0.90A d   (9.28b) s y 2
0.90A jd (9.28c) s y where a
A /0.85
b and jd
d  a/2. s y c 9.46.2 Doubly-Reinforced Rectangular Beams For a rectangular beam with compression-steel area and tension-steel area As, A
s the compression-reinforcement ratio is A
s bd and the tension-reinforcement ratio is As bd where b
width of beam and d
effective depth of beam. For design,  should not exceed s
s
0.75   
  
(9.31a) b y y for 0.85c
1 87,000
s 

(9.31b) b 87,000  y y y where
stress in the compression steel, psi, and other symbols are the same as
s those defined for singly-reinforced beams (Art. 9.46.1). The compression force on the concrete alone in a cross-section (Fig. 9.14) is C
0.85
ba (9.32) 1b c where a
1c is the depth of the stress block and the compression reinforcement FIGURE 9.14 Stresses and strains, at ultimate load in a rectangular beam with compression reinforcement: (a) beam cross-section; (b) strain distribution; (c) two types of stress distribution; (d) compression stress in reinforcement. resists As

s . Forces equal in magnitude to these but opposite in direction stress the tension reinforcement. The depth to the neutral axis c can be found from the maximum compressive strain of 0.003 in / in or by equating the compression and tension forces on the section. (See also Art. 9.64.)

Brass compositions range from higher copper content to zinc contents as high as 40% or more. Brasses with less than 36% zinc are plain alpha solid solutions; but Muntz metal, with 40% zinc, contains both alpha and beta phases. The principal plain brasses of interest in building, and their properties are: Commercial bronze, 90% (90.0% copper, 10.0% zinc). Typical uses are forgings, screws, weatherstripping, and stamped hardware. General properties include excellent cold working and high ductility. Red brass, 85% (85.0% copper, 15.0% zinc). Typical uses are dials, hardware, etched parts, automobile radiators, and tube and pipe for plumbing. General properties are higher strength and ductility than copper, and excellent corrosion resistance. Cartridge brass, 70% (70.0% copper, 30.0% zinc). Typical uses are deep drawing, stamping, spinning, etching, rollingfor practically all fabricating processes cartridge cases, pins, rivets, eyelets, heating units, lamp bodies and reflectors, elec- trical sockets, drawn shapes, etc. General properties are best combination of ductility and strength of any brass, and excellent cold-working properties. Muntz metal (60.0% copper, 40.0% zinc). Typical uses are sheet form, perforated metal, architectural work, condenser tubes, valve stems, and brazing rods. General properties are high strength combined with low ductility. 4.59.2 Leaded Brass Lead is added to brass to improve its machinability, particularly in such applications as automatic screw machines where a freely chipping metal is required. Leaded brasses cannot easily be cold-worked by such operations as flaring, upsetting, or cold heading. Several leaded brasses of importance in the building field are the

These are devices incorporated in pipelines to control the flow into, through, and from them. Valves are also known as faucets, cocks, bibs, stops, and plugs. The term cock is generally used with an adjective indicating its use; for example, a sill cock (also called a hose bib) is a faucet used on the outside of a building for connection with a garden hose. A faucet is a valve installed on the end of a pipe to permit or stop withdrawal of water from the pipe. Valves usually are made of cast or malleable iron, brass, or bronze. Faucets in bathrooms or kitchens are usually faced with nickel-plated brass. The types of valves generally used in water-supply systems are gate, globe, angle, ball, and check valves. Gate valves control flow by sliding a disk perpendicular to the water flow to fit tightly against seat rings when a handwheel is turned. This type of valve is usually used in locations where it can be left completely open or closed for long periods of time. Globe valves control the flow by changing the size of the passage through which water can flow past the valves. Turning a handwheel moves a disk attached at the end of the valve stem to vary the passage area. When the valve is open, the water turns 90
to pass through an orifice enclosed by the seat and then turns 90
again past the disk, to continue in the original direction. Flow can be completely stopped by turning the handwheel to compress the disk or a gasket on it against the seat. This type of valve usually is used in faucets. Angle valves are similar to globe valves but eliminate one 90
turn of the water flow. Water is discharged from the valves perpendicular to the inflow direction. Check valves are used to prevent reversal of flow in a pipe. In the valves, water must flow through an opening with which is associated a movable plug (or flapper). When water flows in the desired direction, the plug automatically moves out of the way; however, a reverse flow forces the plug into the opening, to seal it. Ball valves are quick-closing (1/4 turn to close) valves, which consist of a drilled ball that swivels on its vertical axis. This type of valve creates little water turbulence owing to its straight-through flow design. 14.6.8 Pipe Supports When standard pipe is used for water supply in a building, stresses due to ordinary water pressure are well within the capacity of the pipe material. Unless the pipe is supported at short intervals, however, the weight of the pipe and its contents may overstress the pipe material. Generally, it is sufficient to support vertical pipes at their base and at every floor. Maximum support spacing for horizontal pipes depends on pipe diameter and material. The plumbing code should be consulted to determine maximum horizontal and vertical hanger spacings allowed. While the supports should be firmly attached to the building, they should permit pipe movement caused by thermal dimensional changes or differences in settlement of building and pipe. Risers should pass through floors preferably through sleeves and transfer their load to the floors through tight-fitting collars. Horizontal pipe runs may be carried on rings or hooks on metal hangers attached to the underside of floors. The hangers and anchors used for plumbing piping should be metal and strong enough to prevent vibration. Each hanger and anchor should be designed and installed to carry its share of the total weight of the pipe. All piping installed should be restrained according to the requirements specific to the exact earthquake zone where the building is located. The local code authorities should be consulted about these requirements. 14.6.9 Expansion and Contraction To provide for expansion and contraction, expansion joints should be incorporated in pipelines. Such joints should be spaced not more than 50 ft apart in hot-water pipe. While special fittings are available for the purpose, flexible connections are a common means of providing for expansion. Frequently, such connections consist of a simple U bend or a spiral coil, which permits springlike absorption of pipe