Lecture 35 Design of TwoWay Floor Slab System

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Lecture 35 - Design of Two-Way Floor Slab System

• April 23, 2003
• CVEN 444

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Lecture Goals

• One-way and two-way slab
• Slab thickness, h

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Comparison of One-way and Two-way slab behavior
One-way slabs carry load in one
direction. Two-way slabs carry load in two
directions.
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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 gt
1.5
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Comparison of One-way and Two-way slab behavior
Two-way slab with beams
Flat slab
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Comparison between a two-way slab verses a
one-way slab
For flat plates and slabs the column connections
can vary between
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Comparison of One-way and Two-way slab behavior
Flat Plate
Waffle slab
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Comparison of One-way and Two-way slab behavior
The two-way ribbed slab and waffled slab system
General thickness of the slab is 2 to 4 in.
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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 formwork
• Exposed flat ceilings
• Fast
• Disadvantages
• Low shear capacity
• Low Stiffness (notable deflection)

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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 formwork
• Exposed flat ceilings
• Fast
• Disadvantages
• Need more formwork for capital and panels

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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

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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 are
  relative low
• Expensive formwork expected.

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Comparison of One-way and Two-way slab behavior
ws load taken by short direction wl load taken
by long direction dA dB
Rule of Thumb For B/A gt 2, design as one-way slab
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Two-Way Slab Design
Static 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
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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)
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Two-Way Slab Design
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.
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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
accurate procedures
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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 by
floor.
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Equivalent Frame Method (EFM)
Transverse equivalent frame
Longitudinal equivalent frame
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Equivalent Frame Method (EFM)
Perspective view
Elevation of the frame
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Method of Analysis
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Method of Analysis
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Method of Analysis
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Column and Middle Strips
The slab is broken up into column and middle
strips for analysis
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Minimum Slab Thickness for two-way construction
The ACI Code 9.5.3 specifies a minimum slab
thickness to 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.
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Minimum Slab Thickness for two-way construction
(a) For
fy in psi. But not less than 5 in.
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Minimum Slab Thickness for two-way construction
(b) For
fy in psi. But not less than 3.5 in.
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Minimum Slab Thickness for two-way construction
(c) For
Use the following table 9.5(c)
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Minimum Slab Thickness for two-way construction
Slabs without interior beams spanning between
supports and ratio of long span to short span lt 2
See section 9.5.3.3 For slabs with beams
spanning between supports on all sides.
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Minimum Slab Thickness for two-way construction
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Definition of Beam-to-Slab Stiffness Ratio, a
Accounts for stiffness effect of beams located
along slab edge reduces deflections
of panel adjacent to beams.
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Definition of Beam-to-Slab Stiffness Ratio, a
With width bounded laterally by centerline of
adjacent panels on each side of the beam.
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Beam and Slab Sections for calculation of a
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Beam and Slab Sections for calculation of a
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Beam and Slab Sections for calculation of a
Definition of beam cross-section Charts may be
used to calculate a
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Minimum Slab Thickness for two-way 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
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Example - Slab
A flat plate floor system with panels 24 by 20 ft
is supported on 20 in. square columns. Determine
the minimum slab thickness required for the
interior and corner panels. Use fc 4 ksi and
fy 60 ksi
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Example - Slab
Slab thickness, from table for fy 60 ksi and no
edge beams
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Example - Slab
Slab thickness, from table for fy 60 ksi and no
edge beams for a am 0
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Example a calculations
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
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Example a calculations
The cross-sections are
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Example a calculations
To find h, need to find am therefore Ib, Islab
and a for each beam and slab in long short
direction. Assume slab thickness h 7 in. so
that x y lt 4 tf
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Example a calculations
Compute the moment of inertia and centroid
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Example a calculations
Compute the a coefficient for the long
direction Short side of the moment of inertia
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Example a calculations
Compute the a coefficient for short
direction The average am for an interior panel
is
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Example a calculations
Compute the b coefficient Compute the
thickness for am gt 2
Use slab thickness, 6.5 in. or 7 in.
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Example a calculations
Compute the moment of inertia and centroid for
the L-beam
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Example a calculations
Compute the am coefficient for long
direction Short side of the moment of inertia
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Example a calculations
Compute the am coefficient for the short
direction
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Example a calculations
Compute the am coefficient for the edges and
corner
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Example a calculations
Compute the am coefficient for the edges and
corner
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Example a calculations
Compute the thickness of the slab with am gt
2 The overall depth of the slab is 7 in.
Use slab thickness, 6.5 in. or 7 in.