From Illuminating Engineering Society of North America, 345 East 47th St., New York, NY 10017: Lighting Handbook Recommended Lighting Practices, RP-1 et al. Energy Management Series, EMS-1 et al. From National Fire Protection Association, 1 Batterymarch Park, Quincy, MA National Electrical Code National Electrical Code Handbook From John Wiley & Sons, Inc., New York: B. Stein, et al., Mechanical and Electrical Equipment for Buildings From McGraw-Hill, Inc., New York: T. Croft and W. Summers, American Electricians Handbook M. D. Egan, Concepts for Lighting in Architecture D. G. Fink and H. W. Beaty, Standard Handbook for Electrical Engineers A. E. Fitzgerald and C. Kingsley, Jr., Electric Machinery T. Gonen, Electric Power Distribution System Engineering A. Kusko, Emergency Standby Power Systems E. C. Lister, Electrical Circuits and Machines J. F. McPartland and B. J. McPartland, McGraw-Hills National Electrical Code Handbook L. Watson, Lighting Design Handbook Steven D. Edgett and Allen M. Williams Edgett-Williams Consulting Group, Mill Valley, California Circulation, as usually applied in architecture, is the movement of people and goods between interior spaces in buildings and to entrances and exits. Safe, convenient, rapid circulation is essential for all buildings under both normal and emergency conditions. Such circulation may be channeled through any of several different types of passageways, such as lobbies, corridors, ramps, stairways, and elevator hoistways. General requirements for these have been discussed in previous sections. This section presents in more detail design and construction considerations in provision of means of vertical circulation, the movement of people and goods between floors of multistory buildings. Vertical circulation of traffic in a multistory building is the key to successful functioning of the design, both in normal use and in emergencies. In fact, location of elevators or stairs strongly influences the floor plan. So in the design of a building, much thought should be given to the type of vertical circulation to be provided, number of units needed, and their location, arrangement, and design. Traffic may pass from level to level in a multistory building by ramps, stairs, elevators, or escalators. The powered equipment is always supplemented by stairs for use when power is shut off, or there is a mechanical failure, or maintenance work is in progress, or in emergencies. In addition to conventional elevators, other types of human lifts are occasionally installed in residences, factories, and garages. For moving small packages or correspondence between floors, dumbwaiters, chutes, pneumatic tube systems, powered track conveyors, or vertical conveyors also may be installed. Ladders may be used for occasional access to attics or roofs. Vertical circulation systems may be divided into two classes. Class I systems are intended for movement of both people and goods and include ramps, stairs, escalators, and elevators. Class II systems, including dumbwaiters and vertical conveyors, in contrast, may not be used for movement of people. FIGURE 16.1 Types of ramps: (a) straight ramp; (b) zigzag ramp. Class I systems may be divided into two subclasses, A and B. Class IA systems can be used by people both under normal and emergency conditions as a means of egress. This class includes ramps, stairs, and escalators (powered stairs) that meet requirements for means of egress specified in building codes or the National Fire Protection Association Life Safety Code (see Art. 3.5.10). Systems not acceptable as an emergency means of egress comprise Class IB. (Such systems nevertheless may be used for emergency evacuation of a building, but the capacity of Class IA systems alone must be sufficient for rapid, safe evacuation of the maximum probable building population.) When space permits, a sloping surface, or ramp, can be used to connect different levels or floors (Fig. 16.1). As a means of saving space in some garages, every floor serves as a ramp. Each floor is split longitudinally, each section sloping gradually in opposite directions to meet the next level above and below. Ramps are especially useful when large numbers of people or vehicles have to be moved from floor to floor. So they are frequently adopted for public buildings, such as railroad stations, stadiums, and exhibition halls. And they are either legally required or highly desirable for all buildings, especially to accommodate persons in wheelchairs. In all cases, ramps should be constructed with a nonslip surface. Ramps have been built with slopes up to 15% (15 ft in 100 ft), but 8% is a preferred maximum. Some idea of the space required for a ramp may be obtained from the following: With the 8% maximum slope and a story height of, say, 8 ft, a ramp connecting two floors is 100 ft long (Fig. 16.1a). The ramp need not be straight for the whole distance, however. It can be curved, zigzagged (Fig. 16.1b), or spiraled. Level landings, with a length of at least 44 in in the direction of travel, should be provided at door openings and where ramps change slope or direction abruptly. Ramps and landings should be designed for a live load of at least 100 lb/ ft2. Railings should be designed for a load of 200 lb applied downward or horizontally at any point of the handrail or for a horizontal thrust of 50 lb / ft at top of rail. Guards higher than the minimum required guard height of 42 in should be designed for 50 lb / ft applied 42 in above the floor. Inside Ramps. Local building codes and the National Fire Protection Association Life Safety Code contain general requirements for acceptability of a ramp as a means of emergency egress (see Art. 5.10). Egress ramps are classified as Class A or Class B. The latter may be as narrow as 30 in, whereas Class A must be at least 44 in wide. (This width can accommodate two adults abreast.) Also, the Life Safety Code restricts Class A ramps to slopes of 10% or less and Class B ramps to slopes of not more than 1 in 8. In addition, for Class B, the vertical distance between landings may not exceed 12 ft, but no limit is placed on this distance for Class A. Building codes usually require Class A ramps only for places of assembly of more than 1000 persons. For other types of occupancy, codes may permit the choice of ramp class to be based on emergency exit capacity required. The capacity, in persons per 22-in unit of ramp width, may be taken as 100 in the downward direction and 60 in the upward direction for Class B ramps. For Class A ramps, the capacity may be taken as 100 persons per unit of width in either

Similarly, shearing stresses produced by central shears and twisting moments may be calculated from equations of the form v 
z (5.176) xy t t 3 /12 where D  twisting moment and T  unit shear force along the middle surface. Normal shearing stresses may be computed on the assumption of a parabolic stress distribution over the shell thickness: FIGURE 5.98 Folded-plate structure. V t 2 v 
 z2 (5.177) xz t 3 / t 4 where V  unit shear force normal to middle surface. 5.15.5 Folded Plates A folded-plate structure consists of a series of thin planar elements, or flat plates, connected to one another along their edges. Usually used on long spans, especially for roofs, folded plates derive their economy from the girder action of the plates and the mutual support they give one another. Longitudinally, the plates may be continuous over their supports. Transversely, there may be several plates in each bay (Fig. 5.98). At the edges, or folds, they may be capable of transmitting both moment and shear or only shear. A folded-plate structure has a two-way action in transmitting loads to its supports. Transversely, the elements act as slabs spanning between plates on either side. The plates then act as girders in carrying the load from the slabs longitudinally to supports, which must be capable of resisting both horizontal and vertical forces. If the plates are hinged along their edges, the design of the structure is relatively simple. Some simplification also is possible if the plates, though having integral edges, are steeply sloped or if the span is sufficiently long with respect to other dimensions that beam theory applies. But there are no criteria for determining when such simplification is possible with acceptable accuracy. In general, a reasonably accurate analysis of folded-plate stresses is advisable. Several good methods are available (D. Yitzhaki, The Design of Prismatic and Cylindrical Shell Roofs, North Holland Publishing Company, Amsterdam; Phase I Report on Folded-plate Construction, Proceedings Paper 3741, Journal of the Structural Division, American Society of Civil Engineers, December 1963; and A. L. Parme and J. A. Sbarounis, Direct Solution of Folded Plate Concrete Roofs, EB021D, Portland Cement Association, Skokie, Ill.). They all take into account the effects of plate deflections on the slabs and usually make the following assumptions: The material is elastic, isotropic, and homogeneous. The longitudinal distribution of all loads on all plates is the same. The plates carry loads transversely only by bending normal to their planes and longitudinally only by bending within their planes. Longitudinal stresses vary linearly over the depth of each plate. Supporting members, such as diaphragms, frames, and beams, are infinitely stiff in their own planes and completely flexible normal to their own planes. Plates have no torsional stiffness normal to their own planes. Displacements due to forces other than bending moments are negligible. Regardless of the method selected, the computations are rather involved; so it is wise to carry out the work by computer or, when done manually, in a wellorganized table. The Yitzhaki method offers some advantages over others in that the calculations can be tabulated, it is relatively simple, it requires the solution of no more simultaneous equations than one for each edge for simply supported plates, it is flexible, and it can easily be generalized to cover a variety of conditions. Yitzhaki Method. Based on the assumptions and general procedure given above, the Yitzhaki method deals with the slab and plate systems that comprise a foldedplate structure in two ways. In the first, a unit width of slab is considered continuous over supports immovable in the direction of the load (Fig. 5.99b). The strip usually is taken where the longitudinal plate stresses are a maximum. Second, the slab reactions are taken as loads on the plates, which now are assumed to be hinged along the edged (Fig. 5.99c). Thus, the slab reactions cause angle changes in the plates at each fold. Continuity is restored by applying to the plates an unknown moment at each edge. The moments can be determined from the fact that at each edge the sum of the angle changes due to the loads and to the unknown moments

1b Extreme torsional irregularityto be considered when diaphragms are not flexible D Extreme torsional irregularity shall be considered to exist when the maximum story drift, computed including accidental torsion, at one end of the structure transverse to an axis is more than 1.4 time the average of the story drifts at the two ends of the structure. C and D (this irregularity not permitted in E or F) 2 Re-entrant corners D Plan configurations of a structure and its lateral force-resisting system contain re-entrant corners, where both projections of the structure beyond a re-entrant corner are greater than 15% of the plan dimension of the structure in the given direction. E and F 3 Diaphragm discontinuity D, E, and F Diaphragm with abrupt discontinuities or variations in stiffness, including those having cutout or open areas greater than 50% of the gross enclosed diaphragm area, or changes in effective diaphragm stiffness of more than 50% from one story to