Reinforced concrete stairs (longitudinally spanning): If the flights span longitudinally and are cast monolithically with their landings (i.e., the slab is continuous over landings), the maximum bending moment per metre width is taken as which of the following expressions (with w as the uniformly distributed load per metre width and l as the clear span between supports)?

Introduction / Context:
This question tests the structural design convention for stairs that span longitudinally and are cast integrally with landings. When landings act as supports, the stair slab behaves like a continuous slab, which reduces the midspan bending moment compared to a simply supported case.

Given Data / Assumptions:

• Stair slab spans longitudinally between landings/walls.
• Flights and landings are cast monolithically (continuity provided).
• Uniformly distributed load per metre width = w.
• Clear span between effective supports = l.

Concept / Approach:
For simply supported slabs, the design midspan moment is w l^2 / 8. For continuous slabs with adequate end fixity or continuity, recognized coefficients reduce the midspan moment. A common conservative coefficient for a continuous slab/flight over landings is w l^2 / 10 for the maximum positive moment in the span, acknowledging continuity without performing a full frame analysis.

Step-by-Step Solution:
Model the stair slab as a continuous member over supports at landings.Adopt the standard moment coefficient for a continuous slab: M_max,span ≈ w l^2 / 10.Use this value per metre width for reinforcement design in the flight.

Verification / Alternative check:
Where more accuracy is needed, a continuous-beam analysis (e.g., moment distribution) can be done; the resulting span moments will typically be close to or lower than the w l^2 / 10 coefficient, confirming the conservatism of the rule-of-thumb.

Why Other Options Are Wrong:
w l^2 / 8: Suits simply supported behavior, unconservative for continuous action.w l^2 / 12 or /16: Too small for general continuous stair design without a full analysis.w l^2 / 2: Corresponds to cantilever case; not applicable here.

Common Pitfalls:

• Designing as simply supported despite monolithic landings (overestimates steel at midspan and underestimates negative moments at supports).
• Ignoring effective span definition and support conditions at landings.

Final Answer:
w l^2 / 10