Lecture 36 Design of TwoWay Floor Slab System

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Lecture 36 - Design of Two-Way Floor Slab System

• April 25, 2003
• CVEN 444

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Lecture Goals

• Direct Design Method
• Direct Design Example

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

• 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

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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
Maximum Spacing of Reinforcement At points of
max. /- M Min Reinforcement Requirements
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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
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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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Moment Distribution
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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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Longitudinal Distribution of Moments in Slabs
For a typical interior panel, the total static
moment is divided into positive moment 0.35 Mo
and negative moment of 0.65 Mo. For an
exterior panel, the total static moment is
dependent on the type of reinforcement at the
outside edge.
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Distribution of M0
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Moment Distribution
The factored components of the moment for the
beam.
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Transverse Distribution of Moments
The longitudinal moment values mentioned are for
the entire width of the equivalent building
frame. The width of two half column strips and
two half-middle stripes of adjacent panels.
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Transverse Distribution of Moments
Transverse distribution of the longitudinal
moments to middle and column strips is a function
of the ratio of length l2/l1,a1, and bt.
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Transverse Distribution of Moments
Transverse distribution of the longitudinal
moments to middle and column strips is a function
of the ratio of length l2/l1,a1, and bt.
torsional constant
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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
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)
a1
bt
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Factored Moment in an Interior Strip
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Factored Moment in an Exterior Panel
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Factored Moment in an Exterior Panel
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Factored Moment in Column Strip
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)
a1
bt
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Factored Moment in Column Strip
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)
a1
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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ACI Provisions for Effects of Pattern Loads
The maximum and minimum bending moments at the
critical sections are obtained by placing the
live load in specific patterns to produce the
extreme values. Placing the live load on all
spans will not produce either the maximum
positive or negative bending moments.
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ACI Provisions for Effects of Pattern Loads
The ratio of live to dead load. A high ratio
will increase the effect of pattern loadings. The
ratio of column to beam stiffness. A low ratio
will increase the effect of pattern
loadings. Pattern loadings. Maximum positive
moments within the spans are less affected by
pattern loadings.
1. 2. 3.
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Reinforcement Details Loads
After all percentages of the static moments in
the column and middle strip are determined, the
steel reinforcement can be calculated for
negative and positive moments in each strip.
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Reinforcement Details Loads
Calculate Ru and determine the steel ratio r,
where f 0.9. As rbd. Calculate the minimum
As from ACI codes. Figure 13.3.8 is used to
determine the minimum development length of the
bars.
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Minimum extension for reinforcement in slabs
without beams(Fig. 13.3.8)
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Moment Distribution
The factored components of the moment for the
beam.
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Transverse Distribution of Moments
The longitudinal moment values mentioned are for
the entire width of the equivalent building
frame. The width of two half column strips and
two half-middle stripes of adjacent panels.
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Example 1
Design an interior panel of the two-way slab for
the floor system.The floor consists of six panels
at each direction, with a panel size 24 ft x 20
ft. All panels are supported by 20 in square
columns. The slabs are supported by beams along
the column line with cross sections. The service
live load is to be taken as 80 psf and the
service dead load consists of 24 psf of floor
finishing in addition to the self-weight. Use fc
4 ksi and fy 60 ksi
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Example 1 Previous Example
The cross-sections are
h 7 in.
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Example 1 Previous Example
The resulting cross section
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Example 1 Previous Example
The thickness was calculated in an earlier
example. Generally, thickness of the slab is
calculated at the for the external corner slab.
So use h 7 in.
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Example 1- Loading
The weight of the slab is given as.
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Example 1 calculation d
Compute the average depth, d for the slab. Use
an average depth for the shear calculation with a
4 bar (d 0.5 in)
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Example 1 One-way shear
The shear stresses in the slab are not critical.
The critical section is at a distance d from the
face of the beam. Use 1 ft section.
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Example 1 One-way shear
The one way shear on the face of the beam.
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Example 1 Strip size
Determine the strip sizes for the column and
middle strip. Use the smaller of l1 or l2 so l2
20 ft
Therefore the column strip b 2( 5 ft) 10 ft
(120 in) The middle strips are
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Example 1 Strip Size
Calculate the strip sizes
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Example 1 Static Moment Computation
Moment Mo for the two directions.
long direction
short direction
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Example 1 Internal Panel Moment distribution
Interior panel
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Example 1 Moments (long)
The factored components of the moment for the
beam (long).
Negative - Moment Positive Moment
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Example 1- - Moment (long) Coefficients
The moments of inertia about beam, Ib 22,453
in4 and Is 6860 in4 (long direction) are need
to determine the distribution of the moments
between the column and middle strip.
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Example 1- Moment (long) Factors (negative)
Need to interpolate to determine how the negative
moment is distributed.
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Example 1 - Moment (long) Factors (positive)
Need to interpolate to determine how the positive
moment is distributed.
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Example 1 - Moment (long) column/middle strips
Components on the beam (long).
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Example 1 - Moment (long)-beam/slab distribution
(negative)
When a1 (l2/l1) gt 1.0, ACI Code Section 13.6.5
indicates that 85 of the moment in the column
strip is assigned to the beam and balance of 15
is assigned to the slab in the column strip.
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Example 1 - Moment (long)-beam/slab distribution
(positive)
When a1 (l2/l1) gt 1.0, ACI Code Section 13.6.5
indicates that 85 of the moment in the column
strip is assigned to the beam and balance of 15
is assigned to the slab in the column strip.
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Example 1- Moment (short)
The factored components of the moment for the
beam (short).
Negative Moment Positive Moment
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Example 1 - Moment (short) coefficients
The moments of inertia about beam, Ib 22,453
in4 and Is 8232 in4 (short direction) are need
to determine the distribution of the moments
between the column and middle strip.
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Example 1 - Moment (short) Factors (negative)
Need to interpolate to determine how the negative
moment is distributed.
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Example 1 - Moment (short) Factors (positive)
Need to interpolate to determine how the positive
moment is distributed.
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Example 1- Moment (short) column/middle strip
Components on the beam (short).
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Example 1 - Moment (short) beam/slab distribution
(negative)
When a1 (l2/l1) gt 1.0, ACI Code Section 13.6.5
indicates that 85 of the moment in the column
strip is assigned to the beam and balance of 15
is assigned to the slab in the column strip.
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Example 1 - Moment (short) beam/slab distribution
(positive)
When a1 (l2/l1) gt 1.0, ACI Code Section 13.6.5
indicates that 85 of the moment in the column
strip is assigned to the beam and balance of 15
is assigned to the slab in the column strip.
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Example 1 - Summary
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Example 1- Reinforcement calculation
Use same procedure to do the reinforcement on the
concrete. Calculate the bars from the earlier
version of the problem.
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Example 1 - Reinforcement calculation
Computing the reinforcement uses
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Example 1 - Reinforcement calculation for long
middle strip (negative)
Compute the reinforcement need for the negative
moment in long direction. Middle strip width b
120 in. (10 ft), d 6 in. and Mu 42.5 k-ft
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Example 1 - Reinforcement calculation for long
middle strip (negative)
Compute the reinforcement need for the negative
moment in long direction. Middle strip width b
120 in. (10 ft) d 6 in. and Mu 42.5 k-ft
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Example 1 - Reinforcement calculation for long
middle strip (negative)
The area of the steel reinforcement for a strip
width b 120 in. (10 ft), d 6 in., and h 7
in.
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Example 1 - Reinforcement calculation for long
middle strip (negative)
The area of the steel reinforcement for a strip
width b 120 in. (10 ft), d 6 in., and As
1.62 in2. Use a 4 bar (Ab 0.20 in2 )
Maximum spacing is 2(h) or 18 in. So 13.33 in
lt 14 in. OK!
Use 10 4
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Example 1 Long Results
The long direction using 4 bars
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Example 1 Long summary
The long direction using 4 bars
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Example 1 Short Results
The short direction using 4 bars
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Example 1 Short Summary
The short direction using 4 bars