Stair design basics: For a stair with rise R and tread T spanning horizontally, supported by a wall on one side and a stringer beam on the other, the effective design width of each step (treated as a small beam) is taken as which expression?

Introduction / Context:

In building design, individual stair steps (treads) can be idealized as small cantilevers or simply supported strips depending on their support conditions. When a step is supported by a wall on one side and by a stringer (string) on the other, designers adopt a conventional ‘‘effective width’’ to translate the 2D geometry (rise and tread) into an equivalent one-dimensional beam width for bending checks.

Given Data / Assumptions:

• The stair rises by R per step and has a horizontal going (tread) T per step.
• Support conditions: wall on one side; stringer beam on the other side; step spans horizontally.
• Small-step idealization used in many handbooks for preliminary sizing.

Concept / Approach:

Textbook stair detailing adopts the effective design width of a step as the sum of the vertical rise and the horizontal tread, i.e., (R + T). This consolidates the geometric contribution of both components into a simplified beam-width measure that correlates with load spread and practical reinforcement detailing for solid steps.

Step-by-Step Solution:

Verification / Alternative check:

Design aids and stair examples consistently use R + T for this configuration, yielding conservative and practical steel detailing for reinforced concrete steps.

Why Other Options Are Wrong:

• T − R or R − T: Can be negative and has no design meaning for width.
• R^2 + T^2 or R * T: Incorrect dimensions (area or squared terms), not an effective width.

Common Pitfalls:

• Confusing ‘‘effective width’’ (used for design strip idealization) with the physical plan width of the stair flight.
• Ignoring the support condition; different supports lead to different idealizations.

Final Answer:

R + T