Design of Composite Members and Joints.pdf

European Erasmus Mundus Master Course

Sustainable Constructions

under Natural Hazards and Catastrophic Events 520121-1-2011-1-CZ-ERA MUNDUS-EMMC

Conceptual Design of Buildings (Course unit code 1C2)

Module D

Design of Composite Members and Joints

Rui Simes (University of Coimbra)

F. Dinu (University Politehnica Timisoara)

L28 Composite columns. Resistance of cross-sections.

European Erasmus Mundus

Master Course


under Natural Hazards

and Catastrophic Events

Conceptual Design

of Buildings

List of contents

Introduction

Resistance of

cross sections

Examples

In the scope of EC4-1-1, a composite column may be defined as a composite

member subjected mainly to compression or to compression + bending.

Clause 6.7 of EC4-1-1 includes design rules for concrete encased sections,

partially encased sections and concrete filled rectangular and circular tubes.

Composite columns configurations

This clause applies to columns and compression members (isolated or in framed

structures) with steel grades S235 to S460 and normal weight concrete of

strength classes C20/25 to C50/60; additionally, the steel contribution ratio

should fulfil the following condition: Rdplyda NfA , 9.02.0

Module D Design of Composite Members and Joints

2

Composite column (clause 6.7 of EC4-1-1)



Master Course




Conceptual Design

of Buildings

The main advantages of a composite column are:

- increasing of strength and stiffness due to decreasing of slenderness;

- increasing fire resistance;

- increasing corrosion protection.

A composite column should be checked for:

- resistance of the member in accordance with 6.7.2 (cross section resistance)

or 6.7.3 (buckling resistance);

- resistance to local buckling (taken into account in the cross section

classification);

- introduction of loads in accordance with clause 6.7.4.2 of EC4-1-1;

- resistance to shear between steel and concrete elements in accordance with

6.7.4.3 of EC4-1-1.

EC4-1-1 provides two methods of member design:

- a general method in clause 6.7.2 which allow the design of members with

non-symmetrical cross sections and non-uniform members;

- a simplified method in clause 6.7.3 applicable to the design of members

with cross section doubly symmetric and uniform along the member length.

List of contents

Introduction

Resistance of

cross sections

Examples


3



Master Course




Conceptual Design

of Buildings

The effects of local buckling may be neglected:

- in a steel section fully encased, with concrete cover to a

flange not less than 40 mm, nor less than one-sixth of the

width b of the flange;

- and in other types of cross-section provided the following

maximum values are not exceeded:

cycy b

t

d

290/td

t d

b

52/td 44/ ftbtf

b

yf/235 being fy the characteristic tensile strength of steel.

List of contents

Introduction

Resistance of

cross sections

Examples


4



Master Course




Conceptual Design

of Buildings

Simplified method may be used in the following conditions:

0.2

hcz 3.0 bcy 4.0

List of contents

Introduction

Resistance of

cross sections

Examples


5

Members with cross section doubly symmetric and uniform along the member

length, using rolled, cold-formed or welded steel sections;

The relative slenderness should fulfill the condition: ;

For a fully encased steel section, limits to the maximum thickness of concrete

cover that may be used in calculation are: and ;

The longitudinal reinforcement that may

be used in calculations should not exceed

6% of the concrete area (and should be

not less than 0.3% of concrete area);

The ratio of the depth to the width (hc/bc) of the composite cross-section should be

within the limits 0.2 and 5.0.



Master Course




Conceptual Design

of Buildings

s

sks

c

ckc

Ma

y

aRdpl

fA

fA

fAN 85.0.

Steel

section Concrete

section Reinforcement rebars

The plastic resistance to compression Npl,Rd of a composite cross-section

should be calculated by adding the plastic resistances of its components:

For concrete filled sections the coefficient 0.85 in the concrete contribution

may be replaced by 1.0; for concrete filled tubes of circular cross-section,

this coefficient may be further increased, in accordance with clause

6.7.3.2(6) of EC4-1-1.

List of contents

Introduction

Resistance of

cross sections

Examples


6



Master Course




Conceptual Design

of Buildings

List of contents

Introduction

Resistance of

cross sections

Examples

The plastic resistance to bending + compression of a composite

cross-section should be based in a plastic interaction curve (analytical

expressions are not available) which may be calculated assuming

rectangular stress blocks.

For practical applications, the

interaction curve may be simplified to

a polygonal line, defined by four

points:

A (0 ; Npl,Rd)

B (Mpl,Rd; 0)

C (Mpl,Rd; Npm,Rd)

D (Mmax,Rd; 1/2Npm,Rd)


7



Master Course




Conceptual Design

of Buildings

List of contents

Introduction

Resistance of

cross sections

Examples

0 M

N

A Npl.Rd

0.85fck/ c

Npl.Rd

Concrete Steel Reinf.

fy/ Ma fsk/ s

Point A: Axial compression

Determination of the polygonal line:


8



Master Course




Conceptual Design

of Buildings

List of contents

Introduction

Resistance of

cross sections

Examples

0.85fck/ c


fy/ Ma fsk/ s

+

+

+

2hn

Mpl.Rd

0 M

N

Npl.Rd

Mpl.Rd

A

B

Point B: Simple bending


9



Master Course




Conceptual Design

of Buildings

List of contents

Introduction

Resistance of

cross sections

Examples

0

Npl.Rd

Mpl.Rd M

N

A

C

B

Npm.Rd

0.85fck/ c


fy/ Ma fsk/ s

+ +

2hn Npm.Rd

Mpl.Rd

Point C: Bending +

compression

cdcRdpm fAN ,


10



Master Course




Conceptual Design

of Buildings

List of contents

Introduction

Resistance of

cross sections

Examples

Deduction

cdcRdpm fAN ,


11

0.85fck/ c


2 fy/ Ma 2 fsk/ s

2hn Npm.Rd

cdcRdpm fAN ,

Allow the determination of

hn plastic neutral axis

needed for plastic bending

moment calculation.

22, 2 acRdpm RRN (1)

31 aa RR 31 cc RRBased on symmetry, (2)

For p.n.a in BB, N = 0, and

and

3211 aaca RRRR (3)

312 cca RRRFrom eq. (2) and (3), comes:

cdcccccRdpm fARRRRN 312,Replacing in eq. (1), comes:



Master Course




Conceptual Design

of Buildings

List of contents

Introduction

Resistance of

cross sections

Examples

0.85fck/ c

Mmax.Rd


fy/ Ma fsk/ s

+

+

Npm.Rd/2

Npm.Rd

A

B

0

Npl.Rd

Mpl.Rd M

N

C

Simplified interaction

curve N-M

Mmax.Rd

D 0.5 Npm.Rd

Point D: Maximum resistant

moment


12



Master Course




Conceptual Design

of Buildings

List of contents

Introduction

Resistance of

cross sections

Examples

0

Npl.Rd

Mpl.Rd Mmax.Rd M

N

A

C

D

B

Npm.Rd

0.5Npm.Rd

0.85fck/ c

Mpl.Rd/2


fy/ Ma fsk/ s

+ +

N

Interaction curve N-M

with a 5th point

Point E: 50% of

plastic bending

moment

E

0.5 Mpl.Rd

The interaction curve

defined by five points may

be useful for cases of high

axial force and/or interaction

with minor axis bending.


13



Master Course




Conceptual Design

of Buildings

List of contents

Introduction

Resistance of

cross sections

Examples


14

The plastic bending moment in a double composite cross section may be

determined based on the stress blocks, knowing p.n.a. position or directly

using the following formula:

cdnpcpcsdnpspsydnpapaRdpl fWWfWWfWWM 85.02

1,,,,

Wpa plastic bending modulus of total structural steel in relation to centroid axis;

Wps plastic bending modulus of total reinforcement in relation to centroid axis;

Wpc plastic bending modulus of total concrete (un-cracked) in relation to centroid axis;

Wpa,n plastic bending modulus of structural steel within region 2hn;

Wps,n plastic bending modulus of reinforcement within region 2hn;

Wpc,n plastic bending modulus of total concrete (un-cracked) within region 2hn;

fyd design strength of structural steel;

fsd design strength of reinforcement;

fcd design compressive strength of concrete.

cdpcsdpsydpaRd fWfWfWM 85.02

1max,

The maximum bending moment Mmax,Rd (point D) may be obtained by:



Master Course




Conceptual Design

of Buildings

List of contents

Introduction

Resistance of

cross sections

Examples

Rdpl,

Rda,pl,

EdEda,M

MVV

Eda,EdEdc, VVV

Unless a more accurate analysis is used, the design shear force VEd may

be distributed into two parcels: Va,Ed acting on the structural steel and Vc,Ed

acting on the reinforced concrete section, calculated by:

where: Mpl,a,Rd is the plastic bending moment of the steel section and Mpl,Rd is the

plastic bending moment of the composite section.

The shear force Va,Ed should not exceed the resistance to shear of the steel

section determined according to 6.2.2. The resistance to shear Vc,Ed of the

reinforced concrete part should be verified in accordance with EN 1992-1-1,

clause 6.2.

As a simplification (usually adopted in current composite structures) VEd

may be assumed to be resisted by the structural steel section only.


15



Master Course




Conceptual Design

of Buildings

List of contents

Introduction

Resistance of

cross sections

Examples

Where Va,Ed > 0,5Vpl,a,Rd, the influence of the transverse shear on the

resistance to combined bending and compression should be taken into

account by reducing the design steel strength to (1 - ) fyd along the shear

area Av, in accordance with clause 6.2.2.4(2) of EC4-1-1.


16



Master Course




Conceptual Design

of Buildings

17

EXAMPLE 1


Consider the following cross section of a composite column constituted by a

section HEA 180 in steel S235 (fy = 235 MPa; E = 210 GPa) full encased in

concrete C30/37 (fck = 30 MPa; Ecm = 32 GPa) with 8 rebars 20 mm

(fsk = 500 MPa; E = 210 GPa). Determine the simplified interaction curve for

evaluation the cross section resistance under N+My.

List of contents

Introduction

Resistance of

cross sections

Examples



Master Course




Conceptual Design

of Buildings

18

EXAMPLE 1


Verification of the application conditions of the simplified method of EC4-1-1:

mmbb

c cy 702

180320

2

i) Concrete cover

mmbmmcmm y 7218040.040.07040 mmbc 320

mmhh

c cz 5.742

171320

2

mmhmmcmm z 3.5117130.030.05.7440

mmhc 27417117130.02

OK

Not OK

ii) Percentage of reinforcement

%1.3031.080640

2512

c

s

A

A

2

180 806402512453087680274320 mmAAA sHEAc

2

180 4530mmAHEA2251215.3148 mmAs

%6%1.3%3.0 OK

List of contents

Introduction

Resistance of

cross sections

Examples



Master Course




Conceptual Design

of Buildings

19

EXAMPLE 1


Determination of the cross section resistance:

90.020.0,Rdpl

aya

N

fA

iii) Steel contribution ratio

(To be verified later)

i) Plastic resistance to compression Npl,Rd

kN

fA

fA

fAN

s

sks

c

ckc

a

y

aRdpl

352815.1

10500102512

50.1

103085.01080640

00.1

10235104530

85.0

36

36

36

,

90.030.03528

00.11023510453020.0

36

OK

ii) Plastic bending moment Mpl,Rd

Position of the p.n.a. - hn

kNf

ANc

ckcRdpm 1371

50.1

103085.01080640

85.0 36,

List of contents

Introduction

Resistance of

cross sections

Examples



Master Course




Conceptual Design

of Buildings

20

EXAMPLE 1


mmhh

hhkNN

nn

nnRdpm

20.511020.51106.314215.1

1050022106

00.1

102352

50.1

103085.02106106.31421032021371

363

33

3363

,

hn = 51.20 mm < h/2 - tf = 171/2 - 9.5 = 76 mm, so p.n.a is localized on the web.

cdnpcpcsdnpspsydnpapaRdpl fWWfWWfWWM 85.02

1,,,,

0.85fck/ c


2 fy/ Ma 2 fsk/ s

2hn Npm.Rd

List of contents

Introduction

Resistance of

cross sections

Examples



Master Course




Conceptual Design

of Buildings

21

EXAMPLE 1


kNm

M Rdpl

21050.1

103085.010102.823105455

2

1

15.1

1050010010226

00.1

1023510107.1510325

3933

393

3933

,

33222

, 107.152.5164

2mmht

htW nw

nwnpa

0,npsW

3332

,

2

,

2

, 102.823107.152.513204

2mmWhbW

hbW npannpa

nnpc

iii) Maximum bending moment Mmax,Rd

kNmM Rd 22850.1

103085.010105455

2

1

15.1

105001010226

00.1

102351010325

393

393

393

max,

332

, 1060064

274320mmW totalp

)(10325 33 profilesoftablemmWpa

33

20 10226402

32016.3143240

232 mm

hAW cps

33333 1054551022610325106006 mmWpc

List of contents

Introduction

Resistance of

cross sections

Examples



Master Course




Conceptual Design

of Buildings

22

EXAMPLE 1


iv) Interaction curve N + My

1371

A

B

0

3528

210 M (kNm)

N (kN)

C

Simplified interaction

curve N-My

228

D 685.5

A (0 ; 3528)

B (210; 0)

C (210; 1371)

D (228; 685.5)

List of contents

Introduction

Resistance of

cross sections

Examples



Master Course




Conceptual Design

of Buildings

23

EXAMPLE 2

Consider the following cross section of a composite column.

a) Verify the application conditions of the simplified method of EC4-1-1;

b) Determine the simplified interaction curve for evaluation the cross section

resistance under N+My.


A (0 ; 6275.8)

B (680.9; 0)

C (680.9; 824.3)

D (685.2; 412.2)

S275 fyd = 275 MPa E = 210 GPa

C25/30 fcd = 16.7 MPa E = 31 GPa

A500 fsd = 434.8 MPa E = 210 GPa

List of contents

Introduction

Resistance of

cross sections

Examples

This lecture was prepared for the Edition 1 of SUSCOS

(2012/14) by RUI SIMES (UC) and FLOREA DINU (UPT).

The SUSCOS powerpoints are covered by copyright and are for the exclusive use by the

SUSCOS teachers in the framework of this Erasmus Mundus Master. They may be improved

by the various teachers throughout the different editions.

Thank you

for your attention

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

Design of Composite Members and Joints.pdf

Documents

Transcript of Design of Composite Members and Joints.pdf