Calcul cofraplus60 2xD=3.8 m

7/26/2019 Calcul cofraplus60 2xD=3.8 m

1/7

Date :

Project :

Customer :

Architect :

Engineering office :

Product :

Building codes :

Author :

I . Project data

Country : Romania

Composite slab : Continuous spans Concrete : Normal concrete

Span: Type: NC25/30

n = 2 m c = 2450 kg/m

L1 = 3.8 m fck = 25 MPa

L2 = 3.8 m fctm = 2.6 MPa

ECM = 31000 MPa

Slab depth: a = 0.85

ht = 150 mmLimit of deflection: Steel deck : Cofraplus 60

f/L = 1 / 300 fy = 350 MPa

Fire resistance: Ea = 210000 MPa

RF = 60 min ts = 0.75 mm

h = 58 mm

Charges bbf = 62 mm

Permanent loads (supplementary): bd = 207 mm

gper = 0.00 kN/m buf = 106 mm

Live load: bop = 101 mm

q = 1.50 kN/m gs = 8.5 kg/m

Ap = 1029 mm

Reinforcement bars zcg = 33.3 mm

fya = 300 MPa Ibr = 55.1 cm4

Upper reinforcement: Ieff = 42.6 cm4

d1 = 0 mm Mrd,+ = 4.3 kNm/m

a1 = 0 mm Mrd,- = 4.3 kNm/m

e1 = 0 mm Rw,Ex = 23.5 kN/m

Reinforcement on support: Rw,C = 25.0 kN/m

d2 = 10 mm Mpa = 7.7 kNm/m

a2 = 100 mm zpl = 39.55 mm

e2 = 0 mm m = 230.09 N/mm

Lower reinforcement: k = -0.062 N/mm

d = 0 mm/rib RD = 0.1 MPa

e = 0 mm

Construction stage Hyperstatic

Safety factors f / L = 1 / 180

gM = 1.00 Steel sheet Props : YES

gsb = 1.15 Reinforcement Support width:

gc = 1.50 Concrete Ss,Ex = 50 mm

gvs = 1.25 Shearing Ss,C = 100 mm

g0 = 1.35 Permanent load Number of props:

gq = 1.50 Live load n1 = 1

Y1 = 0.50 Fire n2 = 1

kr = 0.20 Moment redist.

Cofraplus 60

Eurocodes

Diaconescu Razvan

Calculation note

10 March 2016


2/7

II. Longitudinal section and cross section

III. Construction stage

Steel deck : Hyperstatic

Props : YES

Dead load of steel deck and concrete:

g = 2.90 kN/m

1. Deflection checking

d = 2.14 mm 15 = 10% ht

10.56 = L / 180

The ponding effect is ignored.

2. Ultimate limit states

* The loads to be taken into consideration during the conreting operation are the following:

Dead load of the steel deck and of the concrete:

g = 2.90 kN/m

Construction loads during casting of conrete (according to EN 1991-1-6):

qm = 0.75 kN/m

* Calculations of bending moments and support reactions

MEd,+ = 1.40 kNm MEd,- = 1.95 kNm

REd,Ex = 3.77 kN REd,C = 10.95 kN

* Checking of the resistance:

MEd,+/ MRd,+ = 0.32 1 OK MEd,-/ MRd,- = 0.45 1 OK

REd,Ex/ RRd,Ex = 0.16 1 OK REd,C / RRd,C = 0.44 1 OK

MEd,-/MRd,- + REd,C/RRd,C = 0.89 1,25 OK

IV. Verification of the composite deck slab

1. Ultimate limit states

* Three following criteria must be verified to ensure that no ultimat limit state is reached:

Bending resistance

Longitudinal shear

Vertical shear

* Calculation of the maximum design bending moments and vertical shears:

MEd,+ = 7.78 kNm MEd,- = 8.91 kNm

VEd,Ex = 9.80 kNm VEd,C = 14.06 kN

20 %With moment distribution of

cs ggg

cponding gg d7.0

areaworkingtheoutside0.75kN/m

mareaworkingtheinside1.5kN/m)thanmorenotand0.75kN/mthanless(not 3310 cm

g%q

L1 L2

L1/3 L2/3


3/7

a. Sagging bending moment

Position of neutral axis:

Hypothesis: The neutral axis is in the concrete slab and above the steel deck.

Fs = 360150 N

Frib = 0 N

xpl = 25 mm 92 = hc

Moment of resistance:

Mpl,Rd,+ = 37.45 kNm 7.78 OK

b. Hogging bending moment

Hypothesis: the neutral axis is in the steel deck.

F1 = 0 N

F2 = 204886 N

x = 37 mm 58 = h

Mpl,Rd,- = 26.97 kNm 8.91 OK

c. Longitudinal shear

* m-k method This method is not used in this calculation

Shear length:

Ls = 0 mm

The maximum design vertical shear should not exceed the design shear resistance:

Vl,Rd = 0.00 kN VEd,Ex

* Partial connexion method

u,Rd = 0.10 MPa

Fs = 360.15 kN

In order to develop fully plastic moment, the distance of the cross-section being considered to the nearest support:

Lsf = 3602 mm

For fully plastic moment section:

xsr = 0 mm

xf = 25 mm

)2/2(2)2/1(1,,

/)/1000(85.0

/

/

0

21

22

11

plxethFplxethFRdplM

cdck

saya

saya

bbf

FFx

AfF

AfF

g

g

g

)(, kbL

AmbdV

s

p

pRdl

Rdu

ssf

b

FL

,

Fs

Fsr

Ncr= Fsr

Ncf= Fs

spanscontinuousFor

spansingleFor

4/9.0

4/

L

LLs

cb

ckf

ribF

sF

plx

saribA

yaf

ribF

spAyfsF

g

g

g

/85.0

/

/

)2/()2/(,, pl

xrib

et

hrib

Fpl

xp

ds

FRdpl

M

cck

sf

cck

rib

sr

bf

Fx

bf

Fx

g

g

/85.0

/85.0


4/7

For a distance Lx< Lsf, the connexion is partial and expressed by hand the moment of resistance by M Rd:

Mbr = 0.00 kNm Mcp = a*h + b*h

Mpa = 7.65 kNm a = -2.33

Mpr = 1.25Mpa(1-h) Mpa b = 39.78

h

Lx/Lsf Mpr Mcp MRd

0.00 7.65 0.00 7.65

0.11 7.65 4.17 11.82

0.21 7.54 8.29 15.84

0.32 6.54 12.36 18.89

0.42 5.53 16.37 21.90

0.53 4.52 20.34 24.86

0.63 3.51 24.25 27.76

0.74 2.50 28.11 30.610.84 1.49 31.92 33.41

0.95 0.48 35.68 36.16

1.06 0.00 37.45 37.45

OK

e. Vertical shear

* End support

The vertical shear resistance is determined according to EN 1994-1-1 and EN 1992-1-1 :

CRd,c = 0.12

1 = 0.020

h1 = 1.00

k = 2

4.25

MEd

0.00

3.28

5.67

-2.55

Lx

0

0.38

0.76

1.14

1.52

1.90

7.17

7.78

7.49

6.32

-7.283.80

1.30

3.42

2.28

2.663.04

-10

-5

0

5

10

15

20

25

30

35

40

0 0.5 1 1.5 2 2.5 3 3.5 4

M(

kNm)

Lx(m)

Moment of resistance Design moment

cf

c

sf

x

N

N

L

Lh

2/12/3

min

2/12/3

min

0

1

1

1

,,

01min01

3/1

11,

01min01

3/1

1,

,

03.0035.0

/

15.0

0.2/2001

2200/6.04.0

/15.0/18.0

)()100(

)()100(

lcklck

cEdcp

p

sl

p

c

cclRdccRd

pcplpcplckclRd

pcppcpckcRd

cRd

fkVfkV

AN

db

A

k

dk

CC

dbkvdbkfkC

dbkvdbkfkCV

h

gg

h

concretelightFor

concretenormalFor

s

cf

ppfsrcfccp

pa

s

cf

papr

srribtribbr

prcpbrRd

F

NeeexxhNZNM

MF

N

MM

xehFM

MMMM

hhh

h

)()5.0(

)1(25.1

)2/(


5/7

k1 = 0.15

cp = 0

Vmin = 0.495

VRd,c = 40.62 kN 22.74

= 40.62 kN VEd,Ex OK

* Internal support

dp = 150 mm

1 = 0.013

k = 2Vrd,c = 45.58 kN 29.23

= 45.58 kN VEd,C OK

2. Serviceability limit states

a. Deflection control

Modular ratio steel - concrete (average value of the modulus for both long and short term effects):

n = 13.55

* Homogeneous section

xh = 66.95 mm

Ibh = 1.57E+07 mm4

* Cracked section

xf = 44.78 mm

Ibf = 9.93E+06 mm4

* Deflection checking

Average value of the second moment of area:

Ibm = 1.28E+07 mm4

Deflection:

f = 2.27 mm

f/L =1/ 1672 1/ 300 OK

b. Crack control

According to EN1992-1-1, the required minimum areas of reinforcement may be calculated as follows :

kc = 0.4

k = 0.65

As,min = 207.31 mm 119.60 mm

= 207.31 mm

As = 785.40 mm 207.31 OK

c. Vibration control

The frequency of the slab is calculated using the following fomulae

f0 = 10.34 Hz 5 OK

2

3/CM

a

CM

a

E

E

E

E

n

22

2323

2

)()(212212

)(2

hcotcophpp

p

h

pcpcch

ccbh

coppcc

cotcoppppcc

i

ii

h

xehAIxdAhxhnhb

nhbhx

nbh

nbhI

nAnAhbbh

ehnAdnAdhbh

b

A

zAx

22

3

2

)()(3

))((2()(

fcotcopfpp

f

bh

cotcoppcopcop

f

xehAIxdAn

bxI

b

ehAdAn

b

AAn

b

AAnx

2bfbh

bm

III

qqggm percs

Lm

bhIaE

f

5.0

Hz54

1000

20

cts

cteffctcss

AA

AkfkA

0013.0min,

,min,

onconstructiproppedfor

onconstructiunproppedfor

supportedsimplyasdesignedisspancontinuousif

004.0

002.0

min,

min,

cts

cts

AA

AA


6/7

V. Fire resistance

1. Geometry of the steel deck (according to Figure 4.1 of EN 1994-1-2)

h2 = 58 mm 50h2100 OK

l1 = 101 mm 80l1155 OK

l2 = 62 mm 32l2132 OK

l3 = 106 mm 40l3115 OK

A = 4,727 mm/mm Concrete volume in the rib per m rib length

Lr = 184 mm/mm Exposed area of the rib per m rib length

A/Lr = 26 mm Rib geometry factor

F = 0.727 - View factor of the upper flange

a = 71 degrees Angle of the web / horizontal

b = 0.32 Radians Angle of the web / vertical

2. Fire resistance according to thermal insulation "I"

t1 = 118 min 60 OK

3. Integrity criterion "E"

For composite slabs the integrity criterion "E" is assumed to be satisfied (according to EN 1994-1-2).

4. Load bearing criterion "R"

a. Calculation of sagging moment resistance

Temperatures of the lower flange, web and upper flange of the steel decking:

Temperatures of the reinforcement bar in the rib :

Load bearing of each part of the slabs after 60 minutes :

Temperature ky,i Ai Zi Mi

(C) [-] (cm) (cm) (kNcm)

Lower flange

Web

Upper flange

Lower reinforcement

Concrete

Mfi,Rd,+ = kNm

b. Calculation of hogging moment resistance

Temperature ky,i Ai Zi Mi

(C) [-] (cm) (cm) (kNcm)

Upper reinforcement - -

Reinforcement on support - -

Concrete

Mfi,Rd,- = kNm

Fi

(kN)

Fi

(kN)Part of the slab

2

432

3

10

1FF bb

L

Ab

lbb

r

a

3213

5432

2

310

1111 with

1

uuuzlcc

L

Aczc

h

ucc

r

a a


7/7

c. Fire resistance checking of composite slab

Applied load (according to EN 1991-1-2):

Y1,1 =

Pfi,Ed = kN/m

Verification of fire resistance according to EN 1992-1-2 (annex E):

Mfi,Ed,1 = kNm = Mfi,Rd OK

Mfi,Ed,2 = kNm = Mfi,Rd OK

0.35*Mfi,Ed,max = 0.00 kNm = Mfi,Rd,+ OK

1,1,1, kEdfi QGP Y

spanscontinuousFor

spansingleFor

2

8

,,

,,,,,,

,,

,

2

,

,,

Rdfi

eRdfiwRdfi

Rdfi

Rdfi

iEdfi

iEdfi

MMM

M

M

LPM

Mfi,Rd,-,w

Mfi,Rd,-,e

Mfi,Rd,+

Mfi,Ed

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Calcul cofraplus60 2xD=3.8 m