Two Way Slab Systems

8/17/2019 Two Way Slab Systems

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Two-way slab systems

Types

Flat lateDr. Ahmed Shuraim

DDM limitations

Flat SlabFlexure Design: Direct Design method (DDM)CE 472- 2007

SWB

a eFloor Frames and strips

Statical Moment concept

Minimum ThicknessDDM- flat plate-example

M0

DDM- SWB-example

Column Moment

all

M+ve & M-ve

Mcs & Mms

M+ve & M-ve

Mcs & Mms

Beamless slabs

SWB

an ax a oa

RebarsRebarsPunching shear


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Types of two-way slabs-Flat PlateFor relatively light loads

spans : 4.5-6 m

CE 472

2007

Dr. Ahmed

Shuraim


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Types of two-way slabs- Waffle slab

For relatively light loads

- .

CE 472

2007

Dr. Ahmed

Shuraim


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Types of two-way slabs-flat slabFor heavy industrial loads

spans : 6-9 m

CE 472

2007

Dr. Ahmed

Shuraim


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Types of two-way slabs- slabs with beamsFor heavy industrial loads

spans : 6-9 m

CE 472

2007

Dr. Ahmed

Shuraim


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Floor types

SWB

plate

Flat

Slab

Waffle

CE 472

2007

Dr. Ahmed

Shuraim


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Floor Frames

Frame 1 F1

e

C

e

B

m e A

e

DM

o

r

e

Frame 3 F r a

F r a F

r F r a

F3

rame F4

CE 472

2007

Dr. Ahmed

Shuraim


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Defining

design

strips

CE 472

2007

Dr. Ahmed

Shuraim


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SECTION 13.6

DDM Limitations

DIRECT DESIGN METHOD

13.6.1 Limitations

es gn o s a sys ems w n e m a ons o . . . roug . . . y e

direct design method shall be permitted.

13.6.1.1 There shall be a minimum of three continuous spans in each direction.

13.6.1.2 Panels shall be rectan ular with a ratio of lon er to shorter s an center-to-centerof

supports within a panel not greater than2.

13.6.1.3 Successive span lengths center-to-center of supports in each direction shall not

differ by more than one-third the longer span.

13.6.1.4 Offset of columns by a maximum of 10 percent of the span (in direction of offset)rom e t er ax s etween center nes o success ve co umns s a e perm tte .

13.6.1.5 All loads shall be due to gravity only and uniformly distributed over an entire panel.

Live load shall not exceed two times dead load.

13.6.1.6 For a panel with beams between supports on all sides, the relative stiffness of beams

2

12

2

21

ll

α α (13-2)

shall not be less than 0.2 nor greater than 5.0.. . . .

designed by the Direct Design Method. See 13.6.7.

13.6.1.8 Variations from the limitations of 13.6.1 shall be permitted if demonstrated by

analysis that requirements of 13.5.1 are satisfied.CE 4722007

Dr. Ahmed

Shuraim


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Statical Moment

For any continuous mem er eam

or slab), the static moment is given

by

M 0=wl2 /8=M pos+average(M neg)

0

8

2

2

0

nu llw

M =

M

o

r

e

M 0 ln

l2

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2007

Dr. Ahmed

Shuraim


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Assignment of M0 to positive and negative

M

o

r

e

CE 472

2007

Dr. Ahmed

Shuraim


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Assignment of M0 to positive and negative in the end span

CE 472

2007

Dr. Ahmed

Shuraim


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( ) ( )12121 /1/3075 llll −⋅⋅+ α

−

M

o

r

e .

0.1/ 121 ≤llα UseCE 472

2007

Dr. Ahmed

Shuraimα


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13.6.4.2 Column stri s shall be ro ortioned to resist the followin ortions in ercent of exterior negative factored moments:

/ ll 0.5 1.0 2.0

( ) 0/ 121 =llα 0=t β 100 100 1005.2≥t β 75 75 75

( ) 0.1/ 121 ≥llα t

5.2≥t β 90 75 45Linear interpolations shall be made between values shown.

12121 −⋅+− α t t

Use .t .

CE 472

2007

Dr. Ahmed

Shuraim

βt


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Span Statical Moments-FP examples=7.0 m =8 m =7.0 m

Example data:

Live load = 3 kN/m2

dead load = 2 kN/m2

= M 0= 298.31

=6.5 m

Span C-1-2:l n

=6.5-2*.2 = 6.1

m

Span A-1-2:

l n

=6.5-(0.2+.25)

= 6.05 m

mm

Wu=1.4(2+0.25*24)+1

.7*3= 16.3 kN/m2 M 0= 568.62kN-m

kN-m

e C

m

e A

Span C-2-3:*

Span A-2-3:

l n =7.0-2*.25 = 6.5

m M 0= 665.65 C-1-2

F r a F

r= . m n. - . .

m-

0= .

kN-m C-2-3

=6.5 m Frame C:l 2 =8/2+7/2 = 7.5 m

Frame A:

l 2

=7/2+ext = 4.0 m

- -

A-2-3

CE 472

2007

Dr. Ahmed

Shuraim


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Span negative- positive-FP examples=7.0 m =8 m =7.0 m

Live load = 3 kN/m2

dead load = 2 kN/m2

Slab thickness =250

mm

Wu=1.4 2+0.25*24 +147.8477.56

=6.5 m

1.7*3= 16.3 kN/m2

M 0= 568.62 kN-m295.68155.12 M 0= 298.31 kN-m

.

M 0= 665.65 kN-m

432.67

232.98

.

223.82

120.52 M = 344.34 kN-m= . m

C-1-2432.67223.82

=6.5 m Frame C:l 2 =8/2+7/2 = 7.5 m

Frame A:

l 2

=7/2+ext = 4.0 m

C-2-3

A-1-2

A-2-3

CodeCE 472

2007

Dr. Ahmed

Shuraim


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FP- Reinforcement=7.0 m =8 m =7.0 m

6.5/46.5/48/2-6.5/4 7/2-6.5/47/2-6.5/46.5/4

2 5 0

2 5 0

=6.5 m

0 φ 1 4 @ 2 0

0

φ 1 4

@

0 1 2 @ 2 5 0 φ 1

2

φ 2 0 @ 2

4 @

2 8 0

φ 1 2 @ 2

@ 2 5 0

= . m

r i p

r i p

r ps-7/47/48/2-7/4 7/4

7/47/4 φ 1

φ 1

CS bot

=6.5 m Frame C:l 2 =8/2+7/2 = 7.5 m

Frame A:

l 2

=7/2+ext = 4.0 m l u m n

s t

l u m n

s

Strips-A

CS top

MS top

A-1-2 A-2-3

C C MS bot

CE 472

2007

Dr. Ahmed

Shuraim


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FP-Reinforcement detailing in frame C

φ20@240φ20@240 φ14@250φ14@250

φ14@280 φ14@200φ14@200

φ12@250φ12@250 φ12@250φ12@250

Column strip

φ12@250 φ12@250φ12@250

middle strip

Calculation sheets

CE 472

2007

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Shuraim


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Span C-1-2 flexure

CE 472

2007

Dr. Ahmed

Shuraim


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- -

CE 472

2007

Dr. Ahmed

Shuraim


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Span A-2-3 flexure

CE 472

2007

Dr. Ahmed

Shuraim


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- -

CE 472

2007

Dr. Ahmed

Shuraim


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Span A-1-2 flexure

CE 472

2007

Dr. Ahmed

Shuraim


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- -

CE 472

2007

Dr. Ahmed

Shuraim


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Span Static Moments-SWB examples=7.0 m =8 m =7.0 m

Example data:

Live load = 3 kN/m2

dead load = 3.682 M 0= 298.31

=6.5 m

Span C-1-2:

l n

=6.5-2*.2 = 6.1

m

Span A-1-2:

l n

=6.5-(0.2+.25)

= 6.05 m

Slab thickness =180

mm

Wu=1.4(3.68+0.18*24

)+1.7*3= 16.3 kN/m2

M 0= 568.62kN-m

kN-m

e C

m

e A

Span C-2-3:*

Span A-2-3:

l n =7.0-2*.25 = 6.5

m M 0= 665.65 C-1-2

F r a F

r= . m n. - . .

m-

0= .

kN-m C-2-3

=6.5 mFrame C:

l 2 =8/2+7/2 = 7.5 m

Frame A:

l 2

=7/2+ext = 4.0 m

- -

A-2-3

CE 472

2007

Dr. Ahmed

Shuraim

Code


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SWB-Reinforcement

=7.0 m =8 m =7.0 m

6.5/46.5/48/2-6.5/4 7/2-6.5/47/2-6.5/46.5/4

3 0 0

3 0 0

=6.5 m

0 φ 1 2 @ 3 0 0

φ 1 2 @

0 1 4 @ 3 0 0 φ 1

2

Strips-C φ 1 2 @ 3

2 @

3 0 0

φ 1 4 @ 2

@

3 0 0

= . m

CS top

CS bot

r i p

r i p

7/47/48/2-7/4 7/47/47/4

φ 1

φ 1

=6.5 mFrame C:

l 2 =8/2+7/2 = 7.5 m

Frame A:

l 2

=7/2+ext = 4.0 m l u m n

s t

l u m n

s

MS topMS bot

A-1-2 A-2-3

C C

Strips-A beamsCE 472

2007

Dr. Ahmed

Shuraim


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SWB-Reinforcement detailing in frame C

φ12@300φ12@300 φ12@300φ12@300

φ12@300 φ12@300φ12@300

Column strip

φ14@250φ14@250 φ12@300φ12@300

φ12@300 φ14@300φ14@300

middle stripCE 472

2007

Dr. Ahmed

Shuraim


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Minimum thickness- flat plate & slabs9.5.3.2 For slabs without interior beams spanning between the supports and having a ratio of long to short

span not greater than 2, the minimum thickness shall be in accordance with the provisions of Table 9.5(c) and

shall not be less than the following values:

(a) Slabs without drop panels as defined

in Section 13.3.7.1 and 13.3.7.2 120 mm

(b) Slabs with drop panels as defined inSection 13.3.7.1 and 13.3.7.2 100 mm

Without drop panels With drop panels

Exterior panels Interior Exterior panels Interior

Yield

strength,

f MPa

. c -

Without

edge beams

With edge

beams

Without

edge beams

With edge

beams

300nl nl nl nl nl nl

33

36 36 36

40 40

42030

nl 33

nl 33

nl 33

nl 36

nl 36

nl

28

n 31

n 31

n 31

n 34

n 34

n

CE 472

2007

Dr. Ahmed

Shuraim


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Minimum thickness- flat plate & slabs-

Example=7.0 m =8 m =7.0 m

=6.5 mmm Ln 218

306550

30==mm

Ln 25030

7500

30 ==mm Ln 218

306550

30 ==

Ln 7500 == mm L

n 2186550

==mm L

n 2186550

=== . m

3333

=6.5 m mm Ln 21830

655030

==mm Ln 218

306550

30== mm Ln 250

307500

30==

CE 472

2007

Dr. Ahmed

Shuraim


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9.5.3.3 For slabs with beams spanning between the supports on all sides, the minimum

Minimum thickness- Slab with beams

thickness shall be as follows:

(a) For mα equal to or less than 0.2, the provisions of Section 9.5.3.2 shall apply;

(b) For mα greater than 0.2 but not greater than 2.0, the thickness shall not be less than

( )2.053615008.0

−+

⎟⎟ ⎠

⎞

⎜⎜⎝

⎛

+=

m

y

n

f

hα β

l (9-12)

an no ess an mm;

(c) For mα greater than 2.0, the thickness shall not be less than

8.0 ⎟

⎞

⎜⎜

⎛

+ y

n

f

l

β 936+=h (9-13)

and not less than 90 mm;

(d) At discontinuous edges, an edge beam shall be provided with a stiffness ratio α not

less than 0.80 or the minimum thickness required by Eq. (9-12) or (9-13) shall be

increased by at least 10 percent in the panel with a discontinuous edge.α = ratio of flexural stiffness of beam section to flexural stiffness of a width of

slab bounded laterally by centerlines of adjacent panels (if any) on each side

of beam. See Chapter 13

mα = average value of a for all beams on edges of a panel

β = ratio of clear spans in long to short direction of two-way slabsCE 472

2007

Dr. Ahmed

Shuraim


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Minimum thickness- SWB

=7.0 m =8 m =7.0 m

=6.5 m15008.0 ⎟⎟

⎞⎜⎜⎛

+ y

n

f l

08.12.67.6

3.05.63.07 ==

−−= β

h=158.3 mm

24.12.670.7

3.05.63.08 ==−

−= β

= β 936+

= .

15.170.73.08 ==−

= β

=7.0 m

... −

h=179.4 mm

=6.5 m

CE 472

2007

Dr. Ahmed

Shuraim


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CE 472

2007

Dr. Ahmed

Shuraim


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CE 472

2007

Dr. Ahmed

Shuraim


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CE 472

2007

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Shuraim


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Two-way shear- around C2

[ ] kN V u 1.81871.0*61.0)75.6*5.7(3.16 =−=y1=d_avg+yc = 0.21+0.4= 0.61 m

x1=d_avg+yc = 0.21+0.5= 0.71 m

mmmb

c

264064.2)71.061.0(2

25.14.0

.

0 ==+=

== β

kN V c 12011000*6

210*2640*25)1(

25.12 =+= k V c 0.924

1000*3

210*2640*25==

kN V c 11971000*12

210*2640*25)2(

2640210*40 =+=

OK Not

Vu

c .185.0

1.818

..


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Two-way shear- around A1

**

y1=d_avg/2+yc/2 +ext= 0.21/2+0.4/2+0.5= 0.805 m

x1=d_avg/2+xc/2 +ext= 0.21/2+0.4/2+0.5= 0.805 m

u ..... −

c 0.14.0== β

mmmb

210*1610*25

161061.1)805.0805.0(

.

0 ==+= kN V c 5.563

1000*3

210*1610*25==

c1000*6

0.1 =+=

210*1610*25*

c1000*12

1610 ==

V c 5.563*75.0 ==φ

Vu..

9.233

CE 472

2007

Dr. Ahmed

Shuraim


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bw=300 mm

hw=420 mm

hf =180 mm

Span C-1-2

b I =α s

CE 472

2007

Dr. Ahmed

Shuraim


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Torsional member-Slab with beams- βt

bw=300 mm

hw=420 mm

=

CE 472

2007

Dr. Ahmed

Shuraim


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CE 472

2007

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Shuraim


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Distribution of Moments in flat lates

CE 472

2007

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Shuraim


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Effect of edge beams on moments in slabs

CE 472

2007

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Shuraim


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Dr. Ahmed Shuraim

CE 472- 2003

CE 472 2007 Dr. Ahmed Shuraim


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CE 472

2007

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Shuraim


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CE 472

2007

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Shuraim


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Two Way Slab Systems

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