅α
==
for grade 4.6 , αa=0.60
for grade 5.6 , αa=0.60
for grade 8.8 , αa=0.60
for grade 10.9 , αa=0.55
for other grades, αa=0.55
BS
nn*Fnt40.0FV Rd,vRd,vRd +⋅⋅=
sssRd,v A.pPF ==
for grade 4.6 , ps=160 N/mm²
for grade 8.8 , ps=375 N/mm²
for grade 10.9 , ps=400 N/mm²
for other grades, ps=0.4 fub
with nt number of bolts in tension nn number of bolts not in tension
Remark : For anchors, the shear (Fv,Rd, Va,R,d and Ps) are reduced by multiplying them with a factor 0.85
The design shear resistance for preloaded bolts
Suppose we have ntot number of bolts.
EC3
subCd,p Af7.0F ⋅⋅=
( )Ms
Sd,tCd,psRd,s
F8.0FnkF
γ⋅−⋅µ⋅⋅
=
BS
)F(Pk9.0P
Af7.0P
Rd,sossL
subo
=⋅µ⋅⋅=⋅⋅=
Steel Connections
18
with fub the tensile strength of the bolt As the tensile stress area of the bolt n the number of friction interfaces (=1) ks the value for slip resistance
(=1.0 for holes with standard nominal clearances) µ the slip factor Ft,Sd the applied tensile force (=NSd/ntot) γMs the partial safety factor for slip resistance
The design shear force VRd is :
totRd,sRd nFV ⋅=
The stiffness properties
The component stiffness
In EN 1993-1-8 and Eurocode 3 – Revised Annex J, evaluation formulae are provided for each of the basic components.
The following stiffness coefficients are used :
Coefficient Basic component Formula
k1 column web panel in shear
z
A38.0 vc
β⋅
k2 column web in compression
c
wceff
d
tb7.0 ⋅
k3 column flange, single bolt row in tension
3
3fceff
m
tl85.0 ⋅
k4 column web in tension, single bolt row in tension
c
wceff
d
tb7.0 ⋅
k5 endplate, single bolt row in tension
3
3peff
m
tl85.0 ⋅
k7 bolts, single bolt row in tension
b
s
L
A6.1
with Avc
the shear area of the column
z the lever arm β the transformation parameter beff the effective width of the column web dc the clear depth of the column web leff the smallest effective length for the
bolt m the distance bolt to beam/column
web As the tensile stress area of the bolt
19
Lb
the elongation length of the bolt
For a column base, we also consider the stiffness coefficient kc for the compression zone on the concrete block.
eq
cflc Eh
EAk =
with Afl the bearing area under the compression flange
Ec the E modulus of concrete
( ) 3/1ck 8f5.9 +=
(Ec in Gpa, fck in Mpa) E the Young modulus (of steel) heq the equivalent height
( )2
ba effeff +=
where aeff and beff are based on the rectangle for determining Afl Afl=aeff x beff
The stiffness assembly
The initial stiffness Sj,ini is derived from the elastic stiffness of the components. The elastic behaviour of each component is represented by an extensional spring. The spring components are combined into a spring model.
Figure 11 : Spring model for beam-to-column bolted joint
The program calculates 3 stiff nesses :
Sj,ini the initial rotational stiffness Sj the rotational stiffness, related to the actual moment Mj,Sd Sj,MRd the rotational stiffness, related to Mj,Rd (without the influence of
the normal force) The moment-rotation diagram is based on the values of Sj,ini and Sj,MRd.
Steel Connections
20
Sj,MRd
Sj,ini
M
fi
MRd
0.66 MRd
Figure 20 :Simplified Moment-rotation characteristic
The classification on stiffness
The joint is classified as rigid, pinned or semi-rigid according to its stiffness by using the initial rotational stiffness Sj,ini and comparing this with classification boundaries given in EN 1993-1-8 or EC3 – Revised Annex J. If Sj,ini >= Sj,rigid, the joint is rigid. If Sj,ini <= Sj,pinned, the joint is classified as pinned. If Sj,ini<Sj,rigid and Sj,ini>Sj,pinned, the joint is classified as semi-rigid. For braced frames :
b
b
b
b
L
EI5.0pinned,Sj
L
EI8rigid,Sj
=
=
For unbraced frames :
b
b
b
b
L
EI5.0pinned,Sj
L
EI25rigid,Sj
=
=
For column base joints, we use :
c
c
c
c
L
EI5.0pinned,Sj
L
EI15rigid,Sj
=
=
with Ib the second moment of area of the beam
Lb the span of the beam Ic the second moment of area of the
column Lc the storey height of the column
21
E the Young modulus
Figure 21 : Stiffness classification boundaries
Figure 22 : Beam length for stiffness classification
The required stiffness
The actual stiffness of the joints is compared with the required stiffness, based on the approximate joint stiffness used in the analysis model. A lower boundary and an upper boundary define the required stiffness.
Figure 23 : Check of stiffness requirement
When a linear spring is used in the analysis model, we check the following :
Steel Connections
22
When Sj,ini >= Sj,low and Sj,ini<=Sj,upper, the actual joint stiffness is conform with the applied Sj,app in the analysis model. The value of Sj,app is taken as the linear spring value introduced for <fi y> (in the hinge dialog), multiplied by the stiffness modification coefficient η.
Type of joint η
bolted beam-to-column 2
welded beam-to-column 2
welded plate-to-plate 3
column base 3
When a non-linear function is used during the analy sis model, we check the following :
When Sj >= Sj,low and Sj<=Sj,upper, the actual joint stiffness is conform with the applied Sj,app in the analysis model. The value of Sj,app is taken as the analysis stiffness defined by the non-linear function.
Transferring the joint stiffness to the analysis m odel
When requested, the actual stiffness of the joint can be transferred to the analysis model. The linear spring value for <fi y> (in the hinge dialog) is taken as Sj,ini divided by the stiffness modification coefficient η.
Figure 24 : Linear stiffness
For asymmetric joint s which are loaded in both directions (i.e. tension on top and tension in bottom), the linear spring value for <fi y> (in the hinge dialog) is taken as the smallest Sj,ini (from both directions) divided by the stiffness modification coefficient η. At the same time, a non-linear function is generated, representing the moment-rotation diagram.
23
Figure 25 : Non-linear function
Ductility classes The following classification is valid for joints : Class 1 joint : Mj,Rd is reached by full plastic redistribution of the internal forces within the joints and a sufficiently good rotation capacity is available to allow a plastic frame analysis and design. Class 2 joint : Mj,Rd is reached by full plastic redistribution of the internal forces within the joints but the rotational capacity is limited. An elastic frame analysis possibly combined with a plastic verification of the joints has to be performed. A plastic frame analysis is also allowed as long as it does not result in a too high required rotation capacity of the joints where the plastic hinges are likely to occur. Class 3 joint : brittle failure (or instability) limits the moment resistance and does not allow a full redistribution of the internal forces in the joints. It is compulsory to perform an elastic verification of the joints unless it is shown that no hinge occurs in the joint locations.
Ductility classification for bolted joints
If the failure mode of the joint is the situated in the shear zone of the column web, the joint is classified as a ductile, i.e. a class 1 joint . If the failure mode is not in the shear zone, the classification is based on the following :
Classification by ductility Class
df
f36.0t
y
ub≤ Ductile
1
df
f53.0td
f
f36.0
y
ub
y
ub ≤<
Intermediary
2
df
f53.0t
y
ub> Non-ductile
3
Steel Connections
24
with t the thickness of either the column
flange or the endplate d the nominal diameter of the bolts fub the ultimate tensile strength of the
bolt fy the yield strength of the proper basic
component
Figure 26 : Ductility classification for bolted joint
Ductility classification for welded joints
If the failure mode of the joint is the situated in the shear zone of the column web, the joint is classified as a ductile, i.e. a class 1 joint . If the failure mode is not in the shear zone, the joint is classified as intermediary for ductility, i.e. a class 2 joint .
Examples
Calculation of bolted connection
Example
CON_004.esa – Node N1
- See text ‘Design example of a joint with extended end
Figure 27 : Example CON_004.ESA
Calculation of bolted connection
See text ‘Design example of a joint with extended end plate’
: Example CON_004.ESA – NodeN1
25
Steel Connections
26
Calculation of welded connection
Example
CON_005.esa – Node N3 Calculation V wp,Rd : Column web panel in shear
0M
vcyRd,wp
3
'Af9.0V
γ=
When a web doubler is used :
13
2350.9RdVwp,
101724113'A
²mm4113A
280213140A
t(bt2AA
tbA'A
vc
vc
vc
wfvc
ssvcvc
⋅⋅=
⋅+==
⋅−=+−=
+=
Calculation F c,wc,Rd : Column web in compression
.1
1525279.0F
'A
tb3.11
1
9222.17b
5a22tb
105.1t5.1t
ftbF
Rd,wc,c
vc
wceff
1
1
eff
fbeff
wwc
0M
ywceffRd,wc,c
⋅⋅=
+
=ρ
ρ=ρ⋅+=
++=
⋅==γ
ρ=
Calculation F c,fb,Rd : Beam flange in compression
2.17550
595F
1.1
655MM
th
MF
Rd,fb,c
0M
Rd,plRd,c
fbb
Rd,cRd,fb,c
=−
=
=γ
=
−=
Calculation F t,fc,Rd : Column flange in bending
2425.10(F
r2t(F
Rd,fc,c
cwcRd,fc,c
⋅+=
++=
Calculation F t,wc,Rd : Column web in tensio
Calculation of welded connection
Column web panel in shear
When a web doubler is used :
kN6571.1
5919235
²mm59195.10
18)2425.10(18280
t)r2 fw
=⋅=
⋅++⋅+
: Column web in compression
( )
kN6741.
23575.15
79.0
mm252)2418(5
rt5
mm75.155.10
2
wc
fc
=⋅
=
=++
+
=
: Beam flange in compression
kN1116
kNm5951
655
=
=
: Column flange in bending
kN6771.1
23520.17)181724
ft)kt7
0M
ywcfc
=⋅⋅⋅+
γ
: Column web in tensio n
27
( )
kN6441.1
2357.1425281.0F
81.0
'A
tb3.11
1
mm252)2418(59222.17b
rt5a22tb
mm7.145.104.1t4.1t
ftbF
Rd,wc,t
2
vc
wceff
1
1
eff
fcfbeff
wwc
0M
ywceffRd,wc,t
=⋅⋅⋅=
=
+
=ρ
ρ=ρ=++⋅+=
+++=
=⋅==γ
ρ=
Calculation MRd : Design moment resistance 644 kN x 0.532 m = 343 kNm Calculation af The weld size af is designed according to the resistance of the joint. The design force in the beam flange can be estimated as:
kN644532.0
343F
h
MF
Rd
RdRd
==
=
The design resistance of the weld Fw shall be greater than the flange force FRd, multiplied by a factor γ. The value of the factor γ is :
γ = 1.7 for sway frames γ = 1.4 for non sway frames
However, in no case shall the weld design resistance be required to exceed the design plastic resistance of the beam flange Nt.Rd :
kN7711.1
2352.17210N
ftbN
Rd,t
M
ybfbfRd,t
0
=⋅⋅=
γ⋅⋅
=
Fw = min ( Nt.Rd, γ FRd) = min (771, 1.4 x 645)= 771 kN The weld size design for af, using Annex M of EC3
mm23.72210360
8.025.1771000a
2bf
Fa
f
fu
WMwwf
=⋅⋅
⋅⋅≥
⋅⋅β⋅γ⋅
≥
We take af=9 mm. Calculation of a w
Steel Connections
28
Figure 12 : Weld size calculation
The section is sollicitated by the moment M, the normal force N and the shear force D. The moment M is defined by the critical design moment resistance of the connection. The normal force N is taken as the maximum internal normal force on the node, the shear force D is taken as the maximum internal shear force on the node. M = 343 kNm N = 148 kN D = 84 kN To determine the weld size a2 in a connection, we use a iterative process with a2 as parameter until the Von Mises rules is respected (Annex M/EC3).
Figure 13 : Weld size calculation
29
Figure 14 : Example CON_005.ESA – Node N3
Steel Connections
30
Calculation of connections in 3D Frame
Example
CON_008.esa (WSS_002d.esa ����
- copy of connections
- expert system
- wizard for monodrawings
- multiple check of connections
Figure 15 : Example CON_008.ESA
Calculation of connections in 3D Frame
���� CON_008.esa)
wizard for monodrawings
multiple check of connections
: Example CON_008.ESA - Multiple connection check
31
Special features
Use of haunches
lc
ab
tc
hc
alfa
bc
b
tw
tf
h
r
Figure 16 : Haunches
The compression force in the haunch should be transferred by the haunch into the beam. The formula used for the buckling of the column web can also be applied to the check failure of the beam web due to the vertical component of the force transferred by the haunch. This design moment resistance Mj,Rd is compared with the moment Mc at the position where haunch and beam are meeting. For more info about this topic, we refer to Ref.[30].
Steel Connections
32
Example
CON_006.esa – Node N7
Figure 17 : Additional check at haunches
Figure 18 : Example CON_006.ESA
: Additional check at haunches
: Example CON_006.ESA – Node N7
Column in minor axis configuration
In beam-to-column minor-axis jointscausing bending about the minorcolumn web in bending and punching, the following failure mechanisms are considered :
- Local mechanism : the yield pattern is localised in the compression zone or in the tension zone
- Global mechanism : the yield line pattern involves both compression and tension zone. For more info about this topic, we refer to Ref.[30].
Figure 19 : Local and global mechanism
Example
CON_007.esa – Node N4
Figure 20 : Example CON_007.ESA
Column in minor axis configuration
axis joints, the beam is directly connected to the web of an Icausing bending about the minor-axis of the column section. In order to determine the strength of a column web in bending and punching, the following failure mechanisms are considered :
cal mechanism : the yield pattern is localised in the compression zone or in the tension zone
Global mechanism : the yield line pattern involves both compression and tension zone.
For more info about this topic, we refer to Ref.[30].
: Local and global mechanism
: Example CON_007.ESA
33
, the beam is directly connected to the web of an I-section column, axis of the column section. In order to determine the strength of a
column web in bending and punching, the following failure mechanisms are considered :
cal mechanism : the yield pattern is localised in the compression zone or in the tension zone
Global mechanism : the yield line pattern involves both compression and tension zone.
Steel Connections
34
Base plate connections : shear iron, flange widener s
In a column base, 2 connection deformabilities need to be disti
- the deformability of the connection between the column and the concrete foundation
- the deformability of the connection between the concrete foundation and the soil. In the Frame Connect base plate design, the column
Figure 21 : Base plate connection
For more info about base plate design (shear irons, etc…), we refer to Ref.[30].
Example
CON_005.esa – Node N9
Base plate connections : shear iron, flange widener s
In a column base, 2 connection deformabilities need to be distinguished :
the deformability of the connection between the column and the concrete foundation
the deformability of the connection between the concrete foundation and the soil.
In the Frame Connect base plate design, the column-to-concrete “connection’ is
: Base plate connection
For more info about base plate design (shear irons, etc…), we refer to Ref.[30].
the deformability of the connection between the column and the concrete foundation
the deformability of the connection between the concrete foundation and the soil.
concrete “connection’ is considered.
For more info about base plate design (shear irons, etc…), we refer to Ref.[30].
35
Figure 22 : Example CON_005.ESA –Node N9
The use of 4 bolts / row
Figure 23 : Four bolts/row
Steel Connections
36
When 4 bolts/row are used, additional capacity Fcolumn flange and/or the endplate. F
- the capacity of the inner two bolts is equal to the bolt tension resistance (failure mode 3) or is defined by a circular pattern
- the bolt row / group is stiffened- the bolt group contains only 1 bolt row
For more info about this topic, we refe
Example
CON_005.esa – Node N8
Figure 24 : Additonal capacity for 4 bolts/row
When 4 bolts/row are used, additional capacity Fadd is added to the bolt row/group capacity of the column flange and/or the endplate. Fadd is defined for the following conditions :
the capacity of the inner two bolts is equal to the bolt tension resistance (failure mode 3) or is defined by a circular pattern the bolt row / group is stiffened the bolt group contains only 1 bolt row
For more info about this topic, we refer to Ref.[30].
: Additonal capacity for 4 bolts/row
is added to the bolt row/group capacity of the conditions :
the capacity of the inner two bolts is equal to the bolt tension resistance (failure mode 3) or is
37
Figure 25 : Example CON_005.ESA - Node N8
Steel Connections
38
RHS beam
For more info about this topic, we refer to Ref.[30]
Example
CON_005.esa – Node N7
Figure 26 : Example CON_005.ESA
For more info about this topic, we refer to Ref.[30].
: Example CON_005.ESA - Node N7
Frame Connect : pinned joint
Four types of joints are supported :
Type 1 welded plate in beam, welded to column
Type 2 bolted plate in beam, we
Type 3 bolted angle in beam and column
Type 4 short endplate welded to beam, bolted in column
For each type, the design shear resistance Vthe design compression/tension resistance The design shear resistance is calculated for the following failure modes :
- design shear resistance for the connection element- design shear resistance of the beam- design block shear resistance - design shear resistance due to the bolt- design shear resistance due to the bolt distribution in the column
The design compression/tension resistance is calculated for the following failure modes :
- design compression/tension resistance for the connection element- design compression/tension resistance of the beam- design tension resistance due to the bolt distribution in the column
In Ref.[30], more info on the used formulas is given.
Examples
Welded fin plate connection
Example
CON_009.esa – Node N7 Calculat ion Design Shear Resistance VRd for Connection Elem entTransversal section of the plate :
Normal stress : N A=σ
Flexion module : plW =
Design Shear Resistance :
W
a2
Vpl
N
Rd
+⋅σ⋅
−
=
Calculation Design Shear Resistance VRd for BeamShear Area : v AA −=
Frame Connect : pinned joint
Four types of joints are supported :
welded plate in beam, welded to column
bolted plate in beam, welded to column
bolted angle in beam and column
short endplate welded to beam, bolted in column
For each type, the design shear resistance VRd (taking into account the present normal force N ) and the design compression/tension resistance NRd are calculated. The design shear resistance is calculated for the following failure modes :
design shear resistance for the connection element design shear resistance of the beam design block shear resistance design shear resistance due to the bolt distribution in the beam web design shear resistance due to the bolt distribution in the column
The design compression/tension resistance is calculated for the following failure modes :
design compression/tension resistance for the connection element sign compression/tension resistance of the beam
design tension resistance due to the bolt distribution in the column
In Ref.[30], more info on the used formulas is given.
Welded fin plate connection
ion Design Shear Resistance VRd for Connection Elem entTransversal section of the plate : 2
plplpl m003912.0th2A =⋅⋅= (2 plates)
2pl m
N667.67099003912.0
4939.262
A
N ==
32
pl m000106276.06
ht2
pl
=⋅
⋅=
Design Shear Resistance : a= 0.082 m is the centre
240087
A
3
W
a2
f
N
a4
W
a2
2pl
2
2
2M
2y2
N2
22
pl
N
pl
0 =
+⋅
γ−σ⋅
⋅−
⋅σ⋅
Calculation Design Shear Resistance VRd for Beam ( ) 2
fwf m00191276.0tr2ttb2 =⋅⋅++⋅⋅−
39
(taking into account the present normal force N ) and
The design compression/tension resistance is calculated for the following failure modes :
ion Design Shear Resistance VRd for Connection Elem ent (2 plates)
kN240N66.240087 =
Steel Connections
40
Shear Resistance : kN236N57.2359253
fAVRd
0M
yv ==γ⋅
⋅=
Calculation Design Tension Resistance NRd for Conne ction Element Area of the element : 2
plplpl m003912.0th2A =⋅⋅=
Tension Resistance : kN835N45.835745fA
N0M
yplRd ==
γ⋅
=
Calculation Design Tension Resistance NRd for Beam Area of the Beam : 2m003910.0A =
Tension Resistance : kN835N18.835318fA
N0M
yRd ==
γ⋅
=
Weld size Calculation for Plate, Beam and Column To determine the weld size a for the plate on the beam and on the column, we must use a iterative process with a as parameter until the Von Mises rules is respected (Annex M/EC3) :
( )ww
211M
u1
Mw
u222 f and
f3
γ≤σ
γ⋅β≤τ+τ⋅+σ
We’ll only check the weld size for the final value of a. For the weld between plate and beam we find a=4mm and for weld between plate and column, the weld size is a=10mm. Weld size Plate/Beam We define the play as the effective distance between the end of the beam and the flange of the column. In this case, the play is 10mm. By using EC3 and the Chapter 11 of the manual, we compute the following parameters : Weld size : a=0.004 Weld Length : m139.012.02163.0t2hl plpl1 =⋅−=⋅−=
m13.0t2Playbl plpl2 =⋅−−=
m154.001.0164.0Playll pl =−=−=
By EC3 : fuw=360000000N/m2 and βw=0.8 The parameters are :
( )10.104
la414.1la577.0
lla577.0la707.0g
21
11 =⋅⋅+⋅⋅
⋅⋅⋅+⋅⋅=
30377.0la414.1la577.0
la577.0
21
1 =⋅⋅+⋅⋅
⋅⋅=δ
15603.0hla577.0la117.0
la117.0
pl221
21 =
⋅⋅⋅+⋅⋅
⋅⋅=µ
3987.0la14.1la707.0
la707.0
21
1 =⋅⋅+⋅⋅
⋅⋅=Γ
g10L +=
Shear force on one plate : N789.1179622
VD Rd == (for one plate)
Normal force on one plate : N24.1312
NN ==
Moment on the plate : Nm781.13459LDM =⋅=
Weld Check 1: 21
211 mN74.115363040
la2
N
la2
M6
1
==⋅⋅
⋅Γ+⋅⋅
⋅µ⋅=σ=τ
41
21
2 mN72.64449431
la
D =⋅⋅δ=τ
Unity Check : ( )
14.0f
and 1316.0f
3
ww
211
M
u
1
Mw
u
222
≤=
γ
σ≤=
γ⋅β
τ+τ⋅+σ
Weld Check 2 : ( )
22
11 mN8731.55840293
la22
D1 =⋅⋅⋅
⋅δ−=τ=σ
( ) ( )2
222 m
N161.134095932la2
N1
lah
M1 =
⋅⋅⋅Γ−+
⋅⋅⋅µ−=τ
Unity Check : ( )
1193.0f
and 1715.0f
3
ww
211
M
u
1
Mw
u
222
≤=
γ
σ≤=
γ⋅β
τ+τ⋅+σ
Weld size Plate/Column Weld size : a=0.01 m Normal Force : N=262.4939N Moment : Nm89674.19345082.057.235925LDM =⋅=⋅= Stress Calculation :
22pl
11 mN96.154518316
6
ha22
LD
la22
N
W
M
la22
N =
⋅⋅⋅
⋅+⋅⋅⋅
=+⋅⋅⋅
=τ−=σ
22 mN7485.72369806
la2
D =⋅⋅
=τ
Unity Check : ( )
192.0f
3
w
211
Mw
u
222
≤=
γ⋅β
τ+τ⋅+σ
153.0f
wM
u
1 ≤=
γ
σ
Steel Connections
42
Figure 27 : Example CON_009.ESA - Node N2
Bolted fin plate connection
Example
CON_010.esa – Node N7 Calculation Design Shear Resistance VRd for Connect ion Element Transversal section of the plate :
Normal Stress : N =σ
Flexion Module : W =
Bolt Centre : a=0.0995mDesign Shear Resistance :
W
a2
V
N
Rd
+⋅σ⋅
−
=
Calculation Design Shear Resistance VRd for BeamShear Area : v AA −=
Net Area : AA vnet =
For the calculation of VRd in the beam,
Shear Resistance: VRd
Calculation Design Tension Resistance NRd for Conne ction ElementArea : 004512.0ht2A =⋅⋅=Net Area : net 2AA −=Tension Resistance :
⋅
γ⋅
=0M
yRd
9.0,
fAminN
Calculation Design Tension Resistance NRd for Beam
Area : 003910.0A =Net Area : net AA −=
Tension Resistance :
( 1085930,18.835318min=Calculation Design Shear Resistance VRd for Bolt in BeamThe calculation of the shear resistance for bolt in beam is based on the following equation to be solve
I
ca
n
1V
2p
22
22
Rd
+⋅+⋅
Where : 0.0995ma =
4
1i
2ip 66.95rI ∑ ∑==
=
( Rd,vF2minQ ⋅=
Calculation Design Shear Resistance VRd for Connect ion Element Transversal section of the plate : m004512.0012.0188.02th2A =⋅⋅=⋅⋅=
2mN8395.58176
004512.0
4939.262
A
N ==
32
m000141376.06
ht2 =⋅⋅
Bolt Centre : a=0.0995m Design Shear Resistance :
266422
A
3
W
a2
f
N
a4
W
a2
22
2
2M
2y2
N2
22
N
0 =
+⋅
γ−σ⋅
⋅−
⋅σ⋅+
Calculation Design Shear Resistance VRd for Beam ( ) 2
fwf m00191276.0tr2ttb2 =⋅⋅++⋅⋅−
m56.001689.0dt2 0w =⋅⋅−
For the calculation of VRd in the beam, we use Av because vu
ynet A
f
fA ⋅≥
kN236N57.2359253
fAVRd
0M
yv ==γ⋅
⋅=
Calculation Design Tension Resistance NRd for Conne ction Element2m004512
20 m003648.0d2t2 =⋅⋅⋅
γ
⋅⋅
1
net
M
ufA ( ) 96392781.1074501,27.963927min ==
Calculation Design Tension Resistance NRd for Beam 2m003910
20 m0036868.0dt2 =⋅⋅−
γ
⋅⋅
γ⋅
=1
net
0 M
u
M
yRd
fA9.0,
fAminN
) kN836N18.83531818.1085930 == Calculation Design Shear Resistance VRd for Bolt in Beam The calculation of the shear resistance for bolt in beam is based on the following equation to
0Qn
N
nI
dNa2V
I
da 22
2
pRd2
p
22
=−+
⋅⋅⋅⋅⋅+
⋅+
0.0995m 0.094mb = 0.0655mc = 0.07md = 2
2 m036761.066 =
( ))beam,Rd,bplate,Rd,bRd F;Fmin, =31740.8256N for two plates, where
43
Calculation Design Shear Resistance VRd for Connect ion Element 2m (2 plates)
kN266N015.266422 =
2v m00124860.0=
Calculation Design Tension Resistance NRd for Conne ction Element
kN963N27.963927 =
The calculation of the shear resistance for bolt in beam is based on the following equation to
for two plates, where
Steel Connections
44
• kN1.30N30144Af6.0
FMb
subV dR
==γ
⋅⋅=
• kN7.31N8256.31740tdf5.2
FMb
upBeam,Rd,b ==
γ⋅⋅⋅α⋅
=
444.01;f
f;
4
1
d3
p;
d3
eminwith
u
ub
0
1
0
1p =
−=α
• N712.122867tdf5.2
FMb
plupplate,Rd,b =
γ⋅⋅⋅α⋅
=
444.01;f
f;
4
1
d3
p;
d3
eminwith
u
ub
0
1
0
1p =
−=α
By solving the second-degree equation, we find kN9.67N89.67907VRd == Calculation Design Block Shear Resistance The design value of the effective resistance to block shear is determined by the following expression :
eff,veffv,
M
eff,vyRd,eff LtA with
3
AfV
0
⋅=γ⋅
⋅=
We determined the effective shear area Av,eff as follows : m049.0a1 = m155.0a2 = m051.0a3 =
m14.0aahL 21v =−−=
( )
( ) m24.02849.0;24.0min
f
fdnaaL;aaLminL
y
u031v31v3
==
⋅⋅−++++=
( ) m049.0d5;aminL 011 =⋅=
( )
bolt rows 2for 2.5k with
m1685.0f
fdkaL
y
u022
=
=⋅⋅−=
( ) m24.0L;LLLminL 321veff,v =++= 2
eff,v m001488.0A =
kN185N40.1835343
AfV
0M
eff,vyRd,eff ==
γ⋅⋅
=
Figure 28 : Example CON_010.ESA
Bolted cleat connection
Example
CON_011.esa – Node N2 To determine the design shear resistance for bolts in the flange of the column, we use a iterative process with h
We’ll only consider the check for the final value of hm008.0r =
: Example CON_010.ESA - Node N2
To determine the design shear resistance for bolts in the flange of the column, we cess with hD as parameter until we reach a equilibrium :
γγ=σ
00 M
cor,y
M
beam,yD
f,
fmin
We’ll only consider the check for the final value of hD. We have the following data :m03.0a = m006.0s =
45
To determine the design shear resistance for bolts in the flange of the column, we as parameter until we reach a equilibrium :
. We have the following data :
Steel Connections
46
m0128436.0s577.1r4227.0b =⋅+⋅= m0028436.0Playbbs =−=
m011.0hD = 22ipD m029194.0rID
==∑
We compute : 0951.1anI
aK
2pD
=⋅−
=
We define xj=0.03m and zj=0.165m respectively as the maximum horizontal distance between bolts and d and the maximum vertical distance between the bolts and d. Its corresponds to the further bolts how is submitted to the higher force.
( ) 5.0xaKn
1A j =−⋅+= 18069.0zKB j =⋅=
N16224Fn4.1
N1F,FminQ
Rd,tRd,vRd,b =
⋅⋅−⋅= where:
• N16224Af6.0
FMb
subcor,V dR
=γ
⋅⋅= and N24336
Af9.0F
Mb
subRd,t =
γ⋅⋅
=
• N2.22187tdf5.2
FMb
corupcor,Rd,b =
γ⋅⋅⋅α⋅
=
428.01;f
f;
4
1
d3
p;
d3
eminwith
u
ub
0
1
0
1p =
−=α
• kN8.77tdf5.2
FMb
flangeupflange,Rd,b =
γ⋅⋅⋅α⋅
=
0.11;f
f;
4
1
d3
p;
d3
eminwith
u
ub
0
1
0
1p =
−=α
With this values, we have :
N94.61032BA
Q2V
22ColFlange,Rd =
+
⋅= ∑ ∑ =⋅⋅= N64.5948zKVQ jRdh
2DD
hD m
N89.209194259bh
Q=
⋅=σ ∑
View A-
47
Figure 29 : Example CON_011.ESA -Node N2
Steel Connections
48
Flexible end plate connection
Example
CON_012.esa – Node N2
Figure 30 : Example CON_012.ESA
Flexible end plate connection
: Example CON_012.ESA - Node N2
49
References and literature
[1] Eurocode 3 : Part 1.1.
Revised annex J : Joints in building frames
ENV 1993-1-1/pr A2
[2] Eurocode 3
Design of steel structures
Part 1 - 1 : General rules and rules for buildings
ENV 1993-1-1:1992, 1992
[3] P. Zoetemeijer
Bolted beam to column knee connections with haunched beams
Tests and computations
Report 6-81-23
Delft University of Technology, Stevin Laboratory, December 1981
[4] P. Zoetemeijer
Een rekenmethode voor het ontwerpen van geboute hoekverbindingen met een kolomschot in de trekzone van de verbinding en een niet boven de ligger uitstekende kopplaat.
Rapport 6-81-4
Staalcentrum Nederland, Staalbouwkundig Genootschap, Juni 1982
[5] Eurocode 3 : Part 1.1.
Annex L: Design of column bases
ENV 1993-1-1:1992
[6] Eurocode 2
Design of concrete structures
Part 1: General rules and rules for buildings
ENV 1992-1-1:1991
[7] Y. Lescouarc’h
Les pieds de poteaux articulés en acier
CTICM, 1982
[8] Manual of Steel Construction
Load & Resistance Factor Design
Volume II : Connections
Part 8 : Bolts, Welds, and Connected Elements
AISC 1995
[9] U. Portmann
Symbole und Sinnbilder in Bauzeichnungen nach Normen, Richtlinien und Regeln
Wiesbaden, Berlin : Bauverlag, 1979
[10] Sprint Contract RA351
Steel Moment Connections according to Eurocode 3
Simple Design aids for rigid and semi-rigid joints
1992-1996
[11] DIN18800 Teil 1
Stahlbauten : Bemessung und Konstruktion
November 1990
Steel Connections
50
[12] J. Rudnitzky
Typisierte Verbindungen im Stahlhochbau. 2. Auflage
Stahlbau-Verlags-GmbH-Köln 1979
[13] H. Buchenau A.Tiele
Stahlhochbau 1
B.G. Teubner
Stuttgart 1981
[14] F. Mortelmans
Berekening van konstructies Deel 2
Staal Acco
Leuven, 1980
[15] Frame Design Including Joint Behaviour
Volume 1
ECSC Contracts n° 7210-SA/212 and 7210-SA/320
January 1997
[16] F. Wald, A.M. Gresnigt, K. Weynand, J.P. Jaspart
Application of the component method to column bases
Proceedings of the COST C1 Conference
Liège, Sept.17-19, 1998
[17] F.C.T. Gomes, U. Kuhlmann, G. De Matteis, A. Mandara
Recent developments on classification of joints
Proceedings of the COST C1 Conference
Liège, Sept.17-19, 1998
[18] M. Steenhuis, N. Gresnigt, K. Weynand
Pre-design of semi-rigid joints in steel frames
COST C1 Workshop
Prague, October 1994
[19] M. Steenhuis, N. Gresnigt, K. Weynand
Flexibele verbindingen in raamwerken
Bouwen met Staal 126
September/Oktober 1995
[20] O. Oberegge, H.-P. Hockelmann, L. Dorsch
Bemessungshilfen für profilorientiertes Konstruieren
3. Auflage 1997
Stahlbau-Verlagsgesellschaft mbH Köln
[21] M. Steenhuis, JP Jaspart, F. Gomes, T. Leino
Application of the component method to steel joints
Proceedings of the COST C1 Conference
Liège, Sept.17-19, 1998
[22] J.A. Packer, J. Wardenier, Y. Kurobane, D. Dutta, N. Yeomans
Design Guide for rectangular hollow sections (RHS) joints under predominantly static loading
CIDECT
Köln, 1992, Verlag TUV Rheinland
51
[23] Eurocode 3
Part 1.1. Revised Annex J
Joints in building frames, edited
Approved draft : january 1997
[24] Rekenregels voor het ontwerpen van kolomvoetplaten en experimentele verificatie
TNO report N° BI-81-51
[25] Typisierte Anschlüsse im Stahlhochbau
Band 1
DSTV - 2000
[26] Typisierte Anschlüsse im Stahlhochbau
Band 2
DSTV - 2000
[27] Joints in Steel Construction
Moment Connections
BCSA - 1997
[28] Joints in Simple Construction
Volume 1 : Design methods
BCSA - 1994
[29] BS 5950
Structural use of steelwork in building
Part 1 : Code of practice for design - Rolled and welded sections
2000
[30] Scia Engineer Connect Frame & Grid
Theoretical Background
Release : 8.0
Revision : 05/2008