Long-span, precast-concrete floor and roof units are usually prestressed. Short members, 30 ft or less, are often made with ordinary reinforcement. Types of precast units for floor and roof systems include solid or ribbed slabs, hollow-core slabs, single and double tees, rectangular beams, L-shaped beams, inverted-T-beams, and I-beams. Hollow-core slabs are usually available in normal-weight or structural lightweight concrete. Units range from 16 to 96 in. in width, and from 4 to 12 in. in depth. Hollow-core slabs may come with grouted shear keys to distribute loads to adjacent units over a slab width as great as one-half the span. Manufacturers should be consulted for load and span data on hollow-core slabs, because camber and deflection often control the serviceability of such units, regardless of strength. (PCI Design Handbook, Precast / Prestressed Concrete Institute.) Curved shells and folded plates have a thickness that is small compared with their other dimensions. Such structures depend on their geometrical configuration and boundary conditions for strength. Thickness. With closely spaced ribs or folds, a minimum thickness for plane sections of 1 in is acceptable. Reinforcement. Welded-wire fabric with a maximum spacing of 2 in may be used for slab portions of thin-section members, and for wide, thin elements 3 in thick or less. Reinforcement should be preassembled into cages, using a template, and placed within a tolerance of 0 in or 1/8 in from the nearest face. The minimum clear distance between bars should not be less than 11/2 times the nominal maximum size of the aggregate. For minimum concrete cover of reinforcement, see Art. 9.97. Compressive Strength. Concrete for thin-section, precast-concrete members protected from the weather and moisture and not in contact with the ground should have a compressive strength of at least 4000 psi at 28 days. For elements in other locations, a minimum of 5000 psi is recommended. Analysis. Determination of axial stresses, moments, and shears in thin sections is usually based on the assumption that the material is ideally elastic, homogeneous,

ing Code (Art. 9.44) uses factored loads of gravity, wind, earthquake, earth pressure, and fluid pressure to determine factored soil pressure qs, and factored pile or pier load. The factored loadings are used in strength design to determine factored moments and shears at critical sections. For concentrically loaded footings, qs is usually assumed as uniformly distributed over the footing area. This pressure is determined by dividing the concentric wall or column factored load Pu by the area of the footing. The weight of the footing can also be neglected in determining qs because the weight does not induce factored moments and shears. The factored pile load for concentrically loaded pile-cap footings is determined in a similar manner. When individual or wall spread footings are subjected to overturning moment about one axis, in addition to vertical load, as with a spread footing for a retaining wall, the pressure distribution under the footing is trapezoidal if the eccentricity ex, of the resultant vertical load Pu is within the kern of the footing, or triangular if beyond the kern, as shown in Fig. 9.42. Thus, when ex  L/6, where L is the footing length in the direction of eccentricity ex, the pressure distribution is trapezoidal (Fig. 9.42a) with a maximum P 6e q
u 1  x (9.85) s1 BL L

Ease of installation and maintenance Light distribution from fixtures, to summarize, may be accomplished by means of transmission, reflection, refraction, absorption, and diffusion. Reflectors play an important role. Their reflectance, consequently, should be highat least 85%. The shape of a reflectorspherical, parabolic, elliptical, hyperbolicshould be selected to meet design objectives; for example, to spot or spread light in a building space or to spread light over a fixture lens that controls light distribution. (The need for a curved reflector, which affects the size of the fixture, can be avoided by use of a Fresnel lens, which performs the same function as a reflector. With this type of lens, therefore, a smaller fixture is possible.) Light control also is affected by shielding, baffles, and louvers that are positioned on fixtures to prevent light from being emitted in undesirable directions. A wide range of light control can be achieved with lenses. Flat or contoured lenses may be used to diffuse, diffract, polarize, or color light, as required. Lenses composed of prisms, cones, or spherical shapes may serve as refractors, producing uniform dispersion of light or concentration in specific directions. Types of Installations. Luminaires may be classified in accordance with type and location of mountings, as well as with type of lighting distribution: flush or recessed (Fig. 15.13), ceiling mounted (Fig. 15.14), pendent (Fig. 15.15), wall mounted (Fig. 15.16) or structural. Structural lighting is the term applied to lighting fixtures built into the structure of the building or built to use structural elements, such as the spaces between joists, as parts of fixtures. Structural lighting offers the advantage of a lighting system conforming closely to the architecture or interior decoration of a room. Some types of structural lighting are widely used in residences and executive offices. For the purposes of accent or decorative lighting, for example, cornices, valences, coves, or brackets are built on walls to conceal fluorescent lamps. For task lighting, fixtures may be built into soffits or canopies. For general lighting, large, low-brightness, luminous panels may be set flush with or recessed in the ceiling. Lighting objectives can be partly or completely met with portable fixtures in some types of building occupancies. For the purpose, a wide variety of table and floor lamps are commercially available. Because the light sources in such fixtures are usually mounted at a relatively low height above the floor, care should be taken to prevent glare, by appropriate placement of fixtures and by selection of suitable