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Comparison of One way and Two way
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Comparison of One-way and Two-way
slab behavior
One-way and two-way
slab action carry load
in two directions.
One-way slabs: Generally,
long side/short side > 1.5
Comparison of One-way and Two-way
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p y y
slab behavior
Flat slab Two-way slab with beams
Comparison between a two-way
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Comparison between a two-way
slab verses a one-way slabFor flat plates and slabs the column connections
can vary between:
Comparison of One way and Two way
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Comparison of One-way and Two-way
slab behavior
Flat Plate Waffle slab
Comparison of One-way and Two-way
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slab behavior
The two-way ribbed slab and waffled slab system:
General thickness of the slab is 2 to 4 in.
Comparison of One way and Two way
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Comparison of One-way and Two-way
slab behavior Economic Choices
Flat Plate suitable span 20 to 25 ft with LL= 60 -100 psf
Advantages
Low cost formworkExposed flat ceilings
Fast
Disadvantages
Low shear capacity
Low Stiffness (notable deflection)
Comparison of One way and Two way
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Comparison of One-way and Two-way
slab behavior Economic Choices
Flat Slab suitable span 20 to 30 ft with LL= 80 -150 psf
Advantages
Low cost formworkExposed flat ceilings
Fast
Disadvantages
Need more formwork for capital and panels
Comparison of One way and Two way
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Comparison of One-way and Two-way
slab behavior Economic Choices
Waffle Slab suitable span 30 to 48 ft with LL= 80 -150
psf
Advantages
Carries heavy loads
Attractive exposed ceilings
Fast
Disadvantages
Formwork with panels is expensive
Comparison of One-way and Two-way
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Comparison of One-way and Two-way
slab behavior Economic Choices
One-way Slab on beams suitable span 10 to 20 ft with
LL= 60-100 psf
Can be used for larger spans with relatively higher
cost and higher deflections
One-way joist floor system is suitable span 20 to 30 ft
with LL= 80-120 psf
Deep ribs, the concrete and steel quantities arerelative low
Expensive formwork expected.
Comparison of One-way and Two-way
slab behavior
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slab behavior
ws =load taken by short direction
wl = load taken by long direction
dA= dB
Rule of Thumb: For B/A > 2,
design as one-way slab
EI
Bw
EI
Aw
384
5
384
5 4l4s
ls4
4
l
s 162ABFor ww
A
B
w
w
Two-Way Slab Design
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Two Way Slab DesignStatic Equilibrium of Two-Way Slabs
Analogy of two-way slab to plank and beam floor
Section A-A:
Moment per ft width in planks
Total Moment
ft/ft-k
8
2
1wlM
ft-k8
2
12f
lwlM
Two-Way Slab Design
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Two Way Slab Design
Static Equilibrium of Two-Way Slabs
Analogy of two-way slab to plank and beam floor
Uniform load on each beam
Moment in one beam (Sec: B-B) ft-k82
221
lb
lwlM
k/ft
2
1wl
Two-Way Slab Design
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Static Equilibrium of Two-Way Slabs
Total Moment in both beams
Full load was transferred east-west by the planks and then was
transferred north-south by the beams;
The same is true for a two-way slab or any other floor system.
ft-k8
2
21
lwlM
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General Design Concepts
(1) Direct Design Method (DDM)
Limited to slab systems to uniformly distributed
loads and supported on equally spaced columns.
Method uses a set of coefficients to determine the
design moment at critical sections. Two-way slab
system that do not meet the limitations of the ACI
Code 13.6.1 must be analyzed more accurateprocedures
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General Design Concepts
(2) Equivalent Frame Method (EFM)
A three dimensional building is divided into a
series of two-dimensional equivalent frames by
cutting the building along lines midway between
columns. The resulting frames are considered
separately in the longitudinal and transverse
directions of the building and treated floor byfloor.
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Equivalent F rame Method (EFM )
Longitudinalequivalent frame
Transverse equivalentframe
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Equivalent F rame Method (EFM )
Elevation of the frame Perspective view
M h d f A l i
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Method of Analysis
(1) Elastic Analysis
Concrete slab may be treated as an elastic
plate. Use Timoshenkos method of analyzingthe structure. Finite element analysis
Method of Analysis
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(2) Plastic Analysis
The yield methodused to determine the limit state of
slab by considering the yield lines that occur in the
slab as a collapse mechanism.
The str ip method, where slab is divided into strips
and the load on the slab is distributed in two
orthogonal directions and the strips are analyzed as
beams.The optimal analysispresents methods for
minimizing the reinforcement based on plastic
analysis
Method of Analysis
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(3) Nonlinear analysis
Simulates the true load-deformation characteristics
of a reinforced concrete slab with finite-element
method takes into consideration of nonlinearities of
the stress-strain relationship of the individualmembers.
Column and M iddle Str ips
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p
The slab is broken
up into column
and middle strips
for analysis
Minimum Slab Thickness for two-way
construction
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construction
The ACI Code 9.5.3 specifies a minimum slab thicknessto control deflection. There are three 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.
Minimum Slab Thickness for two-way
construction
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construction
22.0 m(a) For
2.0536200,000
8.0
m
y
n
fl
h
fyin psi. But not less than 5 in.
Minimum Slab Thickness for two-way
construction
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construction
m2 (b) For
936
200,000
8.0 y
n
fl
h
fyin psi. But not less than 3.5 in.
Minimum Slab Thickness for two-way
construction
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construction
2.0m (c) For
Use the following table
Minimum Slab Thickness for two-way
construction
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Slabs without interiorbeams spanning
between supports and
ratio of long span to
short span < 2
See section 9.5.3.3
For slabs with beams
spanning between
supports on all sides.
Minimum Slab Thickness for two-way
construction
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construction
The definitions of the terms are:
h = Minimum slab thickness without interior beams
ln =
m=
Clear span in the long direction measured face toface of column
the ratio of the long to short clear span
The average value of for all beams on the sides
of the panel.
Definition of Beam-to-Slab Sti f fness Ratio,
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Accounts for stiffness effect of beams located alongslab edge reduces deflections of panel
adjacent to beams.
slabofstiffnessflexural
beamofstiffnessflexural
Definition of Beam-to-Slab Sti f fness Ratio,
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With width bounded laterally by centerline of
adjacent panels on each side of the beam.
scs
bcb
scs
bcb
EE
/4E/4E
II
lIlI
slabuncrackedofinertiaofMomentI
beamuncrackedofinertiaofMomentI
concreteslabofelasticityofModulusE
concretebeamofelasticityofModulusE
s
b
sb
cb
Beam and Slab Sections for calculation of
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Beam and Slab Sections for calculation of
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Beam and Slab Sections for calculation of
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Definition of beam cross-section
Charts may be used to calculate Fig. 13-21
Minimum Slab Thickness for two-way
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construction
Slabs without drop panels meeting 13.3.7.1 and 13.3.7.2,
tmin= 5 in
Slabs with drop panels meeting 13.3.7.1 and 13.3.7.2,
tmin= 4 in
Example
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Example
A flat plate floor system with panels
24 by 20 ft is supported on 20 in.
square columns. Determine theminimum slab thickness required
for the interior and corner panels.
Use fc= 4 ksi and fy= 60 ksi
Example
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Example
The floor system consists of solid
slabs and beams in two directions
supported on 20 in square columns.Determine the minimum slab
thickness required for an interior
panel. Use fc= 4 ksi and fy= 60 ksi
Example
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The cross-sections are:
Example
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The resulting cross section: