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Transcript of Concrete Floor Systems
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About tie author%
August W. Domel, Jr. is Senior StmctumJ Engineer, Engineered
Stmckues md Cmfes, Portland Cement Association.
S. K. Ghosh is Director, Engineered Stmctures and Codes, Pofi-
kmdCement Association.
This publication is based on the facts, tests, and authorities stated
herein, It is intended for the use of professional personnel
competent to ev.l”ate the significmce and Iimitatiom of the
reported findings a“d who will accept respmsibility for the
application of the material it contains, Obviously, the Pmtkmd
Cement Association disclaims any and all responsibility for
application of the stated principles or for the accuracy of any of
the sources o her than work performed or information developed
by the Association
0 Portland Cement Association 1990
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Contents
lWodution .......................................................................................2
Flat Plate Floor System .....................................................................6
Flat Slab Floor System ...................................................................lO
One-Way Joist Fioor System ..........................................................l4
Two-Way Joist Floor System ...........................................................2O
Wam.SuppoRed Slab System ........................................................26
Overview of Floor Systems ............................................................3O
Publication List Book Contents
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The main objectives of this publication are trx
.
.
Asaiat in the selection of the most econom-
ical cast-in-place concrete floor system for
a given plan layout and a given set of Ioady
Provide a preliminary estimate of material
quantities for the floor system; and
Discuss the effect of different variables in
the selection process.
Five different floor systems are considered in
this publication. These are the flat plate, the flat
slab, the one-way joist, the two-way joist or
waffle, and the slab supported on beams on all
four sides. Material quantity estimates are
given for each floor system for various bay
sizes.
Pricing Trends
The total cost to construct a building depends on
the use for which the structure is designed, the
availability of qualified contractors, and the part
of the country in wh]ch the structure is built.
Figure 1 gives cost comparisons for two differ-
ent types of uses over the past several years.
(The data presented in Figures 1 through 5 and
Table 1 were obtained from Means Concrete
Cost Data, 1990.) ‘Ilte average price per square
foot is considerably greater for office buildings
than for apartment buildings. Part of the higher
Figure 1- Price Comparieorra for Different
Building Typea
.
cost ia because ofi-kc buildings are designed
with more open spaces which in structural terms
means costlier, longer clear spans.
Table 1 gives cost indices for many major
cities in the United States and Cartada. The cost
index includes both labor and materials, with the
value of 100 representing the average cost for
30 major cities. The table shows the wide vari-
ation in costs depending on the locale. In An-
chorage, Alaska (127.9) or New York City
(126.9) the cost of a building can be as much as
60% higher than that of a similar building in
Charleston, South Carolina (80.2), Jackson,
Mksissippi (81) or Sioux Falls, South Dakota
(82.2). Figure 2 shows the relative change in
costs in current dollars of material and labor
over the past 40 years.
too
Sa
Sa
70
m
cost ~
Indsx
4a
30
20
‘TJ_L_—
iwo ?960
tern
ieao
two
Figure 2-
Annual Construction coat
Comperiaona
The majority of the structural cost of a build-
ing typically is the cost of the floor system. This
is particularly true of low-rise buildings and
buildings in low seismic zones. Therefore, it is
imperative to select the most economical floor
system.
In this publication, estimated quantities are.
provided for concrete, reinforcing steel and
formwork for the tive floor systems discussed
in the following sections. Prices for labor and
material for these items over the past several
years are shown in Figores 3 through 5.
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Table l—Relative Construction Costs for Reinforced Concrete
ALABAMA (BIRMINGHAM)
ALASKA (ANCHORAGE)
ARIZONA (PHOENIX)
ARKANSAS (LlllLE ROCK)
CALIFORNIA (LOS ANGELES)
CALIFORNIA (SAN FRANCISCO)
COLORADO (DENVER)
CONNECTICUT (HARTFORD)
DELAWARE (WILMINGTON)
WASHINGTON, D.C.
FLORIDA (MIAMI)
GEORGIA (A~NTA)
HAWAll (HONOLULU)
IDAHO (BOISE)
ILLINOIS (CHICAGO)
INDIANA (INDIANAPOUS)
lOWA (DES MOINES)
KANSAS (WICHITA)
KENTUCKY (LOUISVILLE)
LOUISIANA (NEW ORLEANS)
MAINE (PORTU4ND)
MARYLAND (BALTIMORE)
MASSACHUSElT8 (BOSTON)
MICHIGAN (DETROIT)
MINNESOTA (MINNEAPOUS)
MISSISSIPPI (JACKSON)
MISSOURI (ST. LOUIS)
MONTANA (BILUNGS)
NEBRASKA (OMAHA)
NEVADA (MS VEGAS)
0.6
0.4
W/b
0.2
0_
84.0
127.9
91.9
84.5
112.0
126.0
83.5
lW.1
1CCI.3
95.4
89.9
89.7
111.1
83.3
101,8
97.6
eu.7
88.8
88.3
88.6
89.8
98.1
115.6
108.9
S9.4
61,0
101.6
%?.1
88.6
104.6
t 1 1 I 1
fw
Ieaa la fM7
Im 1969 fw
Figure 3- Cost of Reinforcing Bars in Place
NEW HAMPSHIRE (MANCHESTER)
NEW JERSEY (NEWARQ
NEW MEXICO (ALBUQUERQUE)
NEW YORK (NEW YOR~
NEW YORK (ALBANY)
NORTH CAROUNA (CHARLOTIE)
OHIO (CLEVELAND)
OHIO (CINCINNATl)
OKIA-IOMA (OKIAHOMA CITY)
OREGON (PORWND)
PENNSYLVANIA (PHILADELPHIA)
PENNSYLVANIA (PITTSBURGHI
RHODE ISIAND (PROVIDENCE)
SOUTH CAROUNA (CHARLES1ON)
SOUTH DAKOTA (SIOUX FALLS)
TENNESSEE (MEMPHIS)
TEXAS (DAUAS)
UTAH (SALT LAKE CITY)
VERMONT (BURLINGTON)
VIRGINIA (NORFOLKI
WASHINGTON (SEATTLE)
WEST VIRGINIA (CHARLESTON)
WISCONSIN (MILWAUKEE)
WYOMING (CHEYENNE)
CANADA (EDMONTON)
CANADA (MONTREAL)
CANADA (QUEBEC)
CANADA (TORONTO)
CANADA (VANCOUVER)
CANADA (WINNIPEG)
‘“ ~—
ao
aQ
I
30.3
104.9
91.5
126.9
84.5
80.8
107.3
95.3
89.4
101,0
107.2
1D3.6
100.8
80.2
82.2
87.6
87.8
91.7
8a. 1
83.3
101,6
97.4
97.3
87.4
100.2
100,0
99.0
109.8
105.5
101.5
m
30
20
10
1
a84 1985 1888
1987 1988 1988 1890
Figura 4- Coat of Ready-Mxed Concrete
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f lat skb
2
t
1984
1985
198.S
1987 1988 1989 1990
Figure 5- Cost of Formwork
Presentation of Results
The following pages provide discussion and
quantity estimates for the five floor systems.
These results were obtained using a five bay by
five bay structure. Bay sizes are measured from
centerline of column to centerline of column.
Floors were designed using ACI 318-89 Build-
ing Code Requirements for Reinforced Con-
crete. Concrete, reinforcing steel and formwork
quantities are presented for each of the floor
systems. An overview of the floor systems is
provided, following the discussion of the floor
systems,
Included with each floor system is a discus-
sion of the factors that may affect the estimated
quantities. The factors discussed are column
dimensions, live loads, and aspect ratios. A cost
breakdown is also given in each case. Following
the discussion for each individual floor system
are several tables and graphs. The graphs show
the variation in costs for increased bay size and
higher concrete strength. The tables give quan-
tities for various bay sizes.
Fire Resistance of Concrete
Floor Systems
Fire resistance rated construction will often be
required by the governing building code, or the
owner may desire a highly fire resistant structure
in order to qualify for the lowest fire insurance
rates,
Concrete floor systems offer inherent tire re-
sistance. Therefore, when the floor system is
completed, no additional protective measures
are necessary in order to achieve code required
tire resistance ratings.
On the other hand, for steel floor systems for
instance, additional protection must be provided
by special acoustical ceilings, or fireproofing
sprayed on the underside of the steel deck and/or
beams. In addition, when an acoustical ceiling
is an integral part of a rated floor/ceiling assem-
bly, special ceiling suspension systems, and spe-
cial protective devices at penetrations for light
fixtures and HVAC diffusers are required.
These additional costs associated with pro-
tecting the structural framing members must be
added to the cost of the structural frame to
produce an accurate cost estimate. If this is not
done, the actual cost of the competing floor
system is understated, makkrg a valid compari-
son with a concrete floor system difficult, if not
impossible.
Fire resistance rating requirements vary from
zero to four hours, with two hours typically
being required for high rise buildings. Before
selecting the floor system, the designer should
determine the fire resistance rating required by
the applicable building code. Except for one-
way and two-way joist systems, the minimum
slab thickness necessary to satisfy structural
requirements (usually 5 in.) will normally pro-
vide a floor system that has at least a two hour
fire resistance rating.
Table 2 shows minimum slab thicknesses
necessary to provide fire resistance ratings from
one to four hours, for different types of aggre-
gate. If the thickness necessary to satisfy fire
resistance requirements exceeds that required
for structural purposes, consideration should be
given to using a different type of aggregate that
provides higher fire resistance for the same
thickness. For example, a one-way joist system
may require a 3 in. thick slab to satisfy structural
requirements. However, if a two hour fire resis-
tance rating is desired, a 5 in. thick slab will be
required if siliceous aggregate normal weight
concrete is used. By using lightweight aggre-
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gate concrete, the slab thickness can be reduced
to 3.6 in. This 28% reduction in thickness
translates into approximately a 45% reduction
in dead load.
Table 2—Minimum Slab Thickness for
Fire Resistance Rating
Floor
Construction
Material
r
iliceous Aggregate
Concrete
Carbonate Aggregate
Concrete
Sand-lightweight
Concrete
Lightweight Concrete
Mhimum slab
thickness (in.)
or fire-resistance rating
1 hr
3.5
3.2
2.7
2.5
2 hr
5.0
4.6
3.8
3.6
3
hr
6.2
5.7
4.6
4.4
7.0
6.6
5.4
5.1
Adearrate cover must be provided to keep
reinfor~ing steel temperat~res within cods
prescribed limits. The amount of cover depends
on the element considered (i.e., slab, joist or
beam), and whether the element is restrained
against thermal expansion. All elements of cast-
in-place concrete framing systems are
considered to be restrained.
For positive moment reinforcement in beams
spaced at 4 ft or less on center, and in joists and
slabs, regardless of the type of concrete aggre-
gate used, the minimum cover required by ACI
318 is adequate for ratings of up to four hours.
For beams spaced at more than 4 ft on center,
the cover must not be less than the values given
in Table 3.
Table 3—Cover Thickness for Fire
Resistance Rating for Beams Spaced
More than 4 ft on Center
=
The cover for an individual bar is the mini-
mum cover between the surface of the bar and
the fire-exposed surface of the structural mem-
ber. When more than one bar i:]used, the cover
is assumed to be the average of the minimum
cover to each bar, where the cover for comer
bars used in the calculation is one-half the actual
value. The actual cover for an individual bar
must be not less than one-half the value shown
in Table 3, nor less than 3/4 in. IForbeam widths
between tabulated values, use direct interpola-
tion to determine minimum cover.
The foregoing is intended to give a brief
overview of the subject of fire resistance of
concrete floor systems. While the information
cited is consistent with the three model building
codes in use in the United States, the legally
adopted building code governing the specific
project should be consulted.
7
1
3/4
1
3/4
1
3/4
1
3/4
210
3/4 3/4
3/4 3/4
I
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DATA
SPAN LENGTH:
PracticalRange
= 15 ftt030ft
Wmomicul Range = 15 ft to 25 fl
ADVANTAGES:
.
.
.
Sirrrplecorrstmction and fomrwork
Architectural finish can be applied directly to the
underside of slab
Absence of beams allows lower story heights
Flesibtity of paflition location
Required fire resistance rating Maimed without addi-
tio&l corrcrtte thickness or o~herpmtcctive mea-sums
DISCUSSION
SkdJ Thickness
Floor slab thickness for flat plates under normal
loading conditions (live loada of 50 paf or less) is
usually corrtrokd by deflection considerations. The
Building Code Requirements for Reinforced Cmr-
crete (ACI 318-89) Table 9.5 (c)requires that the slab
thickness for flat plate floors without edge beams he
greater than one-tldrtieth of the span length (for
Grade 60 reinforcing steel) and no less than 5 in.
Becauae deflection controls the slab thickness, the
reinforcing steel required for bending moments will
be about the minimum prescribed by Code. An
increase in slab thickness beyond the minimum re-
quired is not economical. Athickerslab will increaac
the concrete quantity and not reduce the steel rein-
DIMENSIONS:
“ Slab thickness 5 in. to 10 in.
DISAOVANZAGES:
.
l+onomicdh’ viable onlv for short and medium scram
and for mod&’atelive Io;ds
forcing quantity. Also, the minimum code-pre-
scribed slab thickness is independent of the concrete
strength f& A higher strength concrete will increase
the cuat of the concrete without any allowable reduc-
tion in qusntity. Therefore, for normal loading con-
ditions (live loads of 50 paf or less), the most
economical flat plate floor will he the one with the
minimum allowed tfrickneas and an f: of 4000 psi.
When heavier loads are encountered (live loads of
100 psf or more), the deflection criteria may not
control. In that situation the slab th]ckrress is con-
trolled by shear forces at the column face and by
bending moments in the slab. Au increase in the slab
thickness will result in a decrease in the steel rein-
forcing quantity. The reduction in steel cost, how-
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ever, will not offset the increase in concrete costs.
Using a concrete strength of 5000 or6000 psi may
result in a decrease in the slab thickness without a
significant change in the steel reinforcing rm@re-
merrts. Cast analyses show that the decrease in
concrete quantities in conjunction with the increa~
in price for higher strength concrete results in
roughly the same cost as that of tire flate plate with
an & . WOO pai. Therefore, floor cost should be
estimated using a minimum slab thiclmcss with an
~ = 4000 pi, when live
loads are 100 paf or lCSS.
Column Dimension E ects
The height and cross-sectional dimensions of the
columns above and below the slab will affect the
resulting floor slab shears and bending moments.
Column heights can range from 10 ft to 30 ft, but
typi~lly are between 10 ft and 13 ft. A column
height of 12 ft was used in the calculations for this
publication.
Column stiffness is a function of the column
height. Stiffness is determined as EI/L, where E is
the modulus of elasticit y of the column material, I is
the moment of inertia of the column cross-section
and L is the column height. Since the stiffness is
inversely proportional to the column height, it fol-
lows that a longer column is more flexible. A flexi-
ble column will allow greater rotation at the
slab-column joint and larger bending momenta in the
slab. Analyses were performed for a variety of bay
widths and column dimensions, with column heights
ranging between 10 ft and 15 ft. Increasing the floor
height from 10 ft to 15 ft resulted in an increase in
the slab momentx of less than 4~o. This small in-
crease will have minimal effect, if any at all, on the
material quantities. Thus, the floor quantities are
independent of the flnor height under normal loading
conditions.
Column cross-sectional dimensiom will deter-
mine the clear span between the column faces. The
bending momenta are determined using this clear
span length. The shear resisting properties are also
related to the column cross-sectional dimensiofrs. A
larger column width or depth will result in a larger
shear carrying capacity of the slab. In the analyses
of this publication, the column cross-sectional di-
mensions for the different bay widths were chosen
to represent the column sizes used in 10- to 20-story
buildings. If a structure has a column width and
depth considerably different from those used in the
tables, adjustments should be made. The required
adjustment is made by using the same forrnwork and
concrete quantities, with an incrcmsc or decrease in
the reinforcing steel quantity. The steel reinforcing
quantities should be increased by 1% for each 2 in.
decrease in square column dimensions, or decreased
by 1% for the same increase in square column di-
mensions.
Live Load Effects
Gravity loads consist of the floor slab weight, super-
impmed dead loada, and live loads. Typical live
loads rmrge from 40 psf to 50 psf and constitute 20%
to 40% of the total gravity load.
If heavy live
loads
are used (1OOpsf), the resulting stresses and bending
momen~ are increased by 3070 to 4070. Since flat
plate flours have minimum thickness requirements
baaed on deflection considerations, the costs associ-
ated with this incresse is not proportional. Flat plate
floom with live loads of 100 psf are typically onfy
5% to 10% more expensive than those carrying 50
psf of live loads.
Aspect R@”o
The
aspect ratio is defined as the larger dimension of
the slab panel divided by the smaller dimension of
the slab panel. As previously discussed, the flat plate
slab thickness is controlled by the span length. For
a building with square bays (aspect ratio = 1.0), the
slab thickness requirement is the ;same for both di-
rections. A slab with an aspect ratio other than 1.0
will have a different thickness requirement in each
direction. Obviously, the larger of the two is used,
resulting in a loss of economy. Fnr example, a bay
with 625 aq ft of floor area and an a.s~ct ratio of 2.0
will cost 20% more than a square bay with the same
floor area. Unless column layout is dictated by
functional requirements, square ba:ysshould be use~
since they will provide the most economical layouts.
Cost Breakdown
The
formwork costs for flat plates represent approx-
imately 50% of the floor system cost. Concrete
material, placing and finishing account for 30% of
the cost. The remaining 20% is the material and
placing cost of the reinforcing steel.
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.ive Load = 50 psf
superimposed Dead
Load = 20 psf
cost
Index
0.5
0.45
0 .4
0.35
0 .3
1
15
r -c = 4000
psi
,n -
20 25
Squere Bay Size
n
30
Bay Slab
Square
QUANTITIES
Size Thickneea
Column
ft
Concrete Reinforcement
in. Size (in.)
Forme
(ft3/f?)
(psq (f?/f+)
15X15
6.0
14 0.50
2.20
1.0
15x20
7.5 18
0.63
1.95
1,0
15x25 9.5
m 0.79
2.51
1,0
15x30 12.0
22 1.Cxl 3,CQ 1.0
20X20
7.5 20
0.63 2.12
1.0
20x25 9.5
22 0.79 2.55
1.0
20.30
12.0
24 1SW 3,18
1.0
25 X 25
9.5 26
0.79 2.76
1.0
25x30
12.0 30 1CO
3.22
1,0
30XXJ 12.0
32 1.CiJ 3.50
1,0
s
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Live Load .100 psf
Superimposed Dead Load =20 psi
0.5
I
0.45
f ’c . 5000
psl
cost
Index
0 .4
0.35
0 .3
15
20
25
30
Squ are B ay Size
n
Bay
Slab
Size Thickness
it
in.
‘:” km %%
ize (in,)
15X15 7.0
14
0.58
2.24 1,0
15X20 8.5 18
0.71
2.44
1.0
15x25
10,0 22
0.85
2.89
1.0
15X30
12,5 24
1.04
3.52
1,0
2Qxm 9.5 22 0.79 2.48
1.0
20.25
11.0 24
0.92
3.01 1,0
2Qx3a
13.5 26
1.13
3.63 1.0
25 X 25
11,0
28 0.92 3.22
1.0
25x3CI 13.5 32
1.13
3.70
1,0
3QX2KJ
14,0
34
1.17
4.cKl 1,0
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nl
rn
DATA
SPAN LENGTH:
Pmcticd Raoge
= 15tlt030ft
Economical Range = 18 R to 30 ft
ADVANTAGES:
.
Simple construction and fomrwork
Architectural firriah can be applied direzily to the
underside of slab
Abscncc of beams rdlows lower
story
heighta
Reauircd fire reaistancc rating obtained without rrddi-
tioiiaf concrete thickness or O-&r protective measures
DISCUSSION
GenerrrlDiscusa”on
A flat slab floor system is similar tn a flat plate floor
system,
except that the former has drop panels. Drop
panefa are formed by thickening the bottom of the
slab around the columns. This thickerring provides
the slab with increased shear carrying capacity at
locations where the shear is the largest. The discus-
sion on
the flat plate floor system in the preceding
section stated that under normal loading conditions
the slab thickness ia
controlled by deflection con-
straint. Thickening of the slab at the cohrrnn does
little to decreaae the deflections in the span. The
main nae for a drop panel is where the slab has the
proper thickrreas for deflection control, but lacks
sufficient shear capacity at the column. Under nor-
DIMENSIONS:
Slab
thickness 5 in. to 10 in.
Depth of Drop Panels 2~4 in. to 8 in.
DLSADVANZAGES:
.
E.amomicslly viable orrlyforshott and medium, heav.
ily loaded spares
mal loading conditions, ths nccura in spans over 25
ft. For span Iengtha larger than 25 ft, the flat slab can
be more economical than the flat plate. When spana
exceed 35 f~ other systems become more economi-
cal than the flat slab or the flat plate floor system.
Flat slabs are typically economical for heavily
loaded short and rrrcdirrm spans, or possibly when a
relatively flat ceifirrg is required for medium to long
spmrs.
Slab and Drop Panel Dimensions
The
minimum tbickrreas permitted for a slab with
drop
panels
and without beams ia equal to the clear
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span length divided by 33 (ACI 318-89 Table 9.5(c)),
but not less that 4 in. This gives a minimum thick-
ness 10% less than that required for flat plates on
similar spans. This reduction in the required thick-
ness accounts for the decrease in deflection from the
addition of dmp panels around the eolmrrns.
Minimum dimensions for drop panels are given
in Section 13.4.7of the ACI Building Code. The first
restriction requires that the drop panels extend in
each direction from the centerline of the supprt a
distance not less than one-sixth of the span length.
The second restriction is that the projection of the
drop panel below the slab shall beat least one-quarter
the slab thickness.
Drop dlmensiom are also controlled by formwork
considerations. Standard lumber dimensions should
be used when choosing drop depths and should be
limited to either 2.25 in., 4.25 in., 6.25 in., or 8 in.
Any other depth will unnecessarily increase form-
work costs.
A design is begun by choosing a slab thickness
based on the minimum slab thickness requirements
of the ACI Building Code. Drop panel plan dimen-
sions are then chosen on the basis of the spmr lengths.
These drop psnel dimensions are usually adeqnate,
since the shear stress will be critical at the column
face. Analysis should be performed with the mini-
mum drop depth of 2.25 in. If this proves to be
inadequate, the next larger suggested drop depth
should be considered.
Column Dimension Effects
The floor quantities are independent of the floor
height mrder normal loading conditions. If the struc-
ture has columns widths and depths different fmm
those shown in the tables, adjustments should be
made by increasing the steel reinforcing quantities
by three-quarters of 1% for each 2 in. demeuse in
square column dimensions. The qrrarrtities should be
decreased by the same amount for each 2 in. increase
in square column dimensions.
Live LoodEffects
The material quantities required for a flat slab are
typically controlled by deflections. Therefore, an
increase in live loads will not cmrxe a proportional
increase in costs. Alive load of ltXl psf increases the
total cost of a flat slab fleer system by an average of
10% over that of the same system carrying a live load
of 50 pf.
Aspect Rotio
Square bays (aspect ratio = 1.0) represent the most
economical floor layout, since minimum thickness
based on deflection requirements can be exactly met
in both directions. A rectangular bay with an aspect
ratio of 1.5 is 870 more expensive than a square bay
with the same fleer area.
Cost Breokdinvn
The formwork costs for the flat slab are approxi-
mately 51% of the floor system costs. Concrete
material, placing and finishing account for 3070 of
the cost. The remaining 19% is the material and
placing cost of the steel reinforcing.
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Live Load =50 psf
Superimposed Dead Load =20 psf
0 .5
0.45
cost
Index
0 .4
0.35
20
rc = 6000psi
f’c=
5000ps i
fc = 4000p s i
25
Square Bay Size
n
30
3s
Bay
Slab
Drop Size
Square
Size
QUANTITIES
Thi::ess Dimpions Thii;kneea
Column c~ncrat~ ReinfOr~ement
l?
Forms
Size (in.)
(ft3/f )
(I@
(f?/f?)
20.233
7.0
7x7
2.25
m 0,61
2.04 1.01
2Qx25
8,5
81/9 ~
7
2.25
22 0 .73
2 .35 1 01
20X34) 10.5 10X7
4.25 24 0.92
2.78 1.02
20.35 12.0
12x7 4.25 30 1.04 3.29 1.02
25X 25
8 ,5
814 ~ 81/2
2.25 26 0.73
2.54
1.01
25x30 10.0
8172X1(J
4.25
30
0.87 2.78
1.02
25x35
12.0
81, X12
4.25
32
1.04
3.36 1.02
30X30 10.0 10X1O 4.25 32 0,87 3.02
1.02
30X85 12.0 lox 12 4,25 36 1.04 3.51
1.02
35x35
12.0 12X 12
4,25
38 1.04 3.82
1.02
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Live Load = 100 P(
Superimposed Dead Load =20 p:
0.55
I
0.5
fc . Sooo p si
t ’c = 5 00 0 ps i
cost o.
Index
t-c .4000
psi
0.4
0.35
I
I
20
25
30 35
Square B ay Size
n
~~
Thi taas Dimpions Thi:kneaa Column c~ncr~e ReinfOr~emeX
20X30 I
10.5 10x7 I 4.25 I 26 I 0.92 / 3.37
20X35 12,0 12x7 4.25
32
1.04 3.86
—
25 X 25 8.5
f31z x
J31~
4.25
28 0.75
3.02
Forms
(f?/f?)
1.01
1.02
1 02
1,02
1 02
25.30 I
10.0 I 8VZX 10 I
4.25 I 32 I 0.87 I 3.41 I 1.02
25x35 I 12.0 I 8V2X12 4.25 I 34 I 1 ,04 I 4 ,WI I 1 ,02
1 I
1 1 1
1
34)X30 10.0 lox 10
4.25
34 0.87
386 =
30X35
12.0 10X12
6.25
38
1 06
4.02 “~
35x35 I 12.0
12x12 I 6.25 I 40 / 1.0+5 I 4.50 t 1.02
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DATA
SPAN LENGTH:
Practical Range = 15 ft to 40 i?
Emnomical Range .25 ft to @ ft
ADVANTAGES:
Economical for long spans
9 Pan voids rcducc dead loads
Attmctive ceiling
Electrical fixtures can be placed between joiata
DISCUSSION
General
A one-way joist floor system consists of evenly
spaced concrete joista spaming in one direction. A
reinforced concrete slab iscast integral
with the joists
to
form a
monolithic floor system. Reinforcing bars
are located at the top or bottom of the joista, depend-
ing on the sense of the bending moment. The slab
has reinforcement at mid-depth in a direction perpen-
dicular to the direction of the joista. This steel allows
the slab to span bctwcerr the joists, though the amount
of steel required for temperature and shrinkage typ-
ically controls. The one-way joists frame into beams
that span between the cohrmaa, perpendicular to the
joists.
The results presented in this section are for 3 ft
DIMENSIONS:
Slab thicknessvaries
befwccn 3 in. and 5 in. based on
either fire rcsiatancc requirements or structural consid-
erations
Joista extend from 8 in. to 20 in. below the slab, with
web width ranging tlom 5 in. to 7 in.
DISADVANTAGES:
Not economical for short spans
Higher formwork cnsta than for other slab systems.
Deeper members result in greater fkmr heighta
and
5
ft joist spacings. The ACI Building Code
Requirements for Reinforced Concrete (ACI 318-
89) section 8.11.3 restricts the clear diafance between
joista to a maximum of 30 in. (which correspmds to
a 3 ft joist spacing). If the clear spacing exceeds this
value, the floor system mrrat be designed aa a beam-
strpported slab system, rather than as a joist system.
Both systems have the same design requirements,
except for a smaller reinforcing cover and a 10%
increase in the allowable shear stress permitted for
the joist system.
Floor System
The
members that form a complete one-way joist
system are the slab, joista, interior beams and span-
drel beams.
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The slab tldckrreas is controlled by either stnrc-
tural or fire resistance considerations. A 5 in. thick
slab was used in the design of the one-way joists of
th~ section. Thii thickness gives a two hour
fire
rating and is sufficient to span between the joists.
This publication considers only normal weight
concrete for the flcmr systems. But it shordd be noted
that since the slab thickness may be controlled by
tire-resistance, a lightweight concrete may have
aume advantages, bccarrae a two hour
fire
resistance
rating is met by a considerably thkrrrer slab. This will
also result in a sizable dead load reduction.
The dirnensionx of the joists depend on both de-
flection and strcsa considerations. The minimum
depth of the slab plus joist to aatiafy deflection
constraints is gNen in Table 9.5(a) of ACf 318-89.
This table prescribes a minimum slab thickrrcax plus
joist depth of at least the span length divided by 18.5.
The span length for members not built irrtegrully with
supports is defined in section 8.7 of ACI 318-89.
The span length is defined as the lexser of the clear
span plus the depth of the joist or the distance be-
tween suppurt centerlines. The maximum span
lengths for a 5 in. thick slab in combination with
various joist depths arc listed below. Thcxe span
lengths are as defined in .S@ion 8.7 of ACI 318-89
and are not the clear spans. After satisfying deflec-
tion criteria, a joist width is chosen (5 in., 6 in., or 7
in.). The joists are then designed for bending mo-
ments and shear forces.
Joist
Depth
(in.)
8
10
12
14
16
20
Maximum Span
Length
(ft)
20
23
26
29
32
39
Spandrel and interior beam depths are dictated by
the thickness of the slab plrrsthejoist depth, toreduce
formwork costs. The requirement of a level soffit
results
in wide, shallow beams referred to as joist
band beams. Formwork costs are also reduced by
using joist band beams with widths no less than the
column width. Using beams narrower than the col-
mnrr width results in costly formwork details.
In the tables of qrrarrtitiea for this section, the
percentage of pan formwork is shown in the last
column. This represents the percentage of the floor
area that wilf require pans for forrnwork.
Joist OrieW”on
Joists should preferably span in the shorter direction,
and the supporting beams in the longer direction in
rectangular bays, to achieve maximum economy.
This is not crucial for bays with aspct ratios less
than 1.5, since the cost differential is typically leas
than 1%. For baya with aspi?ct ratios between 1.5
and 2.0, orientation of the joists in the short direction
can result in cost suvings of as much as 5%
Column Dimerus”on Effects
Aa
mentioned, the supporting beama should be at
least as wide as the columns they frame into for
reasona of economy of forrrrwork. Other than this
requirement, the width and height of the column
membcm have almost no effect cm the cost of the
one-way joist floor system.
Live LoodEffects
Material quantities are to a large extent controlled by
deflection constraints. An increase in live loads does
not have a proportionate impact on cost. Alive load
of 100 psf increases the total cost by less than 570
over the cost of a one-way joist system designed for
a live load of 50 psf.
Aspect ROtJ-O
The
aspect rutio has a
minimal effect on the qrmrti-
ties for the one-way joist system for aspect ratios less
than 1.5.
Cod Breukdown
The
formwork costs for one-way joist systems are
approximately 58% of the fkmr system costa. Cmr-
crete
material, placing and finishing account for 25’%
of the cost. The remaining 1770 is for material and
placing costs of the reinforcing steel.
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3 ft Module
Live Load =50 psf
Superimposed Dead Load =20 psf
Slab Thickness = 5 in.
0“5 ~
fC = 6000 pSi
0.45
rc = 5000
psi
cost
Index
0 .4
0.3s
I
I
(
I
1
20
25
30
35
40
Square Bay Size
n
Bay
Rib Beam
Square
Size Depth
QUANTrrlES
Rib Width
Width Column
Concrete Reinforcement
ft
in,
Pan Forms
in,
in. Size (in.)
(ft’/fP)
psf
%
20X2U
8
5 25 20 0.59 1,45 89
2Qx25
8 5
39
22
0.62 1.67
84
2UX30 8
5 59 24 0.85 1.77 79
20X35 10
5 58 30 0.71 1.91
79
2QX40 12
5
60
32 0,78 1.93
79
25X 25
10 5 34 26 0.64 1,89 87
25x30 10
5 49 30 0.67 1.98
83
25x35 12
5 53 32 0.73 2.02
83
25X 40 14 5 42 34 0,76 1.42
86
30X30 14
5 35
32
0.73
2.03
68
343 X3.5 14 5 49 36 0.76 2.23 85
30X40 14
5 66 38 0.80
2.46 82
35x35 16 6 46
38
0.82
2.48 87
35.40 20 6 45
40 0.92 2.52 88
40x 40 2U 6 50
42 0.92 2 .83 88
I
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3 ft Module
Live Load = 100 psf
Superimposed Dead Load =20 psf
Slab Thickness = 5 in.
0 .5
0.4s
cost
Index
0 .4
0.35
f ’C = 6 0 00
pSf
fc =
5000 psi
rc .4000
psi
I
I
I
20
25
30
35
40
Squa re Ba y Size
n
Bay
Rib
Beam
Square
Size Depth
QUANTITIES
Rib Width
kWdth
Column
R
Concrete
Reinforcamenl
in.
Pan Form
in. in. Size (in.)
(ft’if?)
paf
%
2QX20 8
6
34
22 0.62
1,86 65
20x25 8
6
53
24 0.66 2.03
79
20.30 10 5 56 26 0.71 2.09 79
233X35 12 5 57
32 0.77 2,13 79
20X40 14 5 61 34
0.65
2.16 79
25X 25 12
5 33
26 0 .69 2 .08
87
25x30 12 5 49 32
0.73
2 .29 83
25x35 14
5
54
34
0 .79 2 .36
82
25x40 16
5 58 36
0 .87 2 .53
81
30 X2J3 14
6 44 34
0 .77 2 .48
85
30X35 2U 5 38
36 0 .89 2 .36 88
30.40 .20
5 40 40
0 .90 2 .52
86
35x35 20
3 40 40
0 .68 2 .79
88
35X40 m
5
42
42
0 .92 3 .CO 86
40x 40 .233
6
44
44
0 .95 3 .38 65
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II Module
~e Load = 50 psf
Jperimposed Dead Load = 20 psf
ab Thickness = 5 in.
0.4s
cost
Index 0“4
0.35
f ’C = 6000 pSi
r’c .5000 psi
rc .4000 psi
20 25
30
35
40
Square B ay Size
n
Bay Rib
Beam Square QUANTITIES
Size Depth
Rib Width
Width Column
Concrete
fr
Reinforcement
Pan Forms
in. in.
in. Size (in.)
(ft’/f?)
Ff
“k
20 X.2CI 16
7
m 20 0.70 1.25
92
.23x25 16 7 22 22 0.71 1.38 91
2QX30 16 7
24
24 0.72 1.43 w
X3X35 16 7 30 WI 0.75
1.58
88
20.40 16
7
37 32
0.77
1.77
85
25X 25 16
7
26 26 0.70 1 55
91
25x3JJ 16
7
30 30
0.72 1,71 80
25x35 16
7
33
32 0.73 1.87 88
25X
40 16 7 44 34 0 .77 2 .00 86
30X30 16
7 32 32
0.71
2.00
90
30X35 16
7
38
36
0.73
2.20
88
30X40 16
7 51 36
0 .77 2 .33
85
35x35 20
7
38
38
0 .80 2 .30
93
35X40 m
7 41
40 0.81 2 .50
69
40X40 m
7 44 42
0,82 2 .80
89
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5 fi Module
Live Load = 100 psf
Superimposed Dead Load =20 psf
Slab Thickness = 5 in.
0.45
cost ~
Index “
0.35
fC = 6000 pSi
fc = 5000 psi
m
,
.
m
I
20
25
30
Square B ay Size
ft
Bay Rib Beam
Square
QUANTITIES
Size Depth Rib Width
Wkfth
Column
ft
Concrete Reinforcement
Pan Forms
in.
in. in.
Size (in.)
(ft3/ft’)
m
%
2QX2U
16 7 22
22
0.71
1.41
91
20x25
16 7 24
24
0.72
1.55 93
2QX30
16 7 26
26
0.73
1.73 89
20X25
16
7 3-5
32 0.77 1.86 66
2QX40
16
7 47
34
0.62
2.06 83
25X 25
16 7 28 28 0,72 1.91 %3
25x30
23
7 32
32 0.81 1,84 89
25x3.5
m
7 34
34
0.82
2.03
88
25x40
Xl
7 39
36
0.s5
2.30
87
30X20
20
7 34
34
0.s0
2,23
89
30X35
20
7
3a
88
0.82 2.45 88
20X40
20
7 45
40
0.84
2,56 86
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DATA
SPANLENGTH:
Practical Range
= 15 ftt040fr
Fxonomical Range .35 ft to 40 ft
ADVANTAGES:
Economical for long, heavily loaded spans
Dome voida reduce dead loads
Attractive ceiling
Electrical fixtures can hc ptacedin the voida
Discussion
General
A two-way joist system consists of evenly spaced
reinforced concrete joists spanning in both direc-
tions. A reinforced concrete slab is cast integral with
the joists to form a monolithic floor system. Rein-
forcing bars are located at the top
or
lmttom of the
joista, depcndirrg on the sense of the bmrding mo-
ment. The slab has reinforcing bar’s at mid-depth to
allow the slab to span between the joists, though the
amount of steel required for temperature and shrin-
kagestrcsaes typically controls.
The perpendicular orientation of the joists results
in evenly spaced square voida on the underside of the
slab (which is the reason why the system is often
referred to ss a waffle slab). These voida, which
DIMENSIONS:
Slab thickness varies from 3 in. to 5 in. baaed on either
fire resistance requirements or structural conaidera-
tiona
. Joists extend frnm 8 in. to 24 in. below the sJab, with
web widths of 6 in. or 8 in.
DISADVANTAGES:
.
.
.
Not ccmromical for short spans or for light to medium
supcrimpascd loads
Higher fonnwork casts than for other slab systems.
Dccpcr members result in greater story heights
allow a considerable reduction iu weigh~ are forrued
by placing steel or tiberglsas domes on top of flat
fonrrwork. The rcxrdting voids from the domes have
aqusre dimensions between 2 ft and 5 ft in even foot
increments. The domes are omitted in the areas
around the cohrmrra to provide a deep sIab with a
high shear csrrying capacity. The solid portion typ-
ically extendx one-sixth of the span length in all four
directions from the column.
The results presented in this wction are for the 3
ft and 5 ft wide domes. ACI code section 8.11.3
restricts the clear distance between joists to a maxi-
mum of 30 in. (which corresponds to a 3 ft dome).
If the clear spacing exceeds this value, the floor
system must be. designed as a beam-supported slab
system. rather than as a joist system. Buth systems
20-’
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have the same design requirements, with the excep-
tion of a artraller reinforcing cover and a 10% in-
crease in the allowable shear stress permitted for
joists. The results for the 5 ft domes are shown in
tfria section, although this system is not considered
by ACf to be a joist system.
Floor System
,
described previously, the slab thickness ia cmr-
trolled by either structural or fire resistance conaid-
erationx. A 5 in. thick slab was used in the dexign of
the two-way joista. This thickrress was chosen tu
provide a two hour fire rating, and more than met the
structural requirements.
The thickness should be
adjuated as required, to obtain the applicable fire
resistance rating.
The standard joist widths for two-way joist sys-
tems rraing 3 ft and 5 ft domes are 5 in. and 8 in.,
respectively. With the slab thickness controlled by
fire resistance requirements and the joist width con-
trolled by indnatry starrdarda, the only geometric
variable to be determined ia the joist depth.
This publication considered only normal weight
concrete for the floor systems. It should be noted that
since the slab thickness may be controlled by fire
resistance requiremerrta, a lightweight concrete may
have some advantages, because a two hour fire rating
is met by a considerably thinner slab. This will alau
result in a sizable dead load reduction.
The depth of the floor system ia controlled by
deflection constraints for the loads used in this pub-
lication. Minimum thickrresa requirements sycified
in Table 9.5(c) of the ACI Code are for solid two-way
slabs. To determine the deflection control rcqrrire-
menta for the two-way joista, the cmaa-section of the
flcor system must be transformed into an equivalent
section of uniform thickness. This is accomplished
by determining a slab thickrre.sa that provides the
same moment of inertia aa the two-way joist section.
Listed below are the maximum clear span lengths for
the two-way joist system baaed on this approxim-
ation.
3 it Modufe
Joist
Joist
Maximum Clear
Depth
ThiCkncss Span Length
(in.)
(in.)
(ft)
8 6 27
10
6 30
12
6 34
14 6 38
16
6
41
5 fl Mndufe
JOixt
Joist Maximum Clear
Depth Thickncm Span Length
(in.) (in.) (ft)
14 8 34
16 8
37
20 8 43
24 8 52
In the tables of quantities for this section, the
pmcentsge of dome formwork is shown in the last
column. ‘Ms reprexenta the percentage of the floor
area which will require domes for forrrrwork.
Column Dimension Effects
The
material quantities are independent of the floor
height under normal loading conditions. Column
dimensiorra rracd in the analyacs of this publication
were chmen to repreaerrt the column sizes used in
10- to 20-story buildings. If a structure has a column
width and depth different from those used in the
tables, adjustments should be made by increasing
steel reinforcing quantities by l% for each 2 in.
decrease in square column dimensions. The quanti-
ties should be decreased by II% for each 2 in. increase
in square column dimensions.
Live Lood Effects
Since the material qrrantities required for a two-way
slab system are typically controlled by deflection
constraints, an increase in live loada dces not have a
proportionate impact on costs. Alive load of 100 psf
increasea the total cost by leas than 5% over the cost
of a two-way joist system designed for a live load of
50 pf.
Aspect Ratio
Square bays (aspect ratio = 1.0) represent the most
economical floor layorr~ since deflection control re-
quirements are exactly met in both directions. A
rectangrdarbay with an aspect ratio of 1.5 is 5% more
expensive than a square bay with the same floor area.
Cost Breukabwn
The
formwork costx for two-way joist systems are
approximately 54% of the floor system coats. Con.
crete material, placing and finishing account for 28%
of the cost. The remaining 18% is for material and
placing costs of the reinforcing steel.
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) fl Module
.ive Load = 50 psf
hperimposed Dead Load = 20 psf
lab Thickness = 5 in.
0.55
r
cost
Index
0.5
0.4s
rC = 6000 /)S/
fk . 5000
psi
r%=
4000
psi
20
25
30
35
40
Square Ba y size
n
Bay
Rib
Solid Head Square
QUANTITIES
Size
Depth Size Column
Concrete
n
Reinforcement Dome Forma
in.
rt Size (in,)
(ft’/ )
@
“/.
20X20 8
81A x 81/9
xl 0.73
2.28
82
20.25 8
81/ 9~
101A
22 0.73
2.58
82
2UX30 10
81,4 ~ 121A
24 0.81 2.85 82
23X35 14
81Ax 141,4
m 0.97 3.19 82
20X40 16
81,4 ~ 161,+
32 1,06 3.58 82
25 X25
8
101/2x 1ol~ 26
0.73 2.82
83
25x30 10
lol~ x 1214 30
0.81
3,03
63
25x35
14
10W x 14V2 32
0.97 3.22
83
25X 40 16
lol~ x 161A 34
1.06 3.52
83
30X30
10
121,+x 121A 32
0.61 2.96
83
30X35 14
121,4 x 141,+ 36
0.97 3.25 83
30X40
16
121,+~ 161A 39
1,06
3.58
83
35x35 14
1414 x 1414 38
0.97
3.56
83
35X40
16
141~ . 161A 40
1.26 3.97 83
40x 40 16
161A x 161+ 42
1,06
4.18
S3
i
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3 ft Module
Live Load = 100 psf
Superimposed Dead Load =20 psf
Slab Thickness = 5
in.
0.55
tb = 6 00 0psi
fc = 5 0U0 ps i
cost
0 .5
Index
20
25
30
35
40
Square B ay Size
n
my
Rib
Solid Heed
Square
Size
Depth
QUANTITIES
Size
Column
Concrete
Reinforcement
Dome Forme
rt
in,
n
Siza on.)
(ft3@
@
“/.
2U X20
8
81A ~ 81/4
22
0.73 2.48 82
20x25 8
81A x lol~
24 0.73 3.15 82
20X30
10
81/9 ~ 121/9
26
0.81 3,50 82
2Q X35
14
81A ~ 141/42
32 0.97
3.72
82
20X40
18
81/9 ~ 161,4
34
1.06
4.10
82
25 X 25
8
lly~ ~ lol~
28
0.73
3.42
83
25x30
10
1ol~ ~ 121,+
32
0.81 3.81 83
25x35 14
lol~ ~ 141/9
~
0.97 3.78 83
25X 40 16
lol~ ~ 1614
36
1.C6
4.24 83
30X30 10
121A ~ 121A
34
0.81
4.00
83
30.35 14
1,314 ~ 141/9
38
0.97
3.93 83
30X40
16
121/9 ~ 161/
40
1.CKr
4.29 83
35x35
14
141A -q141A
40
0.97 4.26 83
35X40
16
ll~x161~
42 1.06
4.53 83
40X40 16
161,4 ~ 161/9
44
1.06
4.98 83
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j ft Module
.ive Load = 50 psf
Superimposed Dead Load = 20 psf
SlabThickness = 5 in.
cost
Index
0.55
I
0.45
I
I
I
I
20 25 30
35 40
.
—
. .
Square-Eay S/ze
ft
Bay Rib Solid Head Square
QUANTITIES
Size
Depth Size Column
Concrete
Reinforcement
n
in.
Dome Forms
ft Size (in.)
(ft’/f?)
psf Y.
2QX2U 14
101,+ ~ ~ol~ 2fJ
0. 32
2.74 72
20x25 14
lol~ ~
101,+ 22
0.s0 2 .70 77
Z) X30 14
lol~
lol~ 24
0,90
2.77 81
2QX35
16
lol~ ~ 151/9 30
0.98
3.01 76
.23 X40 20
lol~ )( 151,+ 32
1.12
3.40 79
25X 25
14
lol~ ~ lol~ 26
0.30
2.40 82
25x30 14
lol~ ~ 101A ~
0.90
2.74 65
25x35 16
fol~ ~ 151A 32
0.9s
3.13 S1
25X 40 m
101~ ~ 151,4
34 1.12
3.29 83
30X30 14
lolfi ~ lol~
32 0.93
2.94 87
30X35
16
11)1~ y. 1514 36
0.9s
3.26 84
30.40 2U
101+ ~ 1514
3s 1.12
3.54 84
35x35 16
1514 ~ 151,4 38
0.98
323
m
35X40 m
151/9 ~ 151,’9 4(3
1.12 3.43 82
40x 40 m
151/ )(
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5 ft Module
Live Load = 100 psf
Superimposed Dead Load =20 psf
Slab Thickness = 5 in.
0.6
0.55
cost
Index
I
0.5
20
25
30
35
40
Squ are B ay Size
n
Bay Rib
‘~
::”)WF
Solid Head
Size Depth
ft in.
20X35
16
lol~ )( 151A
32
0.98
3.51 76
20.40 20
11)1~ ~
151A
34
1.12
3.70 79
25 X 25 14
lIJIA ~ lol~
28
0.90
2.76 82
25x3CI 14
101A ~ lol~
32
0.90
3,04 65
25x35 16
101,+ ~ 1514
34
0.96
3.53
61
25X 40 a
lol~ ~ 151/9
36
1,12
3.91 83
30X30 14
101,+ ~ 101+
34
0.943
3.34 87
30X35
16
lol+ ~ 151A
38
0,98
3.51 84
30X40 m
lol~ )( 151,4
40
1.12
3.S73 84
35 X3.5 16
151zX 151,4
40
0.98
3.84 80
35X40 20
151fix 151A
42 1.12
3.96
82
40X40 m
151/9 ~ 151+
44
1.12
4.26
65
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DATA
SPANLENGTH:
Practical Rarrge = 15 ftt040ft
Ecmromical Range .25 ft to 40 tl
ADVANTAGES:
Economical for longer spans
DISCUSSION
Floor System
The slab thickness for a beam-arrppmttxf slab system
is controlled by deflection constraints. These con-
straint are given by eqnxtimrs 9-11, 9-12, and 9-13
of the Building Code Requirements for Reinforced
Concrete (ACI 318-89). These equations are
/, (0.8+ A)
h=
(9-11)
36+5fl [am- 0.12(1 + ]
but not lexs than
0.8 + A)
h-t.
36+9p
(9-12)
DIMENSIONS:
Slab thickness between 5 in. and 10in.
DISADVANTAGES:
Preserrcc of beams may require greater story height
Flnnr layout maybe dictated by beam lncations
and need not be more than
0.8 + A)
h-t.
36
(9-13)
length of clear span in long direction of two-
way construction, meaaured face-to-face of
columns in slaba without beams and face-to-
face of beams or other supports in other cases.
ratio of clear spans in long to short dkction
of two-way slab.
ratio of flexrrral stiffrresa of beam section to
tlexural stiffness of a width of slab bounded
laterally by centerlines of adjacent panels (if
any) on either side of beam. Values of a can
be obtained from the following two grapha.
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urn = average value of c? for all four edges of a slab
panel.
In no case shall the slab thickness be less than 5
in. for am> 2.0 and 3% in. for a ~s 2.0.
. .
@
2.7
~ ‘+’=;” w H
2.6
2.5
2.4
2.3
2.2
2.1
2.0
1.9
I ,8
1.7
1.2
I .5
1.4
I ,3
I.2
.1
.
“
1
I,5 2345678910
. Ill
2.0
[.9
1e
17
,6
[5
t.4
1,3
1,2
1.1
1.0
13
234567890
Equations 9-11, 9-12, 9-13, are graphically
illktmted below”
L
9.5.3.3- .Wh (fY= 60 ksi)
70 EqQ-11,..= 4
// -
&w <
—2
h
_———
—1
30
——— ~
S13
1.0
M
20
B
The beam depth is also typicully governed by
defktion constraints. Table 9.5(a) of ACI 318-89
requires that the beam shall have a minimum depth
equal to the length of the span as defined in Section
8-7, divided by 18.5. Whh this given beam depth,
the width of the beam is sized to meet loading re-
quirements. Beam widths that are smaller than the
column width should be avoided to reduce formwork
costs.
Column Dimension Effects
The
supprting beams should be at least as wide as
the columns they frame into, for reasons of formwork
simplicity. Other than this rexpriremen~ the width
and height of the column members have minimal
effects on the cost of this flcux system.
Live Load Effects
Material quantities are, for the most par~ controlled
by deflection constraints, and sn increase in live
loads does not have a proportionate impact on costs.
Alive load of 100 psf increases the total cost by less
than 5% over tbe cost of a beam-suppted slab
system d=igrted for a five load of 50 psf.
Aspect Ratio
Square bays (aspect ratio = 1.0) represent the most
economical flour layout, since deflection rwprire-
ments can be exactly met in both directions.
A
rectangular bay with an aspsct ratio of 1.5 is on an
average 470 more expensive than a square bay with
the
same tlcmr area.
Cost Breokdown
The
formwork costs for beam-supported slabs are
af2p?OXi2S?t2tdylvo
of the ffnm system cmts. Ccm-
crete material, placing and finishing account for 21 %
of the cost. The remaining
2570
is for material and
placing costs of the reinforcing steel.
oh
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ive Load =50 psf
Superimposed Dead Load =20 psf
0.5s
fC = 6WOjJSl
4
0.5
cost
Index
fc =
5000psi
0.45
0.4
I
I
15 20 25
30
Square Bsy Size
n
Bay Slab
Beam Squara
Siza
QUANTITIES
Thickness
Depth
Column
Concrata Reinforcement Forms
ft
in.
in. Size (in.)
(ft3/f?)
w
(f?m?
15X 15
5.0 10
14 0.46
3.50 1.15
15X2U 5.5 14
1s 0.55
3.29 1.23
15x25
6.0
16
m 0.88
3.41 1,17
15x31J
7.0 20 22 0.68
3.71 1.16
20 X.ZO 6.0
14
23 0,57 3.54
1.17
20x25 7.0
is
22 0.72 3.59 1.17
.20.30 9.0
20
24 0.83 4.23 1.16
25X 25 70
18
26
0.67
3.86
1.18
25x30 9.5 2U
30 0.89 4.70
1.17
30X30 9.0 20
32 0.s5 5.07 1.17
1
2s
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Live Load = 100 ps
Superimposed Dead Load =20 psi
0.6
0.s5
cost o ~
Index “
0.45
0.4
15
20
25 30
Squ are Ba y Size
ft
Bay
Slab Beam
Sqluare QUANTITIES
Size
Thickness Depth
Column
Concrete Reinforcement
Forms
ft in.
in.
size (in,)
(ft’if?)
Paf
( /ft’)
15X15 5.0 10
14
0.46
4,15
1.15
15X20 5.5 14
118
0. 55
3. 63 1. 23
15x25 6. 0
18 22
0 60 3. 91 1. 22
15X30 7. 0
20
: 14
0. 66
4. 33 1. 16
20x20 6. 0
14
22
0. 57
4. 35
1 16
20x25 7. 0 18
: 14
0. 69
4. 08 1. 17
20X30 9. 0 m
26 0. 83
5. 23
1. 18
25 X 25
7. 0 18
: 8 0. 68
4 78
1. 19
25x30 9. 5
m
32
0. 89
5. 51
1 17
30 X2J I
9. 0 20
34 0. 67 6. 12 1. 19
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General Discussion
This section
provides overall comparisons of the
economics of the various fkmr systems discussed in
this publication. It provides a summary of the factozs
that may influence the costs of cast-in-place concrete
floor systems. These factors include column dimen-
sions, live loads, aspect ratios and proper detailing.
A few other aspects that have an influence on econ-
omy are also discussed.
Overall Comparisons
Four figures that compare the economics of the dif-
ferent structural floor systems
considered are prn-
vided at the end of this publication. The figures
clearly show that the optirrrality of the slab system
depends on two major factors: the span in the long
direction, and the intensity afsrrperimposed dead and
live loads. For a given set of loads, the slab system
that is optimal for short spans, is not necessarily
optimal for longer spans. For a given span, the slab
system that is optimal for light superimposed loads,
is not necessarily optimal for heavier loads. The foor
figures should facilitate the section of a strnctrrral
floor system most appropriate for a certain applica-
tion.
Column Dimenm”ons
Analysis shows that the height between floors has
very little influence on the material qrrantitiea for the
floor system. Column cross-sectional properties de-
termine the clear span length and the shear capacity
of the slab. The column cross-sectional d~mensions
used in this publication were representative of 10- to
20-story buildings Increasing or decreasing the col-
umn dimensions by 2 in. did not affect the concrete
quantities and charrgcd the steel reinforcing quanti-
ties by lCSSthan 1%.
Live Loads
The material quantities for the floor system are typ-
icall y controlled by deflections rather then stresses.
Irrcreusing the live load from 50 psf te ltM paf onfy
resulted in a 4~o to 10% increase in the floor system
cost.
Aspect Ratr”o
Sqrrare bays usually represent the most economical
floor layou~ since deflection control requirements
can be exactly met in both directions. A rectangular
bay with an aspect ratio of 1.5 ranges between 4% to
10% more in cost than a bay with an aspect ratio of
1.0 and the same floor area. This, however, is not
the case for one-way joist systerna. Tfds type of floor
system shordd have the joista span in the short direc-
tion, and is almost unaffected by aspect ratios of UP
to
1.5.
Concrete Strengths
Concrete strengths of 4000 psi, 50@ psi, and @OO
psi were used in this publication. Cost analysis
shows that for gravity loads, 4000 pi concrete is
more economical than higher concrete strengths.
Cost Breakdown
The formwork for the floor systems will absorb from
50% to 58% of the costs. Concrete material, placing
and finishing account for 21’% to 3090. The material
and placing costs of the reinforcing steel amount to
between 17% and 25% of the cost.
Repetition
A cost efficient design utifizes repstitiorr. Changes
should be minimized from floor to floor. Changing
column locations, joist spacing, or the type of floor
system increases the cost of forrnwork, time of corr-
strrrction and the chance of field mistakes, and there-
fore should be avoided.
Column-Beam Intersections
Thebearrra
Orat
frame into columrrashould be at least
aa wide aa the columns. If the beams are narrower
than the columns, the beam forms will require eostl y
field labor to Pas the formwork around the columns.
Stindd Dimenn”ons
Standard available sizea should be used for structural
fornring. For instance, joist fomrwork pans are
available in various web depths of 20 in. and from 8
in. to 16 in. in 2 in. increments. Specifying a depth
different from these sizes will require the fabrication
of costly special forrnwork. When detailing drop
panefs or other changes in the floor system depti
actrral lumber dimensions should be taken into ac-
Corrrrt.
Depth of the Ceibrg Sandwich
This publication haa addrxd the economy of the
structural slab system only. However, the structural
engineer usually has to look beyond. The structural
slab system ia part of the so-called ceiling sandwich
which also includes the mechanical system f,HVAC
ducts), the lighting fixtures, and the ceiling itself.
3tl
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The flnor-to-floor height of a building ia the total
depth of the ceiling sandwich plus the clear tlnor-to-
cciling height. Any variation in the depth of the
ceiling sandwich will have an impact on the total
height of the shearwalls and cohsmna, the mccban-
ical, electrical and plumbing riaezs, the staim and
interior architectural finiahcs, and the exterior clad-
ding. It will also have an impact on the total heating
cooling and ventilation volume. To minimize the
depth of the ceiling sandwich is very often the goal
of the structural engineer. This becnmes particularly
impmiant in cities like Washington, D.C. that impose
a height limit on buildings Optimization of the
ceiling sandwich depth may tranalate intu an extra
story or two accommodated within the prescribed
height limit.
“’’”-l
TT
—
A number of details have been attempted in the
paat to accomplish a reduced depth of the ceiling
sandwich. The HVAC ducts can paas through the
webs of joiata or beams. llrii will reduce the floer-
to-floor height, but will increase formwork and field
labor costs Another alternative is to cut notches at
the bottom of the joist or beam to allow paxsage of
the up~r portions of the HVAC ductx. This altern-
ativealan requires additional forming cmta. Further,
special detailing would be needed to meet the
.WUC.
tural integrity requirements of the ACI 318-89 Cnde.
More importantly, however, such practices take flex-
ibility away from accommodating futrrre changes in
the use of the floor space. Such flexibility is becom-
ing more important in view of the shifting emphasis
towardx corracionaly designing buildings for a long
service life.
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Ne Load = 50 psf
superimposed Dead Load = 20 psf
~= 4000 psi
0.9
0.8
0.7
cost 0.6
Index
0.5 ,
0.3
I
1
1 1
1
[
15 20
25 30
35 40 45
50
Square Bay Si ze
n
Owway
joist
(wi& m-d”k)
. . . . S abandkm
Flat P1.te
— . — Flat dab
Twc-wy joist
Two-nay joist
———
(wi& mod”k?)
15 20 25 w 35
40 45 50
Square Bay Size
rt
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Live Load. 100 ps
Superimposed Dead Load =20 ps
fc’= 4000
ps
0. 8
t
4
.’
/
15
20
25
30 35
40 45
50
Square Say Size
n
—. ‘me way pi
. . . .
S ab and ban
u . FM pl.te
— . — FM ,kb
m m _ Tw..wq joist
Tw.w.y o st
———
[wide m.adub]
15
30
25
30 35 40
45
50
Square Bay Size
ft
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