CONSTRAINED-FLOW ANALYSIS

The constrained-flow approach is appropriate for an egress system that has a point at which a line of waiting people forms. Considering that the constraint is the exterior stairwell door and all occupants start their evacuation simultaneously at time zero, the modeled evacuation time is estimated as:

t_m = t_a + t_c

where:

t_m = modeled evacuation time for an egress route (in minutes)

t_a = time for first person to arrive at the exterior stairwell door (in minutes)

t_c = time for population to pass through the exterior stairwell door (in minutes)

If all stairwell doors are the same width, the constraint will be at the exterior stairwell door. If the width of the exterior door is less than the sum of the widths of the interior stairwell doors that are used for evacuation, the exterior door still is the constraint.

Considering that the first person to reach the exterior stairwell door is walking down the stairs from the floor above, the time to reach the exterior door is about 0.5 min. The time for the population to pass through the exterior stairwell is estimated as:

t_c = ßP

where:

ß = time for a person to pass through the exterior stair door (in minutes)

P = population evacuating through the stairs

The time it takes for a person to pass through the exterior stairwell door, ß, depends on the door's width (Table 3).

EXAMPLE CALCULATION

Let's determine the evacuation time for a five-story building with two stairways and 200 people on each floor (Figure 1). The doors leading into and out of the stairways are 32-in. wide. The pre-movement time, t_pm, is estimated at 8 min, and the evacuation efficiency, ռ, is taken to be 2.

The people on the first floor would exit directly to the outside without using the stairs. The population of the remaining floors using the two stairways is calculated as:

4(200) = 800 people

It is considered that half of the people would use one stairway, and half would use the other. Therefore, the population using a stairway is P = 400. As seen in Table 3, ß = 0.025 for a 32-in.-wide exterior stairwell door. The time for population to pass through the exterior stair is estimated as:

t_c = ßP = 0.025(400) = 10 min

The modeled evacuation time is:

t_m = t_a + t_c = 0.5 + 10 = 10.5 min

The total evacuation time is:

t_t = t_pm + ռt_m = 8 + 2(10.5) = 29 min

SUMMARY

Evacuation time can be estimated by a hydraulic analogy to simulate people as fluid particles. It is important that estimates of evacuation time include pre-movement time and evacuation efficiency. The constrained-flow approach is appropriate for a large number of buildings in which the exterior stairwell door is the flow constraint. For more complex egress routes, a component-by-component analysis can be done, and information about this kind of analysis is available from other sources. For such complicated routes, readers may consider using a computer-evacuation model.

REFERENCES

1. Society of Fire Protection Engineers. (2002). SFPE handbook of fire protection engineering. Quincy, MA: National Fire Protection Association.

2. Quarentelli, E.L. (1979, October). Five papers from the panel session on panic. Paper presented at the Second International Seminar on Human Behavior in Fire Emergencies, Washington, DC.

3. Keating, J. (1982). The myth of panic. Fire Journal, 3, 57-61, 147.

4. Klote, J.H. (1995, April). Design of smoke control systems for elevator fire evacuation including wind effects. Paper presented at Elevators, Fire, and Accessibility, Second Symposium, New York, NY.

5. Bukowski, R.W. (2003, October). Protected elevators for egress and access during fires in tall buildings. Paper presented at the CIB-CTBUH Conference on Tall Buildings, Kuala Lumpur, Malaysia.

6. Klote, J.H., & Milke, J.A. (2002). Principles of smoke management. Atlanta: American Society of Heating, Refrigerating and Air-Conditioning Engineers.

7. Kuligowski, E.D. (2004, June). Review of 28 egress models. Paper presented at the Workshop on Building Occupant Movement During Fire Emergencies, Gaithersburg, MD.

8. Proulx, G., & Sime, J.D. (1991, July). To prevent ‘panic’ in an underground emergency: Why not tell people the truth. Paper presented at the Third International Symposium on Fire Safety Science, Edinburgh, Scotland.

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A smoke-control consultant, John H. Klote, DSc, PE, developed and conducts a series of smoke-control seminars for the Society of Fire Protection Engineers. For 19 years, he conducted fire research for the National Institute of Standards and Technology. He is one of the authors of the books “A Guide to Smoke Control in the 2006 IBC” and “Principles of Smoke Management.”

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