Occupant Load and Egress Capacity: Method

Occupant Load and Egress Capacity

An egress analysis answers four questions for every floor of a building: how many people the code assumes are there, how many exits they need, how wide those exits must be, and how far anyone has to walk to reach one. A fifth question, how long the building takes to empty, is answered by the hydraulic model of people movement. The tool works through all five from the spaces, the floors and the egress components as entered, and prints every comparison as demand against capacity. The model building codes (the International Building Code and NFPA 101) are cited for the rules; their tables are not reproduced. Every factor, threshold and limit is an entered value with its cited default, and the page names the clause each one comes from.

Occupant load

The occupant load of a space is its floor area divided by an occupant-load factor, rounded up to the next whole person, plus any fixed seats; where the actual number is known (a magazine, a locker room at shift change, an existing posted space) an entered count overrides. The factor is expressed as area per person and is applied to the net floor area (the area actually occupied, excluding walls, corridors, stairs and fixed equipment) or the gross floor area, as the use requires. The use selection on each row supplies a default: the values of UFC 3-600-01 Table 10-1 (waiting spaces 15 net, exhibit galleries 30 net, courtrooms 40 net, conference rooms 15 net, shelters 20 net and 7 net for tornado shelters, indoor tennis 50 gross, locker rooms and dormitories 50 gross, mechanical and telecommunications buildings 500 gross, IT rooms 300 gross, manufacturing and parking 200 gross, aircraft hangars 500 gross) are reprinted from that public document; the others (assembly 7 net concentrated, 5 net standing, 15 net with tables and chairs; business 150 gross; classrooms 20 net; mercantile 60 gross; residential 200 gross; industrial 100 gross; storage 500 gross; kitchens 200 gross; libraries 50 net and 100 gross; exercise rooms 50 gross; health care 240 and 120 gross; day care 35 net) are single cited values of IBC Table 1004.5 and NFPA 101 Table 7.3.1.2 and should be confirmed against the edition in force. The business factor was 100 gross in the 2000 and 2003 editions, as NIST NCSTAR 1-7 records for the World Trade Center analysis, and is 150 gross in the current ones.

The load of a floor is the sum of its spaces. UFC 3-600-01 Section 10-3 caps the occupant load of any space at one person per 7 ft² (0.65 m²) of net floor space or the capacity of the required egress components, whichever is less; the tool prints that maximum for each space and each floor, and the posted (signage) load as the lesser of the calculated load and the maximum.

Number of exits

Two exits are the rule: OSHA's 29 CFR 1910.36(b) requires at least two exit routes from a workplace, located as far apart as practical, and more where the number of employees, the size of the building or its arrangement would not allow a safe evacuation by two. The model codes put numbers to it: one exit may serve a small space (49 occupants in the business, assembly, educational and mercantile rows of IBC Table 1006.2.1, within the common-path limit), two exits serve up to 500 occupants, three up to 1,000 and four above that (IBC Table 1006.3.2; NFPA 101 7.4.1.2; both restated in NCSTAR 1-7 for the WTC floors of 429 and of over 1,000 occupants). The three thresholds are entered. A floor above the discharge level counts the exit stairs that serve it; the discharge floor counts its exit doors.

Egress width

The required width of an egress component is the occupant load it serves times a capacity factor: 0.3 in (7.6 mm) per occupant for stairs and 0.2 in (5.1 mm) for doors, corridors and ramps (IBC 1005.3.1 and 1005.3.2; NFPA 101 Table 7.3.3.1), which the IBC reduces to 0.2 and 0.15 in where the building is sprinklered throughout and has an emergency voice/alarm communication system. The factors are entered, and the select fills either set. Each floor is sized for its own load: the stairs for the floor's load, the doors into them likewise, and the exit discharge doors for the largest single floor they serve, since the codes consider the floors individually rather than summing them (IBC 1004.2.1). The provided width is the code width: a door's clear opening per leaf (32 in minimum, 48 in maximum per leaf, measured with the leaf open 90 degrees) times its leaves; a stair's width between walls less any handrail projection beyond the 4.5 in allowed on each side; a corridor's clear width. Minimum widths (44 in for stairs and corridors serving 50 or more, 36 in below) are entered too. The tool reports the provided-to-required ratio of every component group, marks the governing group of each floor, and removes the widest component of the group to check that the remainder keeps at least half the required width (IBC 1005.5). A door serving 50 or more occupants must swing in the direction of travel (OSHA 1910.36(e)(2) says the same for rooms of more than 50 people).

Distances and separation

The measured exit access travel distance, common path of egress travel and dead-end corridor length of each floor are compared with limits typed for the floor's occupancy; the tooltips give the usual values (assembly 250 ft sprinklered and 200 unsprinklered, business 300 and 200, common paths of 75 to 100 ft, dead ends of 20 ft or 50 ft in sprinklered business and mercantile buildings) as single cited figures of IBC Tables 1017.2 and 1006.2.1 and Section 1020.5. Where two exits are required they must be placed apart by at least half the overall diagonal of the area served, one-third where the building is sprinklered throughout (IBC 1007.1.1; NFPA 101 7.5.1.3; both restated in NCSTAR 1-7); the tool computes the diagonal of the entered plan and compares the measured separation with the entered fraction of it.

The hydraulic model

The hydraulic model of the SFPE Handbook treats a crowd as a fluid whose speed falls with its density. As NIST Technical Note 1839 restates it, the speed along the line of travel is S = k (1 − a D) for densities above 0.54 persons/m², with a = 0.266 m² per person and k = 1.40 m/s (275 ft/min) on the level and 1.00, 1.08, 1.16 or 1.23 m/s on stairs of 7.5/10, 7/11, 6.5/12 or 6.5/13 inches riser and tread (the tool fits other geometries with k = 51.8 √(tread/riser) m/min, the form NIST uses for stairs outside the table); below 0.54 persons/m² the speed stays at its free value of 1.20 m/s. The specific flow, persons per unit time per unit width, is S D; it is largest at D = 1/(2a) = 1.88 persons/m², where it equals k/(4a): 24.0 persons/min per foot of effective width on the level and 18.5 on 7/11 stairs, the figures the handbook prints. The effective width of a component is its width less a boundary layer on each side where people keep clear of the surface: 0.15 m (6 in) at a wall or a door jamb and 0.09 m (3.5 in) from the centre of a handrail in the NIST text, 0.20 m (8 in) at a corridor wall in the handbook's table; all four layers are entered. A component's capacity is its maximum specific flow times its effective width.

The tool runs the sequence corridor → door into the stair → stair → discharge door with queues. The occupants of a floor are taken as spread uniformly along its travel distance, so that without congestion they reach the floor's exit doors at a steady rate from the pre-movement time until the farthest occupant arrives at the free speed. Each stage passes at most its capacity per second and holds the rest in a queue: the pooled corridors of the floor, the pooled doors into its stairs, and the entry into the pooled stairs, which can take only what the stair's capacity leaves after the flow already descending from the floors above, which keeps the stair. Occupants who enter the stair descend at the speed belonging to the stair's own flow density (the capacity density when a queue stands at the stair, 1.88 persons/m², where the speed is half the free value) over a storey length of (storey height / riser) steps of √(riser² + tread²) plus the landing travel, and join the discharge-door queue with the discharge floor's own occupants. The cumulative curve of occupants outside against time, the largest queue at every stage with the moments it forms and clears, and the controlling component (the slowest group for the load it carries, which sets the time; the longest queue may stand upstream of it) are printed; the time of the last occupant outside is the evacuation movement time. A hand estimate by the handbook's controlling-component method, pre-movement time plus the load through the slowest group at its capacity plus the last storey of descent, is printed beside it, and so is Nelson's FPETOOL estimate (NISTIR 4380 equations 16 to 21: doors as turnstiles at one person per second per leaf, stairs at 18.3 persons per minute per foot of width less one foot per stair, 250 ft/min on the level and 40 vertical ft/min on stairs with a steepness factor √(1.57 riser/tread)), which NIST developed from the same data of Pauls and the 1988 NFPA 101M appendix.

The model assumes everyone starts at the same moment and moves at the handbook rates, with no counterflow, no merging delays beyond the stair priority rule and no behaviour: NCSTAR 1-7 found the WTC 1 stairs delivering about half the rule-of-thumb flow because of obstacles and crowding. Treat the result as the movement component of the required safe egress time, to which detection, notification and pre-movement time must be added, and as a comparison between layouts rather than a prediction.

Units

Lengths, widths and areas go through the unit dictionary (feet, inches and square feet in USCS mode; metres, millimetres and square metres in SI). The speed constant k, the densities and the pre-movement time are plain numbers in the units of the group title (ft/min and persons per ft², or m/s and persons per m²), which the unit switch does not convert; re-enter them after switching.

Checks and limits

The arithmetic is checked by an independent numpy script on the default building and twenty seeded buildings (occupant loads, exit counts, required widths, diagonals, effective widths, capacities and the queueing simulation step by step), against the printed figures of NCSTAR 1-7 pages 46 and 47 (429 occupants on 42,850 ft² at 100 gross, 129 in and 2.2 m of stair width at 0.3 and 0.2 in, two stairs below 500 and four above 1,000, the one-third diagonal), against the NIST TN 1839 statement of the hydraulic model (the four stair constants, the 0.266 slope, the maximum specific flows 24.0 and 18.5), against the FPETOOL equations and against closed forms of single-stage queues. Not covered: horizontal exits and areas of refuge (which the codes credit with doubled stair capacity), smoke-protected assembly seating, aisle accessways and aisles within assembly rooms, elevators as egress, mezzanines, floors below the discharge level, counterflow of fire fighters, and the behaviour and pre-movement distributions of a full evacuation model. The analysis does not replace the authority having jurisdiction's review of the plans.