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SKILLS Project
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BASE PLATE CONNECTIONS
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Design process for pinned and fixed column base joints
Base-plate resistance
Anchor bolt resistance
Concrete resistance
Weld resistance
Application of the component method to pinned and
fixed column base joint.
3
LEARNING OUTCOMES
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Introduction
Pinned column base joint
Rigid column base joint
Application
Conclusion
4
LIST OF CONTENTS
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INTRODUCTION
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Typical pinned column base joint
6
INTRODUCTION
Grout
Anchor bolt
Concrete foundation
Column
Base plate
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Typical fixed column base joint
7
INTRODUCTION
Concrete foundation
Column
Base plate
Anchor bolts
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Analysis of the joint according to EN 1993-1-8
Joint is modelled by a typical components : T-stub
Two models for loadings :
Resistance in compression : T-stub in compression with concrete,
Resistance in tension : T-stub in tension (anchor bolts + base plate
+ column web).
8
INTRODUCTION
F T,Rd
l eff
F T,Rd
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Recommended partial safety factors according to EN 1993-1-8 :
g M0 =1 : column web in tension, bending of the base-plate
g M2 =1,25 : Anchor bolts in tension/shear, weld resistance
Recommended partial safety factors according to EN 1992-1-1 :
g C =1,5 : Concrete in compression, bond anchorage resistance
The national annexes may give indications
9
INTRODUCTION
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PINNED COLUMN BASE JOINT
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beff
l eff
F c,Rd
jd
Evaluation of the resistance in compression of T-stubs in
contact with concrete.
Resistance in compression of the joint : association of
resistances of T-stubs in compression.
11
PINNED COLUMN BASE JOINT - RESISTANCE IN COMPRESSION
EN 1993-1-8 § 6.2.5
Concrete resistance reached : f jd
Web T-stub : F c,bw,Rd
Flange T-stubs : F c,fc,Rd
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Foundation bearing strength
Where:
a bf coefficient which accounts for diffusion of concentrated
force within the foundation. b j may be taken as 2/3 (see Note)
f cd Concrete design strength :
f ck Compressive cylinder strength of concrete at 28 days
a cc = 1
g c
= 1,512
PINNED COLUMN BASE JOINT - RESISTANCE IN COMPRESSION
EN 1993-1-8 § 6.2.5
EN 1992-1-1 §6.7 jd bf j cd f f a b
ck
cd cc c
f f a
g
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Expression of a bf :
Note : b j = 2/3 if :
Strength of grout ≥ 0,2× f cd
Else :
13
PINNED COLUMN BASE JOINT - RESISTANCE IN COMPRESSION
bf hbf
p p p p
= min 1+ ; 1+2 ; 1+2 ; 3max( , )
ed e
h b h ba
m p
p
50 mm
min 0,2
0,2
e b
h
Axis z-z
Axis y-y
Axis x-x
bp
hp
d f
eb
eh
em
jd cd f f
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Resistance in compression of a T-stub :
Where:
l eff Effective length of the T-stub
beff Effective width of the T-stub such as :
c Additional bearing width of the flange :
f yp Yield strength of base plate
g M0 =1
14
PINNED COLUMN BASE JOINT - RESISTANCE IN COMPRESSION
C,Rd jd eff eff F f b l
EN 1993-1-8 (6.4)
eff 2b t c
yp
p
jd M03
f c t
f g
beff
l eff
F c,Rd
jd t p
c
c
t
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Large and short projections :
Flange T-stub : Flange T-stub :
Web T-stub :
15
PINNED COLUMN BASE JOINT - RESISTANCE IN COMPRESSION
eff fcb t c c b eff fc 2b t c
eff wc 2b t c
t p
t = t fc
c b c c
t p
t = t fc or t wc
c c
a) Short projection b) Large projection
beff beff
jd jd
EN 1993-1-8 §6.2.5
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Resistance in compression of a flange T-stub :
Where:
16
PINNED COLUMN BASE JOINT - RESISTANCE IN COMPRESSION
eff p fcmin ; 2l b b c
eff p c fc c fcmin ; /2 min ; /2b c h h t c h t
c,fc,Rd jd eff eff F f b l
Large projectionShort projection
hc
bfc bp
hp
c
c
l eff
c c
beff
t fc
hc
bfcbp
hp
c
c
l eff
c
beff
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Resistance in compression of the web T-stub :
Where:
17
PINNED COLUMN BASE JOINT - RESISTANCE IN COMPRESSION
c,bw,Rd jd eff eff F f b l
eff c fc2 2 0l h t c
eff wc2b c t
c
c
hc
l eff
c c
beff
t fc
t wc
c
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Resistance in compression of the joint :
Where :
18
PINNED COLUMN BASE JOINT - RESISTANCE IN COMPRESSION
C,Rd c,fc,Rd c,bw,Rd2N F F
C,Rd jd cp cp cp cp wc 2N f h b l b t c
cp p cmin ; 2h h h c
cp p fcmin ; 2b b b c
cp c fc2 2 0l h t c
hc
bfcbp
hp
c
c
c c
t wc
t fc
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Joint modelled by a T-stub (anchor bolts, base plate) in tension
Evaluation of the tensile resistance of the T-stub 6 possible failure modes :
Base plate/anchor bolts (modes 1, 2, 1-2 and 3)
Column web (mode 4) and weld
19
PINNED COLUMN BASE JOINT - RESISTANCE IN TENSION
F T,Rd
l eff
F T,Rd
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Failure modes of base plate/anchor bolts
Mode 1 : Yielding of the base plate Mode 2 : Failure of anchor bolts
Mode 1-2 : Yielding of the base plate Mode 3 : Failure of anchor bolts
20
PINNED COLUMN BASE JOINT - RESISTANCE IN TENSION
Prying
effect
No pryingeffect
F T,1,Rd
Q Q
F T,2,Rd
Q Q
F T,1-2,Rd F T,3,Rd
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Mode 4 : Yielding of the column web in tension
The prying effect has an influence on the choice of failure
modes.
Failure modes 1 and 2 are not possible without prying forceand are replaced by failure mode 1-2.
21
PINNED COLUMN BASE JOINT - RESISTANCE IN TENSION
F T,4,Rd
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Prying effect and failure modes :
PINNED COLUMN BASE JOINT - RESISTANCE IN TENSION
EN 1993-1-8 Table 6.2
Prying effect Presence of prying effect Absence of prying effect
Deformation
Condition
Resistance of
the T-stub
*
b bL L
*
b b>L L
T,1,Rd T,2,Rd
T,Rd
T,3,Rd T,4,Rd
;min
;
F F F
F F
T,1-2,Rd T,3,Rd
T,Rd
T,4,Rd
;min
F F F
F
F T,Rd
Q Q
F T,Rd
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Anchor bolt elongation length :
Where:
t wa Thickness of the washerd Anchor bolt diameter
PINNED COLUMN BASE JOINT - RESISTANCE IN TENSION
EN 1993-1-8 Table 6.2
b m p wa8 0,5L d e t t k
23
t p
em
8d Concrete
grout
base plate
k
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Limit anchor bolt elongation length :
Where:
As Tensile stress area of one anchor bolt
l eff,1 Effective length :
PINNED COLUMN BASE JOINT - RESISTANCE IN TENSION
EN 1993-1-8 Table 6.2
3
* sb 3
eff,1 p
8,8m ALl t
eff,1 eff,cp eff,nc=min ;l l l
wc w/2 /2 0,8 2m p t a
24
m
t pBase plate
aw
p/2
t wc
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Effective lengths of the T-stub :
Circular mechanism Non circular mechanism
PINNED COLUMN BASE JOINT - RESISTANCE IN TENSION
EN 1993-1-8 Table 6.6
eff,cp 2l m eff,nc 4 1,25l m e
mm ee
p
t wc
25
mm ee
Yield line
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Resistance of modes 1 and 1-2:
Where:
PINNED COLUMN BASE JOINT - RESISTANCE IN TENSION
EN 1993-1-8 Table 6.2
Failure mode Mode 1 Mode 1-2
Yielding of
the base
plate
Resistance of
the T-stub
F T,1-2,Rd
pl,1,Rd
T,1,Rd
4MF
m
2
p yp
pl,1,Rd pl,Rd eff,1 pl,Rd eff,1 eff,cp eff,nc
M0
; ; =min ;4
t f M m l m l l l
g
pl,1,Rd
T,1-2,Rd
2MF
m
F T,1,Rd
Q Q
m
26
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Resistance of modes 2 and 3:
Where:
F t,Rd,anchor Resistance of one anchor bolt
PINNED COLUMN BASE JOINT - RESISTANCE IN TENSION
EN 1993-1-8 Table 6.2
Failure mode Mode 2 Mode 3
Failure of
anchor bolts
Resistance of
the T-stub
pl,2,Rd pl,Rd eff,2 eff,2 eff,nc; = ; =min ; 1,25M m l l l n e m
pl,2,Rd t,Rd,anchor
T,2,Rd
2 2M nF
F m n
T,3,Rd t,Rd,anchor
2F F
27
F T,2,Rd
Q Q
emF t,Rd,anchor
F T,3,Rd
F t,Rd,anchor F t,Rd,anchor
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Tensile resistance of anchor bolts :
PINNED COLUMN BASE JOINT - RESISTANCE IN TENSION
28
(b) Washer plate : No bond(a) Hook : bond resistance
1. Base plate
2. Grout
3. Concrete foundation
EN 1993-1-8 §6.2.6.12
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Resistance of one anchor bolt, two failure modes:
Tensile resistance of the anchor bolt section, F t,Rd
,Bond anchorage resistance, F t,bond,Rd.
Design tensile resistance of the anchor bolt section :
Where:
f ub Tensile strength of the anchor bolt
g M2 = 1,25
PINNED COLUMN BASE JOINT - RESISTANCE IN TENSION
29
t,Rd,anchor t,Rd t,bond,Rdmin ;F F F
ub st,Rd
M2
0,9 f AF
g
EN 1993-1-8 Table 3.4
EN 1993-1-8 Table 3.1
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Bond anchorage resistance of a straight bolt :
Where:
d Nominal diameter of an anchor bolt
f bd Design bond strength :If d < 32 mm :
If d ≥ 32 mm :
g c = 1,5
f yb : Yield strength of the anchor bolt.
PINNED COLUMN BASE JOINT - RESISTANCE IN TENSION
30
t,bond,Rd b bdF dl f
F t,Bond,Rd
l b
ck
bd
C
0,36 f f
g
ck
bd
C
0,36 132
100
f d
f g
2
yb 600 /mm f N
INN COLU N AS JOIN SIS ANC IN NSION
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Bond resistance of a bolt with a hook :
Check that :
PINNED COLUMN BASE JOINT - RESISTANCE IN TENSION
31
b bdt,bond,Rd0,7
dl f F
2
yb 300 /mm f N
F t,Bond,Rd
≥5d
90°
l b
EN 1993-1-8 §6.2.6.12 (5)
PINNED COLUMN BASE JOINT RESISTANCE IN TENSION
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Resistance of mode 4:
Where:
f y,wc Yield strength of the column web
PINNED COLUMN BASE JOINT - RESISTANCE IN TENSION
Failure mode Mode 4
Yielding of the column
web in tension
Resistance of the
T-stub
F T,4,Rd
t wc
eff,t wc y,wc
T,4,Rd t,wc,RdM0
b t f F F
g
eff,t eff,1=b l 32
PINNED COLUMN BASE JOINT RESISTANCE IN TENSION
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Weld resistance :
Where:
aw weld throat thickness of the web
b w correlation factor
f u nominal ultimate strength of the weaker joined partl w,wb total effective length of the web welds
Final resistance of the joint in tension :
PINNED COLUMN BASE JOINT - RESISTANCE IN TENSION
33
u
t,w,Rd w,eff,t ww M2
/ 3 f
F l a b g
w,eff,t eff,1 w,wb=2l l l
EN 1993-1-8 Table 4.1
T,Rd T,Rd t,w,Rd t,Edmin ;N F F N
PINNED COLUMN BASE JOINT SHEAR RESISTANCE
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Three ways to transmit shear force to concrete block :
Friction resistance between base plate and concrete (compression),
Shear of anchor bolts (compression/tension),
Use of shear nibs (important tension force).
34
PINNED COLUMN BASE JOINT - SHEAR RESISTANCE
PINNED COLUMN BASE JOINT SHEAR RESISTANCE
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Design friction resistance :
Where:
N c,Ed Compression force
C f,d Coefficient of frictionFor sand-cement mortar :
35
PINNED COLUMN BASE JOINT - SHEAR RESISTANCE
EN 1993-1-8 6.2.2 (6)
f,Rd f,d c,EdF C N
f,d 0,2C
Axial force N c,Ed
Shear force
V Ed<0,2×Nc,Ed
Friction
PINNED COLUMN BASE JOINT SHEAR RESISTANCE
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Shear resistance of an anchor bolt:
Where:
f yb Yield strength of the anchor bolt
36
PINNED COLUMN BASE JOINT - SHEAR RESISTANCE
EN 1993-1-8 6.2.2 (7)
bc ub svb,Rd
M2
f AF
a
g
2 2bc yb yb0,44 0,0003 and 235 N/mm 640 N/mm f f a
F vb,Rd
PINNED COLUMN BASE JOINT SHEAR RESISTANCE
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Shear resistance in presence of compression :
Addition of friction resistance and shear resistance of anchor bolts :
Where:
n Number of anchor bolts
37
PINNED COLUMN BASE JOINT - SHEAR RESISTANCE
EN 1993-1-8 6.2.2 (8)
v,Rd f,Rd vb,Rd EdF F nF V
Axial force N c,Ed
Shear force
V Ed
Friction
Shear of anchor
bolts
PINNED COLUMN BASE JOINT SHEAR RESISTANCE
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Shear resistance in presence of tension :
Where:
F T,Rd Tensile resistance of the T-stub in tension
38
PINNED COLUMN BASE JOINT - SHEAR RESISTANCE
Axial force N t,Ed
Shear force
V Ed
Shear of anchor
bolts
t,EdEd
vb,Rd T,Rd1
1,4
NV
nF F
PINNED COLUMN BASE JOINT SHEAR RESISTANCE
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Shear resistance of welds (in compression) :
Where:
l w,eff total effective length of the welds in the direction of sheara weld throat thickness in the direction of shear
Check of the shear resistance of welds (in tension) :
39
PINNED COLUMN BASE JOINT - SHEAR RESISTANCE
w,Rd vw,d w,eff EdV f a l V
uvw,d
w M2
/ 3 f f
b g
2 2
t,Ed Edw,Ed vw,d
w,eff,t w,eff
N V F f a
l l
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FIXED COLUMN BASE JOINT
FIXED COLUMN BASE JOINT INTRODUCTION
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Calculation of the bending resistance and initial rotational
stiffness in presence of axial force :
Initial rotational stiffness :
FIXED COLUMN BASE JOINT- INTRODUCTION
41
M j,Ed ≤M j,Rd
j,Ed
N j,Ed
M j,Rd
j,Ed
M j,Ed
S j,ini
j,Ed
j,ini
j,Ed
MS
FIXED COLUMN BASE JOINT INTRODUCTION
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Application of the component method :
FIXED COLUMN BASE JOINT- INTRODUCTION
42
beff
l eff
F C F T
M j,Ed ≤M j,Rd
j,Ed F c F T
N j,Ed
T-stub in tension : T-stub in compression :
FIXED COLUMN BASE JOINT INTRODUCTION
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Lever arms :
Tensile force positioned at the centre of anchor bolts,
Compression force at the centre of the column flange.
Bending moment :
Bending resistance : resistance
reach on a T-stub.
43
FIXED COLUMN BASE JOINT- INTRODUCTION
F C
zT zC
F T
M j,Ed
hc
t fc
j,Ed C C T TM z F z F
C C,Rd T T,RdorF F F F
FIXED COLUMN BASE JOINT BENDING RESISTANCE
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Bending resistance depend on eccentricity :
Dominant tensile force : Dominant compression force :
FIXED COLUMN BASE JOINT- BENDING RESISTANCE
44
j,Ed j,Rd
N
j,Ed j,Rd
M Me
N N
2 T-stubs in compression
C N 0z e N T0 e z
2 T-stubs in tension
F T
zT zT
F T,Rd
M j,Rd
N j,Rd
F C,Rd
zC zC
F C
M j,Rd
N j,Rd
FIXED COLUMN BASE JOINT- BENDING RESISTANCE
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FIXED COLUMN BASE JOINT- BENDING RESISTANCE
45
Dominant bending moment :
Joint composed of a tensile part and a compressive part :Resistance reaches in one these parts,
T-stub in tension critical T-stub in compression critical
N T N Core z e z
F C
zT zC
F T,Rd
M j,Rd
N j,Rd
F C,Rd
zT zC
F T
M j,Rd
N j,Rd
FIXED COLUMN BASE JOINT- BENDING RESISTANCE
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Resistance in compression of a flange T-stub :
Where:
46
FIXED COLUMN BASE JOINT- BENDING RESISTANCE
eff p fcmin ; 2l b b c
C,Rd jd eff eff
F f b l
F C,Rd
l eff beff
p cceff fc fcmin , min ,
2 2
h hhb c t t c
g
yp
p
jd M03
f c t
f
hc
bfc bp
hp
c
c
c c
t wc
t fc
l eff
beff
EN 1993-1-8 (6.4)
FIXED COLUMN BASE JOINT- BENDING RESISTANCE
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Resistance of the tensile part of the joint (2 anchor bolts):
Analysis of the resistance of an equivalent T-stub :
Same calculation as for pinned column base joint:
Different effective length, l eff
Replace m by mx, e by ex in resistance of T-stub
FIXED COLUMN BASE JOINT- BENDING RESISTANCE
47
F T,Rd
EN 1993-1-8 Figure 6.10
FIXED COLUMN BASE JOINT- BENDING RESISTANCE
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Effective lengths of the T-stub :
Circular mechanism Non circular mechanism
FIXED COLUMN BASE JOINT- BENDING RESISTANCE
EN 1993-1-8 Table 6.6
48
e w
mx
ex
bp
x
eff,cp x
x
2
min
2
m
l m w
m e
x x
x x
eff,ncx x
p
4 1,25
2 0,625 /2min
2 0,625
/2
m e
m e w l
m e e
b
FIXED COLUMN BASE JOINT- BENDING RESISTANCE
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Loading Lever arm
z
Bending resistance M j,Rd
for a given value of eN
Dominant
compression forcez = zC + zC
N j,Ed < 0 and 0 ≤ eN ≤ +zC N j,Ed < 0 and-zC ≤ eN ≤ 0
The smaller of and
Dominant tension
forcez = zT + zT
N j,Ed > 0 and 0 ≤ eN ≤ +zT N j,Ed > 0 and -zT ≤ eN ≤ 0
The smaller of and
Dominant bendingmoment
z = zT + zC
N j,Ed 0
and eN > +zT or eN < - zT
N j,Ed ≤ 0
and eN < - zC or eN > zC
The smaller of and
M j,Ed > 0 is clockwise, N j,Ed > 0 is tension.
49
FIXED COLUMN BASE JOINT- BENDING RESISTANCE
C,Rd
C N/ 1
F z
z e
j,Ed j,Rd
N
j,Ed j,Rd
M Me
N N
C,Rd
C N/ 1
F z
z e
T,Rd
T N/ 1
F z
z e
T,Rd
T N/ 1
F z
z e
C,Rd
T N/ 1
F z
z e
T,Rd
C N/ 1
F z
z e
Table 6.7
FIXED COLUMN BASE JOINT- INITIAL ROTATIONAL STIFFNESS
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The column base joint can be classified rigid :
for frames where the bracing system reduces the
horizontal displacement by at least 80% :
Otherwise :
Where :
Lc : storey height of the column,
Ic : second moment of area of the column,
: slenderness of the column in which both ends are
assumed to be pinned.50
FIXED COLUMN BASE JOINT INITIAL ROTATIONAL STIFFNESS
c j,ini
c
30EIS
L
0
0 j,ini 0 c c
0 j,ini c c
- if 0,5
- if 0,5 3,93 and 72 2 1 /
- if 3,93 and 48 /
S EI L
S EI L
0
EN 1993-1-8
(2) §5.2.2.5
FIXED COLUMN BASE JOINT- INITIAL ROTATIONAL STIFFNESS
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Otherwise the column base joint is semi-rigid :
Joint model by a rotational stiffener in the global analysis :
51
FIXED COLUMN BASE JOINT INITIAL ROTATIONAL STIFFNESS
Rotational stiffener
S jS j
j j,ini j,Ed j,Rd
j,ini
j j,Rd j,Ed j,Rd
if 2 /3
if 2 /3
S S M M
SS M M M
j,Ed j,Rd(1,5 / ) ; 2,7M M
FIXED COLUMN BASE JOINT- INITIAL ROTATIONAL STIFFNESS
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Model for the calculation of the initial rotational stiffness :
Tensile and compressive parts modelled by axial stiffener.
Initial rotational stiffness :
52
FIXED COLUMN BASE JOINT INITIAL ROTATIONAL STIFFNESS
F C
zT zC
F T
M j,Ed
k T k C
j,Ed
N j,Ed
j,Ed
j,ini
j,Ed
MS
M j,Ed
j,Ed
N j,Ed
FIXED COLUMN BASE JOINT- INITIAL ROTATIONAL STIFFNESS
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Stiffness of compressive part of the joint
Where:
l eff Effective length of the T-stub,
beff Effective width of the T-stub,E c Elastic modulus of concrete (see EN 1992-1-1),
E Elastic modulus of steel.
53
FIXED COLUMN BASE JOINT INITIAL ROTATIONAL STIFFNESS
c eff eff C 13
1,275
E l bk k
E
Concrete
Flange
F C
c
Contact between flange and concrete
EN 1993-1-8 Table 6.11
FIXED COLUMN BASE JOINT- INITIAL ROTATIONAL STIFFNESS
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Stiffness of the tensile part of the joint
Depends on the presence or absence of prying effect.
54
FIXED COLUMN BASE JOINT INITIAL ROTATIONAL STIFFNESS
F T
B B
Q Q
T
F T
B B
T
Presence of prying effect :
*
b bL L*
b b>L L
Absence of prying effect :
EN 1993-1-8 Table 6.11
FIXED COLUMN BASE JOINT- INITIAL ROTATIONAL STIFFNESS
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Stiffness of the tensile part in presence of prying effect :
k 16 : stiffness coefficient of anchor bolts in tension :
k 15 : stiffness coefficient of base plate in bending under tension :
55
T
15 16
1
1 1k
k k
s16
b
1,6A
k L
3
eff p
15 3
0,85 l t k
m
EN 1993-1-8 Table 6.11
FIXED COLUMN BASE JOINT- INITIAL ROTATIONAL STIFFNESS
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Stiffness of the tensile part in absence of prying effect :
k 16 : stiffness coefficient of anchor bolts in tension :
k 15 : stiffness coefficient of base plate in bending under tension :
56
T
15 16
1
1 1k
k k
s16
b
2A
k L
3
eff p
15 3
0,425 l t k
m
EN 1993-1-8 Table 6.11
FIXED COLUMN BASE JOINT- INITIAL ROTATIONAL STIFFNESS
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Rotational stiffness depend on the eccentricity :
Dominant tensile force : Dominant compression force :
57
j,Ed
N
j,Ed
Me
N
2 T-stubs in compression
C N 0z e N T0 e z
2 T-stubs in tension
F T,2
zT zT
F T,1
M j,Ed
k T k T
j,Ed
N j,Ed
F C,2
zC zC
F C,1
M j,Ed
k C k C
j,Ed
N j,Ed
FIXED COLUMN BASE JOINT- BENDING RESISTANCE
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58
Dominant bending moment :
Joint composed of a tensile and compressive part :
N T N Core z e z
F C
zT zC
F T
M j,Ed
k T k C
j,Ed
N j,Ed
FIXED COLUMN BASE JOINT- INITIAL ROTATIONAL STIFFNESS
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Loading Lever arm
z
Initial rotational stiffness S j,ini
for a given value of eN
Dominant
compression forcez = zC + zC
N j,Ed < 0 and 0 ≤ eN ≤ +zC N j,Ed < 0 and-zC ≤ eN ≤ 0
Dominant tension
forcez = zT + zT
N j,Ed
> 0 and 0 ≤ eN
≤ +zT
N j,Ed
> 0 and -zT
≤ eN
≤ 0
Dominant bendingmoment
z = zT + zC
N j,Ed 0
and eN > +zT or eN < - zT
N j,Ed ≤ 0
and eN < - zC or eN > zC
M j,Ed > 0 is clockwise, N j,Ed > 0 is tension.
59
j,Ed
N
j,Ed
Me
N
2
C j,ini
2
E z k S
2
T j,ini
2
E z k S
a
2
j,ini
k
C T
1
11 1
E zS
k k a
C C T Tk
T C
kk
N
× -z ×=
+
=
z k k e
k k
e
e
Table 6.12
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APPLICATION
APPLICATION – PRESENTATION OF THE EXAMPLE
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Detail of the joint and the concrete block
61
Grout of 30 mm thickness
Axial force : NEd
Anchor bolts M24 class 4.6
Column : IPE 450 in S235
Base plate 48022010 in S235
Shear force V z,Ed
Axis z-z
Axis y-y
Axis x-x
Concrete class C25/30
bp=220
hp =480
d f =500mm
eb
eh
400
800
l b=400mm
APPLICATION – PRESENTATION OF THE EXAMPLE
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Detail of the joint
62
15
225
40 40140
225
15
m e 4060,8Web weld : 4 mm
Flange weld : 6 mm
10
2 anchor bolts M24
Class 4.6
190
9,4
14,7
APPLICATION – PRESENTATION OF THE EXAMPLE
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Load Case 1 (compression) :
Nc,Ed = 85 kN
V z,Ed = 35 kN
1-1 – Check the resistance in compression
1-2 – Check the shear resistance
Load Case 2 (tension) :
NT,Ed = 8,86 kN
V z,Ed = 17,5 kN
2-1 – Check the resistance in tension
2-2 – Check the shear resistance
63
APPLICATION – 1-1 RESISTANCE IN COMPRESSION
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Concrete (C25/30) design strength :
The value of b j is equal to 2/3, as :
Coefficient a bf :
64
ckcd cc
c
cd
251 16,7 MPa
1,5
f
f
f
a g
min 1
bf h
bf p p p p
bf
= min 1+ ; 1+2 ; 1+2 ; 3max( , )
500 800 480 400 220; 1 ; 1 , 3 1,67
480 480 220
ed e
h b h ba
a
m p
p
50 mm
30 mm min 0,20,2
e bh
APPLICATION – 1-1 RESISTANCE IN COMPRESSION
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Foundation bearing strength :
Additional bearing width of the flange :
65
jd bf j cd
jd 1,67 2/3 16,7 18,6 MPa
f f
f
a b
yp
p
jd M03
23510 20,5 mm
3 18,6 1,0
f c t f
c
g
APPLICATION – 1-1 RESISTANCE IN COMPRESSION
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Geometrical parameter :
Short projection
Resistance in compression of the column base joint :
66
cp p cmin ; 2 min 480;450 2 20,5 480 mmh h h c cp p fcmin ; 2 min 220;190 2 20,5 220 mmb b b c
cp c fc2 2 450 2 14,7 2 20,5 379,6 mm 0l h t c
C,Rd jd cp cp cp cp wc2
18,6 480 220 379,6 220 9,4 2 20,5 /1000
766,6 kN
N f h b l b t c
APPLICATION – 1-1 RESISTANCE IN COMPRESSION
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Check of the resistance in compression:
67
C,Rd c,Ed
766,6 kN 85 kNN N
bfc =190
b c =15
t fc=
14,7
b c =15
hc = 450
20,5
l eff = 220
hp = 480
c= 20,5
beff
c
c
c
c
t wc = 9,4
APPLICATION – 1-2 SHEAR RESISTANCE (CASE 1)
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Friction resistance :
Shear resistance of one anchor bolt :
Shear resistance of the joint
68
f,Rd f,d c,Ed
f,Rd 0,2 85 17 kN
F C N
F
bc ub svb,Rd
M2
vb,Rd 3
(0,44 0,0003 240) 400 35341,6 kN
1,25 10
f AF
F
a
g
v,Rd f,Rd vb,Rd
v,Rd 17 2 41,6 100,2 kNF F nF F
APPLICATION – 1-2 SHEAR RESISTANCE (CASE 1)
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Shear resistance of welds :
Check of the shear resistance :
69
uw,Rd w,eff
w M2
w,eff
w,Rd
/ 3
2 450 2 14,7 2 21 757,2 mm
360/ 34 757,2/1000 629,5 kN
0,8 1,25
f V a l
l
V
b g
z,Rd v,Rd w,Rd z,Edmin ; 100,2 kN =35kNV F V V
APPLICATION – 2-1 RESISTANCE IN TENSION (CASE 2)
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Length m :
Effective lengths and mechanisms :
Effective lengths of mode 1 and 2 :
70
wc w/2 /2 0,8 2
(140-9,4)= -0,8 2 4 = 60,8 mm
2
m p t a
m
eff,cp
eff,cp
=2=2× ×(60,8)=381,9 mm
l ml
40 40140
m e 4060,8
Web weld :4 mm
eff,nc
eff,nc
=4 +1,25
=4×60,8+1,25×40=293,1 mm
l m e
l
eff,1 eff,cp eff,nc
eff,2 eff,nc
min ; 293,1 mm
293,1 mm
l l l
l l
APPLICATION – 2-1 RESISTANCE IN TENSION (CASE 2)
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Presence of prying effect?
Limit anchor bolt elongation length :
Anchor bolt elongation length :
Prying effect develops and failure modes 1, 2, 3 and 4 will be
considered.
71
b m p wa
*
b b
8 0,5
8 24 30 10 5 0,5 22 248 mm 2382 mm
L d e t t k
L L
3* sb 3
eff,1 p
3*
b 3
8,8
8,8 60,8 3532382 mm
293,1 10
m AL
l t
L
APPLICATION – 2-1 RESISTANCE IN TENSION (CASE 2)
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Bending resistance of the base plate (per unit length) :
Bending resistances of the base plate
Mode 1 :
Mode 2 :
72
2
p yppl,Rd
M0
2
pl,Rd 3
4
10 2355,87kN.mm/mm
4 1,0 10
t f m
m
g
pl,1,Rd eff,1 pl,Rd 293,1 5,87 1722 kN.mmM l m
pl,2,Rd eff,2 pl,Rd 293,1 5,87 1722 kN.mmM l m
APPLICATION – 2-1 RESISTANCE IN TENSION (CASE 2)
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Resistance of one anchor bolt in tension
Design tensile resistance of the anchor bolt section:
Design bond strength :
73
ub st,Rd
M2
t,Rd 3
0,9
0,9 353 400101,6 kN
1,25 10
f AF
F
g
ck
bd
C
bd
0,36
0,36 251,2 MPa
1,5
f f
f
g
APPLICATION – 2-1 RESISTANCE IN TENSION (CASE 2)
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Design bond anchorage resistance:
Design anchor bolt resistance :
74
t,bond,Rd b bd
t,bond,Rd 24 400 1,2/1000 36,2 kNF dl f F
F t,Bond,Rd
l b = 400 mm
t,Rd,anchor t,Rd t,bond,Rdmin ; 36,2 kNF F F
APPLICATION – 2-1 RESISTANCE IN TENSION (CASE 2)
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Resistance in tension of the T-stub : modes 1 and 2
Failure mode Mode 1 Mode 2
Form of the
mode
Resistance of
the T-stub
pl,1,Rd
T,1,Rd
T,1,Rd
4
4 1722 113,3 kN60,8
MF
m
F
75
F T,1,Rd = 113,3 kN
Q Q
m
= min ( ; 1,25 ) = min (40 ; 1,25 60,8) = 40 mmn e m
pl,2,Rd t,Rd,anchor
T,2,Rd
T,2,Rd
2 2
2 1722 40 2 36,262,9 kN60,8 40
M nF F
m n
F
F T,2,Rd=62,9kN
Q Q
emF t,Rd,anchor
APPLICATION – 2-1 RESISTANCE IN TENSION (CASE 2)
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Resistance in tension of the T-stub : modes 3 and 4
Failure mode Mode 3 Mode 4
Form of the
mode
Resistance of
the T-stub
76
T,3,Rd t,Rd,anchor
T,3,Rd
2
2 36,2 72,4 kN
F F
F
eff,t wc y,wc
T,4,Rd
M0
T,4,Rd 3293,1 9,4 235 647,5 kN
1 10
b t f F
F
g
eff,t eff,1= = 293,1 mmb l
F T,4,Rd = 647,5 kN
t wc
F T,3,Rd=72,4 kN
F t,Rd,anchor F t,Rd,anchor
APPLICATION – 2-1 RESISTANCE IN TENSION (CASE 2)
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Resistance of the equivalent T-stub in tension:
Weld resistance :
Check of the resistance of the joint in tension :
77
T,Rd T,1,Rd T,2,Rd T,3,Rd T,4,Rdmin ; ; ; 62,9 kNF F F F F
T,Rd T,Rd t,w,Rd t,Edmin ; 62,9 kN 17 kNN F F N
b g
ut,w,Rd w,eff,t w
w M2
t,w,Rd
/ 3
360/ 3293,1 2 4 487 kN
0,8 1,25 1000
f F l a
F
APPLICATION – 2-2 SHEAR RESISTANCE (CASE 2)
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Check of the shear resistance of bolts :
Check of the shear resistance of weld :
78
t,EdEd
vb,Rd T,Rd
17,5 8,86
0,31 11,4 2 41,6 1,4 62,9
NV
nF N
2 2
t,Ed Edvw,d
w,eff,t w,eff
2 2
1?
8,86 17,5 360/ 3
4 0,033 12 293,1 757,2 0,8 1,25
N V f a
l l
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CONCLUSION
CONCLUSION
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Design methods, based on EC3 and EC2, are presented to
check the resistance of pinned column base joint fordifferent internal forces (compression/tension/shear).
The bending resistance and initial rotation stiffness of rigid
column base joint are determined considering T-stubs intension and compression.
These methods are based on the component method of EN
1993-1-8. The different components are: anchor bolts intension and/or shear, bending of base plate, base plate in
compression with concrete, welds.
80
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REFERENCES
REFERENCES
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EN 1992-1-1 – Eurocode 2 Design of concrete structures Part 1-1:
General rules and rules for buildings
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.