Design of Composite Steel-Concrete Structures to EC4 using ...ssssorgs/images/stories/docs/workshop_10apr2… · • Bondek II • Powerdek • RF55 . 3 How to use the spreadsheets?

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


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


20



Choose the steel

cross-section

21



Choose

concrete grade

22



23



24



Transverse reinforcement

25


Generate Result

26


Check Result OK or Recalculate

Verification for construction stage

27


Verification for composite stage

28


Ok


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30



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32



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



Choose the

steel grade

37


Select Material in designated area Choose the steel

cross-section

38



Choose

concrete grade



40



40

41



42



43



44



Generate Result

Under Axial Compression

Under Biaxial Bending

45



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


Choose

concrete grade

49


Input data

50


Input data

M-k method

N/mm2

N/mm2

51


Input data

mm

52


Check Result

Construction stage

53


Check Result

Composite stage

Documents

Design of Composite Steel-Concrete Structures to EC4 using ...ssssorgs/images/stories/docs/workshop_10apr2… · • Bondek II • Powerdek • RF55 . 3 How to use the spreadsheets?