Criteria for Selection and Design of Residential Slabs-on-Ground (1968) / Chapter Skim
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Part A: Selection and Design of Slabs
Part A: Selection and Design of Slabs
Pages 30-125
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From page 30... ...
Such a slab, however, can, with proper details, be allowed to settle to some degree without detriment either to structure, services, or aesthetic considerations. Wherever a slab also acts as a structural element, transferring the substantive superstructure loads to the foundation soil, of necessity it must be able to do so satisfactorily.
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From page 31... ...
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.
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From page 32... ...
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 reinforcement over its entire area.
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From page 33... ...
3.1.3 Slab Type III Unlike Types I and II, this slab receives and transmits all superstructure loads to the foundation soil. It is used with soils which in all likelihood will undergo substantial volume change with time.
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From page 34... ...
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 slabon-ground primarily through changes in the moisture content of the soil underlying the slab.
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From page 35... ...
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.
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From page 36... ...
~ a study of drought hazards to crops,1 a relationship was noted between soil grain size and moisture availability as affected by rainfall. 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.
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From page 37... ...
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)
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From page 39... ...
The superstructure is supported directly on footings, and the soils on which Type I slabs are founded are practically unaffected by climate 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.
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From page 41... ...
. Since this slab type is expected to receive uniform nonyielding support, the only consideration is judicious placement of joints to induce cracks at the least objectionable location-e.g., under partitions.
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From page 42... ...
4.7 Loads The slab should not be subjected to partition loads greater than 500 plf, nor to equivalent concentrated loads such as chimneys. The slab cannot tolerate loadings of this magnitude without undue deflection.
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From page 43... ...
However, this slab cannot be expected to bridge a void, since the amount of reinforcement provided is based on the premise that the entire slab will remain uniformly supported by underlying soil. The conditions of loading, site drainage, and grading are identical with those of Type I, except that less desirable soils are acceptable as support.
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From page 44... ...
44 RESIDENTIAL SLABS ON GROUND 1 c, . ,, _~_ Rei nforceme nt ~a.
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From page 45... ...
Placement of the fabric in the center of the slab is to ensure that cracks will be kept tightly closed. The sizes recommended are based on the "drag" theory as follows: As= FLwd/2fs where As F L wd area of steel required per foot of width (in.2)
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From page 46... ...
5.6 Loads Since it is reinforced, this slab can accommodate partition loads of up to 500 plf; however, when this loading is exceeded, an additional layer of reinforcement should be provided to extend at least 25 inches on either side, in order to distribute the added stresses. Further, concentrated loads in excess of this amount (500 plf)
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From page 47... ...
6.2 Determination of Slab Type1 Step 1-Soil investigation results show Type of soil: SM win a PI = 2 Thickness: 15 It Relative density: 0-4 It = 25%, and 4-15 It = 50%. Step 2-Determine appropriate slab type From Table I, it is noted that for a loose SM soil the recommended slab is Type II (or Type I if the soil is compacted to a dense state)
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From page 48... ...
Step 3-Check partition loads. All partitions are non-loadbearing, and none exceeds the 500 plf maximum allowable; therefore, partitions may rest on the slab.
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From page 49... ...
. 7.1 Effect of Superstructure Since, with this slab type, the superstructure is supported on the slab itself, the walls and other load-carrying elements of the superstructure will tend to follow any slab deformations.
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From page 50... ...
7.2 Effect of Soil Behavior Some fundamental assumptions relating to the mode of slab support must be made for analysis of Type III slabs. The assumptions adopted for purposes of this report are described in the following paragraphs and lead to the definition of the Support Index (C)
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From page 51... ...
7.3 Support Index Since the exact shape of the pressure distributions is not known, the assumptions that follow have been introduced to permit develop
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From page 52... ...
53) , which defines the boundaries of the supported fraction of slab, is defined as the support index of the slab; this varies with the climatic rating of the site and the plasticity index of the soil upon which the slab rests.
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From page 53... ...
/ / > to to · o o c~ · · a)
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From page 54... ...
The potential volume change of a particular soil is best determined by a swell test on an undisturbed sample of the soil subjected to probable loading and moisture changes which will likely be experienced beneath the structure. However, in the absence of such a test or tests, PI and PVC-meter readings may be used as an indication of potential volume change in determining the support index (C)
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From page 56... ...
-including its own weight-averaged over the area LL' of the slab; and WC = WC/LL = total concentrated dead and live loads (We) , applied Such a case would mist if the water table is, or is maintained, at a sufficiently high level to produce a relatively constant soil moisture condition, e.g., as is accomplished by a system of drainage and controlled pumping in the New Orleans (Louisiana)
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From page 57... ...
. With this definition, it is possible that the support index (C)
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From page 58... ...
58 RES1DENTLAL SLABS ON GROUND b. In the short direction We = 0 (due to the fact that in the short direction, the load We is not acting as a concentrated load)
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From page 59... ...
FIG. 10 Typical Type III Slab Section A special concern in connection with the waffle slab is uniformity of distribution of the rib-stiffening effect along the length of the stiffening beams.
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From page 60... ...
In addition, whereas the ultimate capacity of concrete provides ample margin of safety against failure due to bending moment, there is little ability to accommodate deflections greater ///////D L _ ~ V _ ~ ~ A J_ -Gil vl~ a . Canti lever b.
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From page 61... ...
/2 wL4L'(5- 6C + C3) /384E 'I where w is the per-square-foot average total load on the slab; L and L' are the slab length and width, respectively; I is the moment of inertia of the slab cross section; and E ' is the effective modulus of elasticity, i.e., 1.5 (10~6 psi for concrete under sustained loading.
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From page 62... ...
after cracking of the section, is considered to be 1/3 k3bd3 ~ np (1-k) 2bd3 where k is the ratio of the depth of compression zone to the effective depth of the slab, n is the ratio of the moduli of elasticity for steel and concrete, and p is the steel ratio, i.e., ratio of steel crosssectional area (As)
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From page 63... ...
(7.7d) In the elastic range, the maximum bending moment resisted by the internal stresses of the beam section ¢bd)
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From page 64... ...
normal to the direction along which the analysis is conducted b as the aggregate width of stiffening beams along the dimension ~ for which the design is conducted conditions 7.7g, h, and i obtain the following general form, which is adaptable to the analysis or design of the slab along either of its principal dimensions (L or L ')
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From page 65... ...
/19 or VC 2 75 psi. 7.8.1 Determination of Effective PI, PVC-Meter Reading, or Percentage Swell of Soil An essential design parameter, in addition to the average dead and live load on the slab, is the support index (C)
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From page 66... ...
However, when different soil strata possess different PI's, the determination of a PI value to be used for design purposes is made as follows: If the PI at the layer immediately below the lowest elevation of the slab is the maximum PI of all soil layers within a depth of 15 feet below the lowest elevation of the slab, then the PI of the top layer is considered applicable to the entire foundation soil. In all other cases, the PI to be used for design purposes is taken as the weighted average of PI's within the top 15 feet of the soil immediately below the slab stiffening beams.
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From page 67... ...
is made in terms of Cw and percentage swell of the foundation soil, the percentage swell value also should be derived in a manner similar to that given above; i.e., the percentage swell of the top layer should be considered applicable to the entire foundation soil if it is the highest within a depth of 15 feet below the bottom of the slab.1 Otherwise, the effective percentage swell should be obtained from the percentage swell of the soil strata within 15 feet below the bottom of the slab1 as a weighted average using weight factors 3, 2, and 1, respectively, for the top, middle, and bottom 5 feet of soil below the bottom of the slab.1 The percentage swell for a specific soil stratum should be obtained through swell tests using conventional consolidometer test equipment on undisturbed soil samples under pressure corresponding to the in situ overburden pressure plus the average total dead and live load (w) on the slab (see also, pare.
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From page 68... ...
5. With this adjustment, and in consideration of expressions 7.7g', h', and i', the effective load (w)
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From page 69... ...
empirically obtained as above, must obviously be checked for accuracy after the actual dimensions of the slab, and therefore loads, become known. The value of WS is derived from the total of actual superstructure dead load plus live load calculated on the basis of 30 psf on each floor and 10 psf on the roof, with no reduction for total area.
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From page 70... ...
For average effective loads, i.e., w = w (1-C) `p = 25 to 50 psf, a good design depth (d)
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From page 71... ...
If the steel ratio for the long dimension of a rectangular slab is selected so that critical conditions for bending moment and deflection develop simultaneously, this slab will be stiffer than necessary in the short direction. Thus, in actual design practice, economic design of rectangular slabs often requires that some steel be used to impart stiffness in the long dimension.
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From page 72... ...
\ \ \ \ \ \ W\N \\ °6,, Ls_ U _ 0 eo · rot _ ~ua3Jad U!
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From page 75... ...
Instead, if this happens, changes should be made in b or d, to effect a reduction below the shear line of the minimum required steel ratio (p)
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From page 76... ...
P zl k2 0.003 0.0224 0.216 0.004 0.0277 0.246 0.005 0.0332 0.270 0.006 0.0384 0.291 0.007 0.0433 0.309 0.008 0.0479 0.327 0.009 0.0523 0.344 0.010 0.0565 0.359 0.011 0.0605 0.373 0.012 0.0644 0.386 0.013 0.0681 0.398 0.014 0.0717 0.410 0.015 0.07 52 0.421 0.016 0.0785 0.432 0.017 0.0817 0.442 0.018 0.0848 0.452 0.019 0.0879 0.460 0.020 0.0908 0.464 1 z = 1/3k3 + np(1 - k) 3 2 k =42np + n2p2 _ up n = 10 this curve, the required steel to satisfy the deflection condition 7.8c is greater than the steel ratio required to satisfy the bending moment condition 7.8b-this derivation is as described above.
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From page 77... ...
en 0 ~ Hi ~ 1ua~Jad U!
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From page 78... ...
From these quantities, the designer must determine values for the bottom and top steel ratios (along the two dimensions of the slab) , in terms of widths b and b' and depth d of the stiffening beams.
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From page 79... ...
Step 6-Id terms of the ratio L/L', average load (w) , and support index (C)
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From page 80... ...
~ b. The steel required for deflection control is substantially more than the steel required for bending moment-a condition which is more likely to occur in the long direction.
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From page 81... ...
In both cases, an adjustment should be effected in the value of either B or d, or both, and the design repeated from Step 7. If the minimum required steel ratio (p)
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From page 82... ...
of the beams and redesign from Step 7. If p in the long direction is above the M-D curve, the width of beams running along the short direction is 8 inches, and p in the short direction is less than 0.003, then use 0.003 for p in the short direction (the minimum required steel ratio)
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From page 83... ...
Whether this adjustment will influence only the steel, or both the steel and beam width, depends on how critical the shear criterion is for the beams concerned. If, in determining the steel ratio (p)
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From page 84... ...
Only the properties of the soil itself and its tendency to heave under varying climatic conditions of moisture have been considered. Excluded is any design reference to frost action.
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From page 85... ...
7.9 Design of Type m Slabs on Compressible Soils (7-5>qU/W2 2-5) Compressible soils usually have an unconfined compressive strength (qu)
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From page 86... ...
, it will have to develop support stresses exactly equal to w, in lieu of shear or bending moment. The result will be uniform loading (w)
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From page 87... ...
Therefore, to have a slab-on-ground which will not settle unacceptably, sufficient strength and stiffness must be imparted to the slab to resist the bending moments resulting from uneven support pressures within the limits of the allowable A/L ratio. 7.9.2 Assumed Reactions and Corresponding Support Index (C)
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From page 88... ...
dead and live loads, the weight of the slab itself and all concentrated loads, and is analyzed along its long dimension (L)
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From page 89... ...
Summarizing, w1 = reaction intensity under the slab center W2 = 4w1 = reaction intensity along end strips of width 0.2L w = W/LL' = average total load intensity over the entire slab, including concentrated loads Wc = WC/LL' = total concentrated load (Wc) averaged over the entire slab area.
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From page 90... ...
w. Equating this maximum bending moment to the righthand side of equation 7.9c permits an evaluation of the support index (Cr)
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From page 91... ...
The design is carried out both for the initial value of the support index (C) , and for the reduced value of the support index (Cr)
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From page 92... ...
Such analysis should be conducted on the assumption that the particular portion of the sub involved will be called on to act as a framed slab supported directly on the stiffening beams, and hence that ACI provisions apply 7.10.2 Limiting Reinforcement It is expected that a Type ID slab will be subjected to a variety of support conditions; consequently, deflections will occur in the slab. To ensure that the slab will be able to accommodate these deflections and accompanying stresses, it is essential that a steel ratio no less than 0.003 nor greater than 0.02 be provided.
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From page 93... ...
Special care must be taken to prevent breaking of such pipes by isolation from the slab whenever passage through the slab is necessary. Pipes should pass through the slab vertically and be provided with expansion joints; service lines entering the house should pass beneath the stiffening beams.
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From page 94... ...
Floor plan and outside dimensions: L 42'-0" l , ~ 18-0 ~ -o Type of construction: solid masonry with plaster-on-lath interior Total weight of superstructure = all dead and live loads = 185kips Method of heating: warm-air with ducts in attic Partitions: non-load bearing, weighing 100 plf Openings through slab: none greater than 8 inches; all having expansion joints Concentrated loads: none Concrete: 2 500 psi; VC = 7 5 ps See pare.
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From page 95... ...
c. Compute total superstructure and slab dead load w = wd + WS = 114 ~ 151 = 265 psf.
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From page 96... ...
is found to be 0.72. Since no special circumstances prevent or diminish the expected variations in soil moisture, the support index (C)
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From page 97... ...
Step 7-Develop layout of stiffening beams. The long beams of slab two must coincide with the short beams of slab one.
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From page 98... ...
a. Depth ratios are b.
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From page 99... ...
If Pi > p, and Pi does not exceed p by more than 0.0015, PI is the controlling steel ratio. If PI > P and P1-P > 0.0015, a considerable percentage of steel is needed to impart stiffness rather than strength to the beam.
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From page 100... ...
Therefore, P > Pi, and the bending moment controls in the short direction, for which the required steel ratio (p)
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From page 101... ...
a. Depth ratios are in the long direction, and Q/d= 18
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From page 102... ...
. For this value and for t/d = 18, the required steel ratio obtained from the chart would be 1.18%, and would be located above the limiting-line curve.
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From page 103... ...
c. Determine steel ratios (p)
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From page 104... ...
16) for an 800-psf load index and a depth ratio Q/d = 7.7, the required steel is less than 0.3%.
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From page 105... ...
The beams along the short direction of slab two are equally spaced at 12 feet o.c. This, however, is not the case with the five beams along the short direction of slab one.
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From page 106... ...
107-108, shows a schematic layout of slab and reinforcement as designed above. Step 10-Check slab dead load.
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From page 107... ...
Estimated total average load is w = 265 psf. Actual total average load is w=265 - 114+ 109=260 psf.
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From page 108... ...
o.c.,: b. Slab Section 4 #3 bars 4 #3 bars j:314"~= ::I-~" ~ ,~- 8", ~ 8" ~,~, 8 Section 1-1 Section 2-2 & 3'-3'Sectior' 3-3 & 5-5 c de Note: All stirrups shown are placed for the purpose of positioning reinforcing steel, and are a minimum No.
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From page 109... ...
1 ''I L] 10" 4 #7 bars - 2~" hi Section 7-7 Section 7'-7' & UQ-8 Section 9-9 f 9 ~ 2 #3 bars /1 #7 bar 318'i 8" ~ Section 6-6Section 4-4 ii Note: All stirrups shown are placed for the purpose of positioning reinforcing steel, and are a minimum No.
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From page 110... ...
7.12 Example 2-Design of Type III Slabs Supported on Expansive Soils: Shallow Beams 7.12.1 Determination of Slab Type For purposes of this example, it will be assumed that the slab is the same as that designed in pare. 7.11, subjected to the same loads, and founded on similar soil, but in a different geographic location, i.e., one having a climatic rating (Cw)
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From page 111... ...
d. Effective loads for slab two are w = 0.1w = 0.1 (265)
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From page 112... ...
= 334 psf c. Steel ratios (p)
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From page 113... ...
o.c. Reinforcement used in the short direction is as follows: Bottom steel, 1 No.
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From page 114... ...
= 358 psf c. Steel ratios (p)
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From page 115... ...
7.13 Example 1-Design of Type III Slabs Supported on Compressible Soils The procedures which follow demonstrate the application on compressible soil of the criteria recommended in pare. 1.4, Step 9c, 1.14, and amplified in pare.
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From page 116... ...
21 Slab Layout and Reinforcement-Para. 7.12 Design Example 1 7ji"
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From page 117... ...
11~. 7.13.2 Application of Type III Procedure Step 1-Determine total average load.
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From page 118... ...
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.
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From page 119... ...
Step 5-Determine outside slab dimensions. L =42ft L' = 24 It Step 6-Determine effective loads on the slab.
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From page 120... ...
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)
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From page 121... ...
= 59 [42(12~/40] = 743 psf For the initial value of the support index (C = 0.91)
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From page 122... ...
7.14 Example 2-Design of Type III Slabs Supported on Compressible Soils Assuming that the slab of the preceding example (pare.
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From page 123... ...
(253) = 57.8 psf Effective loads for the initial value C = 0.775 are w = 2 53(1.0 - 0.77 5)
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From page 124... ...
= 57 [42 (12~/40 ~ = 718 psf c. Steel ratios (p)
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From page 125... ...
1.10 ~ (0.985 + 0.335) in.2 Therefore, additional top reinforcement is needed, i.e., A's = (0.985 + 0.335)
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