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

5/19/2018 RC2 Lecture 3.1 - Design of Two-way Floor Slab System

Reinforced Concrete II Hashemite Un

Dr. Hazim Dwairi

The Hashemite University

Department of Civil Engineering

Lecture 3.1Lecture 3.1 Design of TwoDesign of Two--way Floor Slab Systemway Floor Slab System

Reinforced Concrete IIReinforced Concrete IIDr. Hazim DwairiDr. Hazim Dwairi The Hashemite UniversityThe Hashemite Universit y

..

On eOne--w a y a n d Tw o w a y a n d Tw o - -w a y Sl a bw a y Sl a bBehav i o r Behav i o r

OneOne--way slabsway slabs

direction.direction.

TwoTwo--way slabsway slabs

carry load in twocarry load in two

directions.directions.

Reinforced Concrete IIReinforced Concrete IIDr. Hazim DwairiDr. Hazim Dwairi The Hashemite Universit yThe Hashemite Universit y



Dr. Hazim Dwairi

On eOne--w a y a n d Tw o w a y a n d Tw o - -w a y Sl a bw a y Sl a b

Behav i o r Behav i o r

OneOne--way andway and

--

action carryaction carry

load in twoload in two

directions.directions.


OneOne--way slabs: Generally,way slabs: Generally,

long side/short side > 2.0long side/short side > 2.0

T y pes o f Tw oT y p es o f Tw o - -w a y Sl a b s w a y Sl a bs


Flat slab with

drop panels

Two-way slab

with beams



Dr. Hazim Dwairi

T y pes o f Tw oT y p es o f Tw o - -w a y Sl a b s w a y Sl a bs


Flat slab withoutdrop panels

Waffle Slab

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

J o i st Con st r u ct i o n J o i st Con st r u ct i o n

30cm

5075cm2.5cm

Reinforced Concrete IIReinforced Concrete II

The twoThe two--way ribbed slab and waffled slabway ribbed slab and waffled slab

system: General thickness of the slab is 50mmsystem: General thickness of the slab is 50mm

to 100mm.to 100mm.Dr. Hazim DwairiDr. Hazim Dwairi The Hashemite Universit yThe Hashemite Universit y

Econ om i c Ch o i c es i n Sl a bsEcon om i c Ch o i c es i n Sl a bs

Flat Plate without drop panels: suitable spanFlat Plate without drop panels: suitable span22. . .. . . -- ..

AdvantagesAdvantages

Low cost formworkLow cost formwork

Exposed flat ceilingsExposed flat ceilings

FastFast


sa van agessa van ages

Low shear capacityLow shear capacity

Low Stiffness (notable deflection)Low Stiffness (notable deflection)

Dr. Hazim DwairiDr. Hazim Dwairi The Hashemite Universit yThe Hashemite Universit y



Dr. Hazim Dwairi


Flat Slab with drop panels: suitable span 6.0Flat Slab with drop panels: suitable span 6.022 . .. . -- ..


Low cost formworkLow cost formwork

Exposed flat ceilingsExposed flat ceilings

FastFast



Need more formwork for capital and panelsNeed more formwork for capital and panels



Waffle Slabs: suitable span 9.0 to 15 m withWaffle Slabs: suitable span 9.0 to 15 m with22 .. ..


Carries heavy loadsCarries heavy loads

Attractive exposed ceilingsAttractive exposed ceilings

FastFast



Formwork with panels is expensiveFormwork with panels is expensive




Dr. Hazim Dwairi


OneOne--way Slab on beams: sui table span 3.0 toway Slab on beams: suitable span 3.0 to22. .. . -- ..

Can be used for larger spans with relatively higherCan be used for larger spans with relatively higher

cost and higher deflectionscost and higher deflections

OneOne--way jois t floor system is suitable spanway joist floor system is suitable span

6.0 to 9.0 m with LL= 4.06.0 to 9.0 m with LL= 4.0 6.06.0 kNkN/m/m22


,,

relative lowrelative low

Expensive formwork expected.Expensive formwork expected.


Com pa r i so n o f O n e Com pa r i so n o f On e- - a n d Tw o a n d Tw o - -w a y Sl a b s Beha v i o r w a y Sl a b s Beha v i o r

ws =load taken by short direction

w l = load taken by long direction

A = B

LlwLsw 55 4l4

s

=


ls4

4

l

s 162LsLlFor wwLs

Ll

w

w===



Dr. Hazim Dwairi

St a t i c Eq u i l i b r i um f or Tw o St a t i c Eq u i l i b r i um f or Tw o - - w a yw a y

S labsS labs

Analogy of two-way slab to plank and

Consider Section A-A:

Moment per m width in

planks:

m/m-kN2

1wl=


Total Moment( ) m-kN

8

2

12T

lwlM =

St a t i c Eq u i l i b r i um f or Tw o St a t i c Eq u i l i b r i um f or Tw o - - w a yw a yS labsS labs

Uniform load on each beam:

Moment in one beam (Sec: B-B)

kN/m2

1

m-kN82

2

21lb

lwlM

=

2

l


m-8

1w=



Dr. Hazim Dwairi

M et h od o f Desi g nM et h od o f Desi g n

(1)(1) Direct Design Method (DDM):Direct Design Method (DDM):

Limited to slab systems with uniformly distributedLimited 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 determineMethod uses a set of coefficients to determine

the design moment at critical sections. Twothe design moment at critical sections. Two--wayway


the ACI Code 13.6.1 must be analyzed usingthe ACI Code 13.6.1 must be analyzed using

more accurate procedures.more accurate procedures.


M et h od o f Desi g nM et h od o f Desi g n

(2)(2) Equivalent Frame Method (EFM) :Equivalent Frame Method (EFM) :

A threeA three--dimensional building is divided into adimensional building is divided into a

series of twoseries of two--dimensional equivalent frames bydimensional equivalent frames by

cutting the building along lines midway betweencutting the building along lines midway between

columns. The resulting frames are consideredcolumns. The resulting frames are considered


directions of the building and treated floor bydirections of the building and treated floor by

floor.floor.




Dr. Hazim Dwairi

Equ i v a l en t F r am e M et h o d ( EFM )Eq u i v a l en t F r am e M et h o d ( EFM )


Longitudinal

equivalent frame

Transverse

equivalent frame

Equ i v a l en t F r am e M et h o d ( EFM )Eq u i v a l en t F r am e M et h o d ( EFM )

Elevation of

the frame


view



Dr. Hazim Dwairi

Co l um n a n d M i d d l e St r i p s Co l um 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 L/4 L/4 L/4

M i n im um Sl a b T h i ck n ess f o rM i n im um Sl a b T h i ck n ess f o rTw oT w o - -w a y Co n st r u c t i o n w a y Co n st r u c t i o n

The ACI Code 9.5.3 specifies a minimum slabThe ACI Code 9.5.3 specifies a minimum slab

..

empirical limitations for calculating the slabempirical limitations for calculating the slab

thickness (h), which are based on experimentalthickness (h), which are based on experimental

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

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


between supportsbetween supports -- Table 9.5 (c)Table 9.5 (c) and:and:

With drop panels 125 mmWith drop panels 125 mm

Without drop panels .. 100 mmWithout drop panels .. 100 mm




Dr. Hazim Dwairi

M i n im um Sl a b T h i ck n ess f o rM i n im um Sl a b T h i ck n ess f o r

Tw oT w o - -w a y Co n st r u c t i o n w a y Co n st r u c t i o n

For slabs with beams spanning between theFor slabs with beams spanning between the

> 0.2)( fmfora

mm90>


M i n im um Sl a b T h i ck n ess f o rM i n im um Sl a b T h i ck n ess f o rTw oT w o - -w a y Co n st r u c t i o n w a y Co n st r u c t i o n

2.0)( mforc

With drop panels:With drop panels:

h > 125mmh > 125mm

Without dropWithout drop

panels:panels:


h > 100mmh > 100mm




Dr. Hazim Dwairi

M i n im um Sl a b T h i ck n ess f o rM i n im um Sl a b T h i ck n ess f o r

Tw oT w o - -w a y Co n st r u c t i o n w a y Co n st r u c t i o n

Definitions:Definitions:

h = Minimum slab thickness withouth = Minimum slab thickness without

interior beams.interior beams.

llnn = Clear span in the long direction= Clear span in the long direction

measured face to face of columnmeasured face to face of column


= e ra o o e ong o s or c ear= e ra o o e ong o s or c earspanspan

mm== The average value of a for allThe average value of a for allbeams on the sides of the panel.beams on the sides of the panel.


BeamBe am - -t ot o --Sla b St i f f n ess Ra t i o ,Sl a b St i f f n ess Ra t i o ,

Accounts for stiffness effect of beams locatedAccounts for stiffness effect of beams located

panel adjacent to beams.panel adjacent to beams.

beamofstiffnessflexural

=


slabofstiffnessflexural



Dr. Hazim Dwairi

BeamBe am - -t ot o --Sla b St i f f n ess Ra t i o ,Sl a b St i f f n ess Ra t i o ,

bcbbcb E/4E IlI ==scsscs E4E II

beamuncrackedofinertiaofMomentI

slabofelasticityofModulusE

beamofelasticityofModulusE

b

sb

cb

=

=

=


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


slabuncrackedofinertiaofMomentIs=

Beam an d Sl a b Sect i o n s f o rBeam an d Sl a b Sect i o n s f o rca l cu l a t i o n o fca l cu l a t i o n o f




Dr. Hazim Dwairi

Beam an d Sl a b Sect i o n s f o rBeam an d Sl a b Sect i o n s f o r

ca l cu l a t i o n o fca l cu l a t i o n o f


Beam an d Sl a b Sect i o n s f o rBeam an d Sl a b Sect i o n s f o rca l cu l a t i o n o fca l cu l a t i o n o f


Spandrel (Edge) Beam Interior Beam



Dr. Hazim Dwairi

PCA Cha r t s f o r ca l c u l a t i o n o fPCA Cha r t s f o r ca l c u l a t i o n o f


PCA Cha r t s f o r ca l c u l a t i o n o fPCA Cha r t s f o r ca l c u l a t i o n o f




Dr. Hazim Dwairi

E xam p l e : Fl a t Sl a b w i t h o u t B eam s E xam p l e : Fl a t Sl a b w i t h o u t B eam s

A flat plate floor system

. .

is supported on 0.50m

square columns.

Determine the minimum

slab thickness required

for the interior and

corner anels.

Reinforced Concrete IIReinforced Concrete IIDr. Hazim DwairiDr. Hazim Dwairi The Hashemite UniversityThe Hashemite Universit y

Use fc = 28 MPa and

fy = 420 MPa

Ext er i o r Sl a bExt er i o r Sl a b

Slab thickness, from table forSlab thickness, from table for ffyy = 420= 420 MPaMPa andand

ml

lh

n

n

8.65.03.7

30min

==

=


mmusemmh 2307.22630

10008.6min =

=



Dr. Hazim Dwairi

I n t er i o r Sl a b I n t er i o r Sl a b

Slab thickness, from table forSlab thickness, from table for ffyy = 420= 420 MPaMPa andand

ml

lh

n

n

8.65.03.7

33min

==

=


mmusemmh 2101.20633

10008.6min =

=

E xam p l e : Fl a t Sl a b w i t h B eam s E xam p l e : Fl a t Sl a b w i t h B eam s

A flat plate floor system

. .

suppor ted on beams in two

directions which supported

on 0.40m square columns.

Determine the minimum

slab thickness required for

an interior anel.


Use fc = 28 MPa and

fy = 414 MPa



Dr. Hazim Dwairi

F la t Sl a b w i t h B eam s E xam p l e F la t Sl a b w i t h B eam s E xam p l e

Beam crossBeam cross--sectionssectionsAl l Dimensions in mi ll imetersAl l Dimensions in mi ll imeters


IIbb = 1.170 x 10= 1.170 x 101010 mmmm44

IIbb = 7.952 x 10= 7.952 x 1099 mmmm44


10170.1

:*

3

410=beam mmI

DirectionLong

:*

01.4

10916.212

49

==

==

slab

beamlong

slab

DirectionShort

EI

EI

mmI


30.3

10548.312

)180)(7300( 493

==

==

slab

beamshort

slab

EI

EI

mmI



Dr. Hazim Dwairi


avrg

fm

66.33.301.4

:slabinteriorforAverageThe*

=+=

l

l

fm

short

long

2forthicknessCompute

232.14.00.6

4.03.7

:tCoefficientheCompute

>

=

==


mm

fl

h

y

n

4.160

236.19361400

4148.09.6

936

14008.0

=

+

+

=+

+

=

USE

h = 180mm

Thickness of Edge & Corner SlabsThickness of Edge & Corner Slabs

10952.7

:directionlonginCompute*

49=beamL

fm

mmI

:directionshortinCompute*

11.510555.1

10952.7

10555.112

)180)(3200(

9

9

493

=

=

==

fm

long

slab

mmI


25.410871.1

10952.7

10871.112

)180)(3850(

9

9

493

=

=

==

short

slab mmI



Dr. Hazim Dwairi


5.11

93.301.430.311.530.3

=+++

=. .

4.01

5.11

4m


4.25 3.30

4.01

17.44

....=

+++=fm


4.01 89.34

01.430.301.425.4=

+++=fm

4.25 .

4.01

230.130.00.6

30.03.7

:tCoefficientheCompute

....

=

==

==

short

long

n

l

l

m


mm

fl

h

y

n

fm

0.163230.1936

1400

4148.000.7

936

14008.0

=+

+

=+

+

=

h = 180mm

Documents

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