A North Carolina state law requires that stairs have minimum...

Name: Problem 73, Chapter 0: Calculus and Its Applications
Uploaded: 2020-10-30T00:35:34-08:00
Duration: 52 s
Channel: Vishal Parmar
Description: A North Carolina state law requires that stairs have minimum treads of 9 in. and maximum risers of 8.25 in. (Source: North Carolina Office of the State Fire Marshal.) See the illustration below. According to this law, what is the maximum grade of stairs in North Carolina?

A North Carolina state law requires that stairs have minimum treads of 9 in. and maximum risers of 8.25 in. (Source: North Carolina Office of the State Fire Marshal.) See the illustration below. According to this law, what is the maximum grade of stairs in North Carolina?

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Key Concepts

Stair Geometry

Stair geometry refers to the dimensions and proportions of stairs, specifically the relationship between the tread (the horizontal part that is stepped on) and the riser (the vertical part between treads). This concept is fundamental in ensuring that stairs are comfortable, safe, and meet building code specifications, as it directly affects both the usability and the visual appeal of the stairway.

Grade or Slope of a Staircase

The grade or slope of a staircase is defined as the ratio of the riser height to the tread depth, and it quantifies the steepness of the stairs. This ratio is crucial for designing stairs that are not too steep for safe usage. In many building codes, limits are set on this ratio to ensure that stairs are accessible and meet safety standards.

Trigonometric Relationship in Stair Design

The trigonometric relationship in stair design is used to convert the riser-to-tread ratio into an angle of inclination, typically using the arctangent function. This process provides a clear indication of the steepness of the stairs in degrees, allowing for a more intuitive understanding of their incline, which is important for both design and regulatory compliance.

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