"Use stairs not elevator," "In case of fire use stairways" and "In case of fire do not use the elevator, use the stairs" signs are direct, and can graphically portray the importance of using the stairs in a fire emergency.
When fire strikes, people respond. Heading for the exits in an orderly fashion is good. Screaming, running wildly, hiding—not so much. The people in your building might not respond well, if they can't make an informed decision very quickly. When people are panicked and in flight mode exiting through a 6th floor window is not a choice you want them to make, and by equal measure you don't want them to take the elevator. "In case of fire use stairs" signs are essential to getting people to safety.
In a fire, elevator shafts act as a chimney. They draw and funnel heat, smoke, and fire up through the building. People who might be trapped in a stalled elevator have no chance against the kind of heat a fire generates. Elevator doors have been known to open on fire floors, engulfing occupants in flames. Even if the elevator shaft is not near the fire, the mechanical room keeping the elevator operational may be compromised. Electricity interruptions cause elevators to shut down. Rescue from a stalled elevator can take two or three hours. That's not a situation you want to subject yourself or your building patrons to while your building is on fire. Dangers are so many and unpredictable that elevator manufacturers make it very clear to not authorize use of any kind during fires to protect themselves from liability.
Stairs are the way out. In most modern buildings stairwells are built with fire safety in mind, and people not accustomed to taking the stairs, or visiting your building for the first time need to know where to find them in a moment's notice.
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