Loadd Word Document

8/11/2019 Loadd Word Document

1/22

FLOOR CALCULUS

Composite floors with profiled steel sheet-concrete cross-sections

These composite floors can be classified in 2 categories taking into account the loading stages

and the loading carry out mode. In the first category we found floors simply supported du

ring execution and prefabricated floors, where the entire load is taken by the mixed cross-

section steel-concrete.in the second category we found monolith floors unsupported where

the profiled steel sheet is in fact the formwork and takes out the dead load and the concrete

floor load.

The calculus is made in two steps:

1. Profiled steel sheet calculus;

2. Composite section calculus.

To ensure a good collaboration between the profiled steel sheet and the concrete floor at the

contact interface we must consider the floor as a composite element, the profiled steel sheet

having a reinforcement role.

Composite floor calculus

The thickness of the composite floor () will be at least 100 [mm] and the thickness of the

profiled steel sheet it will be at least 0, 7 [mm]. The concrete floor thickness above the

profiled steel sheet () will be at least 50 [mm].

European standards recommended that the dimensions of ribs of the profiled steel sheet and

of the concrete floor will be according to the following conditions:

By taking into account the general configuration of the girders systems it is recommended

that the profiled steel sheet ribs to be disposed normally on the beams. The negative moments

in the supports are taken by the reinforcement on the superior part of the floor (the minimum

reinforcement percentage is 0, 2%).


2/22

The superior surface on the profiled steel sheet which will be in contact with the concrete

must be proper cleaned from paint, rust, greases or from other impurities before putting in

place concrete.

Profiled steel sheet calculus

The self-weight loads of the profiled steel sheet and from the concrete will be taken only by

the profiled steel sheet during execution and can represent a fraction of 20%...50% from the

total load in the service period. The profiled steel sheet has a simply supported beam as static

scheme.

We impose ][21,12

2200*3,0

100*81,87

*

%30 3

1

11 cm

fk

MWk

y

nec

=>T.C. 60/200/0, 75/600-1300

a=6[mm]

b=200[mm]

t=0, 75[mm]

B=600[mm]

l=1300[mm]

][3,12

]/[10

3

2

cmW

cmdaNg

ef

t

yfk

W

M*1

1 Where 1k =0, 2....0, 5 based on the loads from this

stage

][3,1

]/[258

1*2500*06,0*2

085,003,0125,0*1*806,0*25001***2

*1**

*

2

ml

mdaN

Aaceb

lnnhq bribsbkb


3/22

]/[8,3058,28322

]/[8,283258*1,1*

2

2

mdaNqqq

mdaNqnq

bt

k

b

d

b

Where : tq -is the self weight on2m of profiled steel sheet;

-we impose tq = ];/[2220*1,1* 2mdaNqn nt

-q is the load on profiled steel sheet on linear meter;

q=q*1, 35=412, 83 ]/[ 2mdaN ;

]/[21,878

3,1*83,4128

* 2

22

1, mdaNlq

MEd

We impose ][21,122200*3,0

100*81,87

*%30

3

1

11 cm

fk

MWk

y

nec

=>T.C. 60/200/0, 75/600-1300

a=6[mm]

b=200[mm]

t=0, 75[mm]

B=600[mm]

l=1300[mm]

][3,12]/[10

3

2

cmWcmdaNg

ef

t

Loads evaluation from current floor

-cold floor

No. Name of the layer d Loads Loads Loads


4/22

(m) ]/[ 3mdaN

)/( 2mdaN

qk

n

)/( 2mdaN

qd

1. False ceiling gypsum

board

0,02 500 10

1,35

12

2. Profiled steel sheet - - 10 11

3. Reinforced concrete plate 283,8

4. Mosaic cast plates 100 130

Permanent loads from cold floor 378 - 436

Loads from partitioning walls 50 1,2 60

Total permanent loads on floor 428 1,16 496

Imposed loads 300 1,3 390Total 728 - 886

-terrace floor

No. Name of the layer d Loads Loads Loads

(m) ]/[ 3mdaN

)/( 2mdaN

qk

n

)/( 2mdaN

qd

1. False ceiling gypsum

board

0,02 500 10 12

2. Profiled steel sheet - - 22 29,7

3. Reinforced concrete

plate

0,15 2500 258 283,8


5/22

4. Equalization level

M100

0,03 2100 36

1,35

46,8

5. Barrier against

vapors

- - 3,5 4,55

6. Sand 3 3,9

7. Thermo insulation

B.C.A.

114 136,8

8. Slope granulated

concrete

65 71,5

9. M100 cement mortar 36 46,8

10. Hydro insulation 17,5 22,75

11. Precast concrete

plates(20x20x3)

0,15 2500 100 130

Total permanent loads on

floor

663 1,35 780,34

Technological load 200 1,4 280

Snow load 250 -

Total 1113 - 1328,7

Floor design

The floor design implies the pre-dimensioning of the thickness of the floor, the stability of the

reinforcement cross-section (profiled steel sheet), the computation of joints and drawings of

execution details.

The ultimate limit state computation it will be done in the plastic domain, considering that the

steel and concrete reach the effort limit states. It is recommended that the thickness of the

compressed zone shouldnt be more than 0, 5 ah , where ah is calculus height of the

composite floor.

Floor calculus


6/22

Considering that in exploitation limit state, the effort diagram in the compressed area is a

rectangular form, the size of the unit load is cR .In the profiled steel sheet the effort in center

weight is ,Rp where R is steel resistance

Static calculation

The static calculus will be made considering the redistribution of the plastic domain bending

moments.

CLM - longitudinal marginal frame;

CLC - longitudinal current frame;

CTCtransversal current frame;

Gsbeam;

1cM - bending moment in the first field;

1rM - bending moment in the first support;

ccM - bending moment in the current field;

rcM - bending moment in the current support;

2max

22

222

1

222

1

lg0625,0

lg0625,016

lg

lg0151,014

)lg46,0(14

lg0192,011

)lg46,0(11

sqMMM

sqs

qMM

sqsqqlongM

sqsqqlongM

ccrc

ccrc

r

c

Current floor calculus

]m*daN[58,9316

3,1*88616

slgqMM

22

ccrc

Given data:

M max=93, 58[daN*m]


7/22

b=1[m]

steel37OL]cm

daN[2200R

]cm

daN[125R

]cm[62,11

20

100*075,0*)6*2316(

b

100*t*)a*2ec(A

]cm[13]m[13,0h

2

2c

2

t

p

p

]cm[58I

]cm[3,12W

4

3

=> profiled steel sheet

Verification of the maximum unit effort ( p )

]cm[28,13,12

586

W

Ihy 2t

Determination of the computation height of the composite floor

]cm[72,1128,113yhhtpa

- coefficient computation

]cm

daN[97,551)0023216,0*5,01(*72,11*62,11

100*6,64100*58,932,525

)*5,01(*h*A

MM

]cm

daN[3,5253,12

100*6,64

W

M

0023216,00023189,0*211211

]m*daN[6,64M

MMwhere

MMM

4,00023189,0125*72,11*100

6,64100*58,93

R*h*b

M

2

ap

12

1p

21

1

1

max2

12

2

c

2

a


8/22

Designing the composite floor taking into consideration bending moment action in supports

M=93, 58[daN*m]

]cm[100b

]cm

daN[1253R

]cm[5,115,113ahh

]cm[13h

2c

pa

p

The reinforcement is made of PC 52 steel bars (R=3000 ]cm

daN[ 2 )

00713,000710,0*211211

4,000710,0125*5,11*100

100*58,93

R*h*b

M2

c

2

a

P-reinforcement percentage

%2,0p%03,0100*3000

125

*00713,0100*R

R

*p mina

c

We impose %2,0pmin

ml/85]cm[1,25,11*100*100

2,0h*b*

100

2,0A 2aa With ]cm[51,2A

2

eff

Roof terrace computation

Verification of the roof terrace in the maximum bending moment field

]daN[06,11216

3,1*9,1060

16

l*qM

22

q

Given data:


9/22

steel37OL]cm

daN[2200R

]cm

daN[125R

]cm[13h

]cm[100b

]m*daN[06,112M

2

2c

p

q

]cm[58I

]cm[3,12W

4

3

=> profiled steel sheet

]cm

daN[2200R]cm

daN[9,560

]cm

daN[9,560)0033094,0*5,01(*72,11*62,11

100*6,64100*05,1092,525

)*5,01(*h*A

MM

]cm

daN[3,5253,12

100*6,64

W

M

0033094,00033039,0*211211

4,00033039,0125*72,11*100

100*)6,6406,112(

R*h*b

MM

22p

2

ap

121p

21

1

2

c

2

a

12

Designing the terrace roof floor taking into consideration bending moment action in supports

M=112, 06[dan*m]

0081647,00081313,0*211211

4,00081313,0125*5,11*100

100*06,112

R*h*b

M2

c

2

a

P-reinforcement percentage

%2,0p%034,0100*3000

125*0081647,0100*

R

R*p min

a

c

We impose %2,0pmin

ml/85]cm[1,25,11*100*100

2,0h*b*

100

2,0A 2aa With ]cm[51,2A

2

eff

Verification


10/22

Loads:

]cm[44,1f]cm[22,0f

]cm[44,1250

360

250

Lf

]cm[22,03680*10*1,2

)100*6,3(*01,0*6,1014

*384

5

I*E

l*q

*kf

]cm/daN[1300R]cm/daN[25,11603680*26

460*39,2209

I*b

S*T

]cm/daN[2200R]cm/daN[12,705282

45,1988

W

M

]daN[39.22092

6,3*44,1227

2

l*qT

]m*dan[45,19888

6,3*44,1227

8

l*qM

]m/dan[44,12271,1*2,683,1*)35,1*30016,1*428(q*nl*)n*gn*g(q

]m/daN[6,10142,683,1*)300428(ql*)gg(q

aeff

a

6

44

T

n

2

f

2

max

22

max

c

max

22c

max

n

gsgs

n

uech

n

p

c

n

gsgs

n

u

n

p

n

Shear connectors design

Characteristics:

-diameter d=19[mm]

-head diameter de=30[mm]

-height h=100[mm]

25,1

]mm/N[450f

]mm/N[380f

2

ug

2

yg

Strength requirement

)P,Pmin(P 2Rd1RdRd

For shear force we have:

]KN[7,8110*25,1

1

*4

19*

*450*8,0

1

*4

d*

*f*8,0P 3

22

ug1Rd


11/22

For compression we have:

]KN[3,73)7,73P,7,81Pmin(P

]KN[3,7310*25,1

1*30500*25*19*450*1*029P

]mm/N[30500E

]mm/N[25f

43,519100

dhfor1

1*E*f*d*f**029P

2Rd1rdRd

32

2Rd

2

em

ck

c

emck

2

ug2Rd

Computation of number of shear connectors for e structural element

connectors5287,513,73

727,3802

P

VN

Rd

1

Temporary climatic loads

Snow load(according STAS CR 1-1-3/2005)

Snow acts upon structures through exterior systems of forces of staic nature, distributed

on exposed building elements.

The building is in the Iasi area, for which, for a medium interval of recurrence IMR = 50

years, the characteristics value of the snow load on soil is :

= 2.5 KN/.


12/22

The characteristic value of the snow determined load upon the exposed surface of the

considered building element is determined using the relation :

Where:

Facturated intensity of the load given by snow;

:iThe shape coefficient for the snow loading on the roof;

k,0S The characteristic value of the snow loading at the ground level, in the considered

building emplacement [KN/m2];

eC : The exposure coefficient of the construction emplacement;

t

C : Thermal coefficient;


13/22

The exposure coefficient, of the building placement is a function of the exposure

condition of the construction, it`s values being recommanded in the following table:

= 2.5 KN/;

= 1.0;

= 1.0, because the roof has a hydroinsulation;

= 1.0, because the roof is a terrace;

Results: Sk =1 *Ce *Ct *S0,k= 1.0*1.0*1.0*2.5 = 2.5KN/ m2

Wind load(according to NP 082-2004)

The wind effects upon the buildings and structures depends on the properties of the

wind , the shape , dimensions of orientation of the building upon the wind direction , the

dynamic properties of the structures , the emplacement of the structure in the natural

environment and the neighbour constructions .

The wind load action is evaluated by the pressure of the wind , or by the forces of

given by the wind on the construction on structures.

The pressure or the forces given by the wind acts normally on the exposed surface. In

some cases there must be supplementary considered the horizontal friction forces, tangential.

The wind pressure at the level z above the surface of the ground, on the rigid

surfaces of the building is given by the relation:

W(z) = qref * ce(z) * cp , where :

qref = is the reference pressure of the wind, defined on Chapter 6 of NP 082-2004;

ce(z) = the exposure factor at the height z above the ground , defined on Chapter 6 of NP

082-2004;

Exposure time

Complete 0.8

Partial 1.0

Reduced 1.2


14/22

cp= aerodynamic coefficient of pressure in conformity with Chapter 12 from the norms.

Given the location of building, Iasi, the value of the reference pressure of the wind will be

equal to 0, 7 kPa=0,5KN/m 2 .

Taking into consideration the height of the building-30, 77[m], and the placement of theconstruction is Iasi.

Given the dimensions of the building the length 25,5[m], width 12,0[m], and height 30,77

[m] the value of C p will be taken from the tables.

Calculation of wind action on longitudinal frame Because of the wind pressure action is

uniform distributed to a height of 10[m] and then increase linear with the height we calculate

the wind pressure first at a height of 10 [m] and then from floor to floor until the last floor.

a). Wind pressure at height z=10[m]

0926,13054,0*5779,3)10(c*)10(c)10(c

c*)10(c*q)10(w

rge

peref1

Where:

)z(cg =gust factor

)z(c r = roughness factor

5779,3]3682,0*2[5,31)]10(I*2[g1)10(cg

Where:

g=3, 5peak factory

I (z) =turbulence intensity

3054,0)10(ln*24,0)z

10(ln*)z(k)10(c

36828,0)10ln(*5,2

12,2

z

10ln*5,2

I(10)

222

0

0

2

rr

0

Where:


15/22


16/22

9815,2]2830,0*2[5,31)]20(I*2[g1)20(cg

Where:

g=3, 5peak factory


5169,0)20(ln*24,0)z

20(ln*)z(k)20(c

2830,0)20ln(*5,2

12,2

z

20ln*5,2

I(20)

222

0

0

2

rr

0

Where:

)z(k 0r =0, 24- type of terrain factor

0z =1, 0-for high degree of terrain roughness

For each zone the value of pC will be as follows:

;3,0C

;8,0C

;8,0C

;0,1C

pE

pD

pB

pA

Taking into consideration the values already presented, we obtain:

2E

2

D

2

B

2

A

m/KN3236,0)3,0(*5411,1*7,0w

m/KN8630,0)8,0(*5411,1*7,0w

m/KN8630,0)8,0(*5411,1*7,0w

m/KN0788,1)1(*5411,1*7,0w

c).wind pressure at height z=30[m]

8290,16663,0*7451,2)30(c*)30(c)30(c

c*)30(c*q)30(w

rge

peref1

Where :


17/22

)z(cg =gust factor


7451,2]2493,0*2[5,31)]30(I*2[g1)30(cg

Where:

g=3, 5peak factory


6663,0)30(ln*24,0)z

30(ln*)z(k)30(c

2493,0)30ln(*5,2

12,2

z

30ln*5,2

I(30)

222

0

0

2

rr

0

Where:




;3,0C;8,0C

;8,0C

;0,1C

pE

pD

pB

pA


2

E

2

D

2

B

2

A

m/KN3841,0)3,0(*8290,1*7,0w

m/KN0242,1)8,0(*8290,1*7,0w

m/KN0242,1)8,0(*8290,1*7,0w

m/KN2803,1)1(*8290,1*7,0w

d).wind pressure at height z=30,77[m]


18/22

8477,16762,0*7325,2)77,30(c*)77,30(c)77,30(c

c*)77,30(c*q)77,30(w

rge

peref1

Where :

)z(cg =gust factor


7325,2]2475,0*2[5,31)]77,30(I*2[g1)77,30(cg

Where:

g=3, 5peak factory


6762,0)77,30(ln*24,0)z

77,30(ln*)z(k)77,30(c

2475,0)77,30ln(*5,2

12,2

z

77,30ln*5,2

I(30,77)

222

0

0

2

rr

0

Where:





19/22

;3,0C

;8,0C

;8,0C

;0,1C

pE

pD

pB

pA


2

E

2

D

2

B

2

A

m/KN3879,0)3,0(*8477,1*7,0w

m/KN0347,1)8,0(*8477,1*7,0w

m/KN0347,1)8,0(*8477,1*7,0w

m/KN2934,1)1(*8477,1*7,0w

Xxxxxxxxxxxxxxxxxxxxxxx

Calculation of wind action on transversal frame

Xxxxxx

Because of the wind pressure action is uniform distributed to a height of 10[m] and then

increases linear with the height we calculate the wind pressure first at a height of 10[m] and

then at 20[m], 30[m], 30, 77[m].

a). wind pressure at height z=10[m]

0927,13054,0*5779,3)10(c*)10(c)10(c

c*)10(c*q)10(w

rge

peref2

Where :

)z(cg =gust factor


5779,3]3682,0*2[5,31)]10(I*2[g1)10(cg


20/22

Where:

g=3, 5peak factory


3054,0)10(ln*24,0)z

10(ln*)z(k)10(c

3683,0)10ln(*5,2

12,2

z

10ln*5,2

I(10)

222

0

0

2

rr

0

Where:



h>2b30, 77[m]>24, 00[m] => case c)

e=min (b, 2h) =12, 0[m] =>A=e/5=2, 4[m]

=> B * =d-A=25,5-2,4=23,1 [m]


;3,0C

;8,0C

;5,0C

;8,0C

;0,1C

pE

pD

pC

pB

pA


2E

2D

2

C

2B

2A

m/KN2295,0)3,0(*0927,1*7,0w

m/KN6119,0)8,0(*0927,1*7,0w

m/KN3824,0)5,0(*0927,1*7,0w

m/KN6119,0)8,0(*0927,1*7,0w

m/KN7649,0)1(*0927,1*7,0w


21/22

b). wind pressure at height z=20[m]

5411,15169,0*9815,2)20(c*)20(c)20(c

c*)20(c*q)20(w

rge

peref2

Where :

)z(cg =gust factor


9815,2]2830,0*2[5,31)]20(I*2[g1)20(cg

Where:

g=3, 5peak factory


5169,0)20(ln*24,0)z

20(ln*)z(k)20(c

2830,0)20ln(*5,2

12,2

z

20ln*5,2

I(20)

222

0

0

2

rr

0

Where:





22/22

;3,0C

;8,0C

;5,0C

;8,0C

;0,1C

pE

pD

pC

pB

pA


2

E

2

D

2

C

2

B

2

A

m/KN3236,0)3,0(*5411,1*7,0w

m/KN8630,0)8,0(*5411,1*7,0w

m/KN539,0)5,0(*5411,1*7,0w

m/KN8630,0)8,0(*5411,1*7,0w

m/KN0788,1)0,1(*5411,1*7,0w

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