Shear and deflection limit economical flat-plate spans to under about 30 ft for light loading and about 20 to 25 ft for heavy loading. While use of reinforcingsteel or structural-steel shear heads for resisting shear at columns will extend these limits somewhat, their main application is to permit use of smaller columns. A number of other variations, however, can be used to extend economical load and span limits (Arts. 9.60 and 9.61). The ACI 318 Building Code permits two methods of analysis for two-way construction: direct design, within limitations of span and load, and equivalent frame (Art. 9.42). Limitations on use of direct design are: A minimum of three spans continuous in each direction Rectangular panels with a ratio of longer to shorter span, center-to-center of supports within a panel, not greater than 2 Successive span ratios, center-to-center of supports in each direction, not to exceed 2:3 Columns offset from centerlines of successive columns not more than 0.10 span in either direction Specified ratio of live load to dead load (unfactored) does not exceed 2 All loads are due to gravity only and uniformly distributed over the entire panel 9.59.1 Design Procedures for Flat Plates The procedure for either method of design begins with selection of preliminary dimensions for review, and continues with six basic steps. Step 1. Select a plate thickness expected to be suitable for the given conditions of load and span. This thickness, unless deflection computations justify thinner plates, should not be less than h determined from Table 9.16. With Grade 60 reinforcement, minimum thickness is, from Table 9.16, for an interior panel L h
n 5 in (9.71) where Ln
clear span in the direction moments are being determined. Also, as indicated in Table 9.16, for discontinuous panels, the minimum h
Ln/30 5 in if no edge beam is present. TABLE 9.20 Distribution of Mo for the End Span of a Flat Slab

A Water reducer B Set retarder C Set accelerator D Water reducer and set retarder E Water reducer and set accelerator F High-range water reducer G High-range water reducer and set retarder High-range admixtures reduce the amount of water needed to produce a concrete of a specific consistency by 12% or more. 4.13.1 Water-Reducing Admixtures These decrease water requirements for a concrete mix by chemically reacting with early hydration products to form a monomolecular layer of admixture at the cementwater interface. This layer isolates individual particles of cement and reduces the energy required to cause the mix to flow. Thus, the mix is lubricated and exposes more cement particles for hydration. The Type A admixture allows the amount of mixing water to be reduced while maintaining the same mix slump. Or at a constant water-cement ratio, this admixture allows the cement content to be decreased without loss of strength. If the amount of water is not reduced, slump of the mix will be increased and also strength will be increased because more of the cement surface area will be exposed for hydration. Similar effects occur for Type D and E admixtures. Typically, a reduction in mixing water of 5 to 10% can be expected. Type F and G admixtures are used where there is a need for high-workability concrete. A concrete without an admixture typically has a slump of 2 to 3 in. After the admixture is added, the slump may be in the range of 8 to 10 in without segregation of mix components. These admixtures are especially useful for mixes with a low water-cement ratio. Their 12 to 30% reduction in water allows a corresponding reduction in cementitious material. The water-reducing admixtures are commonly manufactured from lignosulfonic acids and their salts, hydroxylated carboxylic acids and their salts, or polymers of derivatives of melamines or naphthalenes or sulfonated hydrocarbons. The combination of admixtures used in a concrete mix should be carefully evaluated and tested to ensure that the desired properties are achieved. For example, depending on the dosage of admixture and chemistry of the cement, it is possible that a retarding admixture will accelerate the set. Note also that all normal-set admixtures will retard the set if the dosage is excessive. Furthermore, because of differences in percentage of solids between products from different companies, there is not always a direct correspondence in dosage between admixtures of the same class. Therefore, it is important to consider the chemical composition carefully when evaluating competing

strength , c psi Aggregates all lightweight, lb/yd3 Sand aggregate lightweight, lb/yd3 weights range from 90 lb / ft3 (all aggregates lightweight) to 115 lb / ft3 (sand lightweight). Typically, compressive strengths range from 2500 to 4000 psi. Highstrength lightweight concretes, however, have been produced with maximum unit weights of 125 lb / ft3 and strengths from 6000 to 9000 psi. Structural lightweight concretes are defined by the ACI as concretes with a 28-day compressive strength more than 2500 psi and air-dry unit weight of 115 lb / ft3 or less. The variable amount of water absorbed in the voids of lightweight aggregates makes use of W/C difficult in design of a lightweight-aggregate mix (Table 4.5). Air entrainment of 4 to 6% is desirable to prevent segregation. Maximum size of the coarse aggregate should not exceed half the depth of cover over the reinforcing steel. Lightweight-aggregate concrete exposed to sulfates should have a compressive strength ranging from 3750 to 4750 psi (see ACI 318). For marine structures, the W/C should not exceed 0.40 and at least seven bags of cement should be used per cubic yard of concrete. The modulus of elasticity Ec of lightweight concrete generally ranges from 1,500,000 to 3,000,000 psi. It may be estimated from E  w1.5
 (4.1) c c where w  unit weight of concrete, lb / ft3