For stairs spanning $$l$$ meters longitudinally between supports at the bottom and top of a flight carrying a load w per unit horizontal area, the maximum bending moment per metre width, is A. $$\frac{{{\text{w}}{l^2}}}{4}$$ B. $$\frac{{{\text{w}}{l^2}}}{8}$$ C. $$\frac{{{\text{w}}{l^2}}}{{10}}$$ D. $$\frac{{{\text{w}}{l^2}}}{{12}}$$ E. $$\frac{{{\text{w}}{l^2}}}{{16}}$$

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

The maximum bending moment per metre width is given by the following equation:

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

where:

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

The equation can be derived by considering the following diagram:

[Diagram of a stair with a load applied at the center]

The force of the load is applied at a distance of $\frac{l}{2}$ from the support, so the bending moment is given by:

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