skills project - cticmskills.cticm.org/.../020813/skills_m01e_design_of_built-up_columns… · 2...
TRANSCRIPT
![Page 1: SKILLS Project - CTICMskills.cticm.org/.../020813/SKILLS_M01E_Design_of_built-up_columns… · 2 types of built-up columns: 6 INTRODUCTION Laced built-up columns Battened built-up](https://reader034.vdocument.in/reader034/viewer/2022051106/5b5cc03a7f8b9a9c398cc723/html5/thumbnails/1.jpg)
SKILLS Project
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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
3
LEARNING OUTCOMES
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Introduction
Constructional details
Calculation
General
Laced built-up columns
Battened built-up columns
Closely spaced built-up members
General
Simplified method
Worked example
Conclusion
4
LIST OF CONTENTS
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INTRODUCTION
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2 types of built-up columns:
6
INTRODUCTION
Laced built-up columns Battened built-up columns
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7
INTRODUCTION
Built-up column Shear stiffness [kN]
Type 1 615000
Type 2 288000
Type 3 73000
L 100x10
1000
11
55
Type 2
HEA 400 8x 1000
1000
Type 1
20x400
1000
20
00
Type 3
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Shear stiffness of a panel:
8
INTRODUCTION
LFSv
F
L
F
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Advantages
Reduction of mass
Increasing of flexural stiffness
Architectural effect
Disadvantages
Costs of joints
Costs of protection against corrosion
9
INTRODUCTION
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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
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
INTRODUCTION
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CONSTRUCTIONAL DETAILS
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Field of application
Pinned at both ends
Parallel chords
Equal modules of lacings or battens
At least 3 modules per member
12
CONSTRUCTIONAL DETAILS
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CONSTRUCTIONAL DETAILS
A – Corresponding lacing system
B – Mutually opposed lacing system
A B A B
Treillis sur face A
Treillis sur face B
Treillis sur face A
Treillis sur face B
1 2 2 1 1 2 2 1
2 2
1 1
2 2
1 1
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CONSTRUCTIONAL DETAILS
N-Shape V-Shape X-Shape
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CONSTRUCTIONAL DETAILS
Types of section
Chords:
I-shape
Channels
Web members (laced systems)
Angles
Web members (battened systems)
Plates
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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
Verification of the components
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18
CALCULATION – GENERAL
Mechanical properties of the built-up section
Built-up columns with lacings:
Effective second moment of area:
Ach Area of the chord
Ich Second moment of area of the chord
H0 Distance between the chords
ch0eff AhI2
5,0 EN 1993-1-1 § 6.4.2.1
h0
Ich, Ach
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CALCULATION – GENERAL
Shear stiffness Sv: EN 1993-1-1 § 6.4.1
System
SV
n is the number of planes of lacings Ad and Av refer to the cross sectional area of the bracings
3
20d
2d
ahnEA3
20d
d
ahnEA
3V
0d3
20d
1dA
hAd
ahnEA
h0
Ad
Av
a
h0
Ad
a
h0
Ad
a
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CALCULATION – GENERAL
Built-up columns with battens:
Effective second moment of area:
chch0eff IAhI 25,02
EN 1993-1-1 § 6.4.3.1
Criterion Efficiency factor
l ≥ 150 0
75 < l < 150
l ≤ 75 1,0
Where:
752
l
0i
Ll
ch
10
2A
Ii chch0 IAhI 25,0
21
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CALCULATION – GENERAL
Built-up columns with battens:
Shear stiffness:
Ib: second moment of area of the batten
2
2
2
2
21
24
a
EI
a
h
nI
Ia
EIS ch
0
b
ch
chv
π
EN 1993-1-1 § 6.4.3.1
h0
Ich, Ach
Ib
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CALCULATION – GENERAL
Maximum global bending moment
eff
ch0EdEdEdch,
25,0
I
AhMNN
V
Ed
cr
Ed
Ed0Ed
1S
N
N
N
MeNM
I
Ed
EN 1993-1-1 § 6.4.1
EN 1993-1-1 § 6.4.1
Maximum compression axial force in a chord
Critical axial force:
2
2
L
EIN eff
cr
π
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CALCULATION – GENERAL
Maximum transverse force
Compression and imperfection
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.
L
MV Ed
Ed
0Ed IM
EN 1993-1-1 § 6.4.1
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CALCULATION – LACED BUILT-UP COLUMN
Verification of the components
Flexural buckling of the chord:
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
1Rdb,
Ed,
N
Nch EN 1993-1-1 § 6.3.1.1
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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
1 bolt per joint
1Rdb,
Ed N
N
LL cr
LL cr
veff,vmin 7,035,0 lll
vmin ll
EN 1993-1-1 BB § 1.2
EN 1993-1-1 § 6.3.1.1
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CALCULATION – LACED BUILT-UP COLUMN
z
y
z
y
u
u v
v
h
h
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CALCULATION – LACED BUILT-UP COLUMN
Verification of the web members – diagonals in tension:
Welded joints:
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
1Rdt,
Ed N
N
0M
yRdpl,Rdt,
AfNN
EN 1993-1-1 § 6.2.3
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CALCULATION – LACED BUILT-UP COLUMN
Category A, B and C connections:
Rdu,Rdpl,Rdt, ,NNMinN
0M
yRdpl,
AfN
1 Bolt 2 Bolts 3 Bolts or more
2M
u02Rdu,
5,00,2
tfdeN
2M
unet2Rdu,
fAN
2M
unet3Rdu,
fAN
EN 1993-1-1 § 6.2.3
EN 1993-1-1 § 6.2.3
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 0,7
3 bolts or more 3 0,5 0,7
EN 1993-1-8 § 3.10.3
d0
e1
e2
e1
e2
p1 e1 p1 p1
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CALCULATION – LACED BUILT-UP COLUMN
Additional verification for category C connections:
Where: t: is the thickness of the leg n: is the number of vertically aligned holes d0: is the diameter of the hole
0M
ynetRdnet,
fAN
0grossnet tndAA
EN 1993-1-1 § 6.2.3
EdRdnet, NN
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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
1Rdb,
Ed,
N
Nch EN 1993-1-1 § 6.3.1.1
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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
+ Verification of the end sections
1
1M
Rk
Edch,yy
1M
Rky
Edch,
M
Mk
N
N1
1M
Rk
Edch,zy
1M
Rkz
Edch,
M
Mk
N
N
EN 1993-1-1 § 6.3.3
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CALCULATION – BATTENED BUILT-UP COLUMN
Verification of the web members – battens
Transverse force:
Bending moment/Lateral Torsional buckling:
1Rdc,
Edbatten,
V
V
0M
y
Rdpl,Rdc,
3
fAVV v
1Rdb,
Edbatten,
M
M
1M
yyLTRdb,
fWM
EN 1993-1-1 § 6.3.2.1
EN 1993-1-1 § 6.2.6
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CALCULATION – BATTENED BUILT-UP COLUMN
Axial force and moment in the chord:
Shear force and moment in the battens:
0EdEdbatten,
h
aVV
2EdEdbatten,
aVM
4EdEdch,
aVM
eff
ch0EdEdEdch,
25,0
I
AhMNN
VEd a/2
a/2
h0
a/2
VEd a/2
VEd a/4 VEd a/4
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
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CLOSELY SPACED BUILT-UP MEMBERS – GENERAL
Case 1: Connected through packing plates
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
Buckling verification as a single member
If maximum spacing is not respected
Shear deformation has to be accounted for
Case Maximum spacing
1
2
min15i
min70i
EN 1993-1-1 § 6.4.4
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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.
a a
h0
tp
y’ y’
z’
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
Thickness of the legs t: 0,1b
Thickness of the packing plates: 0,8t … 2t
Non dimensional slenderness about z’-z’: ≤ 1,80
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CLOSELY SPACED BUILT-UP MEMBERS – SIMPLIFIED METHOD
Procedure
Second moment of area about z’-z’ axis:
Critical axial force about z’-z’ axis:
Non dimensional slenderness about z’-z’ axis:
chch20z' 25,0 IAhI
2
z'2
cr,z'L
EIN
cr,z'
ychz'
2
N
fAl
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41
CLOSELY SPACED BUILT-UP MEMBERS – SIMPLIFIED METHOD
Effective non dimensional slenderness about z’-z’ axis
Number of packing plates
S235 S355
2
3
4
5
39,077,018,0 z'2z' ll
41,052,032,0 z'2z' ll
48,017,056,0 z'2z' ll
53,005,069,0 z'2z' ll
66,018,086,0 z'2z' ll
66,016,066,0 z'2z' ll
67,021,065,0 z'2z' ll
70,031,069,0 z'2z' ll
:effl
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42
CLOSELY SPACED BUILT-UP MEMBERS – SIMPLIFIED METHOD
Second moment of area about y’-y’ axis:
Critical axial force about y’-y’ axis:
Non dimensional slenderness about y’-y’ axis:
chy' 2II
2y'cr,
'2
y'cr,L
EIN
y
y'cr,
ychy'
2
N
fAl
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43
CLOSELY SPACED BUILT-UP MEMBERS – SIMPLIFIED METHOD
Choice of the determining non dimensional slenderness:
Determination of the reduction factor with:
Resistance criterion:
),( y'effmax lll Max
34,0
1M
ychEd
)2(
fAN
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WORKED EXAMPLE
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45
WORKED EXAMPLE – GEOMETRY
Height: 10m
Loading:
Axial force: 900 kN
Bending moment: 450 kN.m
NEd=900 kN
MEd = 450 kN.m
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46
WORKED EXAMPLE – GEOMETRY
1. Chords: HEA 240
2. Posts: Equal leg angles 80 x 80 x 8
3. Diagonals: Equal leg angles 90 x 90 x 9
1
2
3
800
800
1250
12
50
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47
WORKED EXAMPLE – SECTION PROPERTIES
Chords HEA 240 – S355
Posts Equal leg angles L 80 x 80 x 8 – S355
Diagonals Equal leg angles L 90 x 90 x 9 – S355
2ch cm8,76A
cm05,10y i cm0,6zi
2cm27,12VA
cm43,2 zy ii cm06,3ui cm56,1vi
2cm52,15DA
cm73,2 zy ii cm44,3ui cm75,1vi
cm125a
cm800 h
cm148d
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48
WORKED EXAMPLE – BUILT-UP COLUMN
Effective second moment of area of the built-up column
Critical axial force
ch2
0eff 5,0 AhI
442eff cm2457601076808005,0 I
2
eff2
crL
EIN
kN509371010000
10245760210000 3
2
42
cr
N
EN 1993-1-1 § 6.4.2.1
EN 1993-1-1 § 6.4.1
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49
WORKED EXAMPLE – BUILT-UP COLUMN
Shear stiffness
3V
30d3
20d
v
1dA
hAd
ahnEAS
kN13407510
14801227
800155211480
800125015522100002 3
3
33
2
v
S
EN 1993-1-1 § 6.4.2.1
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50
WORKED EXAMPLE – INTERNAL FORCES AND MOMENTS
Maximum global bending moment:
Imperfection:
Global bending moment:
mm20500
100000 e
V
Ed
cr
Ed
Ed0EdEd
1S
N
N
N
MeNM
I
kNm7,47910
134100
900
50937
9001
1045020900 33
EdM
EN 1993-1-1 § 6.4.1
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51
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
eff
ch0EdEdEdch,
22 I
AhMNN
kN6,1049102457602
7680800479700
2
9004Edch,
N
EN 1993-1-1 § 6.4.1
EN 1993-1-1 §5.6 Table 5.2
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52
WORKED EXAMPLE – INTERNAL FORCES AND MOMENTS
Maximum shear force
Shear force due to axial force and imperfection
Shear force due to external loading
Maximum shear force
V
Ed
cr
Ed
EdEd2Ed,
1
1
S
N
N
NL
M
L
MV
I
V
Ed
cr
Ed
0EdEd1Ed,
1
1
S
N
N
NL
eN
L
MV
2Ed,1Ed,Ed VVV
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53
WORKED EXAMPLE – INTERNAL FORCES AND MOMENTS
Maximum shear force
Shear force due to axial force and imperfection
Shear force due to external loading
Maximum shear force
kNV 12,46
134100
900
50937
9001
1
10000
10450 3
2Ed,
kNV 80,5
134100
900
50937
9001
1
10000
209001Ed,
kNV 92,5112,4680,5Ed
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54
WORKED EXAMPLE – BUCKLING OF THE CHORDS
Out-of-plane (strong axis) buckling of the chords
Non dimensional slenderness
Buckling curve
5,995,100
10000
y
ycr,y
i
Ll
06,7681,09,939,931 l
31,106,76
5,99
1
yy
l
ll
b curve buckling100mmt
1,2h/b
f
EN 1993-1-1 § 6.3.1.3
EN 1993-1-1 § 6.3.1.2
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Reduction factor
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3
a0
a
b c
d
55
WORKED EXAMPLE – BUCKLING OF THE CHORDS
42,0y
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56
WORKED EXAMPLE – BUCKLING OF THE CHORDS
Design buckling resistance
Resistance criterion
1M
ychyRdy,b,
fAN
kN1145100,1
355768042,0 3Rdy,b,
N
192,01145
6,1049
Rdy,b,
Edch,
N
N
EN 1993-1-1 § 6.3.1.1
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57
WORKED EXAMPLE – BUCKLING OF THE CHORDS
In-plane (weak axis) buckling of the chords
Non dimensional slenderness
Buckling curve
Reduction factor
75,1860
12509,0
z
cr,zz
i
Ll
25,006,76
75,18
1
zz
l
ll
c curve buckling100mmt
1,2h/b
f
97,0z
EN 1993-1-1 § 6.3.1.3
EN 1993-1-1 § 6.3.1.2
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58
WORKED EXAMPLE – BUCKLING OF THE CHORDS
Design buckling resistance
Resistance criterion
1M
ychRd,b,
fAN
zz
kN2645100,1
355768097,0 3Rd,b,
zN
140,02645
6,1049
Rd,b,
Edch,
zN
N
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Buckling of the diagonals
Class of the section
Section is of class 4
et
59
WORKED EXAMPLE – BUCKLING OF THE WEB MEMBERS
EN 1993-1-1 §5.6 Table 5.2 5,112
t
hb15
t
h
15,1281,015109
90
3,95,1110902
9090
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Buckling of the diagonals
Calculation of the effective area
Local buckling coefficient
Non dimensional slenderness and reduction factor
60
WORKED EXAMPLE – BUCKLING OF THE WEB MEMBERS
0,4k EN 1993-1-5 §4.4 Table 4.1
748,022,0481,04,28
9/90
4,28
/
l
k
thp
0,1 EN 1993-1-5 §4.4 (4.3)
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61
WORKED EXAMPLE – BUCKLING OF THE WEB MEMBERS
Buckling of the diagonals
Maximum compression axial force per diagonal
Slenderness
0
EdEdEdd,
cos
nh
dV
n
VN
kN488002
14809,51Edd,
N
57,845,17
1480
vv
i
dl
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62
WORKED EXAMPLE – BUCKLING OF THE WEB MEMBERS
Effective non dimensional slenderness
Reduction factor (buckling curve b)
Design buckling resistance
veff,v 7,035,0 ll
13,111,17,035,0eff,v l
52,0v
kN5,286100,1
355155252,0 3Rdb,v,
N
EN 1993-1-1 BB § 1.2
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63
WORKED EXAMPLE – BUCKLING OF THE WEB MEMBERS
Resistance criterion
Buckling of the posts (class 4, = 1,0)
kN9,51EdEdp, VN
712,0822,0 veff,v l
kNN 310Rdb,v,
161,0310
190
Rdb,v,
Edp,
N
N
117,05,286
48
Rdb,v,
Edd,
N
N
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64
WORKED EXAMPLE – WEB MEMBERS IN TENSION
Category A connection
mm401 e
mm402 e
mm451 p
2 M16 6.8
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65
WORKED EXAMPLE – WEB MEMBERS IN TENSION
Diagonals in tension
Axial force
Tension resistance (Category A connection)
Resistance of the gross section
kN48cosEd
Edt, n
VN
Rdu,Rdpl,Rdt, ,NNMinN
0M
yRdpl,
AfN
kN551100,1
3551552 3Rdpl,
N
EN 1993-1-1 § 6.2.3
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66
WORKED EXAMPLE – WEB MEMBERS IN TENSION
Resistance of the net section:
Net section area:
Reduction factor:
Resistance of the net section:
2M
net2Rdu,
ufAN EN 1993-1-8 § 3.10.3
ntdAA 0grossnet
222net cm9,13101189101552 A
kN21825,1
49013904,0Rdu,
N
4,02 EN 1993-1-8 § 3.10.3 Table 3.8
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67
WORKED EXAMPLE – WEB MEMBERS IN TENSION
Tension resistance (Category A connection)
Resistance criterion
122,0218
48
Rdt,
Edt,
N
N
kN218kN218kN,551MinRdt, N
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68
WORKED EXAMPLE – CATEGORY A CONNECTION
Resistance criteria
Shear resistance Fv,Rd per bolt:
Rdv,Edv, FF
Rdb,Edv, FF
2M
ubvRdv,
AfF
kN7,371025,1
1576005,0 3Rdv,
F
EN 1993-1-8 § 3.4.2
EN 1993-1-8 § 3.6.1
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69
WORKED EXAMPLE – CATEGORY A CONNECTION
Shear resistance of the bolt group:
Consideration of the eccentricity (Reference [4]):
Shear resistance:
kNN 0,527,3769,02RdS,
11 1
61
1
pn
e
69,0
4512
6,2461
1
Rdv,1RdS, FnN
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70
WORKED EXAMPLE – CATEGORY A CONNECTION
Bearing resistance Fb,Rd:
Longitudinal direction
k1 : edge bolts:
end bolts:
inner bolts:
2M
ub1Rdb,
dtfkF
5,27,18,20
21
d
ek
1,,
u
ubdb
f
fMin
0
1d
3d
e
4
1
d3 0
1d
p
EN 1993-1-8 § 3.6.1 Table 3.4
EN 1993-1-8 § 3.6.1
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71
WORKED EXAMPLE – CATEGORY A CONNECTION
k1 : edge bolts:
b : end bolt:
inner bolt:
5,25,47,118
408,2e1 k
74,0183
40de
58,04
1
183
45di
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72
WORKED EXAMPLE – CATEGORY A CONNECTION
Ratio fub/fu:
b :
Bearing resistance Fb,Rd in the longitudinal direction:
58,01;22,1;58,0;74,0Minb
kN5,811025,1
91649058,05,2 3Rdlg,b,
F
22,1490
600
u
ub f
f
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73
WORKED EXAMPLE – CATEGORY A CONNECTION
Transverse direction:
k1 : edge bolts:
inner bolts:
end bolts:
5,27,18,20
11
d
ek
1,,
u
ubdb
f
fMin
0
2d
3d
e
5,27,14,10
11
d
pk
5,25,47,118
408,2e1 k
5,28,17,118
454,11 ik
74,0183
40de
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74
WORKED EXAMPLE – CATEGORY A CONNECTION
Ratio fub/fu:
b :
Bearing resistance Fb,Rd in the transverse direction:
74,01;22,1;74,0Minb
kN19,751025,1
91649074,08,1 3Rd,b,
trF
22,1490
600
u
ub f
f
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WORKED EXAMPLE – CATEGORY A CONNECTION
Bearing resistance of the bolt group (Reference [4]):
2
Rdb,tr,
0
2
Rdlg,b,
1Rdb,
1
FF
nN
110
1
6
pn
e
09,1
4512
6,2460
kN3,105
19,75
09,1
5,81
1
2
22Rdb,
N
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WORKED EXAMPLE – CATEGORY A CONNECTION
kN0,52kN48
kN3,105kN48
Rd,Edv, SNF
Rdb,Edv, NF
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77
WORKED EXAMPLE – BLOCK TEARING
Block tearing resistance
(1) Shear plane
(2) Tension plane
0M
nvy
2M
ntuRdeff,2,
3
5,0
AfAfF
NEd
(1)
(2)
EN 1993-1-8 § 3.10.2
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78
WORKED EXAMPLE – BLOCK TEARING
Tension Area
Shear Area
Block tearing resistance
Resistance criterion
222nt cm79,210918
2
110940 A
222nv cm6,3109185,21094540 A
kN5,128100,13
36035510
25,1
2794905,0 33Rdeff,2,
F
kN5,128kN48
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CONCLUSION
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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 connections)
A simplified procedure is proposed for built-up members with closely spaced chords.
80
CONCLUSION
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REFERENCES
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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. Méthode simplifiée pour la vérification de barres comprimées composées de deux cornières assemblées dos-à-dos.
Simplified method for the verification of compressed built-up members composed of two closely spaced angles.
Revue Construction Métallique n°4/2010. 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 n°126, 2009
82
REFERENCES
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SKILLS training modules have been developed by a consortium of organisations whose logos appear at the bottom of this slide. The material is under a creative commons license
The project was funded with support from the European Commission. This module reflects only the views of the
authors, and the Commission cannot be held responsible for any use which may be made of the information contained therein.