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Design of Composite Steel-Concrete
Structures to Eurocode 4
- Some Basic Concepts
Chiew Sing-Ping
School of Civil and Environmental Engineering
Nanyang Technological University, SINGAPORE
10 April 2015
2
Scope of Presentation
Design codes
Materials
Composite columns
Composite beams
Composite slabs
3
Design Codes for Composite Structures
Eurocode 1
- for loadings
Eurocode 2
- for concrete properties and some
of the concrete related checks
(such as longitudinal shear)
Eurocode 3 (many Parts)
- for construction stage, design of
pure steel beam and profiled steel
sheeting
Eurocode 4 Part 1-1
- general rules of buildings
Eurocode 4 Part 1-2
- for the structural fire design
Effective 1 April 2015
BS 6399
- for loadings
BS 5950-1
- for construction stage, design of pure
beam
BS 5950-6
- for design of profiled steel sheeting
BS5950-3.1
- for design of composite beam
BS5950-4
- for design of composite slab
BS 5400-5
- for design of composite column
BS 5950-8
- for structural fire design
Superceded (valid till 31 March 2015)
4
Design Safety Factors
Eurocodes British Standards
Load safety factors 1.35 Gk + 1.5 Qk 1.4 Gk + 1.6 Qk (BS5950)
1.2 Gk + 1.5 Qk (BS5400-5)
Material
safety
factors
Structural steel 1.0 1.0 (BS5950)
1.05 (BS5400-5)
Concrete 1.5 1.5
Reinforcement 1.15 1.15
5
BS5950 EC4
Concrete Normal C30 – C50 C20/25 – C60/75
Light weight C25 – C40 LC20/22 – LC60/66
Structural steel ≤ 355 N/mm2 ≤ 460 N/mm2
Concrete and steel strengths in EC4 and BS5950
Cube strength Cylinder strength / Cube strength
Material Strength
The ranges are narrower compared to EC2 (C12/15 – C90/105) and EC3
(≤ 690 N/mm2) because of more limited knowledge and experience in
composite members with very high concrete and steel strengths.
Concrete Strength
6
One of the most noticeable differences in Eurocodes is the way
concrete strength is specified throughout.
In British Standards,
the cube strength fcu is used.
In Eurocodes,
the cylinder strength fck is used.
7
Will different
strength gives
different
resistance ?
BS
Cube strength
25 N/mm2
EC
Cylinder strength
20 N/mm2
Converting from
the concrete
strength to
equivalent plastic
stress block
BS: 0.45 fcu = 0.45×25 = 11.25 N/mm2
EC: 0.85 fck/γc= 0.85×20/1.5 = 11.33 N/mm2
No difference!
8
EC3 has additional ductility requirements compared to
BS5950 in terms of stress ratio, % elongation and strain
ratio.
Steel Strength
Normal strength steel
• fu/fy ≥ 1.10
• Elongation at failure not
less than 15%
• εu ≥ 15εy εy is the yield
stain
high strength steel
• fu/fy ≥ 1.05 (EC3-1-12)
• fu/fy ≥ 1.10 ( UK NA to EC3-1-12)
• Elongation at failure not less
than 10%
• εu ≥ 15 εy
9
Problem Some product standards only have requirements on the nominal yield
and tensile strengths, or their minimum values. The stress ratio calculated
according to these nominal values cannot comply with the EC3 ductility
requirement. Also, % elongation cannot comply. Refer to BC1 for
guidance on minimal requirements and compliance under SS NA.
Standard Grade Nominal yield
strength (MPa)
Nominal tensile
strength (MPa) Stress ratio
AS 1397 G500 500 520 1.04
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-coated
AS 1595: Cold-rolled, unalloyed, steel sheet and strip
EN 10326: Continuously hot-dip coated strip and sheet of structural steels
ISO 4997: Cold-reduced carbon steel sheet of structural quality
10
Profiled Steel Sheeting
Most types of profiled steel sheeting are manufactured from
G500/G550 steel in accordance with AS1397.
11
Headed Stud Shear Connector
In BS 5950, the resistances of headed studs in solid slab
are given for various combinations of height, diameter and
concrete strength but the physics behind these numbers are
not explained.
In EC4, the resistance is expressed in two equations
governed by the strength of concrete and steel.
12
Dimensions of headed stud shear
connectors
Characteristic strength of
concrete (fcu)
Nominal shank
diameter
(mm)
Nominal
height
(mm)
As-welded
height
(mm)
25
N/mm2
30
N/mm2
35
N/mm2
≥ 40
N/mm2
25 100 95 146 154 161 168
22 100 95 119 126 132 139
19 100 95 95 100 104 109
19 75 70 82 87 91 96
16 75 70 70 74 78 82
13 65 60 44 47 49 52
Characteristic Resistance Qk of Headed Studs in
Normal Concrete (BS 5950-3.1 Table 5)
13
2
uRd
V
0.8 4f dP
2
ck cm
Rd
V
0.29 d f EP
Design Resistance of Headed Studs in Solid
Concrete Slab (EC4)
EC4 calculates the resistance as the minimum of two equations,
shown here as (1) and (2).
12.0 sc
d
h
The two equations represent the 2 possible failure modes:
(1)
(2)
(i) failure in the shank of headed stud and (ii) failure in concrete.
14
Push-out Test Specimen
Failure in the headed stud
Failure in concrete
concrete
crushes
steel failure
15
Characteristic resistance of shear stud, PRk (kN)
Headed shear studs embedded
in solid concrete slab of
normal weight concrete
Characteristic strength of concrete (N/mm2)
25 30 35 40
BS5400: Part 5: 2005 90 100 104 109
BS5950: Part 3.1: 2010 95 100 104 109
EC4: Part 1.1: 2004 81.0 92.1 100.6 102.1
Comparison of Characteristic Resistances in
various Design Codes
Notes: Nominal shank diameter = 19mm
Nominal height = 100mm while as-welded height = 95mm
EC4 leads to a 17% reduction of the characteristic resistance.
16
Characteristic Resistance of Stud (EC4 and BS5950)
0
20
40
60
80
100
120
140
160
25 30 35 40 45 50
BS (d=22mm, h=100mm)
EC (d=22mm, h=100mm)
BS (d=19mm,h=100mm)
EC (d=19mm, h=100mm)
BS ( d=16mm, h=75mm)
EC (d=16mm, h=75mm)
PR
k (
kN
)
Concrete strength (N/mm2)
Note: the differences are larger for smaller stud diameters
17
In general, the resistance of headed stud shear connectors
determined by EC4 is lower than BS5950.
more headed studs are needed in EC4 design !
18
Design Resistance of Headed Studs in
Composite Slab
The design resistance of headed stud connector in composite
slab with profiled steel sheeting is more complex than in a solid
slab. It is influenced by the following factors:
The direction of the ribs relative to direction of span of the
composite beam;
The mean breadth b0 and depth hp of profiled steel sheeting;
The diameter d and height hsc of the headed shear stud;
The number nr of the headed studs in one trough;
Whether or not a headed stud is central within a trough.
Reduction Factor kt
Design shear resistance is taken as the resistance in a solid slab
multiplied by the reduction factor kt
b0
hsc
hp
hp/2
b0
hP hsc
maxt,
p
sc
p
0
r
t 17.0
kh
h
h
b
nk
EC4:
BS5950-3.1: The coefficient is 0.85 and 0.6 for re-entrant trough profiles
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
Upper Limit kt,max for the Reduction Factor kt
profiled
steel
sheeting
Number of stud
connectors per
trough
Thickness t
of sheet
(mm)
EC4 BS 5950-3.1
Stud not exceeding
20mm in diameter and
welded through
profiled steel sheeting
Stud not
exceeding
19mm in
diameter
Re-entrant
trough
nr=1 ≤1.0
>1.0
0.85
1.0 1.0
nr=2 ≤1.0
>1.0
0.70
0.8 0.8
Open
trough
nr=1 ≤1.0
>1.0
0.85
1.0 0.82
nr=2 ≤1.0
>1.0
0.70
0.8 0.45
For open trough profiles, the reduction factor in EC4 ≥ BS5950
For re-entrant trough profiles, the reduction factor in EC4 ≤ BS5950
Generally, most profiled sheet sheeting is designed such that their limiting
value dominates, so the reduction factor is independent of the geometry
20
21
Characteristic resistance of shear stud, PRk (kN)
Headed shear studs in
composite slab with profiled
steel sheeting
Characteristic strength of concrete fcu
(N/mm2)
25 30 35 40
BS5950: Part 3:
2010
Re-entrant 95 100 104 109
Open trough 77.9 82 85.3 89.4
EC4: Part 1.1: 2004 68.9 75.5 85.5 86.8
nr=1
Notes: Nominal shank diameter = 19mm
Nominal height = 100mm while as-welded height = 95mm
The resistance of shear stud in composite slab determined in EC4 is up
to 27% lower than that given in BS 5950.
Application of Composite Column
22
23
Kingposts (supporting the roof) which are part of the barrette
piles installed during the foundation stage
Top-Down Construction
24
Installation of a kingpost into the barrette pile
25
Excavation for starter
bars
Install starter bars
KingPost in column
Casting column head
26
Column Design Approach
Cross section resistance (yielding)
Resistance to compression
Resistance to moment
Reduced moment resistance under compressive force, i.e.
interaction between compression and bending
Member buckling resistance
Axial buckling resistance
Reduced moment resistance under compressive force, i.e.
interaction between compression and bending
δ
F
e
LBA
GNIA
Fcr
Types of elastic analysis
and design
27
Simplified Method (EC4 Clause 6.7.3.4)
Design Concepts
Axial
compression
Resistance of
member in
combined
compression
and bending
Design based on the
EC3 buckling curves
(similar to pure steel column)
Design based on second-order
analysis with equivalent member
Imperfection (simplified method)
Design based on second order
analysis with equivalent member
Imperfection (simplified method)
χ
e0
e0
28
Axial Compression Resistance
Compression resistance of composite column
sdscdcydaRdpl, fAfAfAN
= + +
yk a/f ck c/f sk s/f
steel concrete reinforcement
29
Axial Buckling Resistance
The buckling reduction factor
(EC3 approach)
0.1Rdpl,
Ed N
N
0.1
-
1
22
2
2.0-15.0
cr
Rkpl,
N
N
λ
a
b
1.0
0.0 1.0 2.0
x
Plastic resistance
Euler buckling
c
30
Buckling Curve - EC3
Buckling Curve – EC4
Cross-section Limits Axis of
buckling
Buckling curve
S235 - S460
Concrete encased section y-y b
z-z c
Partially concrete encased
section
y-y b
z-z c
Concrete filled circular and
rectangular hollow sections
ρs ≤ 3% any a
3% < ρs ≤ 6% any b
• For steel column, the buckling curve is related to steel section and steel
strength.
• For composite column, the buckling curve is related to the cross-section.
The strength of steel has little influence on the buckling curve.
31
32
Design based on
EC3 buckling
curve
Design based on EC4
simplified approach -
second order analysis &
member imperfection
Buckling curve b
Member
imperfection L/200
Resistance of
axial
compression
N Rd (χ) = 4320 kN N Rd (e0) = 4108 kN
Comparison
NRd(X) / NRd(e0)
1.05
e0
NEd
NEd
Example - Comparison of Design Approach
Note: design based on the use of member imperfection e0 leads to
a maximum difference of 5% in comparison with design based on
the EC3 buckling curve approach.
Design data:
fy=355N/mm2, fck=25N/mm2, fsk=500N/mm2,
Cross-section: 350mm×350mm, steel section: 254×254 UC73.
Column length: 5.0m, 4 bars of 20mm diameter
33
Design based on EC3
buckling curve approach
Design based on EC4
simplified approach
The maximum resistance can be
obtained by:
Second order effect factor k:
0.1
-
1
22
2
2.0-15.0
cr
Rkpl,
N
N
0pl,Rd Rd (e )
pl,Rd pm,Rd
-=
-
N N
N N
Rd( )N 0Rd (e )N
0Rd(e ) 0 M pl,Rd =kN e M
Rd( ) pl,Rd=N N
2
ef,II
cr,eff 2
cr
( )=
EIN
L
N
M Mpl,Rd
NRd(e0)
Npl,Rd
Npm,Rd
μMpl,Rd
Ed,max M pl,RdM M
0Ed,max Rd(e ) 0=M k N e
0Rd (e ) cr,eff
1=
1- /k
N N
Easier approach !
Tedious approach !
Example - Comparison of Design Approach
34
Resistance of Members in combined
Compression and Bending
The EC3 buckling curve approach can be adopted for
composite column under axial compression, however, this
approach is not suitable for 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 the
maximum moment at mid-height of the column.
Similar to slender RC column, equivalent initial bow
imperfections (member imperfections) are used in the design of
composite column for simplification.
35
Bending Moment due to Member Imperfection
e0
NEd
NEd
For the member imperfection e0 caused by the
design axial load NEd on a composite column,
there will be a bending moment of NEde0.
The design bending moment for the composite
column length considered both second-order
effects of end moment and imperfection is given
by:
k1, k2 are the factors of second order effects
0Ed2Ed1Ed.max eNkMkM
Ed cr,eff
=1- /
kN N
related to end moment ratio
36
Cross-section Axis of
buckling
Buckling
curve
Member
imperfection (e0)
Concrete encased section
y-y b L/200
z-z c L/150
Partially concrete encased
Section
y-y b L/200
z-z c L/150
Circular and rectangular
hollow section
y-y a L/300
z-z b L/200
Circular hollow section with
additional I-section
y-y b L/200
z-z b L/200
Partially encased H section
with crossed H section
any b L/200
z
y
y
z
z
y
z y
y z
Member Imperfections for Composite Column
37
Compared to EC4 (1994), the simplified method for
composite columns in EC4 (2004) was improved using
second order analysis and equivalent member (initial bow)
imperfection which takes into account the effects of residual
stresses and geometrical imperfections.
Introducing initial bow imperfections into the simplified
method for composite columns, the scope of the simplified
method can be extended to sway frames.
Improvement in the Design of Column in
Combined Compression and Bending
38
Ed, max
M
d pl,Rd
M
M
(a) EC4: 1994
The member imperfection can be taken
into account in the global analysis and
hence it is not necessary to allow for
the imperfection in the analysis of the
interaction curve.
Ed
M
pl,Rd
M
M
The influence of imperfection is taken
into account indirectly in the interaction
curve. The factor μd is reduced by a
relevant amount to account for the
moment due to the member
imperfection.
1 Ed 2 Ed 0k M k N e
1 Edk M
(b) EC4: 2004
39
Design of Composite Beam
The concrete slab works best in compression while the steel section
works best in tension; hence, a large moment resistance is generated
as a force couple.
Resistance mobilization in both the concrete slab and the steel section
is limited by the shear connection along the concrete interface.
Nc,f
Np
Npl,a
40
Failure Modes of Composite Beam
I-I resistance to sagging moment and vertical shear
II-II resistance to hogging moment and shear and M-V interaction
III-III shear connection @ the steel – concrete interface
IV-IV lateral torsional buckling
V-V Longitudinal shear of the concrete flange
IV
IV
41
Lateral Torsional Buckling Resistance
In BS5950-3.1, no equation is provided to calculate the
lateral torsional buckling resistance of continuous composite
beam under hogging moment over the internal support.
When checking LTB, the methods given in BS5950-1
(design of steel beam) is supposed to be used.
In EC4, the restraint of slab is taken into account compared
with steel beam in EC3.
42
b b xM p S
LT2
LT LT LT
11
Rk
LT
cr
M
M
1/2
2 2
cr c 4 a at s a afz/ /M k C L G I k L E I
BS5950-3.1 EC4
RdLTRdb, MM
Where pb is determined by λTB
TB t t=n uv
0.5
s
t 2 2
s
4 /=
1+ 2 / +0.05 /
a hv
a h x
With:
EC4 EC3 BS5950-3.1 EC4/BS
Ratio
EC4/EC3
Ratio
Lateral-torsional
buckling 546 kNm 531 kNm 479 kNm 1.14 1.03
(EC4)
0.522
cr 1 2 2+w cr Tz
cr z z
I L GIEIM C
L I EI
(EC3)
Inverted- U frame ABCD resisting lateral-torsional buckling
Elastic Critical Moment
43
In this approach, the elastic critical moment Mcr is determined using the
so-called “continuous inverted U-frame model”.
The model given in EC4 takes into account the lateral displacement of the
bottom flange causing bending of the steel web and the rotation of the top
flange that is resisted by bending of the concrete slab.
1/2
2 2
cr c 4 a at s a afz/ /M k C L G I k L E I
44
Composite Slab
Possible modes of failure: Shear failure at end support
Moment failure near mid-span region
Debonding within longitudinal shear span along the interface between concrete slab and decking, i.e. shear bond failure critical
Re-entrant
Trapezoidal Open Trough (Trapezoidal)
45
How can concrete “stick” to profiled sheeting after bending?
How reliable is the shear bond along the interface between
concrete and profiled sheeting ? • Surface bonding due to chemical reaction
- non ductile failure, hence not so reliable.
• Mechanical interlocking due to indentations or
embossments in the profiled sheeting or end anchorage
- ductile failure with rational provision, hence more
reliable.
Longitudinal Shear
46
Longitudinal Shear
End slip
Cracking
Test setup
47
• EC4:
p p
l,Rd
vs s
bd mAV k
bL
• BS5950-4:
r ps ss r cu
s v1.25
m AB dV k f
B L
m-k Method
m= 172.45
k= 0.2491
m= 163.26
k= 0.0312
Concrete
strength
48
EC4 BS5950-4
Short span Long span Short span Long span
m 172.5 163.3
k 0.2491 0.0312
Shear-bond
resistance
Vl,Rd (kN)
79.3 60.1 74.3 56.2
Comparison of Longitudinal Shear
BS5950 provides a more conservative value for longitudinal shear resistance
Test Short span 81.2 kN Long span 61.6 kN
49
Vertical Shear
1/3
v,Rd Rd,c 1 ck 1 pc w p100V C k f k b d
v,Rd,min min 1 cp w pV v k b d
BS 5950-4 EC4
v b s cV b d v
1/3 1/31/4
s cuc
m v
1000.79 400=
25
A fv
b d d
3/2 1/2
min ck0.035v k f
BS 5950-4 EC4 Experiment
153.6 kN 107.8 kN 118.7kN
EC4 provides a more conservative value for vertical shear resistance
50
Punching Shear
BS 5950-4 EC4
p s p cCritical perimeter -V D D v
1/3 1/31/4
s cuc
m v
1000.79 400=
25
A fv
b d d
3/2 1/2
min ck0.035v k f
BS 5950-4 EC4 Experiment
186 kN 139 kN 108kN
BS5950-4 provides a more conservative value for vertical shear resistance
p,Rd p p Rd
1/3
Rd Rd,c 1 ck min100
V C d v
v C k f v
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 areaD D d
51
Conclusions
1. Composite members with high strength steel (≥ S460) and
concrete (≥ C60/75) outside the scope of EC4. Can refer to
BCA/SSSS design guide for S550 steel and C90/105
concrete for CFT members.
2. Common grades of profiled steel sheeting cannot meet
EC3 ductility requirements in terms of stress ratio (fu/fy)
and %elongation after fracture. Design strength will have
to be downgraded. Refer to BC1 design recommendations.
3. The resistance of headed stud shear connectors is
generally lower in EC4 compared to BS5950; BC1 adopts
EC4 design resistance values.
4. For composite columns, the EC4 buckling curves are
different compared to EC3 due to contribution of concrete.
Unlike EC3, no special consideration for composite column
with S460 steel.
52
Conclusions
5. The simplified design approach using second order
analysis and equivalent member imperfection without any
need for member buckling resistance check is much
easier for composite column in combined compression
and bending moment. Approach is more similar to EC2
concrete column design.
6. EC4 provides guidance for lateral-torsional buckling check
for continuous composite beams taking into account the
beneficial effect provided by the concrete slab, i.e. the so-
called ‘ inverted U-frame method’.
7. EC4 provides clear guidance for testing & development of
composite slab system using profiled steel sheeting.
Existing ‘m’ and ‘k’ values from BS5950 cannot be used
directly in EC4 composite slab design.
