SKILLS Projectskills.cticm.org/content/articles/assets/140513/SKILLS_BasePlate... · =1,25 : Anchor bolts in tension/shear, ... Design tensile resistance of the anchor bolt section

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


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


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


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


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


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


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


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


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


FT,1,Rd FT,2,Rd

FT,3,Rd FT,4,Rd

Prying effect and failure modes :


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


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 :


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


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:


EN 1993-1-8 Table 6.2

Failure mode Mode 1 Mode 1-2

Yielding of the base

plate


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


EN 1993-1-8 Table 6.2

Failure mode Mode 2 Mode 3

Failure of anchor bolts


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 :


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


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.


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 :


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


Failure mode Mode 4

Yielding of the column web in tension


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 :


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


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


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


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


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


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 :


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


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


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


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


47

FT,Rd

EN 1993-1-8 Figure 6.10

Effective lengths of the T-stub :

Circular mechanism Non circular mechanism


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


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


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


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


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


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


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


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 :


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


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


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


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


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


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


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


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


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


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


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


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


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



Form of the mode


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



Form of the mode


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


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


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

Documents

SKILLS Projectskills.cticm.org/content/articles/assets/140513/SKILLS_BasePlate... · =1,25 : Anchor bolts in tension/shear, ... Design tensile resistance of the anchor bolt section