Lecture 25 Design of TwoWay Floor Slab System

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Lecture 25 - Design of Two-Way Floor Slab System

• August 6, 2003
• CVEN 444

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Lecture Goals

• Example of DDM
• Panel Design

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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
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Example Two-way Slab (Panels)
Using the direct design method, design the
typical exterior flat-slab panel with drop down
panels only. All panels are supported on 20 in.
square columns, 12 ft long. The slab carries a
uniform service live load of 80 psf and service
dead load that consists of 24 psf of finished in
addition to the slab self-weight. Use fc 4 ksi
and fy 60 ksi
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Example Two-way Slab (Panels)
The thickness of the slab is found using
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Example Two-way Slab (Panels)
From the ACI Code limitation
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Example Two-way Slab (Panels)
From the ACI Code limitation
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Example Two-way Slab (Panels)
Therefore, the panel thickness is
The panel half width are at least L/6 in length.
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Example Two-way Slab (Panels)
Therefore, the drop down panel thickness is 10
in. and has 7 ft x 8 ft.
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Example Two-way Slab (Panels)
The load on the slab is given as
The load on the panel is
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Example Two-way Slab (Panels)
The drop panel length is L/3 in each direction,
then the average wu is
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Example Two-way Slab (Panels)
The punch out shear at center column is
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Example Two-way Slab (Panels)
The punch out shear at center column is
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Example Two-way Slab (Panels)
The punch out shear at panel is
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Example Two-way Slab (Panels)
The punch out shear at panel is
One way shear is not critical.
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Example Two-way Slab (Panels)
Moment Mo for the two directions are
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Example Two-way Slab (Panels)
The column strip will be 10 ft. (20 ft /4 5ft),
therefore the middle strips for long section is
10 ft and the middle strip for the short section
will be 14 ft.
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Example Two-way Slab (Panels)
The factored components of the moment for the
beam (long) is similar to an interior beam.
Negative Moment Positive Moment
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Example Two-way Slab (Panels)
Components on the beam (long) interior.
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Example Two-way Slab (Panels)
Components on the beam (long) interior.
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Example Two-way Slab (Panels)
Computing the reinforcement uses
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Example Two-way Slab (Panels)
Compute the reinforcement need for the internal
moment in long direction. Strip width b 120 in.
(10 ft) d 8.5 in. and Mu 174.5 k-ft
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Example Two-way Slab (Panels)
Compute the reinforcement need for the internal
moment in long direction. Strip width b 120 in.
(10 ft) d 8.5 in. and Mu 174.5 k-ft
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Example Two-way Slab (Panels)
The area of the steel reinforcement for a strip
width b 120 in. (10 ft), d 8.5 in., and h 10
in.
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Example Two-way Slab (Panels)
The area of the steel reinforcement for a strip
width b 120 in. (10 ft), d 8.5 in., and As
4.76 in2. Use a 5 bar (Ab 0.31 in2 )
Maximum spacing is 2(h) or 18 in. So 7.5 in. lt
18 in. OK
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Example Two-way Slab (Panels)
The long direction
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Example Two-way Slab (Panels)
The short direction