Lecture 3.1 Lecture 3.1 Design of Two Design of Two- - way - - PDF document

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Lecture 3.1 Lecture 3.1 Design of Two Design of Two- - way - - PDF document

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Reinforced Concrete II Hashemite University The Hashem ite University Departm ent of Civil Engineering Lecture 3.1 Lecture 3.1 Design of Two Design of Two- - way Floor Slab System way Floor Slab System Dr Hazim Dwairi Dr Hazim

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SLIDE 1

Reinforced Concrete II Hashemite University

  • Dr. Hazim Dwairi

1

The Hashem ite University Departm ent of Civil Engineering

Lecture 3.1 Lecture 3.1 – – Design of Two Design of Two-

  • way Floor Slab System

way Floor Slab System

Dr Hazim Dwairi Dr Hazim Dwairi

Reinforced Concrete II Reinforced Concrete II

  • Dr. Hazim Dwairi
  • Dr. Hazim Dwairi

The Hashemite University The Hashemite University

  • Dr. Hazim Dwairi
  • Dr. Hazim Dwairi

One One-

  • w a y a nd Tw o

w a y a nd Tw o-

  • w a y Sla b

w a y Sla b Beha v ior Beha v ior

  • One

One-

  • way slabs

way slabs carry load in one carry load in one carry load in one carry load in one direction. direction.

  • Two

Two-

  • way slabs

way slabs carry load in two carry load in two directions. directions.

Reinforced Concrete II Reinforced Concrete II

  • Dr. Hazim Dwairi
  • Dr. Hazim Dwairi

The Hashemite University The Hashemite University

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SLIDE 2

Reinforced Concrete II Hashemite University

  • Dr. Hazim Dwairi

2

One One-

  • w a y a nd Tw o

w a y a nd Tw o-

  • w a y Sla b

w a y Sla b Beha v ior Beha v ior

  • One

One-

  • way and

way and two two way slab way slab two two-way slab way slab action carry action carry load in two load in two directions. directions.

Reinforced Concrete II Reinforced Concrete II

  • Dr. Hazim Dwairi
  • Dr. Hazim Dwairi

The Hashemite University The Hashemite University

  • One

One-

  • way slabs: Generally,

way slabs: Generally, long side/short side > 2.0 long side/short side > 2.0

Ty p es of Tw o Ty p es of Tw o-

  • w a y Sla bs

w a y Sla bs

Reinforced Concrete II Reinforced Concrete II

  • Dr. Hazim Dwairi
  • Dr. Hazim Dwairi

The Hashemite University The Hashemite University

Flat slab with drop panels Two-way slab with beams

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SLIDE 3

Reinforced Concrete II Hashemite University

  • Dr. Hazim Dwairi

3

Ty p es of Tw o Ty p es of Tw o-

  • w a y Sla bs

w a y Sla bs

Reinforced Concrete II Reinforced Concrete II

  • Dr. Hazim Dwairi
  • Dr. Hazim Dwairi

The Hashemite University The Hashemite University

Flat slab without drop panels Waffle Slab

Colum n Connections in Fla t Sla bs Colum n Connections in Fla t Sla bs

1 With drop panel

Reinforced Concrete II Reinforced Concrete II

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

Reinforced Concrete II Hashemite University

  • Dr. Hazim Dwairi

4

Joist Construction Joist Construction

30cm 50–75cm 2.5cm Reinforced Concrete II Reinforced Concrete II

  • The two

The two-

  • way ribbed slab and waffled slab

way ribbed slab and waffled slab system: General thickness of the slab is 50mm system: General thickness of the slab is 50mm to 100mm. to 100mm.

  • Dr. Hazim Dwairi
  • Dr. Hazim Dwairi

The Hashemite University The Hashemite University

Econom ic Choices in Sla bs Econom ic Choices in Sla bs

  • Flat Plate without drop panels: suitable span

Flat Plate without drop panels: suitable span 6 0 to 7 5 m with LL= 3 0 6 0 to 7 5 m with LL= 3 0 5 0 5 0 kN kN/m /m2 6.0 to 7.5 m with LL= 3.0 6.0 to 7.5 m with LL= 3.0 -

  • 5.0

5.0 kN kN/m /m2 Advantages Advantages

– Low cost formwork Low cost formwork – Exposed flat ceilings Exposed flat ceilings – Fast Fast

Disad antages Disad antages

Reinforced Concrete II Reinforced Concrete II

Disadvantages Disadvantages

– Low shear capacity Low shear capacity – Low Stiffness (notable deflection) Low Stiffness (notable deflection)

  • Dr. Hazim Dwairi
  • Dr. Hazim Dwairi

The Hashemite University The Hashemite University

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SLIDE 5

Reinforced Concrete II Hashemite University

  • Dr. Hazim Dwairi

5

Econom ic Choices in Sla bs Econom ic Choices in Sla bs

  • Flat Slab with drop panels: suitable span 6.0

Flat Slab with drop panels: suitable span 6.0 to 7 5 to 7 5 m with LL= 4 0 with LL= 4 0 7 0 7 0 kN kN/m /m2 to 7.5 to 7.5 m m with LL= 4.0 with LL= 4.0 -

  • 7.0

7.0 kN kN/m /m2 Advantages Advantages

– Low cost formwork Low cost formwork – Exposed flat ceilings Exposed flat ceilings – Fast Fast

Disad antages Disad antages

Reinforced Concrete II Reinforced Concrete II

Disadvantages Disadvantages

– Need more formwork for capital and panels Need more formwork for capital and panels

  • Dr. Hazim Dwairi
  • Dr. Hazim Dwairi

The Hashemite University The Hashemite University

Econom ic Choices in Sla bs Econom ic Choices in Sla bs

  • Waffle Slabs: suitable span 9.0 to 15 m with

Waffle Slabs: suitable span 9.0 to 15 m with LL= 4 0 LL= 4 0 7 0 7 0 kN kN/m /m2 LL= 4.0 LL= 4.0 – – 7.0 7.0 kN kN/m /m2 Advantages Advantages

– Carries heavy loads Carries heavy loads – Attractive exposed ceilings Attractive exposed ceilings – Fast Fast

Disad antages Disad antages

Reinforced Concrete II Reinforced Concrete II

Disadvantages Disadvantages

– Formwork with panels is expensive Formwork with panels is expensive

  • Dr. Hazim Dwairi
  • Dr. Hazim Dwairi

The Hashemite University The Hashemite University

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SLIDE 6

Reinforced Concrete II Hashemite University

  • Dr. Hazim Dwairi

6

Econom ic Choices in Sla bs Econom ic Choices in Sla bs

  • One

One-

  • way Slab on beams: suitable span 3.0 to

way Slab on beams: suitable span 3.0 to 6 0 m with LL= 3 0 6 0 m with LL= 3 0 5 0 5 0 kN kN/m /m2 6.0 m with LL= 3.0 6.0 m with LL= 3.0 -

  • 5.0

5.0 kN kN/m /m2

– Can be used for larger spans with relatively higher Can be used for larger spans with relatively higher cost and higher deflections cost and higher deflections

  • One

One-

  • way joist floor system is suitable span

way joist floor system is suitable span 6.0 to 9.0 m with LL= 4.0 6.0 to 9.0 m with LL= 4.0 – – 6.0 6.0 kN kN/m /m2

– Deep ribs the concrete and steel quantities are Deep ribs the concrete and steel quantities are

Reinforced Concrete II Reinforced Concrete II

Deep ribs, the concrete and steel quantities are Deep ribs, the concrete and steel quantities are relative low relative low – Expensive formwork expected. Expensive formwork expected.

  • Dr. Hazim Dwairi
  • Dr. Hazim Dwairi

The Hashemite University The Hashemite University

Com p a rison of One Com p a rison of One-

  • a nd Tw o

a nd Tw o-

  • w a y Sla bs Beha v ior

w a y Sla bs Beha v ior

ws =load taken by short direction wl = load taken by long direction δA = δB

EI Ll w EI Ls w 384 5 384 5

4 l 4 s

=

Reinforced Concrete II Reinforced Concrete II

  • Dr. Hazim Dwairi
  • Dr. Hazim Dwairi

The Hashemite University The Hashemite University

EI EI 384 384

l s 4 4 l s

16 2Ls Ll For w w Ls Ll w w = ⇒ = =

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SLIDE 7

Reinforced Concrete II Hashemite University

  • Dr. Hazim Dwairi

7

Sta tic Eq uilibrium for Tw o Sta tic Eq uilibrium for Tw o-

  • w a y

w a y Sla bs Sla bs

  • Analogy of two-way slab to plank and

beam floor

Consider Section A-A: Moment per m width in planks: m/m

  • kN

8

2 1

wl M = ⇒

beam floor

Reinforced Concrete II Reinforced Concrete II

  • Dr. Hazim Dwairi
  • Dr. Hazim Dwairi

The Hashemite University The Hashemite University

Total Moment 8

( )

m

  • kN

8

2 1 2 T

l wl M = ⇒

Sta tic Eq uilibrium for Tw o Sta tic Eq uilibrium for Tw o-

  • w a y

w a y Sla bs Sla bs

wl Uniform load on each beam: Moment in one beam (Sec: B-B) Total Moment in both beams: kN/m 2

1

wl ⇒ m

  • kN

8 2

2 2 1 lb

l wl M ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = ⇒

( )

kN

2 2

l l M

Reinforced Concrete II Reinforced Concrete II

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  • Dr. Hazim Dwairi

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Total Moment in both beams:

( )

m

  • kN

8

2 1

wl M = ⇒

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SLIDE 8

Reinforced Concrete II Hashemite University

  • Dr. Hazim Dwairi

8

Method of Design Method of Design

(1) (1) Direct Design Method (DDM): Direct Design Method (DDM): Limited to slab systems with uniformly distributed Limited to slab systems with uniformly distributed loads and supported on equally spaced columns. loads and supported on equally spaced columns. Method uses a set of coefficients to determine Method uses a set of coefficients to determine the design moment at critical sections. Two the design moment at critical sections. Two-

  • way

way slab system that do not meet the limitations of slab system that do not meet the limitations of

Reinforced Concrete II Reinforced Concrete II

slab system that do not meet the limitations of slab system that do not meet the limitations of the ACI Code 13.6.1 must be analyzed using the ACI Code 13.6.1 must be analyzed using more accurate more accurate procedures. procedures.

  • Dr. Hazim Dwairi
  • Dr. Hazim Dwairi

The Hashemite University The Hashemite University

Method of Design Method of Design

(2) (2) Equivalent Frame Method (EFM) : Equivalent Frame Method (EFM) : A three A three-

  • dimensional building is divided into a

dimensional building is divided into a series of two series of two-

  • dimensional equivalent frames by

dimensional equivalent frames by cutting the building along lines midway between cutting the building along lines midway between

  • columns. The resulting frames are considered
  • columns. The resulting frames are considered

separately in the longitudinal and transverse separately in the longitudinal and transverse

Reinforced Concrete II Reinforced Concrete II

separately in the longitudinal and transverse separately in the longitudinal and transverse directions of the building and treated floor by directions of the building and treated floor by floor. floor.

  • Dr. Hazim Dwairi
  • Dr. Hazim Dwairi

The Hashemite University The Hashemite University

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SLIDE 9

Reinforced Concrete II Hashemite University

  • Dr. Hazim Dwairi

9

Equiv a lent Fra m e Method (EFM) Equiv a lent Fra m e Method (EFM)

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  • Dr. Hazim Dwairi

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Longitudinal equivalent frame Transverse equivalent frame

Equiv a lent Fra m e Method (EFM) Equiv a lent Fra m e Method (EFM)

Elevation of the frame Perspective

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Perspective view

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SLIDE 10

Reinforced Concrete II Hashemite University

  • Dr. Hazim Dwairi

10

Colum n a nd Mid d le Strip s Colum n a nd Mid d le Strip s

The slab is b k i t broken up into column and middle strips for analysis

L/4 L/4 Reinforced Concrete II Reinforced Concrete II

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  • Dr. Hazim Dwairi

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Minim um Sla b Thickness for Minim um Sla b Thickness for Tw o Tw o-

  • w a y Construction

w a y Construction

  • The ACI Code 9.5.3 specifies a minimum slab

The ACI Code 9.5.3 specifies a minimum slab thickness to control deflection There are three thickness to control deflection There are three thickness to control deflection. There are three thickness to control deflection. There are three empirical limitations for calculating the slab empirical limitations for calculating the slab thickness (h), which are based on experimental thickness (h), which are based on experimental

  • research. If these limitations are not met, it will
  • research. If these limitations are not met, it will

be necessary to compute deflection. be necessary to compute deflection.

  • For slabs without interior beams spanning

For slabs without interior beams spanning

Reinforced Concrete II Reinforced Concrete II

For slabs without interior beams spanning For slabs without interior beams spanning between supports between supports -

  • Table 9.5 (c)

Table 9.5 (c) and: and:

– With drop panels …………………… 125 mm With drop panels …………………… 125 mm – Without drop panels ……………….. 100 mm Without drop panels ……………….. 100 mm

  • Dr. Hazim Dwairi
  • Dr. Hazim Dwairi

The Hashemite University The Hashemite University

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SLIDE 11

Reinforced Concrete II Hashemite University

  • Dr. Hazim Dwairi

11

Minim um Sla b Thickness for Minim um Sla b Thickness for Tw o Tw o-

  • w a y Construction

w a y Construction

  • For slabs with beams spanning between the

For slabs with beams spanning between the supports on all sides: supports on all sides: supports on all sides: supports on all sides:

⇓ > . 2 ) (

fm

for a α mm 90 >

Reinforced Concrete II Reinforced Concrete II

  • Dr. Hazim Dwairi
  • Dr. Hazim Dwairi

The Hashemite University The Hashemite University

⇓ < < . 2 0.2 ) (

fm

for b α mm 125 >

Minim um Sla b Thickness for Minim um Sla b Thickness for Tw o Tw o-

  • w a y Construction

w a y Construction

⇓ ≤ 2 . ) (

fm

for c α

  • With drop panels:

With drop panels: h > 125mm h > 125mm

  • Without drop

Without drop panels: panels:

Reinforced Concrete II Reinforced Concrete II

h > 100mm h > 100mm

  • Dr. Hazim Dwairi
  • Dr. Hazim Dwairi

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SLIDE 12

Reinforced Concrete II Hashemite University

  • Dr. Hazim Dwairi

12

Minim um Sla b Thickness for Minim um Sla b Thickness for Tw o Tw o-

  • w a y Construction

w a y Construction

  • Definitions:

Definitions:

h = Minimum slab thickness without h = Minimum slab thickness without interior beams. interior beams. l ln = Clear span in the long direction = Clear span in the long direction measured face to face of column measured face to face of column β β Th ti f th l t h t l Th ti f th l t h t l

Reinforced Concrete II Reinforced Concrete II

β β = The ratio of the long to short clear = The ratio of the long to short clear span span αm= = The average value of a for all The average value of a for all beams on the sides of the panel. beams on the sides of the panel.

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  • Dr. Hazim Dwairi

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Bea m Bea m -

  • to

to-

  • Sla b Stiffness Ra tio,

Sla b Stiffness Ra tio, α

  • Accounts for stiffness effect of beams located

Accounts for stiffness effect of beams located along slab edge reduces deflections of along slab edge reduces deflections of along slab edge reduces deflections of along slab edge reduces deflections of panel adjacent to beams. panel adjacent to beams.

beam

  • f

stiffness flexural = α

Reinforced Concrete II Reinforced Concrete II

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  • Dr. Hazim Dwairi

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slab

  • f

stiffness flexural

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SLIDE 13

Reinforced Concrete II Hashemite University

  • Dr. Hazim Dwairi

13

Bea m Bea m -

  • to

to-

  • Sla b Stiffness Ra tio,

Sla b Stiffness Ra tio, α

b cb b cb

E / / 4E I l l I = = α

s cs s cs

E / 4E I l I

beam uncracked

  • f

inertia

  • f

Moment I slab

  • f

elasticity

  • f

Modulus E beam

  • f

elasticity

  • f

Modulus E

b sb cb

= = =

Reinforced Concrete II Reinforced Concrete II

  • With width bounded laterally by centerline of

With width bounded laterally by centerline of adjacent panels on each side of the beam. adjacent panels on each side of the beam.

  • Dr. Hazim Dwairi
  • Dr. Hazim Dwairi

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slab uncracked

  • f

inertia

  • f

Moment Is =

Bea m a nd Sla b Sections for Bea m a nd Sla b Sections for ca lcula tion of ca lcula tion of α

Reinforced Concrete II Reinforced Concrete II

  • Dr. Hazim Dwairi
  • Dr. Hazim Dwairi

The Hashemite University The Hashemite University

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SLIDE 14

Reinforced Concrete II Hashemite University

  • Dr. Hazim Dwairi

14

Bea m a nd Sla b Sections for Bea m a nd Sla b Sections for ca lcula tion of ca lcula tion of α

Reinforced Concrete II Reinforced Concrete II

  • Dr. Hazim Dwairi
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Bea m a nd Sla b Sections for Bea m a nd Sla b Sections for ca lcula tion of ca lcula tion of α

Reinforced Concrete II Reinforced Concrete II

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Spandrel (Edge) Beam Interior Beam

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SLIDE 15

Reinforced Concrete II Hashemite University

  • Dr. Hazim Dwairi

15

PCA Cha rts for ca lcula tion of PCA Cha rts for ca lcula tion of α

Reinforced Concrete II Reinforced Concrete II

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PCA Cha rts for ca lcula tion of PCA Cha rts for ca lcula tion of α

Reinforced Concrete II Reinforced Concrete II

  • Dr. Hazim Dwairi
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The Hashemite University The Hashemite University

slide-16
SLIDE 16

Reinforced Concrete II Hashemite University

  • Dr. Hazim Dwairi

16

Exa m p le :Fla t Sla b w ithout Bea m s Exa m p le :Fla t Sla b w ithout Bea m s

A flat plate floor system with panels 7 3 by 6 0 m with panels 7.3 by 6.0 m is supported on 0.50m square columns. Determine the minimum slab thickness required for the interior and corner panels.

Reinforced Concrete II Reinforced Concrete II

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p Use f’c = 28 MPa and fy = 420 MPa

Exterior Sla b Exterior Sla b

  • Slab thickness, from table for

Slab thickness, from table for f fy = 420 = 420 MPa MPa and and no edge beams is no edge beams is no edge beams is no edge beams is

m l l h

n n

8 . 6 5 . 3 . 7 30

min

= − = =

Reinforced Concrete II Reinforced Concrete II

  • Dr. Hazim Dwairi
  • Dr. Hazim Dwairi

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mm use mm h

n

230 7 . 226 30 1000 8 . 6

min

⇒ = × =

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SLIDE 17

Reinforced Concrete II Hashemite University

  • Dr. Hazim Dwairi

17

Interior Sla b Interior Sla b

  • Slab thickness, from table for

Slab thickness, from table for f fy = 420 = 420 MPa MPa and and no edge beams is no edge beams is no edge beams is no edge beams is

m l l h

n n

8 . 6 5 . 3 . 7 33

min

= − = =

Reinforced Concrete II Reinforced Concrete II

  • Dr. Hazim Dwairi
  • Dr. Hazim Dwairi

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mm use mm h

n

210 1 . 206 33 1000 8 . 6

min

⇒ = × =

Exa m p le : Fla t Sla b w ith Bea m s Exa m p le : Fla t Sla b w ith Bea m s

A flat plate floor system with panels 7 3 by 6 0 m is with panels 7.3 by 6.0 m is supported on beams in two directions which supported

  • n 0.40m square columns.

Determine the minimum slab thickness required for an interior panel.

Reinforced Concrete II Reinforced Concrete II

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The Hashemite University The Hashemite University

p Use f’c = 28 MPa and fy = 414 MPa

slide-18
SLIDE 18

Reinforced Concrete II Hashemite University

  • Dr. Hazim Dwairi

18

Fla t Sla b w ith Bea m s Exa m p le Fla t Sla b w ith Bea m s Exa m p le

Beam cross Beam cross-

  • sections

sections

All Dimensions in millimeters All Dimensions in millimeters

Reinforced Concrete II Reinforced Concrete II

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Ib = 1.170 x 10 = 1.170 x 1010

10 mm

mm4 Ib = 7.952 x 10 = 7.952 x 109

9 mm

mm4

Interior Sla b Interior Sla b

) 180 )( 6000 ( 10 170 . 1 : *

3 4 10

× =

beam

mm I Direction Long : * 01 . 4 10 916 . 2 12 ) 180 )( 6000 (

4 9 3

= = × = =

slab beam long slab

Direction Short EI EI mm I α

Reinforced Concrete II Reinforced Concrete II

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30 . 3 10 548 . 3 12 ) 180 )( 7300 (

4 9 3

= = × = =

slab beam short slab

EI EI mm I α

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SLIDE 19

Reinforced Concrete II Hashemite University

  • Dr. Hazim Dwairi

19

Interior Sla b Interior Sla b

α

avrg fm

66 . 3 2 3 . 3 01 . 4 : slab interior for Average The * = + = α α l l

fm short long

2 for thickness Compute 232 . 1 4 . . 6 4 . 3 . 7 : t Coefficien the Compute 2 > = − − = = β β

Reinforced Concrete II Reinforced Concrete II

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mm f l h

y n

4 . 160 236 . 1 9 36 1400 414 8 . 9 . 6 9 36 1400 8 . = × + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + = + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + = β

USE h = 180mm Thickness of Edge & Corner Slabs Thickness of Edge & Corner Slabs

10 952 . 7 : direction long in Compute *

4 9

× =

−beam L fm

mm I α : direction short in Compute * 45 . 5 10 458 . 1 10 952 . 7 10 458 . 1 12 ) 180 )( 3000 (

9 9 4 9 3

= × × = × = =

fm long slab

α mm I α

Reinforced Concrete II Reinforced Concrete II

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48 . 4 10 774 . 1 10 952 . 7 10 774 . 1 12 ) 180 )( 3650 (

9 9 4 9 3

= × × = × = =

short slab f

mm I α

slide-20
SLIDE 20

Reinforced Concrete II Hashemite University

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20

Thickness of Edge & Corner Slabs Thickness of Edge & Corner Slabs

5.45 3 30 3 30

02 . 4 01 . 4 30 . 3 45 . 5 30 . 3 = + + + =

f

α

3.30 3.30 4.01 5.45

02 . 4 4

fm

α 01 4 30 3 45 5 48 4 + + +

Reinforced Concrete II Reinforced Concrete II

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4.48 3.30 4.01

31 . 4 4 01 . 4 30 . 3 45 . 5 48 . 4 = + + + =

fm

α

Thickness of Edge & Corner Slabs Thickness of Edge & Corner Slabs

4.01 3 30

95 . 3 4 01 . 4 30 . 3 01 . 4 48 . 4 = + + + =

fm

α

4.48 3.30 4.01

230 . 1 35 . . 6 35 . 3 . 7 : t Coefficien the Compute 95 . 6 15 . 20 . 30 . 7 = − − = = = − − =

short long n

l l m l β β α 2 for thickness Compute >

USE

Reinforced Concrete II Reinforced Concrete II

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mm f l h α

y n fm

8 . 161 230 . 1 9 36 1400 414 8 . 95 . 6 9 36 1400 8 . 2 for thickness Compute = × + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + = + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + = > β

USE h = 180mm