Equation (11.14) indicates that the more absorption present originally the less the improvement provided by added absorption. Thus, in a very hard, bare room, addition of acoustical (sound-absorbent) tile to a full ceiling significantly reduces the noise level. But addition of the same ceiling tile in a room with a thick carpet, upholstered furniture, and heavy draperies would make little change. Heavy carpet, upholstered furniture, heavy draperies, and similar materials are very effective absorbers. In residences, for example, rarely is additional acoustical absorption required in bedrooms, living rooms, and similar spaces. In kitchens, bathrooms, or recreation rooms, with normal hard floors and few additional furnishings or fabrics, however, an acoustical tile ceiling is helpful. This is equally true of offices and similar spaces. In theaters and auditoriums, the large expanse of upholstered seating and aisle carpets is normally adequate for most noise control, but added absorption on some wall surfaces may be required for control of echoes. Reverberation Time. The reverberation within a space is usually expressed as the time required for a sound pulse to decay 60 dB (to one-millionth of its original level). For most purposes, reverberation time T, s, can be calculated from the simple

Final Steps. Receive prices for materials and subcontracts. Review the estimate and carefully note exclusions and exceptions in each subcontract bid and in material quotations. Fill in with allowances or budgets those items or trades for which no prices are available. Decide on the markup. This is an evaluation that should be made by the contractor, weighing factors such as the amount of extras that may be expected, the reputation of the owner, the need for work on the part of the general contractor, and the contractors overhead. Finally, and most importantly, the estimate must be submitted in the form requested by the owner. The form must be filled in completely, without any qualifying language or exceptions, and must be submitted at the time and place specified in the invitation to bid. Figure 17.3 shows part of an estimate and bid summary produced for a multistory apartment building by a computer. Contractors usually submit bids for a lump-sum contract or a unit-price-type contract, when based on complete plans and specifications. When plans and specifications have not yet advanced to a stage where a detailed estimate can be made, the type of contract usually resorted to is a cost-plus-fee type. The bid may be based on either a percentage markup the contractor will receive over and above costs, or may include a lump-sum fee that the contractor charges over and above costs. Sometimes an incentive fee is also incorporated, FIGURE 17.3 Output from a computer spreadsheet program of an estimate and bid summary

z) is to be calculated. The value n is defined as the length of the loaded area (y) divided by the depth (z). The chart is entered with the value of n and upon intersecting the desired m curve, the influence value (I) is then obtained from the vertical axis. As indicated in Fig. 6.16, vertical stress increase ( z) is then calculated as the loaded area pressure (qo) times the influence value (I). Figure 6.16 can also be used to determine the vertical stress increase ( z) below the center of a rectangular loaded area. In this case, the rectangular loaded area would be divided into four parts and then Fig. 6.16 would be used to find the stress increase below the corner of one of the parts. By multiplying this stress by 4 (i.e., 4 parts), the vertical stress increase ( z) below the center of the total loaded area is obtained. This type of analysis is possible because of the principle of superposition for elastic materials. To find the vertical stress increase ( z) outside the loaded area, additional rectangular areas can be added and subtracted as needed in order to model the loading