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Transcript of SKILLS Projectskills.cticm.org/content/articles/assets/140513/SKILLS_BasePlate... · =1,25 : Anchor...
SKILLS Project
BASE PLATE CONNECTIONS
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
Introduction
Pinned column base joint
Rigid column base joint
Application
Conclusion
4
LIST OF CONTENTS
INTRODUCTION
Typical pinned column base joint
6
INTRODUCTION
Grout
Anchor bolt
Concrete foundation
Column
Base plate
Typical fixed column base joint
7
INTRODUCTION
Concrete foundation
Column
Base plate
Anchor bolts
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
FT,1,Rd FT,Rd
FT,3,Rd FT,4,Rd
leff
FT,Rd FT,Rd FT,Rd
b)
Recommended partial safety factors according to EN 1993-1-8 :
gM0 =1 : column web in tension, bending of the base-plate
gM2 =1,25 : Anchor bolts in tension/shear, weld resistance
Recommended partial safety factors according to EN 1992-1-1 :
gC =1,5 : Concrete in compression, bond anchorage resistance
The national annexes may give indications
9
INTRODUCTION
PINNED COLUMN BASE JOINT
beff
leff
Fc,Rd
fjd
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 : fjd
Web T-stub : Fc,bw,Rd
Flange T-stubs : Fc,fc,Rd
Foundation bearing strength
Where:
abf coefficient which accounts for diffusion of concentrated force within the foundation.
bj may be taken as 2/3 (see Note)
fcd Concrete design strength :
fck Compressive cylinder strength of concrete at 28 days
acc = 1
gc = 1,5
12
PINNED COLUMN BASE JOINT - RESISTANCE IN COMPRESSION
EN 1993-1-8 § 6.2.5
EN 1992-1-1 §6.7 jd bf j cdf fa b
ckcd cc
c
ff a
g
Expression of abf :
Note : bj = 2/3 if :
Strength of grout ≥ 0,2×fcd
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
df
eb
eh
em
jd cdf f
Resistance in compression of a T-stub :
Where:
leff Effective length of the T-stub
beff Effective width of the T-stub such as :
c Additional bearing width of the flange :
fyp Yield strength of base plate
gM0 =1
14
PINNED COLUMN BASE JOINT - RESISTANCE IN COMPRESSION
C,Rd jd eff effF f b lEN 1993-1-8 (6.4)
eff 2b t c
yp
p
jd M03
fc t
f g
beff
leff
Fc,Rd
fjd tp
c
c
t
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 cb eff fc 2b t c
eff wc 2b t c
tp
t = tfc
c b c c
tp
t = tfc or twc
c c
a) Short projection b) Large projection
beff beff
fjd fjd
EN 1993-1-8 §6.2.5
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 effF f b l
Large projection Short projection
hc
bfc
bp
hp
c
c
leff
c
c
beff
tfc
hc
bfc
bp
hp
c
c
leff
c
beff
Resistance in compression of the web T-stub :
Where:
17
PINNED COLUMN BASE JOINT - RESISTANCE IN COMPRESSION
c,bw,Rd jd eff effF f b l
eff c fc2 2 0l h t c
eff wc2b c t
c
c
hc
leff
c
c
beff
tfc
twc
c
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
bfc
bp
hp
c
c
c
c
twc
tfc
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
FT,1,Rd FT,Rd
FT,3,Rd FT,4,Rd
leff
FT,Rd FT,Rd FT,Rd
b)
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 prying
effect
FT,1,Rd FT,2,Rd
FT,3,Rd FT,4,Rd
Q Q
FT,1,Rd FT,2,Rd
FT,3,Rd FT,4,Rd
Q Q
FT,1,Rd FT,1-2,Rd
FT,3,Rd FT,4,Rd
FT,1,Rd FT,2,Rd
FT,3,Rd FT,4,Rd
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 force and are replaced by failure mode 1-2.
21
PINNED COLUMN BASE JOINT - RESISTANCE IN TENSION
FT,1,Rd FT,2,Rd
FT,3,Rd FT,4,Rd
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,RdT,3,Rd T,4,Rd
;min
;
F FF
F F
T,1-2,Rd T,3,Rd
T,RdT,4,Rd
;min
F FF
F
FT,Rd FT,2,Rd
FT,3,Rd FT,4,Rd
Q Q
FT,1,Rd FT,Rd
FT,3,Rd FT,4,Rd
Anchor bolt elongation length :
Where:
twa Thickness of the washer
d Anchor bolt diameter
PINNED COLUMN BASE JOINT - RESISTANCE IN TENSION
EN 1993-1-8 Table 6.2
b m p wa8 0,5 L d e t t k
23
tp
em
8d
Concrete
grout
base plate
k
Limit anchor bolt elongation length :
Where:
As Tensile stress area of one anchor bolt
leff,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 AL
l t
eff,1 eff,cp eff,nc=min ;l l l
wc w/2 /2 0,8 2m p t a
24
m
dw
tp Base plate
aw
p/2
twc
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
m m e e
p
twc
25
m m e e
Yield line
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
FT,1,Rd FT,1-2,Rd
FT,3,Rd FT,4,Rd
pl,1,RdT,1,Rd
4MF
m
2p yp
pl,1,Rd pl,Rd eff,1 pl,Rd eff,1 eff,cp eff,nc
M0
; ; =min ;4
t fM m l m l l l
g
pl,1,RdT,1-2,Rd
2MF
m
FT,1,Rd FT,2,Rd
FT,3,Rd FT,4,Rd
Q Q
m
26
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,anchorT,2,Rd
2 2M nFF
m nT,3,Rd t,Rd,anchor2F F
27
FT,1,Rd FT,2,Rd
FT,3,Rd FT,4,Rd
Q Q
e m Ft,Rd,anchor
FT,1,Rd FT,2,Rd
FT,3,Rd FT,4,Rd
Ft,Rd,anchor Ft,Rd,anchor
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
Resistance of one anchor bolt, two failure modes:
Tensile resistance of the anchor bolt section, Ft,Rd,
Bond anchorage resistance, Ft,bond,Rd.
Design tensile resistance of the anchor bolt section :
Where:
fub Tensile strength of the anchor bolt
gM2 = 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
Bond anchorage resistance of a straight bolt :
Where:
d Nominal diameter of an anchor bolt
fbd Design bond strength :
If d < 32 mm :
If d ≥ 32 mm :
gc = 1,5
fyb : Yield strength of the anchor bolt.
PINNED COLUMN BASE JOINT - RESISTANCE IN TENSION
30
t,bond,Rd b bdF dl f
Ft,Bond,Rd
lb
ckbd
C
0,36 ff
g
ckbd
C
0,36 132
100
f df
g
2yb 600 /mmf N
Bond resistance of a bolt with a hook :
Check that :
PINNED COLUMN BASE JOINT - RESISTANCE IN TENSION
31
b bdt,bond,Rd
0,7
dl fF
2yb 300 /mmf N
Ft,Bond,Rd
≥5d
90°
l b
EN 1993-1-8 §6.2.6.12 (5)
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
FT,1,Rd FT,2,Rd
FT,3,Rd FT,4,Rd
twc
eff,t wc y,wc
T,4,Rd t,wc,Rd
M0
b t fF F
g
eff,t eff,1=b l32
Weld resistance :
Where:
aw weld throat thickness of the web
bw correlation factor
fu nominal ultimate strength of the weaker joined part
lw,wb total effective length of the web welds
Final resistance of the joint in tension :
PINNED COLUMN BASE JOINT - RESISTANCE IN TENSION
33
ut,w,Rd w,eff,t w
w M2
/ 3fF 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
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
Design friction resistance :
Where:
N c,Ed Compression force
C f,d Coefficient of friction
For 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
Effort
tranchant
Vz
Bêche
a)
Axial force Nc,Ed
Axe z-z
Axe y-y
eh
hp
hf
eb
bp bf
Vz
Effort axial N
Axe z-z
Axe y-y
Axe x-x
Vz
b)
Shear force VEd<0,2×Nc,Ed
Friction
Shear resistance of an anchor bolt:
Where:
fyb 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/mmf fa
Fvb,Rd
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
Effort
tranchant
Vz
Bêche
a)
Axial force Nc,Ed
Axe z-z
Axe y-y
eh
hp
hf
eb
bp bf
Vz
Effort axial N
Axe z-z
Axe y-y
Axe x-x
Vz
b)
Shear force VEd
Friction
Shear of anchor bolts
Shear resistance in presence of tension :
Where:
FT,Rd Tensile resistance of the T-stub in tension
38
PINNED COLUMN BASE JOINT - SHEAR RESISTANCE
Effort
tranchant
Vz
Bêche
a)
Axial force Nt,Ed
Axe z-z
Axe y-y
eh
hp
hf
eb
bp bf
Vz
Effort axial N
Axe z-z
Axe y-y
Axe x-x
Vz
b)
Shear force VEd
Shear of anchor bolts
t,EdEd
vb,Rd T,Rd
11,4
NV
nF F
Shear resistance of welds (in compression) :
Where:
lw,eff total effective length of the welds in the direction of shear
a 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
/ 3ff
b g
2 2
t,Ed Edw,Ed vw,d
w,eff,t w,eff
N VF f a
l l
FIXED COLUMN BASE JOINT
Calculation of the bending resistance and initial rotational stiffness in presence of axial force :
Initial rotational stiffness :
FIXED COLUMN BASE JOINT- INTRODUCTION
41
Mj,Ed ≤ Mj,Rd
j,Ed
Nj,Ed
Mj,Rd
j,Ed
Mj,Ed
Sj,ini
j,Edj,ini
j,Ed
MS
Application of the component method :
FIXED COLUMN BASE JOINT- INTRODUCTION
42
beff
leff
Tronçon en T
comprimé
Aire de répartition
uniforme de pression
entre la platine et son
appui
FC
FT
Mode 2
Mécanisme partiel et
rupture des tiges
e m
FT,2,Rd =(2Mpl, 2, Rd +nFt, Rd)/(m +n)
Q Q n n
Mode 3
Rupture des tiges
FT,3,Rd = Ft, Rd
e m
Mode 4
Plastification de l’aile tendue
(âme du poteau)
FT,4,Rd = Ft,wc, Rd
e m
Mj,Ed ≤ Mj,Rd
j,Ed
Fc FT
Nj,Ed
T-stub in tension : T-stub in compression :
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
FC
zT zC
FT
Mj,Ed
hc
tfc
j,Ed C C T TM z F z F
C C,Rd T T,Rd or F F F F
Bending resistance depend on eccentricity :
Dominant tensile force : Dominant compression force :
FIXED COLUMN BASE JOINT- BENDING RESISTANCE
44
j,Ed j,Rd
Nj,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
FT
zT zT
FT,Rd
Mj,Rd
Nj,Rd
FC,Rd
zC zC
FC
Mj,Rd
Nj,Rd
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 C or e z e z
FC
zT zC
FT,Rd
Mj,Rd
Nj,Rd
FC,Rd
zT zC
FT
Mj,Rd
Nj,Rd
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 effF f b l
FC,Rd
leff beff
p cceff fc fcmin , min ,
2 2
h hhb c t t c
g
ypp
jd M03
fc t
f
hc
bfc
bp
hp
c
c
c
c
twc
tfc
leff
beff
EN 1993-1-8 (6.4)
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, leff
Replace m by mx, e by ex in resistance of T-stub
FIXED COLUMN BASE JOINT- BENDING RESISTANCE
47
FT,Rd
EN 1993-1-8 Figure 6.10
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 wl
m e e
b
Loading Lever arm
z Bending resistance Mj,Rd
for a given value of eN
Dominant compression force
z = zC + zC
Nj,Ed < 0 and 0 ≤ eN ≤ +zC Nj,Ed < 0 and-zC ≤ eN ≤ 0
The smaller of and
Dominant tension force
z = zT + zT
Nj,Ed > 0 and 0 ≤ eN ≤ +zT Nj,Ed > 0 and -zT ≤ eN ≤ 0
The smaller of and
Dominant bending moment
z = zT + zC
Nj,Ed 0
and eN > +zT or eN < - zT
Nj,Ed ≤ 0
and eN < - zC or eN > zC
The smaller of and
Mj,Ed > 0 is clockwise, Nj,Ed > 0 is tension.
49
FIXED COLUMN BASE JOINT- BENDING RESISTANCE
C,Rd
C N/ 1
F z
z e
j,Ed j,Rd
Nj,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
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
cj,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
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
Sj Sj
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
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
FC
zT zC
FT
Mj,Ed
kT kC
j,Ed
Nj,Ed
j,Edj,ini
j,Ed
MS
Mj,Ed
j,Ed
Nj,Ed
Stiffness of compressive part of the joint
Where:
leff Effective length of the T-stub,
beff Effective width of the T-stub,
Ec 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 131,275
E l bk k
E
Concrete
Flange
FC
c
Contact between flange and concrete
EN 1993-1-8 Table 6.11
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
FT
B B
Q Q
T
FT
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
Stiffness of the tensile part in presence of prying effect :
k16 : stiffness coefficient of anchor bolts in tension :
k15 : stiffness coefficient of base plate in bending under tension :
55
FIXED COLUMN BASE JOINT- INITIAL ROTATIONAL STIFFNESS
T
15 16
11 1
k
k k
s16
b
1,6A
kL
3eff p
15 3
0,85 l tk
m
EN 1993-1-8 Table 6.11
Stiffness of the tensile part in absence of prying effect :
k16 : stiffness coefficient of anchor bolts in tension :
k15 : stiffness coefficient of base plate in bending under tension :
56
FIXED COLUMN BASE JOINT- INITIAL ROTATIONAL STIFFNESS
T
15 16
11 1
k
k k
s16
b
2A
kL
3eff p
15 3
0,425 l tk
m
EN 1993-1-8 Table 6.11
Rotational stiffness depend on the eccentricity :
Dominant tensile force : Dominant compression force :
FIXED COLUMN BASE JOINT- INITIAL ROTATIONAL STIFFNESS
57
j,Ed
Nj,Ed
Me
N
2 T-stubs in compression
C N 0z e N T0 e z
2 T-stubs in tension
FT,2
zT zT
FT,1
Mj,Ed
kT kT
j,Ed
Nj,Ed
FC,2
zC zC
FC,1
Mj,Ed
kC kC
j,Ed
Nj,Ed
FIXED COLUMN BASE JOINT- BENDING RESISTANCE
58
Dominant bending moment :
Joint composed of a tensile and compressive part :
N T N C or e z e z
FC
zT zC
FT
Mj,Ed
kT kC
j,Ed
Nj,Ed
Loading Lever arm
z Initial rotational stiffness Sj,ini
for a given value of eN
Dominant compression force
z = zC + zC
Nj,Ed < 0 and 0 ≤ eN ≤ +zC Nj,Ed < 0 and-zC ≤ eN ≤ 0
Dominant tension force
z = zT + zT
Nj,Ed > 0 and 0 ≤ eN ≤ +zT Nj,Ed > 0 and -zT ≤ eN ≤ 0
Dominant bending moment
z = zT + zC
Nj,Ed 0
and eN > +zT or eN < - zT
Nj,Ed ≤ 0
and eN < - zC or eN > zC
Mj,Ed > 0 is clockwise, Nj,Ed > 0 is tension.
59
FIXED COLUMN BASE JOINT- INITIAL ROTATIONAL STIFFNESS
j,Ed
Nj,Ed
Me
N
2C
j,ini2
E z kS
2T
j,ini2
E z kS
a
2
j,inik
C T
1
11 1
E zS
k k a
C C T Tk
T C
kk
N
× -z ×=
+
=
z k ke
k k
e
e
Table 6.12
APPLICATION
Detail of the joint and the concrete block
61
APPLICATION – PRESENTATION OF THE EXAMPLE
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 Vz,Ed
Axis z-z
Axis y-y
Axis x-x
Concrete class C25/30
bp=220
hp =480
df=500mm
eb
eh
400
800
lb=400mm
Detail of the joint
62
APPLICATION – PRESENTATION OF THE EXAMPLE
15
225
40 40 140
225
15
m e 40 60,8 Web weld : 4 mm
Flange weld : 6 mm
10
2 anchor bolts M24 Class 4.6
190
9,4
14,7
Load Case 1 (compression) :
Nc,Ed = 85 kN
Vz,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
Vz,Ed = 17,5 kN
2-1 – Check the resistance in tension
2-2 – Check the shear resistance
63
APPLICATION – PRESENTATION OF THE EXAMPLE
Concrete (C25/30) design strength :
The value of bj is equal to 2/3, as :
Coefficient abf :
64
APPLICATION – 1-1 RESISTANCE IN COMPRESSION
ckcd cc
c
cd
251 16,7 MPa
1,5
ff
f
ag
min 1
bf hbf
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 0,2
0,2
e b
h
Foundation bearing strength :
Additional bearing width of the flange :
65
APPLICATION – 1-1 RESISTANCE IN COMPRESSION
jd bf j cd
jd 1,67 2/3 16,7 18,6 MPa
f f
f
a b
ypp
jd M03
23510 20,5 mm
3 18,6 1,0
fc t
f
c
g
Geometrical parameter :
Short projection
Resistance in compression of the column base joint :
66
APPLICATION – 1-1 RESISTANCE IN COMPRESSION
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 wc 2
18,6 480 220 379,6 220 9,4 2 20,5 /1000
766,6 kN
N f h b l b t c
Check of the resistance in compression:
67
APPLICATION – 1-1 RESISTANCE IN COMPRESSION
C,Rd c,Ed 766,6 kN 85 kNN N
bfc =190
bc =15
tfc= 14,7
bc =15
hc = 450
20,5
leff = 220
hp = 480
c= 20,5
beff
c
c
c
c
twc = 9,4
Friction resistance :
Shear resistance of one anchor bolt :
Shear resistance of the joint
68
APPLICATION – 1-2 SHEAR RESISTANCE (CASE 1)
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 kN
F F nF
F
Shear resistance of welds :
Check of the shear resistance :
69
APPLICATION – 1-2 SHEAR RESISTANCE (CASE 1)
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
fV a l
l
V
b g
z,Rd v,Rd w,Rd z,Edmin ; 100,2 kN =35kNV F V V
Length m :
Effective lengths and mechanisms :
Effective lengths of mode 1 and 2 :
70
APPLICATION – 2-1 RESISTANCE IN TENSION (CASE 2)
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 m
l
40 40 140
m e 40 60,8
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
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
APPLICATION – 2-1 RESISTANCE IN TENSION (CASE 2)
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
Bending resistance of the base plate (per unit length) :
Bending resistances of the base plate
Mode 1 :
Mode 2 :
72
APPLICATION – 2-1 RESISTANCE IN TENSION (CASE 2)
2p yp
pl,RdM0
2
pl,Rd 3
4
10 2355,87kN.mm/mm
4 1,0 10
t fm
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
Resistance of one anchor bolt in tension
Design tensile resistance of the anchor bolt section:
Design bond strength :
73
APPLICATION – 2-1 RESISTANCE IN TENSION (CASE 2)
ub st,Rd
M2
t,Rd 3
0,9
0,9 353 400101,6 kN
1,25 10
f AF
F
g
ckbd
C
bd
0,36
0,36 251,2 MPa
1,5
ff
f
g
Design bond anchorage resistance:
Design anchor bolt resistance :
74
APPLICATION – 2-1 RESISTANCE IN TENSION (CASE 2)
t,bond,Rd b bd
t,bond,Rd 24 400 1,2/1000 36,2 kN
F dl f
F
Ft,Bond,Rd
lb = 400 mm
t,Rd,anchor t,Rd t,bond,Rdmin ; 36,2 kNF F F
Resistance in tension of the T-stub : modes 1 and 2
APPLICATION – 2-1 RESISTANCE IN TENSION (CASE 2)
Failure mode Mode 1 Mode 2
Form of the mode
Resistance of the T-stub
pl,1,RdT,1,Rd
T,1,Rd
4
4 1722113,3 kN
60,8
MF
m
F
75
FT,1,Rd = 113,3 kN FT,2,Rd
FT,3,Rd FT,4,Rd
Q Q
m
= min ( ; 1,25 ) = min (40 ; 1,25 60,8) = 40 mmn e m
pl,2,Rd t,Rd,anchorT,2,Rd
T,2,Rd
2 2
2 1722 40 2 36,262,9 kN
60,8 40
M nFF
m n
F
FT,1,Rd FT,2,Rd=62,9kN
FT,3,Rd FT,4,Rd
Q Q
e m Ft,Rd,anchor
Resistance in tension of the T-stub : modes 3 and 4
APPLICATION – 2-1 RESISTANCE IN TENSION (CASE 2)
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 3
293,1 9,4 235647,5 kN
1 10
b t fF
F
g
eff,t eff,1 = = 293,1 mmb l
FT,1,Rd=647 FT,2,Rd
FT,3,Rd FT,4,Rd = 647,5 kN
twc
FT,1,Rd FT,2,Rd
FT,3,Rd=72,4 kN FT,4,Rd
Ft,Rd,anchor Ft,Rd,anchor
Resistance of the equivalent T-stub in tension:
Weld resistance :
Check of the resistance of the joint in tension :
77
APPLICATION – 2-1 RESISTANCE IN TENSION (CASE 2)
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
fF l a
F
Check of the shear resistance of bolts :
Check of the shear resistance of weld :
78
APPLICATION – 2-2 SHEAR RESISTANCE (CASE 2)
t,EdEd
vb,Rd T,Rd
17,5 8,860,31 1
1,4 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 / 34 0,033 1
2 293,1 757,2 0,8 1,25
N Vf a
l l
CONCLUSION
Design methods, based on EC3 and EC2, are presented to check the resistance of pinned column base joint for different internal forces (compression/tension/shear).
The bending resistance and initial rotation stiffness of rigid column base joint are determined considering T-stubs in tension and compression.
These methods are based on the component method of EN 1993-1-8. The different components are: anchor bolts in tension and/or shear, bending of base plate, base plate in compression with concrete, welds.
80
CONCLUSION
REFERENCES
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.
82
REFERENCES