sbsfid12683dif.pdf

8/10/2019 sbsfid12683dif.pdf

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Design of Flat Slabs

Dr. Ayman Hussein Hosny

Professor of RC Structures


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Lecture Layout

Types Analysis Concrete dimensions

Slab thickness

Empirical analysis

Frame Analysis Drop thickness

Columns

Finite element

Check unchin Column heads Beams (if any)

Examples


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Types of Flat Slabs

Regular flat slabs

Slab

co umn


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Flat slab with Drop Parts

Slab

drop

column


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Flat slab with Drop Parts


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Failures of Flat Slab


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Punching failure


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Punching failure


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Flat slab with Column Heads

Flat slab

Column head or

column capital

column


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Flat slab with Column Heads


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Flat Slab with Drop Part and

o umn ea

Flat slab


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REAL BUILDING


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Concrete Dimensions

Minimum thickness (ts)= 150 mm

Thickness depends on L

11 22

Without drop

ts Lext/32 t L /36

With drop

s ext

ts Lint/40


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Example 1:

Without drops

ts is bigger of

150 mm

6000/32=187.5 mm

= .

Take ts = 200 mm


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Example 2:

ts

is bigger of

6000/36=166.6 mm

= mm

Take ts = 180 mm

Note slight effect of

dro anel here


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When to use drop?

If ts is large

If heavy live load (> 5-8 kN/m2)

In general, drop parts are not common in

residential buildings The are common in factories and buildin s

with false ceilings


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Drop panels

Drop panels below

s a

ona pane s

above slab


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d

td

ts

/4

, d s

Drop panel width (X) min

XLmin/2

= m n

Example

t =80mm X=2750 mm


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Columns

Bmin=bigger of

300 mm

h/15 Spacing/20


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Column Head

Mostly used to

safeguard against

unchin max= 45 degrees

max= min

What if >45 degrees?


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Marginal Beams

Might be used

Carry walls

Resist lateral loads


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Analysis of Flat Slabs

Empirical method 3rd civil

Frame analysis 3rd civil

Yield line analysis


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Empirical method conditions

Columns lay on straight lines (or maximum

eccen r c y=

Number of spans at least three in each direction erence etween two a acent spans w t n

Maximum difference between largest and smallest

span n e same rec on w n

Inner spans larger or equal outer spans

ax mum span m n mum span .

Constant slab thickness, ts

ve oa < ea oa


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Example

Columns lay on straight lines (or

=

Number of spans at least three

in each direction

spans within 10%

Maximum difference between

arges an sma es span n e

same direction within 20%

Inner spans larger or equal outer

spans

Maximum span/minimum

span1.30

Constant slab thickness, ts

Live load< 2* Dead load


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Analysis Procedure

Obtain loads, Ws Consider wall loads

Get straining actions in long and short

rec ons Divide into strips

Design of sections


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SOLUTION

Divide slab into

column and field

strips in bothdirections


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In case of drop panels

Calculation in Long


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Calculation in Long

In long direction, L1

Mo=WsL2(L1-2/3D)2/8

o

length L1 having a width of

2 Distribute Mo between

column and field strips as

er the followin table


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Design

Compute moment per meter

Choose rft (same regulations as solid

5-10 bars/meter

n mum ame er= mm

Preferable to have constant number of bars

per meter

Calculation in Short


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Calculation in Short

In short direction, L2

Mo=WsL1(L2-2/3D)2/8

o 2having a width of L1

Distribute Mo between column and fieldstrips as per same table

Note that larger moment results in longer-

N t


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Notes

Table ratios are based on column strip

width equals field strip width

,field strip moment by the following ratio, R

=rea w o e s r p a . . o . .

Reduce column strip moments accordingly

E l


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Example

F.S.=4.25 m

C.S.=2.75 m


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D t il f RFT


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Details of RFT


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Effect of transferred moment on slab


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Effect of transferred moment on slab

Moment transferred to column partially by flexure and

par a y y ors on

fflexure =

1

qtorison

12

1

bf

+

2

s flexure . s

Punching


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Punching

q up

=

o

up

o=15.1=

bo=2A+B bo

=A+B30.1= 50.1=

Punching check


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Punching check

=qq

d columnexterior.......3

.......

=

0

]20.0[80.0b

qc

cucup +=

columncorner.......2=

]50.0[316.0 fbaq cucup +=

fcu=

2

.c

cup The least

shall be.cup considered

EXAMPLE


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EXAMPLE

Data

Walls=3 kN/m2

= 2Flooring=2 kN/m2

cu= a

Example


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Example

LLWallsFCtw css +++=

2/143322524.0 mkNxws =+++=

210

/215.114

mmd

mkNxwus

=

==

257]5.35.3[21 kNxxQ ==

0

25700050.1

9104552

x

mmxb ==

.210910

mmx

q ==

]200[800 fd

q cu+=EXAMPLE


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]20.0[80.0qcu +=EXAMPLE

2

0

302102x

c

==

.5.1

.910

.

a

cup

..b

qc

cup =

2/11.2

5.1]

35050.0[316.0 mmNq

cup =+=

316.0qc

cucup =

cupqq >

2/41.1

5.1

30316.0 mmNqcup ==

USE

COLUMN2

/6.1 mmNqcup =

HEAD

EXAMPLE


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EXAMPLE

]20.0[80.0 fd

q cucu +=

2/14.125700050.1 mmNxq ==

2

0

/64.130

20.02102

80.0 mmx

c

=+=

50.0316.0

5.11610

fa cu+=

2/11.2

3080550.0316.0 mmN

c

=+=

316.0

5.1805

fcu

cup

=

230

c

==

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