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Design of Composite Steel-Concrete
Structures to EC4 using Excel
Spreadsheets
Chiew Sing-Ping
School of Civil and Environmental Engineering
Nanyang Technological University
10 April 2015
2
EC4 Design Spreadsheets
Composite beam
Composite column
• Concrete-encased composite column
• Concrete-filled rectangular tube (CFT)
• Concrete-filled circular tube (CFT)
Composite slab
• Bondek II
• Powerdek
• RF55
3
How to use the spreadsheets?
Check whether spreadsheets apply to your design
Input data in designated area
Select material in designated area
Generate results
Check results
4
Example of Composite beam
beff
130mm hc
hp= 55 mm
ha
How to design a simply supported composite beam
using the excel spreadsheet ?
5
Properties of materials
Structural steel:
Grade S275 fy = fyd = 275 N/mm2 Ea = 210 kN/mm2
Concrete:
C25/30 fck = 25 N/mm2 fcd = 16.7 N/mm2 Ecm = 3.1 kN/mm2
Reinforcement:
fsk = 500 N/mm2 fsd = 435 N/mm2
Shear connectors:
19 mm studs with 95 mm height fu = 450 N/mm2 one stud per trough
Profiled steel sheeting:
RF55 fyp = 550 N/mm2 t = 1.0 mm
Properties of the IPE A 270 steel section
bf=135 mm, ha=267 mm, tf= 8.7 mm, tw=5.5 mm, Aa= 39.2 cm2, W pl = 412.5 cm3,
Ia = 4917 cm4
Design data
Span length: 6 m, Bay width: 3 m
Slab depth: ht = 130 mm
6
Loadings
Self-weight of slabs:
The concrete wet density is 2400 kg/m3, dry density is 2350 kg//m3. The
volume of concrete in composite slab is 0.125 m3/m2 , self-weight of
decking is 0.14 kN//m2. Then,
1= 0.125 9.81 2400+0.14 3 = 9.25 kN/mkg
Characteristic Load (kN/m) ULS loading (kN/m)
Construction stage
Self-weight of composite slab 9.25 12.49
Self-weight of steel beam 0.3 0.41
Construction load 2.25 3.38
Total 11.8 16.27
Composite stage
Self-weight of composite slab 9.07 12.24
Self-weight of steel beam 0.3 0.42
Floor finishes 3 4.05
Imposed load 15 22.5
Total 27.37 39.19
The loadings for composite beam spacing of 3 m are given in Table
7
Verification of construction stage
The total load in construction stage is 16.27 kN/m, then
Bending moment at mid-span is:
The design vertical shear is:
The plastic moment resistance of steel beam is:
Check: Mpl,a,Rd > MEd
It is ok.
2 2
Ed
16.27 6= = = 73.2 kN m
8 8
qLM
Ed
16.27 6= = = 48.8 kN
2 2
qLV
3
pl,a,Rd pl yd= 412.5 275 10 113.44 kN mM W f
8
Verification of construction stage
The total load in serviceability limit state is 9.55 kN/m, then
The maximum deflection is:
Allowable deflection is:
Check deflection:
It is ok.
The mid-span bending moment is:
Maximum bending stress is
Check stress:
It is ok.
The section is still in elastic region at the end of construction.
All design checks are OK at both the ultimate limit state and the
serviceability limit state.
45 = =15.61 mm
384 a ay
wL
E I
1
= min( ;30 mm) 30 mm200
L
<
2 2
Ed
9.55 6= = = 42.98 kN m
8 8
qLM
2Edmax
el,y
= =116.69 N/mmM
W
max yf
9
Verification for composite stage
Cross-section classification:
Flange:
Web:
The flange and the web is Class 1, therefore the cross-section is Class 1
Effective width of concrete flange
Single line of shear studs, therefore, nr = 1, b0 = 0
The effective width of compression flange of the composite beam
y
235 235= = = 0.92
275f
f
= 5.72 < 9 = 8.32c
t
w
= 39.93 < 72 = 66.56d
t
eff 0 ei e = + = 0 + 2 /8 = 2 6/8 =1.5 mb b b L
10
The design shear resistance of headed studs
19mm headed stud, d = 19 mm, hsc = 95 mm, fu = 450 N/mm2, then,
so, α= 1.0
Then,
For sheeting with ribs transverse to the supporting beam, the reduction factor is:
The design shear resistance of headed studs is
95= =5 > 4
19
sch
d
2 2-3u
Rd,1
V
0.8 4 0.8 450 3.14 19 /4= 10 =81.61 kN
1.25
f dP
2 2ck cm -3
Rd.2
V
0.29 0.29 1.0 19 25 31000= 10 =73.73 kN
1.25
d f EP
0 sc
t t max
p pr
0.7 = 1 1.2 = 0.85
b hk k
h hn
Rd t,max Rd1 Rd2 = min( ; ) = 62.67 kNP k P P
11
Degree of shear connection
Number of shear connectors for half span: n = 15
Total resistance of shear connectors is:
Compression resistance of concrete slab is:
Tensile resistance of steel beam is
Degree of shear connectors is
Checking the condition of minimum degree of partial shear connection
Then,
It is ok.
q Rd = 940 kNN nP
cf cd eff c = 0.85 = 1593.75 kNN f b h
pl,a a yd = 1078 kNN A f
q
cf pl,a
= 0.87 1.0 partial shear connectionmin( , )
N
N N
min e
y
35525 ; 1 0.75-0.03 , 0.4 L m L
f
min = 0.4
12
Verification of bending resistance (plastic moment resistance)
Total loads (factored load used for ULS) is 39.19 kN/mm2
The mid-span bending moment is
The design vertical shear is:
As Nc,f > Npl,a, P.N.A in concrete slab.
The depth of plastic neutral xpl measured from the upper surface of the slab is
The moment resistance in full shear connection is
Plastic moment resistance of steel section is
Interpolation method:
The resistance moment MRd with partial shear connection is
It is ok.
2
Ed = / 8 = 176.37 kNmM wL
Ed = / 2 = 117.58 kNV wL
pl pl,a eff cd c = / ( 0.85 ) 50.73 mm 75 mmx N b f h
pl,Rd pl,a a c p pl = 0.5 0.5 256.71 kNmM N h h h x
pl,a,Rd pl yd = =113.44 kNmM W f
Rd pl,Rd pl,a,Rd pl,a,Rd Ed = 238.38 kNm > M M M M M
13
Verification of vertical shear
The shear area of steel section is
The shear resistance is
It is ok.
So, verification for shear buckling is not required.
So, reduction to bending resistance is not required.
2
v f w f = - 2 + ( +2 ) 1879.85 mmaA A bt t r t
pl,a,Rd v yd Ed = / 3 = 298.5 kN > V A f V
w w/ =39.93 72 / = 66.56h t
Ed pl,a,Rd/ 0.39 0.5V V
14
Longitudinal shear resistance
The plastic longitudinal shear stresses is
To prevent crushing of the compression struts in the concrete flange, the
following condition should be satisfied, assuming θf= 45:
It is ok.
Continuous profiled decking with ribs perpendicular to the beam span
the area of transverse reinforcement per unit length is
The reinforcement is 10 mm bars at 200mm c/c spacing
The reinforcement provided per unit length is
It is ok.
2
Ed
f
= =2.09 N/mm2 / 2
qNv
h L
ck0.6 1 / 250 = 0.54 f
2
Ed cd f f sin cos =4.5 N/mm v f
sf yd f Ed f f/ /cot A f s v h
2
sf f Ed f yd f/ / cot =360.36 mm /m A s v h f
As/ss= 393 mm2/m
15
Deflection
The modular ratio for variable loading is n0, and the modular ratio for permanent
load is around 3n0. But, for simplicity, creep will be allowed for by using n = 2n0
for all loading.
Distance from the top surface of the concrete slab to centre of area
The second moment of area of the composite section is calculated. Assuming
that the neutral axis depth exceeds hc, the depth of neutral axis is given by:
Then, the second moment of area of the section is
0 a cm2 =2 / =13.55 n n E E
g a t= /2+ =263.5 mm z h h
eff c c
a g
- 2- =
b h x hA z x
n
2
a g eff c
c
a eff c
+ 2= =109.98 mm > h
+
A z b h nx
A b h n
2
2 2 6 4
a a g eff c c = - + / /12 ( / 2) 189 10 mmcI I A z x b h n h x h
16
The mid-span deflection of steel beam is:
The mid-span deflection of composite beam is
The total deflection is:
δ = 27.24 mm
Allowable deflection is:
Check:
It is ok.
4
1
a a
5= = 15.61 mm
384
g L
E I
4
2
a
5= = 11.63 mm
384
g L
E I
= / 200 30 mmL
17
Spreadsheets of Composite beam
Check whether spreadsheets apply to you design
Input data in designated area
Select material in designated area
Generate result
Check results
assumptions
Input data
Choose steel/concrete grade
Ok or Recalculate
Procedure
18
Spreadsheets of Composite beams
Restrictions:
Simply-supported beam
Internal beam
Sheeting with ribs transverse to the
supporting beam (cross-beam)
Equal concrete flange
Check whether the spreadsheet is applicable to your
design based on the following restrictions.
19
Select Material in designated area
Choose the
steel grade
Spreadsheets of Composite beams
20
Select Material in designated area
Spreadsheets of Composite beams
Choose the steel
cross-section
21
Select Material in designated area
Spreadsheets of Composite beams
Choose
concrete grade
22
Input data in designated area
Spreadsheets of Composite beams
23
Input data in designated area
Spreadsheets of Composite beams
24
Input data in designated area
Spreadsheets of Composite beams
Transverse reinforcement
25
Spreadsheets of Composite beams
Generate Result
26
Spreadsheets of Composite beams
Check Result OK or Recalculate
Verification for construction stage
27
Spreadsheets of Composite beams
Verification for composite stage
28
Spreadsheets of Composite beams
Ok
Check Result OK or Recalculate
29
Spreadsheets of Composite beams
Check Result OK or Recalculate
30
Spreadsheets of Composite beams
Check Result OK or Recalculate
31
Spreadsheets of Composite beams
Check Result OK or Recalculate
32
Spreadsheets of Composite beams
Check Result OK or Recalculate
33
Worked Example of Composite Column
tw
tf
bc
cy
cy b
cz
h
cz
hc
34
Design Data
Column length: Ly= Lz = 5.0m
Design axial force: NEd = 2500kN with permanent load NG,Ed = 1500kN
Design bending moment about y-y axis: My,Ed,top = 80 kNm, My,Ed,bot = 0 kNm
Design bending moment about z-z axis: Mz,Ed,top = 30 kNm, Mz,Ed,bot = 0 kNm
Material
Structural steel: Grade S355, 254×254 UC 89
Concrete: C25/30
Reinforcement: fsk = 500 N/mm2, 4 bars, diameter d=20mm
Shear connector: fu = 450 N/mm2, d=19mm, hsc = 95mm
Properties of cross-section:
Concrete depth: hc = 350 mm
Concrete width: bc = 350 mm
Concrete cover: c = 30 mm
Additional factors
creep coefficient φ(t0)=3
α = 0.34 for buckling curve b, α = 0.49 for buckling curve c
Ke = 0.6, Ke,II =0.5, Ko = 0.9
αc= 0.85
35
Spreadsheets of Composite column
Restrictions on simplified method:
Columns: doubly symmetrical & uniform cross section
Steel contribution ratio 0.2 ≤ δ ≤ 0.9
Non-dimensional slenderness
Steel reinforcement area 0.3% ≤ As/Ac < 0.6%
Depth to width ratio 0.2 < hc/bc <5.0
Concrete cover minimum: 40mm
maximum: cz = 0.3hc & cy = 0.4bc
Check whether the spreadsheet could apply to you
design based on assumptions
36
Spreadsheets of Composite column
Select Material in designated area
Choose the
steel grade
37
Spreadsheets of Composite column
Select Material in designated area Choose the steel
cross-section
38
Spreadsheets of Composite column
Select Material in designated area
Choose
concrete grade
Input data in designated area
Spreadsheets of Composite column
40
Input data in designated area
Spreadsheets of Composite column
40
41
Input data in designated area
Spreadsheets of Composite column
42
Input data in designated area
Spreadsheets of Composite column
43
Input data in designated area
Spreadsheets of Composite column
44
Spreadsheets of Composite column
Check Result OK or Recalculate
Generate Result
Under Axial Compression
Under Biaxial Bending
45
Spreadsheets of Composite column
Check Result OK or Recalculate
Shear
Shear connectors
46
Worked example of Composite slab
Composite slab
Bondek II
47
Design Data
Span: L = 3.0m
Depth: ht = 130 mm
Material
Concrete: C20/25
Concrete wet density, ρwc =2400 kg/m3
Concrete dry density, ρc =2350 kg/m3
Volume of concrete vc = 0.125 m3/m2
Reinforcement: fsk = 500 N/mm2
Properties of profiled sheeting:
Depth of decking: hp = 54 mm
Yield strength: fyp=550 N/mm2 (G550)
Thickness: tp=1.0 mm
Width of Per rib: bs = 200 mm, b0 = 168 mm
Effective steel area: Ap=1678 mm2/m
Second moment of area: Ip=64.1x104mm4/m
Plastic bending resistance: Mpa=9.18 kNm/m
Distance of centroid above base: e = 15.6mm
Characteristic resistance to vertical shear: Vpa=39.5 kN/m
For resistance to longitudinal shear: m =184N/mm2, k = 0.0530N/mm2
For partial-interaction design: τu,Rd =0.2448N/mm2
48
Spreadsheets of Composite slab
Select Material in designated area
Choose
concrete grade
49
Spreadsheets of Composite slab
Input data
50
Spreadsheets of Composite slab
Input data
M-k method
N/mm2
N/mm2
51
Spreadsheets of Composite slab
Input data
mm
52
Spreadsheets of Composite slab
Check Result
Construction stage
53
Spreadsheets of Composite slab
Check Result
Composite stage