Bolts, welds, column base - eurocodes.jrc.ec.europa.eu · Eurocodes - Design of steel buildings...

Bolts, welds, column base

František Wald Czech Technical University in Prague

Eurocodes - Design of steel buildings with worked examples Brussels, 16 - 17 October 2014

Motivation

To present

o Content/principles

o Selected particularities

o Questions

To offer

o Worked examples

for design according to EN1993-1-8: 2005 of

Bolts

Welds

Column bases


Scope of the lecture

Bolts o General o Design resistance of individual fasteners

o Non-preloading bolts o Slotted holes

o Design for block tearing o Worked example o Summary

Welds o General o Fillet weld

o Design model o Design example o Welding to flexible plate

o Summary

Column bases o Basis of design o Components

o Base plate and concrete in compression o Base plate in bending and bolt in tension o Anchor bolt in shear

o Assembly o Resistance o Stiffness

o Classification o Worked examples o Summary


Scope of the lecture Bolts oGeneral oDesign resistance of individual fasteners oNon-preloading bolts oSlotted holes

oDesign for block tearing oWorked examples oSummary



o Summary Column bases

o Basis of design o Components





Connections made with bolts, rivets or pins in EN1993-1-8: 2005 3.1 Bolts, nuts and washers pg. 20

3.1.1 General 20 3.1.2 Preloaded bolts 20

3.2 Rivets 20 3.3 Anchor bolts 21 3.4 Categories of bolted connections 21

3.4.1 Shear connections 21 3.4.2 Tension connections 21

3.5 Positioning of holes for bolts and rivets 23 3.6 Design resistance of individual fasteners 24

3.6.1 Bolts and rivets 24 3.6.2 Injection bolts 28

3.7 Group of fasteners 29 3.8 Long joints 29 3.9 Slip resistant connections using 8.8 or 10.9 bolts 30

3.9.1 Design Slip resistance 30 3.9.2 Combined tension and shear 31 3.9.3 Hybrid connections 31

3.10 Deductions for fastener holes 31 3.10.1 General 31 3.10.2 Design for block tearing 32 3.10.3 Angles connected by one leg and other unsymmetrically connected members in tension 33 3.10.4 Lug angles 34

3.11 Prying forces 34 3.12 Distribution of forces between fasteners at the ultimate limit state 34 3.13 Connections made with pins 35

3.13.1 General 35 3.13.2 Design of pins 35


Bolt standards

EN 15048

Non-preloaded structural bolting assemblies

o Part 1: General requirements

o Part 2: Suitability test

EN 14399

High-strength structural bolting for preloading


High-strength structural bolting for preloading

EN 14399 Part 1: General requirements

Part 2: Suitability test for preloading Part 3: System HR — Hexagon bolt and nut assemblies Part 4: System HV — Hexagon bolt and nut assemblies Part 5: Plain washers

Part 6: Plain chamfered washers Part 7: System HR – Countersunk head bolt and nut assemblies Part 8 : System HV – Hexagon fit bolt and nut assemblies


Part 3: System HR — Hexagon bolt and nut assemblies


Part 4: System HV — Hexagon bolt and nut assemblies


Mechanical properties

EN ISO 898-1, Mechanical properties of fasteners made of carbon steel and alloy

steel — Part 1: Bolts, screws and studs (ISO 898-1:1999)

EN 20898-2, Mechanical properties of fasteners — Part 2: Nuts with specified

proof load values — Coarse thread (ISO 898-2:1992)

EN ISO 3506-1, Mechanical properties of corrosion-resistant stainless-steel fasteners —

Part 1: Bolts, screws and studs (ISO 3506-1:1997)

EN ISO 3506-2, Mechanical properties of corrosion-resistant stainless-steel

fasteners — Part 2: Nut (ISO 3506-2:1997)


Material Bolts made of carbon steel and alloy steel:

4.6, 4.8, 5.6, 5.8, 6.8, 8.8, 10.9

Nuts made of carbon steel and alloy steel: 4, 5, 6, 8, 10, 12

Bolts made of austenitic stainless steel: 50, 70, 80

Nuts made of austenitic stainless steel: 50, 70, 80

Washers (if appropriate) according to hardness class HV 100 or HV 200


EN 1993-1-8 Material Properties

Nominal values for bolts fyb is yield strength fub is ultimate tensile strength

Bolt class 4.6 4.8 5.6 5.8 6.8 8.8 10.9

fyb (N/mm2)

240 320 300 400 480 640 900

fub (N/mm2)

400 400 500 500 600 800 1000


Holes

o Normal

+1 mm for M 12

+2 mm for M 16 up M 24

+3 mm for M 27 and bigger

o Oversized with 3 mm (M12) up 8 mm (M27)

o Slotted (elongated)

o Close fitting – flushed bolts

for bolt M20 must be the clearance d < 0,3 mm

EN 1090-2 Execution of steel structures and aluminium structures – Part 2: Technical requirements for steel structures



oDesign for block tearing oWorked example oSummary









Resistance in shear in one shear plane

M2

ubvRdv,

fAF

where the shear plane passes through the unthreaded portion of the bolt

v = 0,6

A is the gross cross section of the bolt fub is ultimate tensile strength for bolt γM2 s partial safety factors for resistance of bolts


Resistance in shear in one shear plane

M2

ubvRdv,

fAF

where the shear plane

passes through the threaded portion of the bolt

- for classes 4.6, 5.6 and 8.8: v = 0,6

- for classes 4.8, 5.8, 6.8 and 10.9 v = 0,5

A is the tensile stress area of the bolt As

fub is ultimate tensile strength for bolt γM2 s partial safety factors for resistance of bolts


Resistance in bearing

p 1e

1

d

d

0

Fb.Sd

M2

ub1Rdb,

ftdakF

u

ub

f

f

0

1d

3 d

e

4

1

3 0

1d

d

p

71820

2 ,d

e,

71410

2 ,d

e,

where b is the smallest of d, or 1,0

, for inner bolts

Perpendicular to the direction of load transfer

or 2,5

or 2,5

In the direction of load transfer

- for inner bolts k1 is the smallest of

- for end bolts:

- for edge bolts k1 is the smallest of


Bearing of Plate and Bolt

Inner bolt Outer bolt


Resistance in Bearing

Load on a bolt not parallel to the edge

the bearing resistance may be verified separately

for the bolt load components parallel and normal to the edge in oversized holes reduce bearing by 0,8

e30

L

t

p1

w pt

1

e1

10

IPE 200

14060

5,6

40

40

44

5010

V = 110 kNSd

P 10 - 140 x 100

M 20 - 5.6

10

R 1020


Influence of distances to force

Prallel to acting force

M2

ub1

Rd,b

ftdkF

p1 p1e1 e1 a1 a1e1 e1a1

p2

e2

e2

p2

a2

e2

e2

a2F F

1

f

f

25,0d3

p

d3

e

min

u

ub

0

1

0

1

b


M2

ub1

Rd,b

ftdkF

p1 p1e1 e1 a1 a1e1 e1a1

p2

e2

e2

p2

a2

e2

e2

a2F F

5,2

7,1d

p4,1

7,1d

e8,2

mink0

2

0

2

1

Perpendicular to acting force


Influence of distances

Nomimal transversal distances:

e1 = 1,2 d0

p1 = 2,2 d0

e2 = 1,2 d0

p2 = 2,4 d0

66,1

5,2

66,1

66,1

min

5,2

7,1d

d4,24,1

7,1d

d2,18,2

min

5,2

7,1d

p4,1

7,1d

e8,2

mink0

0

0

0

0

2

0

2

1

400,0d3

d2,1

d3

e

0

0

0

1

bEnd bolts

Internal bolts

483,025,0d3

d2,225,0

d3

p

0

0

0

1

b

M2

u

M2

u

M2

ub1

Rd,b

ftd664,0

ftd400,066,1ftdakF

p1e1 e1

p2

e2

e2

F

e1 = 1,2 d0

p1 = 3,0 d0

e2 = 1,5 d0

p2 = 3,0 d0

M2

u

M2

u

M2

ub1

Rd,b

ftd802,0

ftd483,066,1ftdakF

WE WE


Sum p1e1 e1

p2

e2

e2

F

e1 = 1,2 d0

p1 = 3,0 d0

e2 = 1,5 d0

p2 = 3,0 d0

Sum of resistances

Minimal resistance

M2

u

M2

u

M2Rdb, 75,500,12875,12

ftdftdftdF u

M2

u

M2

uRdb, 0,40,14

ftdftdF

WE WE


Pitch distances

Min

p1 = 2,2 d0

p2 = 2,4 d0

optimum e1 from 1,2 d0 to 1,45 d0

e2 = 1,2 d0

Large

p1 = 3,75 d0

p2 = 3,0 d0

e1 = 3,0 d0

e2 = 1,5 d0

M2

u

M2

u

M2

ub1

Rd,b

ftd5,2

ftd0,15,2ftdakF

M2

u

M2

u

M2

ub1

Rd,b

ftd802,0

ftd483,066,1ftdakF

WE


Last-VerformungskurveVersuch VL-100-220-385

Fu = 297kN

Fb,R = 234kN

0

50

100

150

200

250

300

350

0 2 4 6 8 10 12

Verformung ux [mm]

Kra

ft

Fx

[kN

]

= 27%

B1

B3

B2

B3 B2 B1

Last-VerfromungskurveVersuch VL-240-320-385

Fu,test =

432kN

Fb,R,max = 426

Fv ,R = 438

0

100

200

300

400

500

0 2 4 6 8 10 12

Verschiebung ux [mm]

Kra

ft

Fx

[kN

]

B3 B2 B1

e1 = 1,0 d0 < min. e1 = 1,2 d0

B1

B3

B2

e1 = 2,4d0 and p1 = 3,2 d0

Comparison to EN e1 and p1 min. Fu/FEN3 = 1,27

e1 and p1 max. Fu/FEN3 1,02

University of Dortmund,

Institute of Steel Structures

Steel S690 Experiment bolts M12 10.9 minimal and maximal pitch


Comparison of simulation VL-100-220-385

Numerical model • Good agreement

• Diffference D=5,5%

University of Dortmund,

Institute of Steel Structures












Bearing resistance in slotted holes

Loaded perpendicular to the long direction of the slot 60% of resistance in circular holes

110

25

50

35

10

40 40 8 16

18

8

M 16

110

25

50

35

10

40 40

22 18

M 16

Displacement , mm

0

20

40

60

80

100

120

140

160

0 5 10 15 20 25 30 35 40

Force, F, kN

Slotted holes,

Circular holes, 180

(test 1c-16-1-d+2)

(test 5c-16-1-d+2,5)

8 16 8

45

200












Block tearing

Failure in shear at the row of bolts along the shear face of the hole group

accompanied by Tensile rupture along the line of bolt holes

on the tension face of the bolt group

N Ed

N Ed

N Ed

N Ed


Test

Orbison J.G., Wagner M. E., Fritz W.P. 1999, Tension plane behavior in single-row bolted connections subject to block shear, Journal of Constructional Steel Research, 49, 225 – 239


FE model

Topkaya C., 2004, A finite element parametric study on block shear failure of steel tension members, Journal of Constructional Steel Research, 60, 1615 – 1635, ISSN 0143-974X.

Rupture


Design model

Symmetric bolt group subject to concentric loading

Veff,1,Rd = fu Ant / M2 + (1/√3) fy Anv / M0

Ant net area subjected to tension

Anv net area subjected to shear

Eccentric loading

Veff,2,Rd = 0,5 fu Ant / M2 + (1/√3) fy Anv / M0


Worked Example - Angle 40

35

25

8 x M16; 70

P10; 1.4401

L - 100 x 100 10

30 + 7 x 30 +30

70

100

70

materiál 1.4401

240

60

35

240

In plate (staggered rows)

In angle (staggered rows)

M0

nvy

M2

ntuRdeff,1,

γ

Af

3

1

γ

AfV

kN39736236

101,0

10911872402220

3

1

101,25

1092355300,533

M0

nvpy,

M2

ntpu,Rdeff,2,

γ

Af

3

1

γ

Af0,5V

kN24517570

101,0

10184240220

3

1

101,25

10918605300,533

Worked Example – Angle connected by one leg WE


Worked example – Fin plate connection

45

70

70

45

3 x M20, 8.8

50 50

35

60

10

IPE 300S235

meteriál S235

5

P10 - 230 x 110HEA 200S235

230

= 100 kNV Sd

WE


Worked Example – Fin Plate connection Shear Resistance

80

70

70

50

50

45

70

70

45

230

kN kN 1991599,39

100,1

1,711222220235

3

1

1025,1

1,711503605,033

M0

nvb1y,

M2

b1u,Rd,11

Af

AfV

3

15,0

nt

WE


Worked example – Fin plate, Tying resistance

In beam web

70

70

50

50

45

70

70

45

M0

nvb1y,

uM,

ntb1u,u,6Rd,

Af

AfN

3

1

kN2981.75223

0,1

11501,72235

3

1

1,1

2221401,7360

WE












Bolted connection of double angle bar

Angle net section

40

2× L80 × 6

N Ed

8 70

6 6

45

35e =2

70 70 4070

e1 p1

Bolts M20 class 5.6 fully treated Loading NEd = 400 kN

kN400kN3,416

25,1

36062293529,09,0Ed

M2

unetRdu,

N

fAN

Satisfactory

WE



Bolts in shear

40

2× L80 × 6

N Ed

8 70

6 6

45

35e =2

70 70 4070

e1 p1

Two shear planes Shear in bolt thread Resistance for one bolt kN6,117

25,1

5002456,022

M2

ubsvv.Rd

fAF

WE



Bearing of end bolt

40

2× L80 × 6

N Ed

8 70

6 6

45

35e =2

70 70 4070

e1 p1

5,2k5,2;75,2min5,2;7,122

358,2min5,2;7,1

d

e8,2mink 1

0

21

606,0

0,1

389,1

606,0

min

0,1

360

500

223

40

min

0,1

f

f

d3

e

minu

ub

0

1

b

kN3,8725,1

360820606,05,2ftdkF

2M

u1Rd,b

WE



Bearing of internal bolt

40

2× L80 × 6

N Ed

8 70

6 6

45

35e =2

70 70 4070

e1 p1

5,2k5,2;75,2min5,2;7,122

358,2min5,2;7,1

d

e8,2mink 1

0

21

811,0

0,1

389,1

811,0

min

0,1

360

500

4

1

223

70

min

0,1

f

f

4

1

d3

p

minu

ub

0

1

b

kN4,9325,1

360820811,05,2F Rd,b

WE



Check of bolts

Shear resistance 117,6 kN Bearing resistance – end bolt 87,3 kN Bearing resistance – internal bolt 93,4 kN Shear is not guiding the resistance, e.g. bearing as sum For connection with five bolts

EdkN400kN5,4573,873,9433,87 N Satisfactory

Conservatively elastic (minimal) resistance

Lower resistance from bearings

EdkN400kN5,4363,875 N Unsatisfactory

WE












Summary for bolted connections

o Connections made with bolts, rivets or pins in Chapter 3 of EN 1993-1-8

o Non-preloaded bolts

o Preloaded bolts preload (0,7 fub)

o Injection bolts replacement of rivets; bolts 8.8 and 10.9

o Pins including serviceability


Future? Advanced models of bolted connections

o FEM research models o Validated on experiments

o FEM design models o Verified against

analytical and numerical models

o Bars and springs model

o In tension – stiffness, resistance

o In shear - contact

Fan model of bolts


Scope of the lecture Bolts

o General o Design resistance of individual fasteners


o Design for block tearing o Worked example

o Summary

Welds oGeneral oFillet weld oDesign model oDesign example oWelding to flexible plate

oSummary Column bases






Welded connections in EN1993-1-8: 2005 4.1 General 38 4.2 Welding consumables 38 4.3 Geometry and dimensions 38

4.3.1 Type of weld 38 4.3.2 Fillet welds 38 4.3.3 Fillet welds all round 40 4.3.4 Butt welds 40 4.3.5 Plug welds 41 4.3.6 Flare groove welds 41

4.4 Welds with packings 41 4.5 Design resistance of a fillet weld 42

4.5.1 Length of welds 42 4.5.2 Effective throat thickness 42 4.5.3 Design Resistance of fillet welds 42

4.6 Design resistance of fillet welds all round 44 4.7 Design resistance of butt welds 45

4.7.1 Full penetration butt welds 45 4.7.2 Partial penetration butt welds 45 4.7.3 T butt joints 45

4.8 Design resistance of plug welds 45 4.9 Distribution of forces 46

4.10 Connections to unstiffened flanges 46 4.11 Long joints 48 4.12 Eccentrically loaded single fillet or single sided partial penetration butt welds 48 4.13 Angles connected by one leg 48 4.14 Welding in cold-formed zones 49


Electrode classification

EN 499 classification of carbon and low alloy steel electrodes

E 38 0 RC 1 1

Strength & elongation

Impact properties (47J at 0oC)

Recovery and type of current

Welding position (all positions)

Covered electrode / manual metal arc welding

Type of electrode covering (rutile-cellulosic)






o Summary








Fillet welds – Definition of effective throat thickness a

The effective throat thickness of a fillet weld should not be less than 3 mm


Design Model of Fillet Welds

a effective throat thickness of the fillet weld

┴ normal stresses perpendicular to the throat

║ normal stresses parallel to the axis of weld (omitted)

┴ shear stresses perpendicular to the axis of weld

║ shear stresses parallel to the axis of weld


53

Plane Stresses

Huber-Mises-Henckey condition of plasticity (HMH) o Triaxial state of stress (needed exceptionally only) oPlane state of stress (needed very often) x

2 + z2 - x

2 z2 + 32 ≤ (fy / M) 2

oUniaxial state of stress (from the material tests) ≤ fy / M0

≤ fy / (M0 √3)

x

z


Design Resistance of Filet Weld

2 II

2 2 3 ^ ^ Mw w u f b

^ Mw u f

f u Ultimate tensile strength of connected material

b w Correlation factor

γ Mw Partial safety factor for material of welds


55

Correlation factor bw for fillet welds Standard and steel grade Correlation factor

βw EN 10025 EN 10210 EN 10219

S 235

S 235 W S 235 H S 235 H 0,80

S 275

S 275 N/NL

S 275 M/ML

S 275 H

S 275 NH/NLH

S 275 H

S 275 NH/NLH

S 275 MH/MLH

0,85

S 355

S 355 N/NL

S 355 M/ML

S 355 W

S 355 H

S 355 NH/NLH

S 355 H

S 355 NH/NLH

S 355 MH/MLH

0,90

S 420 N/NL

S 420 M/ML S 420 MH/MLH 1,00

S 460 N/NL

S 460 M/ML

S 460 Q/QL/QL1

S 460 NH/NLH S 460 NH/NLH

S 460 MH/MLH 1,00






o Summary








Two fillet welds in parallel shear

l a 2 F

From plane stress analysis is

3 f a 2 F Mw w u b l

Throat thickness, not leg length

WE


0 II

2 R ^ ^

Has to be satisfied

Mw w u

2 2 f 3 b ^ ^

After substitution

Mw w u

2 R

2

R

2

R f 2 2 3 2 b +

2 f Mw w u R b

Fillet weld in normal shear

Ignored parallel fillet weld

WE


Connection of cantilever Shear force

h a 2 F Sd II

=

Bending moment

Transferred by the shape of weld .

Centre of gravity, Iwe and cross section modulus we

For weld at lower flange cross section modulus and stress is

( ) 1 , we Sd 1 1 W 2 M = = ^ ^

For upper weld on flange is

( ) 2 , we Sd 2 2 W 2 M = = ^ ^

Sd = F Sd . V

Sd = F Sd e M

W

we,1 W

Transferred by web

fillets

WE


Flange - web weld

VSd

Vl

Welds are loaded by longitudinal shear force

I S V V Sd =

l

where V Sd

S static moment of flange to neutral axis

I moment of inertia

This longitudinal force is carried by two welds effective thickness a

Shear stress

3 f a 2 V Mw w u II b =

l

Maximum stress is at the point of maximum shear force

shear force

WE






o Summary








Welds to flexible plate

Effective width of unstiffened column flanges

EN 1993-1-8 Chapter 4.10 twc thickness of column web tfc thickness of column flange tfb thickness of beam flange s equal to fillet radius rc for hot rolled column sections

fcwceff 72 tstb

yb

yc

fb

2fc

wceff 72f

f

t

tstb

beff

t fb

t fc

twc

rc

σ


Effective Width

Unstiffened column flanges In EN1993-1-8 Clause 6.2.4.4 twc is thickness of column web tfc thickness of column flange tfb thickness of beam flange s is equal to fillet radius rc for hot rolled column sections

M0

ybfbfcwcRdfc,t, 72

fttkstF

1;min

fbyb

fcyc

tf

tfk






o Summary








Summary

o Chapter 4 in EN1993-1-8: 2005 o Rules for connection of open sections

o Chapter 7 in EN1993-1-8: 2005 o Rules for connection of hollow sections

o New rules for high strength steels

o Size of welds o Weld design for full resistance


66

Weld design for full resistance Loading by normal by connecting member

Not directly in code σ = FSd / (t h) FSd is the acting design force fu is plate design strength t is the thinness of connecting plate b is width of connecting plate Full capacity of a plate the thickness for steel S235

Mwu /7,0

f

ta

ttt

f

tfa 5,047,0

25,1/360

)0,1/235(7,0

/

)/(7,0

Mwu

M0y

w

F

t

Sd

WE


h

t

VSd

Weld design for full resistance Loading by shear force by connecting member

= VSd / (t h) VSd is the design shear force in weld

For full capacity of a plate thickness S235

ttt

f

tf

f

ta

Mwu

My

Mww

3,033,025,1/360

)3 0,1/(23585,0

/

)3/(85,0

/85,0

0

WE


Weld Design or Full Resistance of Connecting Members Loading by normal force 0,5 t

Loading by shear force 0,3 t

Compare to AISC is less economical design

AISC – LRFD – matching with SMAW EN1993-1-8: 2005

fy (N/mm2)

fEXX (ksi – N/mm2)

a Steel grade fw.u.side

(N/mm2) a

235 60 – 414 70 – 483

0,37 t 0,33 t

S235 208 0,37 t

355 70 – 483 0,49 t S355 262 0,45 t

420 80 – 552 0,51 t S420 M S420 N

230 240

0,61 t 0,58 t

485 90 – 621 0,52 t S460 M S460 N

245 254

0,63 t 0,61 t








o Summary

Column bases o Basis of design o Components o Base plate and concrete in compression o Base plate in bending and bolt in tension o Anchor bolt in shear


o Classification oWorked examples o Summary


70

Column bases in chap. 6 of EN 1993-1-8: 2005

Unfortunately in 6 clauses

o Resistance in cl. 6.2.8, cl. 6.2.5(7)

o Stiffness in cl. 6.3.1(4)

o Classification in cl. 5.2.2.5

o Component concrete block in compression and base plate in bending in cl. 6.7(2)

o Component anchor bolt in tension and base plate in bendingin cl. 6.2.6.11(2)

o Component anchor bolt in shear cl. 6.2.2(6)


71

Component method cl. 6.2.8

Concrete block in compression

and base plate in bending

Column web in shear

Anchor bolts in shear

Anchor bolts in tension

and base plate in bending

Components

o Concrete block in compression and base plate in bending

o Anchor bolt in tension and base plate in bending

o Component anchor bolt in shear

o Column web and flange in compression


Background materials Wald F., Sokol Z., Steenhuis M. and Jaspart, J.P.,

Component Method for Steel Column Bases,

Heron. 2008, vol. 53, no. 1/2, 3-20, ISSN 0046-7316

Steenhuis M., Wald F., Sokol Z. and Stark J.W.B.,

Concrete in Compression and Base Plate in Bending,

Heron. 2008, vol. 53, no. 1/2, 51-68, ISSN 0046-7316.

Wald F., Sokol Z. and Jaspart J.P.,

Base Plate in Bending and Anchor Bolts in Tension,

Heron, 2008, vol. 53, no. 1/2, 21-50, ISSN 0046-7316.

Gresnight N., Romeijn A., Wald F., and Steenhuis M.,

Column Bases in Shear and Normal Force,

Heron, 2008, vol. 53, no. 1/2, 87-108, ISSN 0046-7316.

EN 1992-4 Eurocode 2:

Design of concrete structures — Part 4: Design of Fastenings for Use in Concrete








o Summary





74

Component Concrete in compression and base plate in bending

Design principles

• 3D behaviour od concrete D

• Design bearing strength of the joint fjd

• Flexible base plate on concrete block

• Effective rigid area under the flexible plate Aeff

• Deformation of concrete block

• Stiffness coefficient for concrete deformation under the flexible plate kc

c

fj

L

Column flange

Base plate

F

t

c tw

Sd FRd

Wald F., Sokol Z., Steenhuis M. and Jaspart, J.P., Component Method for Steel Column Bases, Heron 53 (2008) 3-20.


75

3D behaviour Concentrated force for at concrete resistance FRd,u

o Design bearing strength of joint cl. 6.2.5(7)

o Area of crushing of the concrete Ac0

o According to cl. 6.7(2) in EN 1992-1-1

Ac0 = b1 d1

Ac1 = b2 d2

h b2 – b1; h d2 – d1

3 b1 b2 a 3 d1 d2

cdc0

c0

c1cdc0uRd, fA

A

AfAF 0,3

Load axes

h


Load axes

h

Area

Area

Cursing of the concrete cl. 6.7(2) in EN 1992-1-1

Homogenous forces on area Ac0


77

Concrete design strength in joint

bj = 2/3 is joint coefficient Fcd is concrete compressive strength

cd

c0

cdc0

c0

c1cd

c0

c0

c1cdc0j

efef

Rduj

jd fA

fA

A

Af

A

A

AfA

lb

Ff 0,3

0,3 jb

bb

Load axes

h


Flexible base plate on concrete block

o Effective rigid plate

o Elastic deformation of plate only

Elastic bending moment of the base plate per unit length is

M′ =1

6 t2

fy

γM0

and the bending moment per unit length on the base plate of span c and loaded by distributed load is

M′ =1

2fj c

2

where fj is concrete bearing strength

c

f j

Column

Base plate

F

t

c t w

Sd F Rd

L

t


Effective width of flexible plate c

M0jd

y

f

ftc

3

Aeq

Ap A

c c

c

c

c

c

Aeq

Ap A

c c

c

c

c

c

Effective width

where

t is the plate thickness

fy is the base plate yield strength

fjd is the design bearing strength of the joint

M0 is the partial safety factor for concrete

Effective area


Stiffness

Deformation of an elastic hemisphere Stiffness coefficient Width of effective T stub ar in elastic stage

E

LaE

E

LaE

E

Fk

275,185,05,1

eleq,celeq,c

c

= a t, + ta steq,weleq, 52

M0jd

y

wwf

f t + c = t + = t

322

LaE

F

E

aF

c

r

rl

r

85,0

E Ip

x

cfl


Validation to experiments

0

200

400

600

800

1000

1200

1400

1600

1800

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 Deformation, mm

Force, kN

Concrete and grout

Concrete

Experiment

Prediction based on local and global deformation,

Prediction based on local deformation only

Calculated strength

L

F

d

t

t w


Influence of grout o Grout higher quality than concrete block

b1 = 2/3 1,0

o Grout lower quality than concrete block

o Model as plate on liquid

bj = 2 / 3

fc.g 0,2 f c

tg 0,2 min (a ; b)

tg 0,2 min (a ; b) h

t

tg

gt

45o

tg

g45o t

Lower nut

Packings








o Summary





Component Anchor bolts in tension and base plate in bending

eff

Column flange

Base plate

F

t

em

l

o Base plate compare to end plate

o Base plate is thicker

o Anchor bolt is longer

o In most cases no prying forces


Contact of edge of T stub on experiment


Question of contact

o End plate – contact or no contact

o Base plate – no contact

F

B

Rd.3

t.RdB

t.Rd

F

B

Rd.1

B

Q Q

e

n m

Q Q

B t.RdBt.Rd

FRd.2

Mode 3 Mode 1 Mode 2a) b) c)

nm

F

Q = 0 Q = 0

F1-2


Failure Mode 1-2

Bt.Rd is bolt tensile resistance

Mpl,Rd is base plate bending resistance of unique length

F B/ T,Rd

0,0

0,2

0,4

0,6

0,8

1,0

0 0,5 1 1,5 2

porušení 1

Failure mode 2Failure mode 3

Failure mode 1-2

Tvar

4 eff mpl,Rd / B T,Rdl


Free length of anchor bolt embedded in concrete

o Bolt effective free length Lbe = 8 d

o No prying force o For Q = 0 o Limiting bolt length

Lbf

L

d

be

L b

nm

F

Q = 0

p

b

b = p n

Q = 0

b3

eff

s

3

lim.b LtL

Am82,8L

Wald F., Sokol Z., Jaspart J.P., Base Plate in Bending and Anchor Bolts in Tension, Heron 53 (2008) 21-50.


Failure mode 1- 2

Design resistance in collapse 1 -2 where m is the lever arm of the anchor bolt Plastic moment resistance For the effective length ℓeff the yield line method may be used.

m

MF

Rdpl,1,Rd2,T,1

2

M0effRdpl,1, /25,0 2ftM l


Length of effective T stub Bolts inside the flanges

For bolts inside the section In case of prying

m42 l

emm 25,1421 l e m

m22 l

emm 25,1421 l


Length of effective T stub Bolts outside the flanges

Prying case No prying case

ℓ1 = 4 α mx + 1,25 ex ℓ1 = 4 α mx + 1.25 ex

ℓ2 = 2 π mx ℓ2 = 2 π mx

ℓ3 = 0.5 bp ℓ3 = 0.5 bp

ℓ4 = 0.5 w + 2 mx + 0.625 ex ℓ4 = 0.5 w + 2 mx + 0.625 ex

ℓ5 = e + 2 mx + 0.625 ex l5 = e + 2 mx + 0.625 ex

ℓ6 = π mx + 2 e ℓ6 = 2 π mx + 4 e

ℓ7 = π mx + w ℓ7 = 2 (π mx + w )

ℓeff,1 = min (ℓ1 ; ℓ2 ; ℓ3 ; ℓ4 ; ℓ5 ; ℓ6 ; ℓ7 ) ℓeff,1 = min (ℓ1 ; ℓ2 ; ℓ3 ; ℓ4 ; ℓ5 ; ℓ6 ; ℓ7 )

ℓeff,2 = min (ℓ1 ; ℓ2 ; ℓ3 ; ℓ4 ; ℓ5 ) ℓeff,2 = min (ℓ1 ; ℓ2 ; ℓ3 ; ℓ4 ; ℓ5 )

bp

mx

ex

e w e

a, 280

ll


Length of effective T stub for hollow sections

m

b

m

b

a

ac

bc

eaeb

m

mL .eff 1

2

bL 2.eff

22

22

38

cc

ba

ba

.eff bbaamee

eeL

22

22

2ba

ccee

bbaam

)L;L;L;L;L(minL 5.eff4.eff3.eff2.eff1.effeff

2

aL 4.eff

mL .eff 5

(a)

Wald F., Bouguin V., Sokol Z., Muzeau J.P., Component Method for Base Plate of RHS, Proceedings of the

Conference Connections in Steel Structures IV: Steel Connections in the New Millenium, Roanoke

2000, IV/8- IV/816.

Heinisuo M., Perttola H., Ronni H., Joints between circular tubes, Steel Construction, 5(2) (2012) 101-107.


93

Stiffness coefficients of component anchor bolts in tension and base plate in bending

For base plate of thickness t For bolt

3

3425,0

m

tk eff

p

l

b

sb

L

Ak 0,2


Model anchor bolts for resistence in CEB documents Eligehausen R., Mallée R., Silva J. F., Anchorage in Concrete Construction, Ernst and Sohn Verlag, Darmstadt, 2006, ISBN 978-433-01143-0

0

20

40

60

80

100

120

140

160

180

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6Deformation, mm

Force, kN

Experiment W13/98

Experiment W14/97

Prediction

50

10

40

40

315 365

6

5

9595

P10 - 95 x 95

P6 - 40 x 50 5

24 - 355

10

Comparison to experiments Stiffens and resistance of anchor bolt with header plate


Comparison to experiments

95

m = 32

W97-02

0

50

100

150

200

250

300

350

0 2 4 6 8

Force, kN

Deformation, mm

Simplified prediction

Complex calculation

m = 67

W97-12

0

50

100

150

200

250

300

350

0 2 4 6 8

Force, kN

Deformation, mm

Simplified prediction

Experiment

Complex calculation

Wald F., Sokol Z., Jaspart J.P.,

Base Plate in Bending and Anchor Bolts in Tension, Heron 53 (2008) 21-50.








o Summary





Components in Shear


98

In EN1993-1-8 cl. 6.2.2(6) - Anchor Bolt in Shear

Simplification by limiting of shear where fub is bolt design strength (in range 640 MPa fub 235 N/mm2) b = 0,44 – 0,0003 fyb Mb is safety factor for bolts

Fh

h

0

Fh

h

Shear and bending resistance

Reduced tensile resistance

Tensile resistance

Mb

subbRdvb,2,

AfF

Gresnigt N., Romeijn A., Wald F., Steenhuis M.,

Column Bases in Shear and Normal Force, Heron (2008) 87-108.








o Summary





NEd

MEd

Ft,pl,Rd

z

zt zc

Fc,pl,Rd

Affective area

Activated part

of affective area

Axis of compressed part

Neutral axis

100

Assembling of components for bending resistance

o Plastic design

o Force equilibrium

Rdl,t,rc,EdEd F

z

zN

z

M

RdR,C,T,1EdEd F

z

zN

z

M

Wald F., Sokol Z., Steenhuis M. and Jaspart J.P.,

Component Method for Steel Column Bases, Heron 53 (2008) 3-20.


M - N interaction diagram

M

NN0Ft.Rd

Compression

M

M , N2 2

M , N1 1

Tension

M=0

N=0








o Summary





103

Assembling of components for bending stiffness

From the component deformation stiffness for two cases • Bolts activated • Bolts not activated

NEd

MEd

NEd

MEd

t,lc,r

c,l c,r

zz

zt,l zc,r zc,l zc,r

Wald F., Sokol Z., Steenhuis M. and Jaspart, J.P.,



Stiffness Simplified contact area round the axes of compressed flange

cc

c

c c c

k

k

kp

kbc

t

k c k c

c

c

MSd / NSd = konst. xc <NSd / MSd <

i

2

SdSd

SdSd

j

k

1

zE

N/M

N/MS

tc

ttcc

kk

kzkz

1 52 7

,,

12

2

r

M N

M Nr

M N

Sd Sd

Rd Sd

Sd Sd

/

/

//

/


105

History of loading

o Influence to stiffness o No influence to resistance

Moment

Rotation

MRd

Sd

S j.ini

Plastification of one component

Anchor bolts in tension and one flange in compression

Nonlinear part of the curve

Non-proportional loading

Proportional loading

0 Normal force

Moment

Non-proportional

Proportional

resistance

e N0

0

Column base

loading

loading


Sensitivity study of base plate thickness

10

15

20

25

30Moment, kNm

Rotation, mrad

t =

0

20

40

60

80

100

120

0 5 10 15 20 25 30

t

HE 160 B

MRd

M 20 - 10.9

400 kN


Validation on experiment

Force, kN

Anchor bolt

E kb

Base plate

Deformation, , mm

Concrete

E k c

E kp

200

100

00,5

200

100

00,5

200

100

00,5

W7-4.20-prop

Experiment

Prediction

Moment, kNm

0

20

40

60

80

0 10

t = 20

HE 160 B

h = 500

NM

Rotation, mrad

Force, kN

Force, kN

Components Assembly

Wald F., Sokol Z., Jaspart J.P.,

Base Plate in Bending and Anchor Bolts in Tension, Heron 53 (2008) 21-50.


Validation on experiment

Proportional loading, bolt failure

Nonproportional loading, concrete failure

W7-4.20-prop

0

20

40

60

80

0 2 4 6 8 10 12

Moment, kNm

Model

Experiment

HE 160 B - 480

4 M 24 - 4.6 - 420 P 20 - 300 x 220

550 x 550 x 550 30 x 330 x 250

Rotation, mrad

0

10

20

30

40

50

60

70

80

0 500 1000

Normal force, kN

Moment, kNm

W7-4.20-prop

0

20

40

60

80

100

120

140

0 5 10 15 20 Rotationí, mrad

Moment, kNm

Model

Experiment

S220-190

HE 220 B - 900

2 M 20 - 10.9 - 320P 20 - 280 x 280

1200 x 600 x 600

30 x 250 x 250

0

20

40

60

80

100

120

140

160

0 500 1000 Normal force síla, kN

Moment, kNm S220-190








o Summary





Classification

According to stiffness Asked accuracy of design 5% in resistance 10% in serviceability Similar to beam-to-column joints

Wald F., Sokol Z., Steenhuis M. and Jaspart, J.P.,



0,6

0,7

0,8

0,9

1

0,0001 0,01 1,00 100,0 S_

S

j,ini,pinS

j,ini,stif

b =F

Fcr,res

cr.pin

t = 12 mm

a1 = b1 = 280 mm

a = b = 500 mm

h = 1000 mm

M 24 -420

S = 7 100 kNm / rad

t = 40 mm

a1 = b1 = 420 mm

a = b = 500 mm

h = 1000 mm

M 24 -420S = 74 800 kNm / rad

log

j,ini,stif

j,ini,pin

Non-sway frames by resistance


Sway frames for serviceability

115 kN

5 m

4 m

115 kN

HE 200 B

HE 200 B

5 kN

y / yP

y

S

1,0

0

0,2

0,4

0,6

0,8

0,0001 0,01 1 100log S

j,ini,pinS

S j,ini,stif


113

Classification based on stiffness Accuracy - 5% for resistance and 20% for serviceability

0

0,2

0,4

0,6

0,8

0 0,1 0,2 0,3

1,0

S j,ini,c,s

S j,ini,c,n = 30 E I / Lc

Pinned

Semirigid

Rigid

= 12 E I / L 36,1o =

Rotation,

M j / Mpl,Rd

c

c


114

Non-sway frames by resistance

For 0,5 Sj,ini 0 For 0,5 < < 3,93 Sj,ini 7 (2 - 1) E Ic / Lc and for 3,93 Sj,ini 48 E Ic / Lc where is relative stiffness for simple supported column at both ends For limited stiffness 12 E Ic / Lc For sway frames

ccinij, LIES / 30

o

o

o








o Summary





Worked example – Simple base plate

Base plate resistance?

o Column HE 200 B

o Concrete block 850 x 850 x 900 mm concrete C 12/15

o Base plate 18 mm, steel S 235

o c = 1,50, M0 = 1,00

4xP30-40x40RdF

t = 18

HE 200 B b = 850

b = 340

2

d = 850d = 34021

h = 900

30

1

WE


Concrete strength in joint

Under the base plate

MPaMPa cdjd 245,1/120,30,33,13 ff

340340

850850

11

22cd

c0

c1cdjd 5,1/12

3

2 =

d b

d b f

A

Aff jj bb

WE


Plate effective width

mm7,430014133

23518

M0j

y

,,f 3

f t =c

c c

c

c

cc

t = 15

t = 9h = 200 w

f

c

b = 200c

WE


Base plate compression resistance

Effective area under I cross section The base plate resistance

c c

c

c

cc

t = 15

t = 9h = 200 w

f

c

b = 200c

chacbbA 2;min2;min fceff

0;22max0;22;minmax fcfc cthctcbb

7,4322007,432200effA

2mm722667771559982

7,4321522007,43297,432200

N108873,1372266 3jdeffRd fAN

WE WE


120

Work example – rigid base plate

Bending resistance of base plate?

• Column HE 200 B loaded by FEd = 500 kN

• Concrete block C16/20 of 1 600 x 1 600 x 1000 mm

• Base plate 30 mm from steel S235

• c = 1,50; M0 = 1,00 and Mb = 1,25

r = 160

b = 1600

b = 420

t = 30

HE 200 B

2

1d = 420 d = 16002

MFEd Ed

b

30

h = 1000

M 24

e = 50

e = 90

p = 240

b

a

e = 60c

1

WE WE


Component Anchor bolt and plate in bending

Bolt resistance

for M 24; As = 253 mm2

mb

sub

Rdt,RdT,3,

9,022

AfBF

N100,18325,1

3533609,02 3

WE WE


Component anchor bolt and plate in bending Bolt distance for weld 6 mm

Length of effective T stub T stub resistance

mm2,53268,06028,060 wf am

2,81424022,53π22π2

2,6949042,5324π2

7,2125090625,02,532625,02

7,2822405,090625,02,5325,0625,02

2104205,05,0

6,6682,53π4π4

3,2755025,12,53425,14

min

b

ab

b

a

eff,1

pm

πem

eem

pem

b

m

em

l

N100,37000,1604

235302102

4

2 32

M0

y2

eff,1

Rd2,-T,1

m

ftLF

mm210eff,1 l

WE WE


Component Concrete block and plate in bending Concrete crushing resistance Force equilibrium Contact force for full bolt resistance

MPaMPa24,0 cd 325,1/160,30,3 f

420420

14201420

11

22cdj

c0

c1cdjjd 5,1/16

3

2 =

d b

d b f

A

Aff bb

RdT,jeffEd FfAF

2

d

Rd,3Edeff mm45828

0,24

100,18310500 33

jf

FFA

WE WE


Effective width of base plate

The effective width of the area in contact

M0jd

y

γ f

f= t c

3mm 54,2

0010243

23530

,,

mm4,1232,542152mm3,922,542200

45828

2f

c

effeff

ct

cb

Ab

c

c c

c

c

rt

rc

c

beff

c

cf= 15t

c= 200h

f= 15t

c = 200b

w= 9t

WE WE


Bending moment resistance for acting normal force

Lever arm Bending resistance

for normal force FEd = 500 kN

cjdeffbRdT,3,Rd rfArFM

mmeffcc 1,108

2

3,922,54

2

200

22

bc

hr

1,1080,2445828160100,183 3

kNmNmm 1,103101,103 6

WE WE


Bending stiffness

Stiffness coefficient o Anchor bolt

o Base plate

mm7,25,261

3530,20,2

b

sb

L

Ak

mm0162,53

30210425042503

3

3

3effb,

b ,,

m

tL,k

t f

t

= 15

a eq

b c = 15

WE WE


Bending stiffness

Stiffness coefficient

Lever arm in tension zt and in compression zc to column neutral axes For part in tension

mm8,1320090000210275,1

50027

275,1ceq

s

cc

ba

E

Ek

mmcc 16060

2

200

2t e

hr

mmcc 5,92

2

15

2

200

22f

thz

mm

pb

t 310,2

0,16

1

7,2

1

1

11

1

kk

k

WE WE


Bending stiffness

Lever arm Eccentricity Bending stiffness

mm5,2525,92160ct rrr

mm4,563,28,13

1603,25,928,13

tc

ttcc

kk

rkrka

mm2,20610500

101,1033

6

Ed

Rd

F

Me

78,13

1

31,2

11

5,252000210

4,562,206

2,206

1

22

i i

s

k

rE

ae

eS

inij,

radkNm79920radNmm79920,

WE WE


Classification

Bending stiffness for column HE 200 B of length Lc = 4,0 m the base plate is semi-rigid for braced frames and also for unbraced frames

96,61096,56000210

000410799,20

6

9

cs

cinij,inij,

IE

LSS

3,sECini,j,inij, 3096,6 SS

n3,ECini,j,inij, SS 1296,6

0

0,2

0,4

0,6

0,8

0 0,1 0,2 0,3

1,0

S j,ini,c,s

S j,ini,c,n = 30 E I / Lc

Pinned

Semirigid

Rigid

= 12 E I / L 36,1o =

Rotation,

M j / Mpl,Rd

c

c

WE WE


Base plate M-N interaction diagram

0

1 000

100 Moment, kNm

Normal force, kN

30

40

25

15

20

HE 200 B

t =

MN

RdRd

30

h =

M 24

1 600

340 630

630

340

1 600

pl.Rd

pl.RdN

M

t =

End column resistance

1 835

151,0

1 000

WE WE


Influence of contact in column web

Moment, kNm

Normal force, kN

Base plate thickness, mm

30

40

25

15

20

pl,Rd

pl,RdN

M

One bolt row activated

Both bolt rows activated

Model contact column web and flanges

Contact of flanges only

Column end resistance

WE WE








o Summary





Summary

o Component method o Good accuracy of prediction

o In EN 1993-1-8 in 6 closures

o Plastic distribution of forces for resistance o Concrete 3D strength o Effective rigid area under flexible base plate

o Questions for next edition o Embedded columns? o Column bases with base plate and anchor plate? o Advanced models?


RFCS project INFASO+

o Design Manual I o Design Manual II o Software toll

http://www.steelconstruct.com/site http://steel.fsv.cvut.cz/infaso

Component based model of column base with base plate and anchor plate

http://www.steelconstruct.com/site

http://www.steelconstruct.com/site

http://steel.fsv.cvut.cz/infaso


Component based FEM

oAdvanced design model based on FEM oComponents integrated FEM o Welds

o Bolts

o Compressed plates

Allows for column bases o Generally loaded by N and My, Mz o Irregular shape of base plate o Arbitrary positions of anchors o Opening in column web

True stress-strain

Experimental

Design

Material nonlinear design model of plate

Fan model of anchor bolt

http://www.idea-rs.com

http://www.idea-rs.com/




Thank you for your attention

František Wald Czech Technical University in Prague

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