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Overview Waffle Slab
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Quiz - 1
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Two Way Joist Slab
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Two-Way Joist
Introduction
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Two-Way Joist
Introduction
• A two-way joist system, or waffle slab, comprises
evenly spaced
directions
and
concrete
joists
spanning
in
both
a reinforced concrete slab cast
integrally with the joists.
Joist
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Two-Way Joist
• The joists are commonly formed by using standard
square “dome” forms and the domes are omitted
around the columns to form the solid heads.
Solid Head
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Two-Way Joist
• Like one-way joist system, a two way system will be
called as two-way joist system if clear spacing between
ribs (dome width) does not exceed 30 inches.
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Two-Way Joist
Introduction
•
Standard Dome Data
• Generally the dome for waffle slab can be of any size.
However the commonly used standard domes are discussed as
follows:
•
30-inch × 30-inch square domes with 3-inch flanges; from which 6inch wide joist ribs at 36-inch centers are formed: these
are available in standard depths of 8, 10, 12, 14, 16 and 20 inches.
•
19-inch × 19-inch square domes with 2 ½-inch flanges, from which
5-inch wide joist ribs at 24-inch centers are formed. These are
available in standard depths of 8, 10, 12, 14 and 16 inches.
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Two-Way Joist
•
Standard Dome Data
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Two-Way Joist
Behavior
• The behavior of two-way joist slab is similar to a two way flat Slab
system.
Characteristics
• Dome voids reduce dead load.
• Attractive ceiling (waffle like appearance).
• Electrical fixtures can be placed in the voids.
• Particularly advantageous where the use of longer spans
and/or heavier loads are desired without the use
of deepened drop panels or supported beams.
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Two-Way Joist
Sizes
• Minimum Joist Depth
• For Joist depth determination, waffle slabs are considered as flat
slab (ACI 13.1.3, 13.1.4 & 9.5.3).
• The thickness of equivalent flat slab is taken from table 9.5 (c).
• The thickness of slab and depth of rib of waffle slab can
be
then computed by equalizing the moment of inertia of
equivalent flat slab to that of waffle slab.
• However since this practice is time consuming, tables
have been developed to determine the size of waffle slab from
equivalent flat slab thickness.
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Two-Way Joist
Sizes
• Minimum Joist Depth
• Equivalent Flat Slab Thickness
ACI 318-05 – Sect. 9.5.3
• Minimum thickness = ln/33
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Two-Way Joist
Sizes
• Minimum Joist Depth
• Slab and rib depth from equivalent flat slab thickness
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Two-Way Joist
Sizes
• Minimum Joist Depth
• Slab and rib depth from equivalent flat slab thickness
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Two-Way Joist
Sizes
• Minimum Width of Rib
•
ACI 8.11.2 states that ribs shall be not less than 4 inches in width.
• Maximum Depth of Rib
• ACI 8.11.2 also states that ribs shall have a depth of not more than 3½
times the minimum width of rib.
• Minimum Slab Thickness
• ACI 8.11.6.1 states that slab thickness shall be not less than onetwelfth the clear distance between ribs, nor less than 2 inch.
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Two-Way Joist
Sizes
• Solid Head
• Dimension of solid head on either side of column centerline is
equal to l/6.
• The depth of the solid head is equal to the depth of the
combined depth of ribs and top slab.
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Two-Way Joist
Load
• Solid Head
• Floor dead load for two-way joist with certain dome size, dome
depth can be calculated from the table shown for two options of
slab thicknesses (3 inches and 4 ½ inches).
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Two-Way Joist
Load
• Solid Head
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Two-Way Joist
Load
• Floor dead load (wdj) for two-way joist can
also be calculated as follows:
Volume of solid:
Vsolid = (36  36  11)/1728 = 8.24 ft3
Volume of void:
Vvoid = (30  30  8)/1728 = 4.166 ft3
Total Load of joists per dome:
wdj = (Vsolid – Vvoid)  γconc
= ( 8.24 – 4.166)  0.15 = 0.61 kips/ dome
Total Load of joists per sq. ft:
wdj/ (dome area) = 0.61/ (3  3) = 0.0679 ksf
= 68 psf ≈ 71 psf (from table 03)
The difference is because sloped ribs are not considered.
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Two-Way Joist
Load
• Taking a panel out of the system:
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Two-Way Joist
Load
• If the complete area l1 × l2 is assumed to occupy
joists alone, then the dead load in the area l1 × l2 will be wdj.
•
However
since
there
are
solid
head
regions
present, therefore additional dead load due to solid head
region shall be:
• Wdsh = hsolid x γconc - wdj
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Two-Way Joist
Load
• ACI code allows use of DDM for analysis of waffle slabs
(ACI R13.1).
In
such
a
case,
waffle
slabs
are
considered as flat slabs, with the solid head acting as drop
panels (ACI 13.1.3).
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Two-Way Joist
Design
• Design of slab for punching shear.
• The solid head shall be checked against punching shear.
• The critical section for punching shear is taken at a section d/2
from face of the column, where d is the effective depth at solid
head.
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Two-Way Joist
Design
l1
• Design of slab for punching
shear.
•
Load on tributary area will
l2
cause punch out shear.
•
Within
tributary
area,
two
types of loads are acting:
•
•
Solid head load
•
Joist load
d
/
2
Both types shall be considered
while
calculating
punching
shear demand.
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Two-Way Joist
Design
l1
• Design of slab for punching
shear.
•
Total area (At) = l1  l2
•
Solid head area = Asolid
•
Critical perimeter area = Acp
•
Vu =At wuj + Asolid (wish − wuj)
•
Where,
l2
wuj = Factored load considering
joist alone
wsh = Factored solid head dead
load
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Two-Way Joist
Design
• Design of slab for punching shear.
• ΦVn = ΦVc + ΦVs
• ΦVc is least of:
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Φ4√ (fc′)bod
• (2 + 4/βc) √ (fc′)bod
• {(αsd/bo +2} √ (fc′)bod
βc = longer side of column/shorter side of column
αs = 40 for interior column, 30 for edge column, 20 for corner columns
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Two-Way Joist
Design
• Design of Joist for Beam Shear:
• Beam Shear Demand
• Beam shear is not usually a problem in slabs including waffle
slabs. However
for
completion
of
design
beam
shear
may also be checked. Beam shear can cause problem in
case where larger spans and heavier loads with relatively
shallow waffle slabs are used.
• The critical section for beam shear is taken at a section d from
face of the column, where d is the effective depth at solid head.
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Two-Way Joist
Design
• Design of Joist for Beam Shear:
• Beam shear capacity of concrete joist:
• ΦVn = ΦVc + ΦVs
• ΦVc is least of:
• Φ2√ (fc′)bribd
• ΦVs = ΦAvfy/bribs
• For joist construction, contribution of concrete to shear strength Vc shall
be permitted to be 10 percent more than that specified in Chapter 11.
• If required, one or two single legged stirrups are provided in the rib to
increase the shear capacity of waffle slab.
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Two-Way Joist
ACI Recommendations on Reinforcement Requirement
of Waffle Slab:
• Recommendations for Ribs:
• ACI 10.6.7 states that if the effective depth d of a beam or
joist exceeds 36 inches, longitudinal skin reinforcement shall be
provided as per ACI section 10.6.7.
•
Recommendations for Slab:
• According to ACI 13.3.2, for cellular or ribbed construction
reinforcement shall not be less than the requirements of ACI 7.12.
• As per ACI 7.12, Spacing of top bars cannot exceed 5h or 18 inches.
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Two-Way Joist
Other Important Points:
• The amount of reinforcement and, if necessary, the top slab
thickness
can be changed to vary the
load capacities for
different spans, areas, or floors of a structure.
• Each joist rib contains two bottom bars. Straight bars are
supplied over the column centerlines for negative factored
moment.
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Two-Way Joist
Other Important Points:
• For layouts that do not meet the standard 2-feet and 3-feet
modules, it is preferable that the required additional width be
obtained by increasing the width of the ribs framing into the
solid column head.
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Two-Way Joist
Other Important Points:
• The designer should sketch out the spacing for a typical panel
and correlate with the column spacing as a part of the early
planning.
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Moment Coefficient Method
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Two-Way Slab
Moment Coefficient Method (Introduction)
• The Moment Coefficient Method included for the first time
in 1963 ACI Code is applicable to two-way slabs supported
on four sides of each slab panel by walls, steel beams
relatively deep, stiff, edge beams (h = 3hf).
• Although, not included in 1977 and later versions of ACI code, its
continued use is permissible under the ACI 318-08 code
provision (13.5.1).
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