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SKILLS Project SKILLS Project
BUILT-UP COLUMNS
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Special features for the design of built-up columns
Design procedure
Design of closely spaced built-up members
LEARNING OUTCOMES
3
Introduction
Constructional details
Calculation
General
Laced built-up columns
LIST OF CONTENTS
Battened built-up columns
Closely spaced built-up members
General
Simplified method
Worked example
Conclusion
4
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INTRODUCTION
2 types of built-up columns:
INTRODUCTION
Laced built-up columns Battened built-up columns
6
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INTRODUCTION
1000
11
55
Type 2
1000
Type 1
1000
20
00
Type 3
7
Built-up column Shear stiffness [kN]
Type 1 615000
Type 2 288000
Type 3 73000
L 100x10
HEA 400
8x 1000 20x400
Shear stiffness of a panel:
INTRODUCTION
LFSv
=
F
8
L
F
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Advantages
Reduction of mass
Increasing of flexural stiffness
Architectural effect
Disadvantages
INTRODUCTION
Disadvantages
Costs of joints
Costs of protection against corrosion
9
Modelling using design software
One bar-type element using effective section properties
Area A = Area of the chords
Inertia about strong axis = Ieff
Inertia about weak axis = 2 x Iy,chord
Shear stiffness Sv
INTRODUCTION
v
Advantage: Rapidity of the modelling process
Sets of elements using common section properties
Advantage: Knowledge of internal forces and moments of the
elements of the built-up column
10
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CONSTRUCTIONAL DETAILS
Field of application
Pinned at both ends
Parallel chords
Equal modules of lacings or battens
At least 3 modules per member
CONSTRUCTIONAL DETAILS
At least 3 modules per member
12
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CONSTRUCTIONAL DETAILS
A Corresponding lacing
system
B Mutually opposed lacing
system
A BA B
1 2 2 1 1 2 2 1
2 2
1 1
2 2
1 1
13
Treillis sur
face A
Treillis sur
face B
Treillis sur
face A
Treillis sur
face B
CONSTRUCTIONAL DETAILS
14
N-Shape V-Shape X-Shape
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CONSTRUCTIONAL DETAILS
Types of section
Chords:
I-shape
Channels
Web members (laced systems)
15
Web members (laced systems)
Angles
Web members (battened systems)
Plates
CALCULATION
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CALCULATION GENERAL
Design steps
Mechanical properties of the built-up section
Critical axial force of the built-up column
Maximum global bending moment
Maximum axial force
Maximum transverse force
17
Maximum transverse force
Verification of the components
CALCULATION GENERAL
Mechanical properties of the built-up section
Built-up columns with lacings:
Effective second moment of area:
ch0eff AhI25,0= EN 1993-1-1 6.4.2.1
h0
18
Ach Area of the chord
Ich Second moment of area of the chord
H0 Distance between the chords
h0
Ich, Ach
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CALCULATION GENERAL
Shear stiffness Sv: EN 1993-1-1 6.4.1
System
Ad
Av
a
Ad
a
Ad
a
19
SV
n is the number of planes of lacings
Ad and Av refer to the cross sectional area of the bracings
3
20d
2dahnEA
3
20d
dahnEA
+ 3
V
0d3
20d
1dAhAd
ahnEA
h0h0h0
CALCULATION GENERAL
Built-up columns with battens:
Effective second moment of area:
chch0eff IAhI 25,0 2 += EN 1993-1-1 6.4.3.1
Criterion Efficiency factor
20
150 0
75 < < 150
75 1,0
Where:
752 =
0iL
=ch
10 2A
Ii = chch0 IAhI 25,02
1 +=
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CALCULATION GENERAL
Built-up columns with battens:
Shear stiffness:
2
2
2
221
24a
EI
a
hnII
a
EIS ch0
b
ch
chv
+
= EN 1993-1-1 6.4.3.1
h0
21
Ib: second moment of area of
the batten
b h0
Ich, Ach
Ib
CALCULATION GENERAL
Maximum global bending moment
MeN I+
Critical axial force:
2
2
LEIN effcr
=
22
eff
ch0EdEdEdch, 2
5,0I
AhMNN +=
V
Ed
cr
Ed
Ed0Ed
1SN
NN
MeNMI
Ed
+= EN 1993-1-1 6.4.1
EN 1993-1-1 6.4.1
Maximum compression axial force in a chord
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CALCULATION GENERAL
Maximum transverse force
Compression and imperfection
Attention: In case of a bending moment caused by external
LMV EdEd pi=
( )0Ed =IMEN 1993-1-1 6.4.1
23
Attention: In case of a bending moment caused by external
loads, this formula is not applicable.
Transverse force due to external loads has to
be accounted for.
CALCULATION LACED BUILT-UP COLUMN
Verification of the components
Flexural buckling of the chord:
Buckling length:
1Rdb,
Ed, NNch
EN 1993-1-1 6.3.1.1
24
Buckling length:
in plane buckling: I or H sections: 0,9 a
other sections : 1,0 a
out of plane buckling: distance between lateral supports
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CALCULATION LACED BUILT-UP COLUMN
Flexural buckling of the compressed web members (angle
sections):
Buckling length and slenderness ratio:
welded connection/at least 2 bolts per joint
1Rdb,
Ed NN EN 1993-1-1 6.3.1.1
25
welded connection/at least 2 bolts per joint
1 bolt per joint
LL =cr
LL =cr
veff,vmin 7,035,0 +==
vmin =
EN 1993-1-1 BB 1.2
CALCULATION LACED BUILT-UP COLUMN
z
uvh
26
y
z
y
u vh
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CALCULATION LACED BUILT-UP COLUMN
Verification of the web members diagonals in tension:
Welded joints:
1Rdt,
Ed NN
0M
yRdpl,Rdt,
AfNN ==
EN 1993-1-1 6.2.3
27
Bolted joints: According to connection type
Category A connections: Bearing type
Category B connections: Slip resistant at service limit state
Category C connections: Slip resistant at ultimate limit state
0M
CALCULATION LACED BUILT-UP COLUMN
Category A, B and C connections:
( )Rdu,Rdpl,Rdt, ,NNMinN =
0M
yRdpl,
AfN =
EN 1993-1-1 6.2.3
EN 1993-1-1 6.2.3
28
1 Bolt 2 Bolts 3 Bolts or more
( )2M
u02Rdu,
5,00,2
tfdeN =2M
unet2Rdu,
fAN =2M
unet3Rdu,
fAN =
EN 1993-1-8 3.10.3
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CALCULATION LACED BUILT-UP COLUMN
Constants 2 and 3:
Pitch p1 2,5 d0 5,0 d0
2 bolts 2 0,4 0,73 bolts or more 3 0,5 0,7
EN 1993-1-8 3.10.3
29
d0
e1
e2
e1
e2
p1 e1 p1 p1
CALCULATION LACED BUILT-UP COLUMN
Additional verification for category C connections:
0M
ynetRdnet,
fAN = EN 1993-1-1 6.2.3
EdRdnet, NN
30
Where: t: is the thickness of the leg
n: is the number of vertically aligned holes
d0: is the diameter of the hole
0grossnet tndAA =
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CALCULATION BATTENED BUILT-UP COLUMN
Verification of the chord
Flexural buckling perpendicular to the battens
Buckling length = distance between lateral supports
Chord subjected to axial force
31
1Rdb,
Ed, NNch EN 1993-1-1 6.3.1.1
CALCULATION BATTENED BUILT-UP COLUMN
Flexural buckling in the plane of the battens:
Buckling length = distance between battens
Chord subjected to axial force and local bending moment
1Rk
Edch,yy
Rky
Edch, +
M
MkN
N1
Rk
Edch,zy
Rkz
Edch, +
M
MkN
N
32
+ Verification of the end sections
1M1M 1M1M
EN 1993-1-1 6.3.3
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CALCULATION BATTENED BUILT-UP COLUMN
Verification of the web members battens
Transverse force:
1Rdc,
Edbatten, V
V
( )0M
y
Rdpl,Rdc,
3
fA
VVv
== EN 1993-1-1 6.2.6
33
Bending moment/Lateral Torsional buckling:
0M
1Rdb,
Edbatten, M
M
1M
yyLTRdb,
f
WM =EN 1993-1-1 6.3.2.1
CALCULATION BATTENED BUILT-UP COLUMN
Axial force and moment in the
chord:
Shear force and moment in
4EdEdch,aVM =
eff
ch0EdEdEdch, 2
5,0I
AhMNN +=
VEd a/2
a/2
h0
a/2
VEd a/2
VEd a/4 VEd a/4
34
Shear force and moment in
the battens:
0EdEdbatten, h
aVV =
2EdEdbatten,aVM =
h0
VEd a/h0
a/2
h0
a/2
VEd/2
VEd/2 VEd/2
VEd/2
VEd a/h0
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CLOSELY SPACED BUILT-UP MEMBERS
CLOSELY SPACED BUILT-UP MEMBERS GENERAL
Case 1: Connected through packing plates
36
Case 2: Connected by pairs of battens
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CLOSELY SPACED BUILT-UP MEMBERS GENERAL
Calculation
Shear stiffness is set to infinity if maximum spacing for
joints are respected
Case Maximum spacing
1 15i
EN 1993-1-1 6.4.4
37
Buckling verification as a single member
If maximum spacing is not respected
Shear deformation has to be accounted for
1
2
min15i
min70i
CLOSELY SPACED BUILT-UP MEMBERS SIMPLIFIED METHOD
Simplified calculation for sections composed of 2 equal
leg angles (Reference [3])
when the spacing is > 15 imin.
h0
z
38
a atp
yy
z
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CLOSELY SPACED BUILT-UP MEMBERS SIMPLIFIED METHOD
Scope of application
Spacing of the packing plates a: 15imin 50 imin
Number of packing plates: 2 5
Width of the legs b: 50 mm 200 mm
39
Thickness of the legs t: 0,1b
Thickness of the packing plates: 0,8t 2t
Non dimensional slenderness about z-z: 1,80
CLOSELY SPACED BUILT-UP MEMBERS SIMPLIFIED METHOD
Procedure
Second moment of area about z-z axis:
Critical axial force about z-z axis:
chch20z' 25,0 IAhI +=
z'2EIN pi=
40
Non dimensional slenderness about z-z axis:
2z'
cr,z' LEIN pi=
cr,z'
ychz'
2N
fA=
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CLOSELY SPACED BUILT-UP MEMBERS SIMPLIFIED METHOD
Effective non dimensional slenderness about z-z axis
Number of packing
platesS235 S355
2 39,077,018,0 2 ++ 66,018,086,0 2 +
:eff
41
2
3
4
5
39,077,018,0 z'2z' ++
41,052,032,0 z'2z' ++
48,017,056,0 z'2z' ++
53,005,069,0 z'2z' +
66,018,086,0 z'2z' +
66,016,066,0 z'2z' +
67,021,065,0 z'2z' +
70,031,069,0 z'2z' +
CLOSELY SPACED BUILT-UP MEMBERS SIMPLIFIED METHOD
Second moment of area about y-y axis:
Critical axial force about y-y axis:
chy' 2II =
2y'cr,
'
2
y'cr, LEI
N ypi
=
42
Non dimensional slenderness about y-y axis:
y'cr,L
y'cr,
ychy'
2N
fA=
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CLOSELY SPACED BUILT-UP MEMBERS SIMPLIFIED METHOD
Choice of the determining non dimensional
slenderness:
Determination of the reduction factor with:
),( y'effmax Max=
34,0=
43
Resistance criterion:
34,0=
1M
ychEd
)2(
fAN
WORKED EXAMPLE
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WORKED EXAMPLE GEOMETRY
Height: 10m
Loading:
Axial force: 900 kN
Bending moment: 450 kN.m
NEd=900 kN
MEd = 450 kN.m
45
WORKED EXAMPLE GEOMETRY
1
2
800
800
12
50
46
1. Chords: HEA 240
2. Posts: Equal leg angles 80 x 80 x 8
3. Diagonals: Equal leg angles 90 x 90 x 9
2
3
12
50
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WORKED EXAMPLE SECTION PROPERTIES
Chords HEA 240 S355
Posts Equal leg angles L 80 x 80 x 8 S355
2ch cm8,76=A
cm05,10y =i cm0,6=zi
2cm27,12=VA
cm125=a
cm800 =h
47
Diagonals Equal leg angles L 90 x 90 x 9 S355
cm27,12=VA
cm43,2== zy ii cm06,3=ui cm56,1=vi
2cm52,15=DA
cm73,2== zy ii cm44,3=ui cm75,1=vi
cm800 =h
cm148=d
WORKED EXAMPLE BUILT-UP COLUMN
Effective second moment of area of the built-up column
Critical axial force
ch2
0eff 5,0 AhI =442
eff cm2457601076808005,0 == I
2EIpi
EN 1993-1-1 6.4.2.1
48
2eff
2
cr LEIN pi=
kN509371010000
10245760210000 32
42
cr =pi
=N
EN 1993-1-1 6.4.1
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WORKED EXAMPLE BUILT-UP COLUMN
Shear stiffness
+
=
3V
30d3
20d
v
1dAhAd
ahnEAS
800125015522100002 32
EN 1993-1-1 6.4.2.1
49
kN13407510
14801227800155211480
800125015522100002 3
3
33
2
v =
+
=
S
WORKED EXAMPLE INTERNAL FORCES AND MOMENTS
Maximum global bending moment:
Imperfection:
Global bending moment:
mm20500
100000 ==e
MeN I+ EN 1993-1-1 6.4.1
50
V
Ed
cr
Ed
Ed0EdEd
1SN
NN
MeNMI
+=
kNm7,47910
134100900
509379001
1045020900 33=
+=
EdM
EN 1993-1-1 6.4.1
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WORKED EXAMPLE INTERNAL FORCES AND MOMENTS
Maximum compressive axial force of the chord
Class of the section:
Class 1
Maximum axial force in the chord
AhMN EN 1993-1-1 6.4.1
EN 1993-1-1 5.6 Table 5.2
51
eff
ch0EdEdEdch, 22 I
AhMNN +=
kN6,10491024576027680800479700
2900
4Edch, =
+=N
EN 1993-1-1 6.4.1
WORKED EXAMPLE INTERNAL FORCES AND MOMENTS
Maximum shear force
Shear force due to axial force and imperfection
Shear force due to external loading
V
Ed
cr
Ed
0EdEd1Ed,
1
1
SN
NNL
eNL
MV
== pipi
52
Shear force due to external loading
Maximum shear force
V
Ed
cr
Ed
EdEd2Ed,
1
1
SN
NNL
ML
MV
I
==
2Ed,1Ed,Ed VVV +=
-
WORKED EXAMPLE INTERNAL FORCES AND MOMENTS
Maximum shear force
Shear force due to axial force and imperfection
Shear force due to external loading
kNV 80,5
134100900
509379001
110000
209001Ed, =
= pi
53
Shear force due to external loading
Maximum shear force
kNV 12,46
134100900
509379001
110000
10450 32Ed, =
=
kNV 92,5112,4680,5Ed =+=
WORKED EXAMPLE BUCKLING OF THE CHORDS
Out-of-plane (strong axis) buckling of the chords
Non dimensional slenderness
5,995,100
10000y
ycr,y === i
L
06,7681,09,939,931 ===
54
Buckling curve
31,106,765,99
1
yy ===
b curve buckling100mmt
1,2h/b
f
==k
73
end bolts:
= 1,,
u
ubdb f
fMin
0
2d 3d
e=
0
5,28,17,118454,11 ==ik
74,0183
40de =
=
WORKED EXAMPLE CATEGORY A CONNECTION
Ratio fub/fu:
b :
( ) 74,01;22,1;74,0Minb ==
22,1490600
u
ub==
ff
74
Bearing resistance Fb,Rd in the transverse direction:
kN19,751025,1
91649074,08,1 3Rd,b, =
=
trF
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WORKED EXAMPLE CATEGORY A CONNECTION
Bearing resistance of the bolt group (Reference [4]):
2
Rdb,tr,
02
Rdlg,b,
1Rdb,
1
+
=
FF
nN
( )6e
=
75
( ) 110 16
pne
+=
( ) 09,145126,246
0 =+
=
kN3,105
19,7509,1
5,811
222Rdb,
=
+
=N
WORKED EXAMPLE CATEGORY A CONNECTION
kN0,52kN48
kN3,105kN48
Rd,Edv, SNF
Rdb,Edv, NF
76
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WORKED EXAMPLE BLOCK TEARING
Block tearing resistance
0M
nvy
2M
ntuRdeff,2, 3
5,0AfAfF +=
NEd
(2)
EN 1993-1-8 3.10.2
77
(1) Shear plane
(2) Tension plane
(1)
WORKED EXAMPLE BLOCK TEARING
Tension Area
Shear Area
Block tearing resistance
222nt cm79,2109182
110940 == A
( ) 222nv cm6,3109185,21094540 =+= A
78
Resistance criterion
kN5,128100,13
3603551025,1
2794905,0 33Rdeff,2, =
+
=
F
kN5,128kN48
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CONCLUSION
The buckling verification of a built-up member is based on a
calculation that takes into account an equivalent geometric
imperfection (L/500) and 2nd order effects.
Then the resistance of each component has to be checked
(cross-section resistance, buckling resistance, resistance of
CONCLUSION
(cross-section resistance, buckling resistance, resistance of
connections)
A simplified procedure is proposed for built-up members
with closely spaced chords.
80
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REFERENCES
EN 1993-1-1 Eurocode 3 Design of steel structures Part 1-1:General rules and rules for buildings
EN 1993-1-8 Eurocode 3 Design of steel structures Part 1-8:Design of joints.
A.Bureau/P.-L. Chouzenoux. Mthode simplifie pour la vrification de barres comprimes composes de deux cornires assembles
REFERENCES
de barres comprimes composes de deux cornires assembles dos--dos.
Simplified method for the verification of compressed built-up
members composed of two closely spaced angles.
Revue Construction Mtallique n4/2010. CTICM.
J.-P. Jaspart, J.-F. Demonceau, S. Renkin, M.L. Guillaume, European Recommendation for the Design of Simple Joints in Steel Structures, ECCS, Publication n126, 2009
82