RC2 Lecture 3.1 - Design of Two-Way Floor Slab System

Reinforced Concrete II

Hashemite University

The Hashemite University Department of Civil Engineering

Lecture 3.1 – De Desi Design sign gn of TwoTwo Tw o way Floor Slab Slab System .

Dr. D r . Hazim Hazi m Dwairi Dw ai r i

The Th e H Hashe Hashemite ash emite m i t e Universit Un i v er s i ty


One e -w a y a n d T w o - w a y Sl a b Behavior • OneOne-way -way slabs direction. • TwoTwo-way -way slabs carry load in two directions.

Dr. Hazim Dwairi

Dr Hazim Dwairi

The Hashemite Hashemite Universit y


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One e --w w a y a n d T w o -w - w a y Sl a b Behavior • OneOne-way and action carry load in two directions.

• OneOne-way slabs: Generally, long side/short side > 2.0 The Hashemite Universit y

Dr. Hazim Dwairi


T y p es o f T w o -w - w a y Sl a b s

Two-way slab with b eams

Flat slab with drop panels Dr. Hazim Dwairi

Dr Hazim Dwairi

The Hashemite Universit y


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T y p es o f T w o -w - w a y Sl a b s

Waffle Slab

Flat slab without drop panels Dr. Hazim Dwairi



Co l u m n C o n n ect i o n s i n F l a t Sl a b s

. 2. Without drop panel 3. With column capital or crown 4. Without column capital or crown Dr. Hazim Dwairi

Dr Hazim Dwairi



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J o i s t Co n st r u ct i o n 30cm 50–75cm

2.5cm

• The two two--way ribbed slab and waffled slab system: General thickness of the slab is 50mm to 100mm. The Hashemite Universit y

Dr. Hazim Dwairi


E co n o m i c Ch o i c es i n Sl a b s • Flat Plate with out d rop p anels: suitable span 2 . . . - . Advan tages – Low cost formwork – – Exposed flat ceilings – – Fast –

sa van ages – Low shear capacity – – Low Stiffness (notable deflection) –

Dr. Hazim Dwairi

Dr Hazim Dwairi



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E co n o m i c Ch o i c es i n Sl a b s • Flat Slab wi th dr op p anels: s uit able span 6.0 2 . . - . Ad vantages – Low cost formwork – – Exposed flat ceilings – – Fast –

sa van ages – Need more formwork for capital and panels –


Dr. Hazim Dwairi


E co n o m i c Ch o i c es i n Sl a b s • Waffle Slabs: su itable span 9.0 to 15 m with 2 . – – . Ad vantages – Carries heavy loads – – Attractive – Attractive exposed ceilings – Fast –

sa van ages – Formwork with panels is expensive –

Dr. Hazim Dwairi

Dr Hazim Dwairi



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E co n o m i c Ch o i c es i n Sl a b s • OneOne-way Slab on beams: sui suittable able span 3.0 to 2 . . - . – Can be used for larger spans with relatively higher – cost and higher deflections

• OneOne-way jois joistt floor system is suitable span 6.0 to 9.0 m wit h L L= 4.0 – – 6.0 kN/m kN/m 2 –

, relative low

– Expensive formwork expected. –


Dr. Hazim Dwairi


Co m p a r i so n o f O n e e-- a n d T w o - - w a y Sl a b s B eh a v i o r w s =load taken by short directio n w l = load taken by long di rection

A

5ws Ls 4

ws wl

=

Ll 4 Ls 4

Dr. Hazim Dwairi

Dr Hazim Dwairi

=

=

B

5wl Ll 4

For Ll = 2Ls ⇒ ws

= 16wl



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St a t i c E q u i l i b r i u m f o r T w o - w w ay Slabs • Analogy o f t wo-way s lab t o p lank an d Consider Section A-A: Moment per m width in planks:

⇒

=

wl 12

kN - m/m

Total Moment l 12 ⇒ M T = (wl 2 ) kN - m 8 Dr. Hazim Dwairi



St a t i c E q u i l i b r i u m f o r T w o - w w ay Slabs Uniform l oad on each beam:

⇒

1

2

kN/m

wl 1 ⎞ l 22 ⎛ ⎟ kN - m Moment in one beam (Sec: B-B) ⇒ M lb = ⎜ ⎝ 2 ⎠ 8 2

⇒

Dr. Hazim Dwairi

Dr Hazim Dwairi


= w1

l

8

-m


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M et h o d o f D e si g n (1) Direct Design Metho Method d (DDM): Limited to slab systems with uniformly distributed loads and supported on equally spaced columns. Method uses a set of coefficients to determine the design moment at critical sections. TwoTwo-way the ACI Code 13.6.1 must be analyzed using more accurate procedures. Dr. Hazim Dwairi



M et h o d o f D e si g n (2) Equiv Equivalent alent Frame Method (EFM) : A threethree-dimensional building is divided into a series of twotwo -dimensional equivalent frames by cutting the building along lines midway between columns. The resulting frames are considered directions of the building and treated floor by floor. Dr. Hazim Dwairi

Dr Hazim Dwairi



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E q u i v a l en t F r a m e M et h o d ( E F M )

Longitudinal equivalent frame

Dr. Hazim Dwairi

Transverse equivalent frame



E q u i v a l en t F r a m e M et h o d ( E F M ) Elevation of the frame

view

Dr. Hazim Dwairi

Dr Hazim Dwairi



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Co l u m n a n d M i d d l e St r i p s The slab is ro en up nto column and middle strips for analysis L/4 L/4

L/4 L/4

L/4 Dr. Hazim Dwairi

L/4

L/4


L/4


M i n i m u m Sl a b T h i ck n ess f o r Tw o o -w -w a y Co n st r u c t i o n • The ACI Code 9.5.3 specifies a minimum slab . empirical limitations for calculating the slab thickness (h), which are based on experimental research. If these limitations are not met, it will be necessary to compute deflection. • between supports - Table 9.5 (c) and: – With drop panels …………………… 125 mm – – Without drop panels ……………….. 100 mm – Dr. Hazim Dwairi

Dr Hazim Dwairi



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M i n i m u m Sl a b T h i ck n ess f o r Tw o o -w -w a y Co n st r u c t i o n • For slabs with beams spanning between the the

(a ) for α fm

> 2.0 ⇓ > 90 mm

(b) for 0.2 < α fm

< 2.0 ⇓ > 125mm The Hashemite Universit y

Dr. Hazim Dwairi


M i n i m u m Sl a b T h i ck n ess f o r Tw o o -w -w a y Co n st r u c t i o n (c) for α m

≤ 0.2 ⇓

• With drop panels: h > 125mm • Without drop panels: h > 100mm

Dr. Hazim Dwairi

Dr Hazim Dwairi



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M i n i m u m Sl a b T h i ck n ess f o r Tw o o -w -w a y Co n st r u c t i o n

• Definitions: 



h = Minimum slab thickness without interior beams. ln = Clear span in the long direction measured face to face of column

ββ =



e ra o o

e ong o s or c ear

span

α αm= The average value of a for all



beams on the sides of the panel. The Hashemite Universit y

Dr. Hazim Dwairi


Beam m --tt o o -Sl - Sl a b St i f f n ess R a t i o , • Accounts Accounts for stiffness effect effect of beams located panel adjacent to beams.

α =

flexural stiffness of beam flexural stiffness of slab

Dr. Hazim Dwairi

Dr Hazim Dwairi



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Beam m --tt o o -Sl - Sl a b St i f f n ess R a t i o , α =

4E cb I b / l 4E cs I s

=

E cb I b E cs I s

= Modulus of elasticity of beam E sb = Modulus of elasticity of slab I b = Moment of inertia of uncracked beam Is = Moment of inertia of uncracked slab

E cb

• With width bounded laterally by centerline of adjacent panels on each side of the beam. Dr. Hazim Dwairi



B ea m a n d S l a b Sect i o n s f o r ca l c u l a t i o n o f

Dr. Hazim Dwairi

Dr Hazim Dwairi



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Dr. Hazim Dwairi




Spandrel (Edge) Beam

Dr. Hazim Dwairi

Dr Hazim Dwairi


Interior Beam


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P CA Ch a r t s f o r ca l c u l a t i o n o f

Dr. Hazim Dwairi



P CA Ch a r t s f o r ca l c u l a t i o n o f

Dr. Hazim Dwairi

Dr Hazim Dwairi



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E x a m p l e : Fl a t S l a b w i t h o u t B e a m s A fl at plate floo r system . . is su pport ed on 0.50m square columns. Determine the minimu m slab thickness required for the interior and corner anels. Use f’ c = 28 MPa and f y = 420 MPa

The Hashemite Hashemite Universit University y

Dr. Hazim Dwairi


E x t er i o r Sl a b • Slab thickness, from table for f y = 420 MPa and

hmin

=

hmin

=

l n

30 l n = 7.3 − 0.5 = 6.8m

Dr. Hazim Dwairi

Dr Hazim Dwairi

6.8 × 1000 30

= 226.7mm ⇒ use 230mm The Hashemite Universit y


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I n t er i o r Sl a b • Slab thickness, from table for f y = 420 MPa and

hmin

=

l n

33 l n = 7.3 − 0.5 = 6.8m hmin

=

6.8 × 1000 33

Dr. Hazim Dwairi

= 206.1mm ⇒ use 210mm The Hashemite Universit y


E x a m p l e : F l a t S l a b w i t h B ea m s A fl at plate floo r system . . suppor ted on beams in two directions which supported on 0.40m square col umns. Determine the minimu m slab thickness required for an interior anel. Use f’ c = 28 MPa and f y = 414 MPa Dr. Hazim Dwairi

Dr Hazim Dwairi



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F l a t Sl a b w i t h B ea m s E x a m p l e Beam cross cross--sections Al l Dim ens io ns in mi ll im eter s

Ib = 7.952 x 10 9 mm 4 Ib = 1.170 x 10 10 mm 4 The Hashemite Universit y

Dr. Hazim Dwairi


I n t er i o r Sl a b * Long Direction : I beam

= 1.170 ×1010 mm 4 3

I slab

=

α long =

= 2.916 ×109 mm4

12 EI beam EI slab

= 4.01

* Short Direction : I slab

=

(7300)(180) 3

α short = Dr. Hazim Dwairi

Dr Hazim Dwairi

12 EI beam EI slab

= 3.548 ×109 mm 4

= 3.30 The Hashemite Universit y


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I n t er i o r Sl a b

* The Average α fm for interior slab : 4.01 + 3.3

α avrg =

= 3.66

Compute the β Coefficient : β =

l long l short

=

7.3 − 0.4 6.0 − 0.4

= 1.232

Compute thickness for α fm

⎛ ⎝ h=

>2

⎞ 414 ⎞ ⎟⎟ 6.9⎛ 0.8 + ⎜ ⎟ 1400 ⎠ 1400 ⎠ ⎝ = 36 + 9 β 36 + 9 × 1.236

l n ⎜⎜ 0.8 +

f y

USE h = 180mm

= 160.4mm The Hashemite Universit y

Dr. Hazim Dwairi


Thickness of Edge & Corner Slabs * Compute α fm in long direction : I L −beam I slab

=

= 7.952 ×109 mm 4 (3200)(180)3 12

= 1.555 ×109 mm 4

7.952 × 109

= 5.11 1.555 × 109 * Compute α fm in short direction :

α long

I slab

=

=

(3850)(180)3

α short = Dr. Hazim Dwairi

Dr Hazim Dwairi

12 7.952 × 109 1.871× 10

9

= 1.871×109 mm4 = 4.25 The Hashemite Universit y


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Thickness of Edge & Corner Slabs 5.11 .

α m

=

3.30 α fm

=

.

3.30 + 5.11 + 3.30 + 4.01 4

= 3.93

4.01 5.11 4.25

+ . + .

.

+ .

= 4.17

4

4.01 The Hashemite Universit y

Dr. Hazim Dwairi


Thickness of Edge & Corner Slabs 4.01

α fm .

4.25

4.25 + 4.01 + 3.30 + 4.01

=

4 n

= .

− .

− .

= 3.89

= . m

Compute the β Coefficient : 4.01

β =

l long l short

=

7.3 − 0.30 6.0 − 0.30

= 1.230

fm

⎛ h = ⎝

⎞ 414 ⎞ h = 180mm ⎟⎟ 7.00⎛ 0.8 + ⎜ ⎟ 1400 ⎠ 1400 ⎠ ⎝ = = 163.0mm 36 + 9 β 36 + 9 × 1.230

l n ⎜⎜ 0.8 +

Dr. Hazim Dwairi

Dr Hazim Dwairi

f y



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RC2 Lecture 3.1 - Design of Two-Way Floor Slab System

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