lecture 2 by chiew sing ping for civil and structure

7/27/2019 Lecture 2 by Chiew Sing Ping FOR CIVIL AND STRUCTURE

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and Concrete Structures

Chiew Sing-Pingv v

Nanyang Technological University, Singapore

12 J uly 2013


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Scope of Presentation

M t ri l

Com osite columns

Composite beams Composite slabs

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Design Codes for Composite Structures

Effective 1 st April 2015: Till 31 st March 2015:

Eurocode 1- for loadings

BS 6399- for loadings

- - for concrete properties and some

of the concrete related checks- for construction stage, design of pure

beam(such as longitudinal shear)

Eurocode 3 (many Parts)BS 5950-6- for design of profiled steel sheeting

- ,pure steel beam and profiled steelsheeting

- .- for design of composite beamBS5950-4

Eurocode 4 Part 1-1- general rules of buildings - for design of composite slabBS 5400-5-

- for the structural fire design-BS 5950-8

- for structural fire desi n

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Design Safety Factors

Eurocodes British Standards

Load safet factors 1.35 G + 1.5 1.4 G + 1.6 BS5950 1.2 G k + 1.5 Q k (BS5400-5)

Material

Structural steel 1.0 1.0 (BS5950)

1.05 (BS5400-5)sa etyfactors

Concrete 1.5 1.5

Reinforcement 1.15 1.15

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Material Strength

Concrete and steel strengths in EC4 and BS5950

BS5950 EC4

ConcreteNormal C30 C50 C20/25 C60/75

Structural steel 355 N/mm 2 460 N/mm 2

Cube strength Cylinder strength / Cube strength

The ranges are narrower compared to EC2 (C12/15 C90/105) and EC32

composite members with very high concrete and steel strengths.

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Concrete Strength

One of the most noticeable differences in Eurocodes is the wayconcre e s reng s spec e roug ou .

the cube strength f cu is used.

,the cylinder strength f ck is used.

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BS

Cube strength2

Will differentstrength gives Converting from

the concrete

resistance ? strength toequivalent plastic

Cylinder strength

20 N/mm 2

. cu . .

= = 2

No difference!7


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Steel Strength

EC3 has additional ductility requirements compared toBS5950 in terms of stress ratio, elongation and strainratio.

Normal strength steel high strength steel

f u/f y 1.10

f u/f y 1.05 (EC3-1-12)

f /f 1.10 UK NA to EC3-1-12 less than 15%

Elongation at failure not less than

10%u y y

stain u 15 y

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ProblemSome product standards only have requirements on the nominal yieldand tensile strengths, or their minimum values. The stress ratio calculatedaccor ng to t ese nomna va ues cannot comp y w t t e uct tyrequirement.

Standard Grade omna y estrength (MPa) omna ens estrength (MPa) Stress ratio

AS 1397.

G550 550 550 1.00

AS 1595 CA 500 500 510 1.02

EN 10326 S550GD 550 560 1.02

ISO 4997 CH550 550 550 1.00

AS 1397: Steel sheet and strip hot-dip zinc-coated or aluminium/zinc-coatedAS 1595: Cold-rolled, unalloyed, steel sheet and strip

-ISO 4997: Cold-reduced carbon steel sheet of structural quality

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Profiled Steel Sheeting

Most types of profiled steel sheeting are manufactured from.

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Headed Stud Shear Connector

In BS 5950, the resistances of headed studs in solid slabare given for various combinations of height, diameter andconcrete strength but the physics behind these numbers are

not explained.

n , e res s ance s expresse n wo equa onsgoverned by the strength of concrete and steel.

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Characteristic Resistance Q k of Headed Studs inNormal Concrete (BS 5950-3.1 Table 5)

mens ons o ea e s u s ear connectors

arac er s c s reng oconcrete (f cu )

Nominal shank Nominal As-welded diameter

(mm)

height(mm)

height(mm)

N/mm 2 N/mm 2 N/mm 2 N/mm 2

25 100 95 146 154 161 168

22 100 95 119 126 132 13919 100 95 95 100 104 109

16 75 70 70 74 78 82

13 65 60 44 47 49 52

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Design Resistance of Headed Studs in Solidoncre e a

shown here as (1) and (2).

2u

Rd V

0.8 4 f d P

= (1)

2

ck cm0.29 d f E = = schV

.d

The two equations represent the 2 possible failure modes:i failure in the shank of headed stud and ii failure in concrete.

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steel failure

Failure in the headed stud

- concretecrushes

14Failure in concrete


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Comparison of Characteristic Resistances invar ous es gn o es

arac er s c res s ance o s ear s u , RkHeaded shear studs embedded Characteristic strength of concrete (N/mm 2)

n so concre e s a onormal weight concrete 25 30 35 40

: ar :

BS5950: Part 3.1: 2010 95 100 104 109EC4: Part 1.1: 2004 81.0 92.1 100.6 102.1

o es: omna s an ame er = mm

Nominal height = 100mm while as-welded height = 95mm

.

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Characteristic Resistance of Stud (EC4 and BS5950)

160

120

140BS (d=22mm, h=100mm)EC (d=22mm, h=100mm)

100 BS (d=19mm,h=100mm)EC (d=19mm, h=100mm)BS ( d=16mm, h=75mm) ( k

N )

60

EC (d=16mm, h=75mm) P

R k

40

0

Concrete strength (N/mm 2)

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In general, the resistance of headed stud shear connectorsdetermined by EC4 is lowe than BS5950.

more headed studs are needed in EC4 design !

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Design Resistance of Headed Studs inompos e a

The design resistance of headed stud connector in compositeslab with profiled steel sheeting is more complex than in a solidslab. It is influenced by the following factors:

The direction of the ribs relative to direction of span of thecom osite beam;

The mean breadth b0 and depth hp of profiled steel sheeting;

The diamete d and height h sc of the headed shea stud;

The numbe n of the headed studs in one trou h;

Whether or not a headed stud is central within a trough.

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Reduction Factor k

Design shear resistance is taken as the resistance in a solid slabt

b 0 b 0

s c c

h p

p /

2

h P

h

sc07.0 hb maxt,

p pr

t

hhn

- . . . -and 0.63 and 0.34 for open trough profiles

For the EC4 these values are about 17% lower than the BS for re-entrant profiles, but about 40% higher than the BS for open trough profiles.19


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Upper Limit k t,max for the Reduction Factor k tGenerally, most profiled sheet sheeting is designed such that their limitingvalue dominates , so the reduction factor is independent of the geometr

EC4 BS 5950-3.1

steelsheeting

connectors per

trough

of sheet

(mm)Stud not exceeding20mm in diameter and

welded through

Stud notexceeding19mm in

profiled steel sheeting diameter

- n r=11.0 0.85

1.0 trough

. .

n r=21.0>1.0

0.700.8 0.8

Opentrough

nr=1 .

>1.0

.

1.00.82

= 1.0 0.70> . .

For open trough profiles , the reduction factor in EC4 BS5950or re-en ran roug pro es , e re uc on ac or n

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Characteristic resistance of shear stud P kN

Headed shear studs incom osite slab with rofiled

Characteristic strength of concrete f cu(N/mm 2)

steel sheeting 25 30 35 40

BS5950: Part 3:2010

e-en ran

Open trough 77.9 82 85.3 89.4

EC4: Part 1.1: 2004 68.9 75.5 85.5 86.8

n =1

Notes: Nominal shank diameter = 19mmNominal height = 100mm while as-welded height = 95mm

The resistance of shear stud in composite slab determined in EC4 is upto 27% lower than that given in BS 5950.

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Top-Down Construction

piles installed during the foundation stage

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Installation of a kingpost into the barrette pile

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KingPost in column

bars

24Casting column head

C l i h


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Column Design ApproachCross section resistance (yielding)

Resistance to com ression Resistance to momentReduced moment resistance under com ressive force i.e. interaction between compression and bending

Member bucklin resistance Axial buckling resistance

interaction between compression and bending

LBAF cr

Types of elastic analysisand design

25 e

Si lifi d M h d (EC4 Cl 6 7 3 4)


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Simplified Method (EC4 Clause 6.7.3.4)

Desi n Conce ts

Design based on the

Axial(similar to pure steel column)

Design based on second-order

analysis with equivalent member e 0mper ec on s mp e me o

member incombined Design based on second orderanalysis with equivalent membe

and bending Imperfection (simplified method)e 0

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A i l C i R i


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Axial Compression Resistance

Compression resistance of composite column

A A A N ++= ssccya p ,

= + +

steel concrete reinforcement

yk a ck c/ f sk s/ f

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A i l B kli R i t


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Axial Buckling Resistance

N .

Rd pl, N

The buckling reduction factorEC3 a roach Plastic resistance

0.1

12 =

a1.0

x Euler buckling-+

( ) 22.0-15.0 ++= c

Rk pl, N = 0.0 1.0 2.0cr

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Bucklin Curve - EC3

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B kli C EC4


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Buckling Curve EC4

Cross-section Limits Axis of Buckling curveuc ng S235 - S460

Concrete encased sectiony-y b

z-z c

Partially concrete encased y-y b

z-z c

Concrete filled circular and s 3% any a

s

For steel column, the buckling curve is related to steel section and steelstrength.

For composite column, the buckling curve is related to the cross-section..

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Example Comparison of Design Approach


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Example - Comparison of Design Approach

Design based on Design based on seconduc ng

curve

equivalent member

imperfection

Ed

Buckling curve bMember L/200 e

Resistance of

axial N = 4320 kN N = 4108 kNcompression

Comparison 1.05Rd(X) Rd(e0) Ed

Note: design based on the use of member imperfection e 0 leads to

the EC3 buckling curve approach.Design data:

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f y=355N/mm 2, f ck =25N/mm 2, f sk =500N/mm 2,Cross-section: 350mm 350mm, steel section: 254 254 UC73.Column length: 5.0m, 4 bars of 20mm diameter

Example Comparison of Design Approach


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Example - Comparison of Design Approach

Design based on the EC3 Design based on second order analysisbuckling curve approach with equivalent member imperfection

approachRd N Rd e N

Rd( ) pl,Rd = N N N0Ed,max Rd(e ) 0= k N e

The maximum resistance can be0.1

-

122

+

=

Npl,RdEd,max M pl,Rd M

( ) 22.0-15.0 ++= 0Rd(e ) 0 M pl,Rd =kN e M Rd(e0)

Npm,Rd

cr

Rk pl,

N N =

0 pl,Rd Rd (e )

pl,Rd pm,Rd

-= -

N N

N N M

Second order effect factor k:2

ef,II( )

=

EI

Mpl,Rd Mpl,Rd

1=k Easier approach !

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cr,e 2cr L0Rd(e ) cr,eff -

Resistance of Members in combined


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ompress on an en ng The EC3 bucklin curve a roach can be ado ted focomposite column under axial compression, however, thisapproach is not suitable fo composite column subjected to

axial compression and bending moment.

In design of slender RC column, an accidental eccentricity of

the axial load in the column is introduced to calculate themaximum moment at mid-height of the column.

Simila to slende RC column, equivalent initial bowimperfections (member imperfections) are used in the design of compos e co umn o s mp ca on.

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Bending Moment due to Member Imperfection


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Bending Moment due to Member Imperfection

NEd 0

design axial load NEd on a composite column,.

The design bending moment for the compositee 0 co umn engt cons ere ot secon -or e

effects of end moment and imperfection is given

0Ed 2Ed 1Ed.max e N k M k M +=

NEd k1, k 2 are the factors of second order effects

Ed cr,eff

=1- /

k N N

re a e o en momen ra o

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Member Imperfections for Composite Column


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p p

Cross-sectionAxis of

bucklingBuckling

curveMember

imperfection (e )Concrete encased section y-y b L/200

-y

Partially concrete encasedSection

y-y b L/200z

z-z c L/150

Circular and rectangular y-y a L/300

z

o ow sec onz-z b L/200

Circular hollow section with

zy

additional I-section

-

z-z b L/200zy

Partially encased H sectionwith crossed H section

any b L/200y

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Improvement in the Design of Column in


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p gom ne ompress on an en ng

Compared to EC4 (1994), the simplified method for

second order analysis and equivalent member (initial bow)im erfection which takes into account the effects of residualstresses and geometrical imperfections.

method for composite columns, the scope of the simplified.

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Ed M 1 Edk M


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Ed 1 Ed pl,Rd

The influence of imperfection is takeninto account indirectly in the interaction

. d relevant amount to account for themoment due to the member

(a) EC4: 1994 imperfection.

Ed, max M 1 Ed 2 Ed 0k M k N e+d pl,Rd

The member im erfection can be takeninto account in the global analysis andhence it is not necessary to allow for

37e mper ec on n e ana ys s o e

interaction curve.(b) EC4: 2004

Design of Composite Beam


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Design of Composite Beam

Nc,f

p

The concrete slab works best in com ression while the steel section

,

works best in tension; hence, a large moment resistance is generatedas a force couple.

Resistance mobilization in both the concrete slab and the steel sectionis limited b the shear connection alon the concrete interface.

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Failure Modes of Composite Beam


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p

IV

IV

I-I resistance to sagging moment and vertical shearII-II resistance to hogging moment and shear and M-V interactionIII-III shear connection @ the steel concrete interfaceIV-IV lateral torsional buckling

- ong u na s ear o e concre e ange

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Lateral Torsional Buckling Resistance


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g

In BS5950-3.1, no equation is provided to calculate thelateral torsional buckling resistance of continuous compositebeam under hogging moment over the internal support.

When checking LTB, the methods given in BS5950-1.

,with steel beam in EC3.

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BS5950-3.1 EC4


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b b x p S =

Rd LTRd b, =1=

Where pb is determined by TB With:

2

LT LT LT + TB t t

0.5

LTcr M

=( ) ( )

st 2 2

s

4 /=

1+ 2 / +0.05 /

a hv

a h x ( ) ( )2 2cr c 4 a at s a afz/ / M k C L G I k L E I = + (EC4)

0.522

cr 1 2 2+w cr T z

cr z z

M C L I EI

=

(EC3)

EC4 EC3 BS5950-3.1 EC4 /BSRatioEC4/EC3

Ratio

41a era - ors ona

buckling 546 kNm 531 kNm 479 kNm 1.14 1.03

Elastic Critical Moment


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Inverted- U frame ABCD resisting lateral-torsional buckling

, cr so-called continuous inverted U-frame model.

The model iven in EC4 takes into account the lateral dis lacement of thebottom flange causing bending of the steel web and the rotation of the topflange that is resisted by bending of the concrete slab.

( ) ( )1/2

2 2cr c 4 a at s a afz/ / M k C L G I k L E I = +

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Composite Slab


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p

TrapezoidalOpen Trough (Trapezoidal)

Re-entrant

Possible modes of failure:

Moment failure near mid-span regionDebonding within longitudinal shear span along the interface between

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concrete slab and decking, i.e. shear bond ailure critical

Longitudinal Shear


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g

How reliable is the shear bond alon the interface between

concrete and profiled sheeting ?

- non ductile failure, hence not so reliable.

Mechanical interlocking due to indentations or

- ductile failure with rational provision, hence morereliable.

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Longitudinal Shear


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End slip

es se up

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m-k Method


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BS5950-4:

p pbd mAV k = +

r ps ss r cu

m A B d V k f

= + Concretestren th,vs s

bL

s v.

m= 163.26

m= 172.45k= 0.2491

k= 0.0312

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Comparison of Longitudinal Shear


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EC4 BS5950-4Short span Long span Short span Long span

. .

k 0.2491 0.0312

-resistance

V (kN)

79.3 60.1 74.3 56.2

,

Test Short span 81.2 kN Long span 61.6 kN

BS5950 provides a more conservative value for longitudinal shear resistance

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Vertical Shear


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BS 5950-4 EC4

1/3

v,Rd Rd,c 1 ck 1 pc w p

v Rd min min 1 c wV v k b d = +

v b s c

1/3 1/31/4s cu1000.79 400=

A f c

m v 25b d d 3/ 2 1/2min ck 0.035v k f =

BS 5950-4 EC4 Experiment

153.6 kN107.8 kN118.7kN

EC4 provides a more conservative value for vertical shear resistance

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Punching Shear


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BS 5950-4 EC4

( ) p s p cCritical perimeter -V D D v= p,Rd p p Rd V C d v=1/3

1/31/4s cu

c1000.79 400=

25 A f v

b d d 3/ 2 1/20.035v k =

Rd Rd,c 1 ck min100v C k f v = m n c

( ) ( ) p c p f p f p c2 2 2 2 2 2 2C h b h a h d h = + + + + + ( ) ( )s p sCritical perimeter = 4 - +4 +4 length of load area D D d

BS 5950-4 EC4 Experiment

186 kN139 kN108kN

-

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Conclusions


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1. Composite members with high strength steel and concreteou s e e scope o .2. Common grades of profiled steel sheeting cannot meet

,downgraded.

.generally lower in EC4 compared to BS5950; Important to

.4. For composite columns, the EC4 buckling curves are

.

However, unlike EC3, no special consideration for

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Conclusions


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5. The simplified design approach using second orderanalysis and equivalent membe imperfection without anyneed for member buckling resistance check is mucheas e o compos e co umn n com ne compress onand bending moment.

. prov es gu ance o a era - ors ona uc ng c ecfor continuous composite beams taking into account the

.7. EC4 also provides clear guidance for prototype testing

profiled steel sheeting.

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lecture 2 by chiew sing ping for civil and structure

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