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OCR for page 30
30 RESK)ENTIAL SLABS ON GROUND
procedures. All this information is intended to amplify and clarify
the recommendations set forth in Section II.
PART A: Selection and Design of Slabs
1. O FUNCTIONS OF SLABS- ON- GROIJND
Slabs-on-ground constitute an element of residential construction
performing in at least the first and frequently both of the following
two capacities: as a separating element between the ground and
habitable space; as a structural element receiving part or all of
the loads of and on the superstructure and transmitting such loads
to the foundation soil. While slabs-on-ground act in the former
capacity at all times, the degree to which they function in the latter
capacity depends upon engineering definition.
Wherever a slab-on-ground acts simply as a separator between
living space and ground, it carries no load-bearing or large load-
producing elements of the superstructure. In this case, satisfactory
performance may be defined to include no unsightly cracks, and no
large differential settlements which may be functionally or aestheti-
cally objectionable, such as a noticeable "out-of-plumb" condition
affecting trafficability or equipment and building elements supported
on the slab, an exposure of the foundation, and/or an effect upon the
performance of any mechanical/electrical services which pass
through the slab. Such a slab, however, can, with proper details, be
allowed to settle to some degree without detriment either to struc-
ture, services, or aesthetic considerations.
Wherever a slab also acts as a structural element, transferring
the substantive superstructure loads to the foundation soil, of neces-
sity it must be able to do so satisfactorily. In this case, the differ-
ential settlement of the slab, unless confined within prescribed
limits, may have critical consequences for the superstructure-for
example, if a wall is supported on a slab which settles unevenly, it
may rack or crack. Therefore, a slab which receives superstructure
loads should be made stiff enough to support such loads without
excessive deflection or uneven settlements; this requires that it
OCR for page 31
SUPP LE ME NTARY INFORMATION 31
behave as nearly as necessary like a monolithic rigid body which,
if it should settle, will do so uniformly.
Stating these two situations in another way, slabs to be treated
solely as separators must be founded on firm ground and soil not
subject to substantial changes in volume as a result of changes in
water or moisture content. The separate structural supports must
similarly be well founded. In those areas where either or both are
not possible, slabs may as well be made monolithic with the founda-
tion and thus act both as separators and as receivers of all imposed
loads for transmittal to the ground.
Even though those instances where a structural or monolithic
slab and foundation system will be needed are limited in number,
they are the most demanding of attention and design effort. This
circumstance is reflected in this report in the disproportionately
large number of pages devoted to the analysis and design of slabs
which act both as separators and as structural elements, even
though the need for such slabs is limited to a small percentage of
all residential construction in the nation.
2.0 FUNDAMENTAL FACTORS OF SLAB DESIGN AND
CONSTRUCTION
The design of slabs-on-ground consists of three basic operations,
namely:
a. Selection of slab type to be used
b. Dimensioning the slab (layout)
c. Reinforcing the slab (wherever necessary).
To perform these operations successfully under a specific set of
conditions, the designer must analyze many factors which directly
or indirectly influence his decisions. Those assuming dominant
importance in the great majority of cases are:
a. Soil properties of the ground on which the slab is to be
supported
b. Climate at the building site
OCR for page 32
32 RESH)ENTIAL SLABS ON GROUND
c. Type of superstructure (for slabs which transmit super-
structure loads to the foundation)
d. Quality control in materials use and in construction.
These four principal factors are, for this report, the bases on
which procedures are developed for selection, and specification
or design, of slabs-on-ground. The first three (soil, climate, and
superstructure) are presented and analyzed below, in relation to
slab selection, and specification or design; the fourth and equally
important factor of quality control will be presented independently
in Part B of this section.
3.0 SELECTION OF SLAB TYPE
The slab appropriate to any given set of conditions should be ade-
quate in terms of performance and economy. Below is a descrip-
tion of each of the four types, under one or another of which almost
all slabs encountered in practice can be classified. Selection of the
appropriate type to be applied in each case depends on only two of
the four fundamental factors-soil and climate. The impact of these
factors on slab-type selection is analyzed following the descriptions.
3.1 Types of Slab- On- Ground
3.1.1 Slab Type I
This 4-inch-thick slab, intended for use on firm ground which
will develop no change in volume with time, is cast directly on a
properly prepared building site and slab base and carries no rein-
forcement over its entire area. Its use is limited to that of separa-
tor between ground and living space. Its maximum dimensions are
limited by the need to avoid shrinkage cracking. Successful per-
formance depends on compliance with a set of specifications.
3.1.2 Slab Type II
Also limited to the function of separating ground from living
space, this 4-inch-thick slab, which may be of larger dimension
OCR for page 33
SUPPLEMENTARY INFORMATION 33
than Type I, is applicable to ground which may undergo small
movements (shrinkage and expansion) with weather changes and
under loading. To withstand these small movements as well as
to accommodate the stresses of drying shrinkage and thermal
change without serious damage, it is provided with light reinforce-
ment. Successful performance depends on compliance with a set
of specifications.
3.1.3 Slab Type III
Unlike Types I and II, this slab receives and transmits all super-
structure loads to the foundation soil. It is used with soils which
in all likelihood will undergo substantial volume change with time.
Use of spread footings for the foundation is not advisable on such
ground; therefore, loads are distributed by the slab over its entire
ground-support area. This reduces the bearing stresses on the
ground and also forces the foundation, the slab, and the superstruc-
ture to act as a monolithic structure (somewhat like a rigid boulder
in a soft mass of ground). To assure that the slab will actually be-
have in this manner, the designer must impart to the slab the
necessary rigidity and strength. Hence, slabs of this type need to
be carefully analyzed and designed so that dimensions (for stiffness)
and reinforcement (for strength) will be accurately determined
and provided.
3.1.4 Slab Type rv
This slab also receives and transmits all superstructure loads to
the foundation soil. Unlike Type III, however, this slab does not it-
self rest on the ground. Rather, it is supported on beams which are
in turn carried by caissons, piles, footings, or similar special foun-
dations carrying the loads to solid ground well below the level of the
slab. It is used on very poor soils which are extremely sensitive
to weather, have negligible bearing capacity, or are high in organic-
materials content. This type is designed in the same manner as
structural floor slabs of concrete, in accordance with the ACI code.
Each of the four types discussed above is considered minimal for
the condition described. Obviously, a slab type of greater capability
can be selected-e.g., Type II instead of Type I; however, any de-
cision in this respect should be predicated on the desire to improve
quality of performance within predetermined economic limits.
OCR for page 34
34 RESIDENTIAL SLABS ON GROUND
3.2 Soil Investigation
The importance of determining the nature and properties of the soil
on the site where a residential slab is to be used cannot be over-
emphasized; proper identification of the foundation soil is a critical
factor in slab selection.
For purposes of this report, the Unified Soil Classification Sys-
tem has been adopted.1 Details and specifics relating to soils are
provided in Part C of this section; here, only the basic specifica-
tions on minimum requirements for soil investigation are given.
Unless competent engineering advice indicates otherwise (see
also Step 1, p. 10), it is advisable to perform at least one test boring
on each slab site. When the boring reveals unusual conditions, such
as organic soils, soft or loose soils, highly plastic soils, or rock,
additional borings should be made. These test borings can be made
with simple tools, the important thing being to determine soil types
and extent of each to a depth of at least 15 feet, or to a solid layer
of rock.2 A record of the class of soil, its depth, consistency, and
moisture content should be kept. Where CL, OL, CH, or OH soils
are encountered, it is also necessary, for the appropriate selection
of slab type, to determine the unconfined compressive strength (qu).
It may be helpful In the site investigation to examine existing resi-
dences in the immediate area, but it must first be determined that
the same conditions prevail with respect to soil type, topography,
and construction type; also, that the existing structures examined
are old enough to have experienced the design range of climatic
variations likely to occur in the area.
3.3 Climatic Rating
Along with soil classification, climate is the other important factor
in the selection of slab type. Climate affects the behavior of a slab-
on-ground primarily through changes in the moisture content of the
soil underlying the slab. If there are wide variations in the amount
of moisture in the supporting soil, and if this soil is water-content
sensitive, expanding as it absorbs water and shrinking with its loss,
then the slab is subjected to a sequence of uplift (as the soil swells)
1See Appendix D, p. 289.
2Bucket augers or helical-blade augers are usually satisfactory, since
pieces of undisturbed soil can often be obtained.
OCR for page 35
SUPPLEMENTARY INFORMATION 35
and settling (as the soil shrinks). Whenever a time of high water
content is followed by drought, the moisture at and beneath the
perimeter of the slab will generally evaporate much more rapidly
than that under its center, where it is trapped and sealed from
direct exposure. Moisture will often remain under the slab center
even after extended periods of drought (one year or several years),
and/or accumulate there due to capillary action as well as migra-
tion, even though the soil around the periphery has dried to a con-
siderable depth. A similar but opposite phenomenon develops when
the ground moves from low to high moisture content. Particularly
if prolonged periods of alternating drought and wetting occur, con-
siderable difference in moisture content can develop between one
and another of the various points underlying a slab. If the soil
happens to be such that substantial change in volume will occur
with change in moisture content, one of the following two conditions
may ensue:
a. If the slab is relatively flexible, it will follow the uneven con-
tour of the soil which will result from the uneven change of volume;
the superstructure, if it rests on the slab, then will be exposed to
distortions which may cause damage.
b. If the slab is sufficiently rigid, it will refuse to follow the
uneven contour of the ground. As a result, higher soil pressure
will develop on the slab over the high plateaus, with greatly re-
duced pressure over the valleys. The slab will be subjected to
bending as it endeavors to accommodate to the uneven contour,
and the soil may deform in areas of high bearing pressure, trans-
ferring load to adjoining areas. If the slab carries the superstruc-
ture, the latter thus will be provided protection against damage.
Obviously, it is difficult to assign exact values to the amount of
precipitation, its variation in occurrence, or its effect on soil under-
lying slabs-on-ground. The important consideration is whether or
not climatic conditions will be likely to change the moisture content
of the soil during and after construction. Involved may be such
matters as freezing, which, in some soils, will cause volume change
through the formation of ice lenses; or the presence of trees and
shrubbery in the immediate proximity of the slab perimeter, which
will affect soil moisture content by providing a shield from natural
precipitation and by extracting moisture during growth.
Studies of weather data disclose at least five variables affecting
consistency of climate. They are:
OCR for page 36
36 RESIDENTIAL SLABS ON GROUND
a. Yearly annual precipitation
b. Degree of uniformity through the year in distribution of
precipitation
c. Number of times precipitation occurs
d. Duration of each occurrence
e. Amount of precipitation at each occurrence.
~ a study of drought hazards to crops,1 a relationship was noted
between soil grain size and moisture availability as affected by rain-
fall. Even though the principal concern of this study was something
other than soil moisture retention, its findings bear out the accepted
premise that, the finer the soil grain size, the slower the loss or
gain of total moisture.
U.S. Weather Bureau studies have further disclosed a strong ~n-
verse correlation between two factors: the amount of rainfall for
any particular period and the number of occurrences. Without de-
tailed explanation of how these values are obtained, it suffices, for
purposes of this report, that the frequency function provides an
excellent measure of the potential for soil activity; for it gives a
sound indication of the likelihood of extended periods during which
the normal soil-moisture balance may be upset through evaporation
by reason of low rainfall, or through concentration in fewer-than-
normal occurrences. ~ either instance, cohesive soils can be
expected to shrink during dry periods. Upon restoration of the
normal rainfall pattern, cohesive soils can be expected to swell.
The rate at which moisture is lost or gained by soils is not at
this time thoroughly understood. It is generally accepted, however.
that air movement accelerates loss of soil moisture. Since air
movement is independent of rainfall, it can be assumed to increase
loss of soil moisture, especially during extended periods of little
or no precipitation.
While it is recognized that other factors such as temperature
and relative humidity also influence loss or gain of soil moisture,
the effects exerted are comparatively unimportant.
On the basis of U.S. Weather Bureau data, a climatic rating
(Cw) has been assigned to all points in the continental United States,
1Gerald L. Barger and H. C. S. Thom, "Evaluation of Drought Hazard,"
Agronomy Journal, Vol. 41, No. 11, November 1949, pp. 519-526.
OCR for page 37
SUPPLEMENTARY INFORMATION 37
as shown in Fig. 1, p. 38. The Cw for any particular locality not
directly on an isoline can be determined simply by interpolation to
the nearest whole number; for example, Jackson, Mississppi, would
be assigned a Cw of about 37, while for Columbia, Missouri, Cw
would be about 33.
3.4 Correlation of Climate and Soil for Selection of Slab
Once the foundation soil of a slab is classified, and the severity of
the climate at the site is identified with the help of Fig. 1, the proper
slab type can be selected. When the soil is basically cohesionless,
selection of slab type depends exclusively on the density and con-
sistency of the foundation soil, without regard to climate. Thus,
a Type I slab can be successfully used on all gravelly soils (GW,
GP) under all climatic conditions. It can also be used on all sandy
soils with or without silts and clays (GM, GC), as well as on silts
(ML, MH), provided they are classified as medium or dense.
Table VI, p. 142, provides a quantitative measure of the various
densities of cohesionless soils In terms of the number of blows
required to drive a standard 2-~nch OD sampler 1 foot into the
ground by means of a standard 140-lb hammer falling 30 inches.1
Whenever cohesionless soils or soils of low plasticity (GM, GO,
SW, SP, SM, SC, ML, MH) are present in loose condition, a Type II
slab is the more suitable (regardless of climatic conditions), since
such soils in loose condition are subject to a limited degree of
uneven settlement after the erection of the superstructure.
Light reinforcement, therefore, will be required to protect the
slab from cracking.
A Type II slab can also be used over clay (CL) or organic soils
(OL) when the plasticity index rating is less than 15 and the ratio
qu/w (where w is the average total slab dead and live load, and qu
is the unconfined compressive strength of the soil) is more than
7.5, thus permitting superstructure loads to be supportable directly
on spread footings. Where PI ~ 15 but the soil is relatively firm
(qu/w > 7.5), a Type II slab is still adequate provided the climate
is optimum, i.e., the climatic rating (Cw) is at least 45.
Type HI slabs have a limited application, in the sense that they
are needed only where clays or organic soils (CL, OL, CH, OH)
1ASTM Designation D 1586-64T (or most recent edition), Standard Pene-
tration Test. Philadelphia: American Society for Testing and Materials.
OCR for page 38
(A
W\,o S: \
. ~ ~ ~ Q
O ~ ~ ~ ~
it ~ §'! ~
o 3 5] - ;
u, o ~ 1
~ f(_:
if:
/ ,_
of_
~ ~1
~ _
~° ~
0 CO
C.
U]
I:
Ct
% ~
C)
O
3
U]
._
8 c)
_ ·_
·_.
~4
~ o~
OCR for page 39
SUPPLEMENTARY INFORMATION 39
occur in localities having a climate which is less than ideal (i.e.,
Cw < 45), or where the average load (w) is high relative to the un-
confined strength (qu) of the supporting soil (qu/w ~ 7.53.
When CL, OL, CH, and OH soils having a low compressive bear-
ing capacity (qu/w < 2.5) are encountered, a Type IV slab resting
on special foundations should be used.
Table I, p. 11, correlates the various combinations of soil type
and climate and classifies them with respect to the type of slab
recommended for use.
4.0 CRITERIA FOR TYPE I SLABS
4.1 General
Type I slabs (Fig. 2, p. 40) are not affected either by the type of
superstructure or by the climate at the construction site. The
superstructure is supported directly on footings, and the soils on
which Type I slabs are founded are practically unaffected by cli-
mate and water content changes.
This type of slab, by its very nature, possesses only limited
capabilities; specifically, it has only compressive strength and
cannot tolerate appreciable amounts of tension or warping. It may
crack during drying, but, when used under controlled conditions,
such cracks as do occur should not become excessively wide nor
prove a detriment to the serviceability of the slab.
The controlling factors in the successful performance of these
slabs are the quality of materials and construction, size, and cer-
tain other basic details. Aspects of quality control are described
fully in Part B. pp. 126-136, and the other factors are discussed
below.
4.2 Site
Any site upon which this slab is to be placed should be well drained
and properly graded.1 The soil should be one of those appropriate
for supporting a slab of this type, and should be uniformly and
1This report, Part B. pp. 126-136.
OCR for page 40
40 RESIDENTIAL SLABS ON GROUND
. . .
· ~ . ~
i'<
-Insulation or
Expansion Joint
-
~ .
. a, ., ~ .
_ =
Insulation or
Expansion Joint_
~!
. ~ ' ~ 'I
a\
c.
:~ Insulation or
b
b.
~ .
Expansion Joint
Grooved to Typical
Separate Weakened
Aggregated ~PIane Jointed
. ~Z2, . ~ , .
. `,
~ . ^' :~
1~ ~ 1/3 1 o. Add
Non-cellulosic:
Strip Separator
Insulation or
Expansion Joint
-
Note: This type of construction,
entailing ledge support
di rec tly under slab, with
or without insulation or
expansion loins, es nor
recommended.
d.
FIG. 2 Typical Type I Slabs
adequately compacted] to provide the support necessary to ensure
that warping and tensile stresses which contribute to cracking are
not induced in the slab.
1This report, Part B. Fig. 22, p. 128.
OCR for page 115
SUPP LE ME NTARY INFORMATION 1 15
Step 9a-Reinforcement used in both directions is as follows:
Bottom steel, 1 No. 6 bar per beam (area = 0.44 in.2)
Top steel, No. 2 bars in the slab at 9 in. o.c. (area = 0.067 in.2/ft)
for a requirement of 0.18 (0. 34) = 0.061 in.2 /ft.
Note: Slab reinforcement (No. 2 bars at 9 in. o.c.) exceeds the
WAIF reinforcement specified for the corresponding Type II slab.
Steps lea and lla-Not applicable.
The full slab layout is shown in Fig. 21, p. 116. No steel adjust-
ment is made for unequal beam spacing, because the steel provided
in excess of the minimal steel required is ample compensation.
Since beams are shallow, the use of stirrups (No. 3 at 5 ft-O in.) is
optional-bottom steel can be easily placed and secured by other
means. However, if stirrups are not used, chairs or other means
should be provided to assure that bottom steel will be held clear a
minimum of 2 inches from the soil as recommended herein. It
should be noted too, that for smaller slabs or for slabs on less
active soils or in less unfavorable climates, the depth of beams
would be even less, approaching a flat slab or Type II slab.
7.13 Example 1-Design of Type III Slabs Supported on
Compressible Soils
The procedures which follow demonstrate the application on com-
pressible soil of the criteria recommended in pare. 1.4, Step 9c,
1.14, and amplified in pare. 7.9-7.9.3, pp. 85-91.
7. 13.1 Given Conditions
Location: Alexandria, Louisiana
Floor plan and outside dimensions.
Bear~ngWa11; total load
at base = 15^
- 1
i .
18'- 0" ~24'- 0" l
L 42'- 0"
,
OCR for page 116
116 RESIDENTIAL SLABS ON GROUND
~ 9~-08' ~ 96-0~' ~128-0~. ~12'-0" ~' N
-2 1
,
C~
,
'
I .. J
_ J-8" 1kg" 3' L~.'J3'
I I I I I ~
L ~J L~ JL_ _~.
r ~ r~ ,~ ~
11 a'
2L!'~t2 ~J~8
l
~ _ ~_ _ ~ ~ _~ _ _ ~ ~ _ _
r-~r~~ =~ ' ~~]
1 L ,_~1 , 1 3 L .
I ~o I I = I
L_~__] L =~__u
~-t
1
1
I ~ Oe, 1:
-i''-0 J
~ I
1 1 _
5 t 11
-1 J5
l
8$'
J l
1
_
J I
~#3at 12in. o.c. inE-Wdirection
thickness2I :_~:y,~
#2 at 9 in. o.c. in N-S direction
a. Slab Layout b. Slab Section
i/r :] i6~ ~ 1 \7i "
8" 8" 8"
~ ~. ~Y .H ~
Section 1-1 & 6-6 Section 2-2, 3'-3' & 4-4 Section 3-3 & 5-5
c d
176 "
a
a .~/
D i 2 #6 bars
·- II-2t
Q.'
~,,
Section 7-7
f
~2116~ ~
'~ 8" ~ ~ 8" `,
Section 7'-7' 8' 8-8 Section 9-9
9 h
FIG. 21 Slab Layout and Reinforcement-Para. 7.12 Design Example
1 7ji"
OCR for page 117
SUPPLEMENTARY INFORMATION 117
Type of construction: wood frame; masonry veneer and plaster-
board interior
Total weight of superstructure = all dead and live loads, includ-
ing concentrated loads = 140 kips
Openings through slab: none greater than 8 inches; all having
expansion joints
Concentrated loads: one bearing wall, with a total dead and live
load of 15 Rips, located as shown above.
Step 1-Summarize soil investigation results.
a. Soil type: CH with PI = 35 to a depth of 8 It and
OH with PI = 44 from 8-20 It in depth
b. Consistency of CH soil: qu = 1200 psf.
Step 2-Determine climatic rating.
Referring to Fig. 1, p. 38, Cw = 35 for Alexandria, Louisiana.
Step 3-Determine appropriate slab type.
Since the soil is CH and OH, PI > 15, and Cw = 45, a Type Ill
slab is required unless qu/w < 2.5, In which case a Type IV slab
would be needed (Table I, p. 11~.
7.13.2 Application of Type III Procedure
Step 1-Determine total average load.
a. Compute psf-superstructure load.
ws= 140,000/24~42) = 139 psf
b. Compute estimated dead weight of slab.
wd= 2L+ 30 =2~42) + 30 = 114 psf
c. Compute total superstructure and slab dead load.
w = wd + WS = 114 + 139 = 253 psf
Resee pare. 7.9.3, p. 91.
OCR for page 118
1 18 RE SIDENTIA L SLABS ON GROUND
Step 2-Establish controlling soil properties.
a. The minimum qu in the top 15 feet of the soil immediately
below the bottom of the slab stiffening beams is the qu for the CH
soil stratum, i.e ., qu = 1200 psf. Therefore
qu/w= 1200/253 = 4.75
and
2.5 ~ qu/w ~ 7.5.
b. ~ accordance with the provisions of 7.8.1a, p. 66, PI of the
soil is determined as follows:
The top 3 It are devoted to the depth of stiffening beams
From 3 to 8 ft. PI = 35 (total depth = 5 It and weight factor = 3)
From 8 to 13 ft. PI = 44 (total depth = 5 It and weight factor = 2)
From 13 to 18 ft. PI = 44 (total depth = 5 It and weight factor = 1)
From which
PI = 1/30 [3~5) 35 + 2~5) 44 + 1~5) 44]
=
- 5/30 (105 + 88 + 44)
= 1/6 (237)
= 39.5
Step 3-Determine support index.
From Fig. 6, p. 53, for PI = 39.5 and Cw = 35' C = 0.91.
No special circumstances prevent or diminish the expected varia-
tions in soil moisture; therefore
Cm = C = 0.9.
Since 2.5 ~ qu/w < 7. 5, the support index (C) must be reduced
and equated to Cr. in accordance with 7.5, p. 56 and 7.9, p. 85, and,
since C > 0.65, Cr is determined from the equation
qu/w= 4.75.
OCR for page 119
SUPPLEMENTARY INFORMATION 119
Total superstructure load (W) is
w (24) 42 = 0.253 (24) 42 = 255 Rips
Wc = 15 Rips
and
w W
c c
-
w W
Therefore, in the long direction
= 2~55= 0.059.
Cr = (2.5 - 4.75~0.13 - 0.2 (0.059) - 0.2 (0.91~] + (0.65 - 0.059)
= -2.25 (-0.064) + 0.591
= 0.735.
Because the concentrated load is uniformly distributed along the
short direction, Wc = 0 for the short direction, and
Cr = (2.5 - 4.75)[0.13 - 0.2 (0.91)] + 0.65 = O.767.
Step 4-E stablish deflection ratio .
From Table III, p. 50, allowable l`/L = 1/300.
Step 5-Determine outside slab dimensions.
L =42ft
L' = 24 It
Step 6-Determine effective loads on the slab.
Then
~ = 1.4 - 0.4 (L/L') = 1.4 - 0.4 (42/24) = 0.7.
w= (1-Cr) w = (1.0 - 0.7673~255) = 59.4 or 59 psf
OCR for page 120
120 RES~ENTL9^L SLABS ON GROUND
in the short direction, and
w = (1-Cr~w~p= (1.0 - 0.735~255) 0.7 = 47.3 psf
in the long direction.
The initial value of the support index is
C = 0.91,
and the effective load in the short direction is
w = 255 (1.0 - 0.91) = 23 psf,
and the effective load in the long direction is
w = 23ro psf = 23 (0.7) = 16.1 or 16 psf.
Step 7-Layout of the slab
Three stiffening beams will be placed along the 42-foot dimen-
sion at 12 feet o.c., and five stiffening beams along the short
dimension at approximately 10 feet o.c.
1 1 1~1'
~L l
l 10' - 5" 10' - 5" 10' - 5'il0' - 5"l
Step 8-Select basic beam dimensions.
d = 28 in.
B = 3 (8) = 24 in.
B'= 5 (8) = 40 in.
Step 9-Select basic parameters.
a. Depth ratios are
- ~
'
'
cow .
OCR for page 121
SUPPLEMENTARY INFORMATION 121
L/d = 42 (12)/28 = 18
L'/d = 24(12)/28 = 10.3.
b. Load indices are
in the long direction, and
in the short direction.
w(L'/B) = 47.3 t24(12~/24] = 568 psf
w(L/B') = 59 [42(12~/40] = 743 psf
For the initial value of the support index (C = 0.91), the load
indices are
in the long direction, and
in the short direction.
w(L'/B) = 16 t24(12~/24~= 192 psf
w(L/B') = 23 [42(12~/40] = 290 psf
c. Determine steel ratios (p).
Referring to Fig. 15 for A/L - 1/300, ordinate w(t'/b) is
568 (p= 0.95%) for Q/d= 18
743 (p= 0.39%) for t/d= 10.3
192 ~=0.31%)forQ/d= 18
290 (Pmin= 0.3%) for Q/d= 10~3.
d. Reinforcing steel required per beam in the long direction is
As= 0.009 (28) 8 = 2.13 in.2 (bottom)
and in the short direction is
As= 0.0039 (28) 8 = 0.87 in.2 (bottom).
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122 RESIl)ENTIAL SLABS ON GROUND
For the initial value of the support index (C = 0.91), the required
steel in the long direction is
As= 0.0031 (28) 8 = 0.69 in.2 (bottom)
As = 0.69 - 0.65 = 0.0 in.2 (top)
and in the short direction is
As = 0.003 (28) 8= 0.67 in.2 (bottom)
A's = 0.67 in.2 _ 0.65 in.2 = 0.02 in.2 (top).
Compare require 2ents in the long direction.
Since the 2.13 in. bottom reinforcement exceeds the sum
of bottom plus additional reinforcement obtained for the initial
value,
C = 0.91 (i.e., since 2.13 ~ (0.69 + 0.04) in.2, no additional top
reinforcement is required).
Compare requirements in the short direction.
0.87 ~ (0.67 + 0.02) in.2
Therefore, no additional top reinforcement is needed in the short
direction either.
7.14 Example 2-Design of Type III Slabs Supported on
Compressible Soils
Assuming that the slab of the preceding example (pare. 7.12) was
to be applied in Dallas, Texas, instead of Alexandria, Louisiana,
the design would have been affected as follows:
Cw for Dallas (Fig. 1, p. 38) would have been 20
From Fig. 6, p. 53, for PI= 39.5 and Cw = 20, the value of C
would have been 0.775.
Continuing with step 3 of the previous example and referring to
equation Age, p. 90, the value of Cr in the long direction is
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SUPP LE ME NTARY INFORMATION 12 3
\
=
(2.5 - qu/w)[O. 13 - 0.2 (wc/w) - 0.2C ] + (0.65 - wc/w)
(2.5 - 4.75)[0.13 - 0.2(0.059) - 0.2(0.775)] + 0.65 - 0.059
= 0.674.
In the short direction, WC = 0 (because the concentrated load W
is uniformly distributed along the short direction), and
Cr = (2.5 - 4.75)[0.13 - 0.2 (0.775)] + 0.65 = 0.706.
Steps 4 and 5 remain unchanged from the preceding example.
Step 6-In determining effective loads on the slab, lo = 0.7 as
.
before; however, the effective loads for the reduced value of C are
w = (1 .0 - 0.706) (2 53) = 74.4 psf
in the short direction, and
in the long direction.
w = (1.0 - 0.674)(0.7)(253) = 57.8 psf
Effective loads for the initial value C = 0.775 are
w = 2 53(1.0 - 0.77 5) = 57 psf
in the short direction, and
in the long direction.
w = 57 lo = 57 (0.7) = 40 psf
Steps 7 and 8 remain unchanged from the preceding example.
Step 9-Select basic parameters.
a. Depth ratios are
L/d = 18
L'/d = 10.3.
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124 RESIDENTIAL SLABS ON GROUND
b. Load indices are
w(L'/B) = 57.8 [24(12)/24~ = 694 psf
for the reduced value of C in the long direction, and
w(L/B') = 74.4 [42~12~/40] = 937 psf
in the short direction.
For the initial value C = 0.775, load indices are
w(L'/B) = 40 t24~12~/24] = 480 psf
in the long direction, and
in the short direction.
w(L/B ') = 57 [42 (12~/40 ~ = 718 psf
c. Steel ratios (p), Fig. 15, p. 73, are for the reduced value Cr;
therefore
wtQ,/b) = 694 (p= 1.12%) for t/d= 18
937 (p= 0.49%) for I/d= 10.3.
=
For the initial value C = 0.755
w(L'/b) = 480 (p = 0.78%) for L/d = 18
= 71 (p = 0.39%) for L/d = 10.3.
d. Reinforcing steel required per beam for the reduced value
of Cr is
in the long direction, and
in the short direction.
A s = 0.011 (28) 8 = 2.47 In .2 (botto m)
As = 0.0049 (28) 8 = 1.10 in.2 (bottom)
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SUPPLEMENTARY INFORMATION 125
Reinforcing steel required per beam for the initial value C =
0.775 is
As = 0.0078 (28) 8 = 1.75 in.2 (bottom)
A' = 1.75- 0.65= 1.0 in.2 (top)
in the long direction, and
AC! = 0.0039 (28) 9 = 0.985 in.2 (bottom)
~7
A's = 0.985 - 0.65= 0.335 in.2 (top)
in the short direction.
Compare requirements in the long direction.
2.47 < (1.75 + 1.0) in.2
Therefore, additional top reinforcement is needed, i.e.,
A's = (1.75 + 1.0) - 2.47 = 0.28 in.2 (top).
Compare requirements in the short direction.
1.10 ~ (0.985 + 0.335) in.2
Therefore, additional top reinforcement is needed, i.e.,
A's = (0.985 + 0.335) - 1.10 = 0.22 in.2 (top).
Summarizing,
in the long direction, and
in the short direction.
As = 2.47 in.2 (bottom)
As = 0.28 in.2 (top)
As = 1.10 in.2 (bottom)
A's = 0.22 in.2 (top)
Representative terms from entire chapter:
support index
