specified concrete compressive strength, psi d
effective depth of wall, but not to be taken larger than 80% of the wall length h
wall thickness Shear carried by the concrete should not exceed the smaller of the values of Vc computed from Eq. (9.112) or (9.113). N d V
3.3

hd  u (9.112) c c 4Lw where Nu
factored vertical axial load on wall acting with Vu, including tension due to shrinkage and creep (positive for compression, negative for tension). L (1.25

 0.2N /L h) w c uw V
0.6

  hd (9.113) c c M /V  L /2 u u w where Mu
factored moment at section where Vu acts. Alternatively, Vc
may be used if Nu 2

hd causes compression. Shear c strength Vc computed for a section at a height above the base equal to Lw/2 or onehalf the wall height, whichever is smaller, may be used for all lower sections. When Vu  0.5Vc, the area of horizontal shear reinforcement within a distance s2 required for shear is given by (V /  V )s A
u s 2 0.0025hs (9.114) h d 2 y where s2
spacing of horizontal reinforcement (max  Lw/5  3h  18 in) and y
yield strength of the reinforcement. Also, when Vu  0.5Vc, the area of vertical shear reinforcement with spacing s should be at least FIGURE 9.57 Components of a fixed arch. L A A
0.0025  0.5 2.5  h  h  0.0025 hs 0.0025hs (9.115) vh L nL w h where Lh is the wall height. But Avh need not be larger than Ah computed from Eq. (9.114). Spacing s should not exceed Lw/3, 3h, or 18 in. Arches are used in roofs for such buildings as hangars, auditoriums, gymnasiums, and rinks, where long spans are desired. An arch is essentially a curved beam with the loads, applied downward in its plane, tending to decrease the curvature. Arches are frequently used as the supports for thin shells that follow the curvature of the arches. Such arches are treated in analysis as two-dimensional, whereas the thin shells behave as three-dimensional elements. The great advantage of an arch in reinforced concrete construction is that, if the arch is appropriately shaped, the whole cross section can be utilized in compression under the maximum (full) load. In an ordinary reinforced concrete beam, the portion below the neutral axis is assumed to be cracked and does not contribute to the bending strength. A beam can be curved, however, to make its axis follow the lines of thrust very closely for all loading conditions, thus virtually eliminating bending

g(t)  F d2A r rn n  2 r1  A  (5.276) dt 2 n n j  W 2 r rn r1 where An  displacement in the nth mode of an arbitrarily selected mass n  natural frequency of the nth mode Fr(t)  varying force applied to the rth mass Wr  weight of the rth mass j  number of masses in the system rn  ratio of the displacement in the nth mode of the rth mass to An g  acceleration due to gravity We define the modal static deflection as j g  F r rn r1 A  (5.277) n j 2  W 2 n r rn r1 Then, the response for each mode is given by A  D A (5.278) n n n where Dn  dynamic load factor. Since Dn depends only on n and the variation of force with time (t), solutions for Dn obtained for one-degree systems also apply to multidegree systems. The total deflection at any point is the sum of the displacements for each mode, An rn, at that point. Beams. The response of beams to dynamic forces can be determined in a similar way. The modal static deflection is defined by L  p(x) (x) dx n 0 A  (5.279) n w L 2 2  (x) dx n n

Pumps 75 Generators 75 Compressors 75 Impact Pile drivers 95 Jackhammers 75 Rock drills 80 Pneumatic tools 80 Other Saws 75 Vibrators 75 or three-shift construction work and delaying work that requires overtime. Also, some Federal agencies have promulgated regulations requiring noise readings on projects (Table 17.2). In accordance with such readings, local officials may place a construction project in one of the following categories: Unacceptable: Noise levels exceed 80 dB for 1 h or more per 24 h, or 75 dB for 8 h per 24 h. Normally unacceptable (discretionary): Noise exceeds 65 dB for 8 h per 24 h or loud repetitive noises on site. Normally acceptable (discretionary): Noise does not exceed 65 dB for more than 30 min per 24 h. Acceptable: Noise does not exceed 45 dB for more than 30 min per 24 h. Energy conservation in construction projects is part of the overall problem of the conservation of energy resources of the nation as a whole. Contractors should be alert to and aware of any ways to bring this about. They can help by using recycled building materials, recycling materials used during demolition, and demonstrating sensitivity to depletion of endangered natural resources. The term systems building is used to define a method of construction in which use is made of integrated structural, mechanical, electrical, and architectural systems. The ultimate goal is integration of planning, designing, programming, manufacturing, site operation, scheduling, financing, and management into a disciplined method of mechanized production of buildings. Application of these systems should be controlled by an engineer-construction management firm rather than by use of prevailing contract building-management procedures. Housing Production. The greatest concentration of effort has occurred in the realm of structural framing, leading to development of mass-production methods. These have, in general. been of the following types: Panel type, consisting of floors and walls that are precast on site or at a factory and stacked in a house-of-cards fashion to form a building. Volumetric type, consisting of boxes of precast concrete or preassembled steel, aluminum, plastic, or wood frames, or combinations of these, which are erected on the site after being produced in a factory. Component type, consisting of individual members of precast-concrete beams and columns or prefabricated floor elements, which are brought to the site in volume, or mass produced. These systems have displayed inherent disadvantages that came about through lack of opportunity to use the entire systems-building process, and because the systems often were not able to attain sufficient volume production to pay for the many fixed costs and start-up costs for the component factories that were built. Experience has shown, however, that housing can be built efficiently and economically from standardized, modular designs. Some examples are as follows: Mobile homes manufactured, complete with floor, roof, walls, electric wiring, plumbing, and cabinetry, by techniques similar to those used by automobile manufacturers. Built in factories, mobile homes are trucked to the sites and then installed and finished by on-site builders. Packaged homes, also known as prefabricated or panelized. They are factory subassembled and, with an assortment of other building components, are delivered to the site for final assembly. Modular homes, also known as sectional homes, manufactured in off-site factories, usually on an assembly line similar to that used by mobile-home manufacturers. Completely furnished, three-dimensional sections, including mechanical systems, of one or more rooms are factory assembled and then delivered to the sites by truck, railroad, or barge. (A. D. Bernhardt. Building Tomorrow: The Mobile/Manufactured Housing Industry, The MIT Press, Cambridge, Mass.) The lessons learned from past experiences offer the following guidelines for construction managers: Early commitment must be made to use of a specific system in the design stage. The systems builder must control the design. Shop drawings should be started early and refined during the design. Preparations of schedules, cost estimate, and bids must involve all the members of the team, that is, the designers, owner, and contractor, because there will be many last-minute proposed changes and details that will have to be challenged