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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

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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

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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

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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.

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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.

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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:

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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.

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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.

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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.

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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.

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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" ,

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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"

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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.

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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.

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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

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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 .

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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)