Lecture 23 Design of TwoWay Floor Slab System

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Lecture 23 - Design of Two-Way Floor Slab System

• November 27, 2001
• CVEN 444

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Lecture Goals

• One-way and two-way slab
• Direct Method

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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
Flat Plate
Waffle slab
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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 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/Agt2, 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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Basic Steps in Two-way Slab Design

• Choose layout and type of slab.
• Choose slab thickness to control deflection.
  Also, check if thickness is adequate for shear.
• Choose Design method
• Equivalent Frame Method- use elastic frame
  analysis to compute positive and negative moments
• Direct Design Method - uses coefficients to
  compute positive and negative slab moments

1. 2. 3.
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Basic Steps in Two-way Slab Design

• Calculate positive and negative moments in the
  slab.
• Determine distribution of moments across the
  width of the slab. - Based on geometry and beam
  stiffness.
• Assign a portion of moment to beams, if present.
• Design reinforcement for moments from steps 5 and
  6.
• Check shear strengths at the columns

4. 5. 6. 7. 8.
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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
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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Minimum Slab Thickness for two-way construction
Maximum Spacing of Reinforcement At points of
max. /- M Max. and Min Reinforcement
Requirements
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Direct Design Method for Two-way Slab
Method of dividing total static moment Mo into
positive and negative moments.
Limitations on use of Direct Design method

• Minimum of 3 continuous spans in each direction.
  (3 x 3 panel)
• Rectangular panels with long span/short span
  2

1. 2.
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Direct Design Method for Two-way Slab
Limitations on use of Direct Design method

• Successive span in each direction shall not
  differ by more than 1/3 the longer span.
• Columns may be offset from the basic rectangular
  grid of the building by up to 0.1 times the span
  parallel to the offset.

3. 4.
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Direct Design Method for Two-way Slab
Limitations on use of Direct Design method

• All loads must be due to gravity only (N/A to
  unbraced laterally loaded frames, from mats or
  pre-stressed slabs)
• Service (unfactored) live load 2 service dead
  load

5. 6.
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Direct Design Method for Two-way Slab
Limitations on use of Direct Design method

• For panels with beams between supports on all
• sides, relative stiffness of the beams in the 2
• perpendicular directions.
• Shall not be less than 0.2 nor greater than 5.0

7.
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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 Fig. 13-21
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Distribution of Moments
Slab is considered to be a series of frames in
two directions
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Distribution of Moments
Slab is considered to be a series of frames in
two directions
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Distribution of Moments
Total static Moment, Mo
where
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Column Strips and Middle Strips
Moments vary across width of slab panel
Design moments are averaged over the width of
column strips over the columns middle strips
between column strips.
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Column Strips and Middle Strips
Column strips Design w/width on either side of a
column centerline equal to smaller of
l1 length of span in direction moments are being
determined. l2 length of span transverse to l1
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Column Strips and Middle Strips
Middle strips Design strip bounded by two column
strips.
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Positive and Negative Moments in Panels
M0 is divided into M and -M Rules given in ACI
sec. 13.6.3
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Positive and Negative Moments in Panels
M0 is divided into M and -M Rules given in ACI
sec. 13.6.3
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Distribution of M0
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Distribution of M0
ACI Sec 13.6.3.4 For spans framing into a common
support negative moment sections shall be
designed to resist the larger of the 2 interior
Mus ACI Sec. 13.6.3.5 Edge beams or edges of
slab shall be proportioned to resist in torsion
their share of exterior negative factored moments
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Factored Moment in Column Strip
a1
Ratio of flexural stiffness of beam to stiffness
of slab in direction l1. Ratio of torsional
stiffness of edge beam to flexural stiffness of
slab(width to beam length)
bt
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Factored Moment in Column Strip
a1
Ratio of flexural stiffness of beam to stiffness
of slab in direction l1. Ratio of torsional
stiffness of edge beam to flexural stiffness of
slab(width to beam length)
bt
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Factored Moments
Factored Moments in beams (ACI Sec. 13.6.3)
Resist a percentage of column strip moment plus
moments due to loads applied directly to beams.
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Factored Moments
Factored Moments in Middle strips (ACI Sec.
13.6.3)
The portion of the Mu and - Mu not resisted by
column strips shall be proportionately assigned
to corresponding half middle strips. Each middle
strip shall be proportioned to resist the sum of
the moments assigned to its 2 half middle strips.
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Example Distribution of Moments by Direct Method
A plan view of a typical interior bay of a
two-way slab system is shown in the figure.
Assume that all adjacent interior bays have the
same dimension. 8in slab SDL20 lb/ft2 LL75
lb/ft2 Determine The appropriate design moments
that would be used to size the flexural
reinforcement for slab strips running east-west
direction. Use direct design method to compute
factored design moments/ft (a) interior support
-column strip,(b) interior support middle strip
(c ) midspan- column strip, (d) midspan middle
strip