Assumptions in design of total losses in tendon stress of 35,000 psi for pretensioning and 25,000 psi for posttensioning to allow for elastic shortening, frictional losses, slip at anchorages, shrinkage, creep, and relaxation of the prestressing steel FIGURE 9.61 Prestressed-concrete beam: (a) with straight tendons; (b) with curved tendons; (c) midspan stresses with straight or curved tendons; (d) stresses between midspan and supports with curved tendons. Net stresses near the supports become tensile with straight tendons. usually gives satisfactory results. Losses greater or smaller than these values have little effect on the design strength but can affect service-load behavior, such as cracking load, deflection, and camber. Elastic Shortening of Concrete. In pretensioned members, when the tendons are released from fixed abutments and the steel stress is transferred to the concrete by bond, the concrete shortens under the compressive stress. The decrease in unit stress in the tendons equals PsEs /AcEc
nc, where Es is the modulus of elasticity of the steel, psi; Ec the modulus of elasticity of the concrete psi; n the modular ratio, Es /Ec; c the unit stress in the concrete, psi; Ps the prestressing force applied by the tendons; and Ac the cross-sectional area of the member. In posttensioned members, the loss due to elastic shortening can be eliminated by using the members as a reaction in tensioning the tendons. Frictional Losses. In posttensioned members, there may be a loss of prestress where curved tendons rub against their enclosure. The loss may be computed in terms of a curvature-friction coefficient . Losses due to unintentional misalignment may be calculated from a wobble-friction coefficient K (per lin ft). Since the coefficients vary considerably, they should, if possible, be determined experimentally. A safe range of these coefficients for estimates is given in the Commentary on ACI 318-99, American Concrete Institute. Frictional losses can be reduced by tensioning the tendons at both ends, or by initial use of a larger jacking force which is then eased off to the required initial force for anchorage. Slip at Anchorages. For posttensioned members, prestress loss may occur at the anchorages during the anchoring. For example, seating of wedges may permit some shortening of the tendons. If tests of a specific anchorage device indicate a shortening L, the decrease in unit stress in the prestressing steel is equal to EsL/L, where L is the length of the tendon. This loss can be reduced or eliminated by overtensioning initially by an additional strain equal to the estimated shortening. Shrinkage of Concrete. Change in length of a member caused by concrete shrinkage results in a prestress loss over a period of time. This change can be determined from tests or experience. Generally, the loss is greater for pretensioned members than for posttensioned members, which are prestressed after much of the shrinkage has occurred. Assuming a shrinkage of 0.0002 in / in of length for a pretensioned member, the loss in tension in the tendons is 0.0002Es
0.0002  30  106

If a porous, sound-absorbent blanket is inserted in the void between layers, the standing waves in the air layers are minimized. Furthermore, such a blanket has the effect of reducing the stiffness of the air, as well as absorbing some of the energy of the air as it pumps back and forth through the blanket. The result is an additional increase in sound transmission loss. The performance of various barriers, and rating systems for their performance, are shown in Table 11.27. 11.79.2 Bypassing of Sound Barriers Rarely is a sound barrier the sole transmission path for the acoustic energy reaching it. Some energy invariably travels via the connecting structures (floors, ceilings, etc.), or through openings in or around the barrier. FIGURE 11.94 Structural flanking: (a) poor isolation at a partition; (b) adequate isolation at a partition; (c) poor isolation at an exterior wall (balloon framing); (d ) adequate isolation (platform framing). Structural flanking via edge attachments and junctions of walls, partitions, floors, and ceilings can seriously degrade the performance of a barrier. Figure 11.94 shows some typical flanking paths and how to avoid such flanking. Even trivial openings through a sound barrier seriously degrade its performance. An opening with an area of only about 1 in2 transmits as much acoustical energy as a 6-in-thick concrete block wall of 100-ft2 area. Figure 11.95 shows the effect of openings of various sizes on walls of various effectiveness. (Note: Sound transmission class STC is a rating system described in Art. 11.80.) The better the wall, the more serious the effect of openings or leaks. The more common points of leakage through or around barriers include perimeter of pipes, ducts, or conduits penetrating the barriers; relief grilles for return air; perimeter of doors or glazing; shrinkage or settlement cracks at partition heads or sills; joints between partitions and exterior curtain-wall mullions; joints around or openings through back-to-back electrical outlet boxes, medicine cabinets, etc.; common supply or return ducts with short, unlined runs between rooms; and operable windows opening to a common court. Such openings should be avoided, when possible, and all cracks, joints, and perimeters should be calked and sealed. In some spaces (an open-plan school, landscaped office, etc.), screens, or partial-height barriers are used. Their effectiveness is much less than that of fullheight partitions or walls. See also Art. 11.79.7. 11.79.3 Structure-Borne Sound Transmission Acoustical energy transmission from sound sources to distant parts of the structure via the structure itself is often a major annoyance in building acoustics. One reason, FIGURE 11.95 Effects of leaks on STC of partitions (for a 100

For control of large, separate loads, the live copper blades of the various switches are concealed in steel enclosures, and the movable blades are operated by insulated levers on the front of the board. The equipment is called a dead-front switchboard. 15.7.4 Protective Devices for Circuits In an electrical distribution system for a building, each electric service must have a means of disconnection, but it may not consist of more than six service switches. Each service switch may disconnect service to a panelboard from which lighter feeders extend to other distribution points, up to the final branch circuits with the minimum size wire, No. 12. This panelboard contains switches with lower disconnecting ratings than that of the service switch and that serve as disconnecting means for the light feeders. The rating and type of each switch must correspond to the size and kind of load and the wire size. There must also be in every circuit some protective device to open the circuit if there is an unexpected overload, such as a short circuit or a jammed motor that prolongs a high inrush current. These protective devices may be fuses combined with knife switches, or circuit breakers, which provide both functions in one device. In addition, electrical systems should be protected against power surges caused by lightning strokes. See Art. 15.19.1. Fuses in lighting and applicance circuits with loads up to 40 A may be the screwed plug type, with a metallic melting element behind a transparent top. For each rating, plug fuses are given different colors and the screw size is made intentionally different, to prevent errors. Cartridge fuses are another type of fuse. They are cylindrical in form and are available in any size. They are classified for special purposes, and the rating is clearly marked on the cylinder. So-called HI-CAP fuses (high capacity) are used for fused service switches that have the capacity to interrupt very high short-circuit