Similarly, the carry-over factor toward support L is given by  Since the carry-over factors are positive, the moment carried over has the same sign as the applied moment. For prismatic beams,   L/6EI and   L/3EI. Hence, For beams with variable moment of inertia,  and  can be determined from Eqs. (5.105) and (5.106) and the carry-over factors from Eqs. (5.109) and (5.110). If an end of a beam is free to rotate, the carry-over factor toward that end is zero. FIGURE 5.62 Determination of fixed-end stiffness: (a) elastic curve for moment KR causing a unit end rotation; (b) the moment diagram for condition (a). 5.11.3 Fixed-End Stiffness The fixed-end stiffness of a beam is defined as the moment that is required to induce a unit rotation at the support where it is applied while the other end of the beam is fixed against rotation. Stiffness is important because, in the moment-distribution method, it determines the proportion of the total moment applied at a joint, or intersection of members, that is distributed to each member of the joint. In Fig. 5.62a, the fixed-end stiffness of beam LR at end R is represented by KR. When KR is applied to beam LR at R, a moment ML  CLKR is carried over to end L, where CL is the carry-over factor toward L (see Art. 5.11.2). KR induces an angle change R at R, where R is given by Eq. (5.105). The carry-over moment induces at R an angle change CLkR, where  is given by Eq. (5.106). Since, by the definition of stiffness, the total angle change at R is unit, KRR  CLKR  1, from which when CR is substituted for /R [see Eq. (5.109)]. In a similar manner, the stiffness at L is found to be With the use of Eqs. (5.107) and (5.111), the stiffness of a beam with constant moment of inertia is given by where L  span of the beam E  modulus of elasticity I  moment of inertia of beam cross section Beam with Hinge. The stiffness of one end of a beam when the other end is free to rotate can be obtained from Eqs. (5.112) or (5.113) by setting the carry-over factor toward the hinged end equal to zero. Thus, for a prismatic beam with one end hinged, the stiffness of the beam at the other end is given by FIGURE 5.63 Determination of fixed-end moments in beam LR: (a) Loads on the fixed-end beam are resolved (b) to (d ) into the sum of loads on a simple beam. (e) to (h) Bending-moment diagrams for conditions (a) to (d ), respectively.

A. Damusis, Sealants, Van Nostrand Reinhold Company, New York. Protective and decorative coatings generally employed in building are the following: Oil Paint. Drying-oil vehicles or binders plus opaque and extender pigments. Water Paint. Pigments plus vehicles based on water, casein, protein, oil emulsions, and rubber or resin latexes, separately or in combination. Calcimine. Water and glue, with or without casein, plus powdered calcium carbonate and any desired colored pigments. Varnish. Transparent combination of drying oil and natural or synthetic resins. Enamel. Varnish vehicle plus pigments. Lacquer. Synthetic-resin film former, usually nitrocellulose, plus plasticizers, volatile solvents, and other resins. Shellac. Exudations of the lac insect, dissolved in alcohol. Japan. Solutions of metallic salts in drying oils, or varnishes containing asphalt and opaque pigments. Aluminum Paint. Fine metallic aluminum flakes suspended in drying oil plus resin, or in nitrocellulose. Following are descriptions of the most commonly used vehicles and binders for

All metal connectors should be insulated with either tape or manufactured insulated covers and should be enclosed in a metal box with cover. Several connections properly insulated can be enclosed in the same metal box if the box is adequate in size. The number of spliced conductors in a box is limited by building codes. 15.6.7 Raceways A raceway is a general term used to describe the supports or enclosures of wires. For most power distribution systems in buildings, rigid conduit or tubing is used. The dimensions of such conduit or tubing and the number of wires of each size permitted is fixed by tables in the National Electrical Code. Three or more conductors may not occupy more than 40% of the interior area, with some exceptions for lead-sheathed cable. All metallic raceways must be continuously grounded. One wide use of rigid steel conduit, galvanized, is for branch circuits buried in the concrete slabs of multistory buildings. Electrical metallic tubing is a thin-walled tube that is permitted by codes in locations where the raceway is not subject to physical damage. For economy in industrial installations, a continuous, rigid structure may be designed to carry both power and signal wiring. This structure may be in the form of a trough, a ladder run, or a channel. It is limited in use to certain cables specifically approved by Underwriters Laboratories for such use. Flexible metallic conduit, also known as Greenfield, is a continuous winding of interlocking metal stripping similar to that used for Type AC metal-clad cables (BX). These conduits are often used in short lengths at the terminal connection of a feeder to a motor. For wet locations, a watertight-type (Sealtite) is available. Surface raceways are usually oval shaped and flat. When painted the same color as the wall or ceiling, they are less conspicuous than round pipe conduit. Surface raceways with a larger, rectangular cross section may be used to mount receptacles or telephone or data outlets, in addition to housing wiring. FIGURE 15.5 Raceways incorporated in a concrete floor, with outlet cover at the top of the floor. FIGURE 15.6 Cellular steel decking serves as underfloor electric ducts. Wires in headers distribute power to wires in the cells. Underfloor raceways are ducts placed under a new floor in office spaces where desks and other equipment are frequently moved. Laid in parallel runs 6 to 8 ft apart, with separate ducts for power, signal, and telephone wires, these raceways may have flat-plate outlet covers spaced 4 to 6 ft along each run. Large retail stores also find these installations a great convenience. The alternative is feeder runs above the hung ceiling of the story below, with firerated, poke-through construction to reach new outlets above the floor. Underfloor raceways may be singlelevel (Fig. 15.5) or two-level (Fig. 15.6). In steel-frame buildings, with cellular steel decking, single-level raceways may be included in the structure of the floor itself. A concrete header across the cellular runs provides the means of entering from the finished floor. A similar arrangement can be used in cellular precast-concrete decks, with metal headers for connections. Wireways to carry large numbers of conductors carrying lightcurrent signal or control circuits are commercially available in fixed lengths. 15.6.8 Access Floor Systems In large computer rooms and in offices with heavy computer or communications usage, such as a brokerage or a data center, an access floor system may be used. This offers a false floor above the structural floor. The system consists of 2-ft by 2-ft removable panels, topped with a floor covering, which are supported from 6 to 36 in, or more, above the structural floor by pedestals and stringers. The space below the access floor is used for routing electrical, computer, and communication wiring. It is also used as a plenum for distributing conditioned air to the equipment and the occupied space. Since virtually the entire underfloor space is available and accessible, this system, though relatively expensive, offers flexibility for making changes in space use, such as adding equipment or rearranging room layouts. 15.6.9 System Furniture Most modern offices undergo frequent relocation of staff due to workload, project teaming, or organizational changes. This high churn rate is made less of a burden to building managers by the use of system furniture. System furniture is a coordinated system of components including partitions, work surfaces, and storage elements that can be assembled into a variety of workstation configurations. Although, design of system furniture is not an electrical item of work, the task lighting, power, and voice / data elements are integral to the system. Individually controlled task lighting is provided for each workstation, as are power and voice / data outlets. To accommodate the required services, the specifications must include clear definition of the types and configuration of the electrical components. Furniture specifications will include wiring harness, power, lighting, and voice / data distribution as integral parts of the system. Particular attention should be paid to the method for feeding the system furniture from building services, capacity and bending restrictions of voice / data raceways (network cables) (see Fig. 15.7), and increased neutral currents caused by harmonic loads. Often, a wiring harness will have eight conductors; three phases, three neutrals (one per phase), an equipment ground conductor, and an isolated ground conductor. 15.6.10 Flat Conductor Cables (FCC) These offer similar flexibility to that of an access floor system in that such cables permit outlets to be located anywhere in a room and allow easy relocation of an outlet. Flat conductor cables are available not only as power circuits but also in multiconductor, twisted pair, coaxial, and fiber-optic cables for use in communication and data systems. Manufacturers offer complete lines of power, data, and communication floor fittings for FCC system use. Use of FCC is limited to installation under carpet squares and is most commonly used in renovation work. Most buildings, commercial, industrial, institutional, and residential, receive their power from a public utility. Usually, the customer is given a choice of voltages. For example, 240/120-V single-phase, three-wire service is, very common in suburban and rural areas. This service comes from a single-phase, 240-V transformer, with one wire from each end of the secondary coil and with the neutral from the midpoint of its secondary coil. The voltage between the end terminal connections is 240 V and between each end wire and the neutral, 120 V (Fig. 15.3b). In large cities, the service to large buildings can be 208/120 V, three-phase, four-wire, with 208 V available between phase wires and 120 V between a phase wire and the neutral (Fig. 15.3c). Another choice is 480/277 V, three-phase, fourwire, with 277 V available between a phase leg and the neutral. It is more economical to use the higher voltage, 480/277 V, for motors and industrial lighting. FIGURE 15.7 Space beneath a raised access floor can be used for routing power and voice / data network cables to equipment. Care must be taken to use cables listed for use in air-handling spaces of buildings. The lower voltage 208/120 V is required for residential or commercial lighting and