If longitudinally spanning stairs are casted along with their landings, the maximum bending moment per metre width, is taken as A. $$\frac{{{\text{w}}{l^2}}}{4}$$ B. $$\frac{{{\text{w}}{l^2}}}{8}$$ C. $$\frac{{{\text{w}}{l^2}}}{{10}}$$ D. $$\frac{{{\text{w}}{l^2}}}{{12}}$$

The correct answer is $\frac{{{\text{w}}{l^2}}}{8}$.

The maximum bending moment per metre width of a longitudinally spanning stair is given by the following equation:

$$M = \frac{{{\text{w}}{l^2}}}{8}$$

where:

• $M$ is the maximum bending moment per metre width
• $w$ is the uniform load per metre length
• $l$ is the span length

The equation is derived from the following assumptions:

• The stair is simply supported at both ends.
• The stair is a uniform beam.
• The load is uniformly distributed along the length of the stair.

The equation can be used to calculate the maximum bending moment in a stair for a given set of loading and geometric conditions.

The other options are incorrect because they do not represent the correct value of the maximum bending moment per metre width of a longitudinally spanning stair.