If $${{l_1}}$$ and $${{l_2}}$$ are the lengths of long and short spans of a two way slab simply supported on four edges and carrying a load w per unit area, the ratio of the loads split into w1 and w2 acting on strips parallel to $${{l_2}}$$ and $${{l_1}}$$ is A. $$\frac{{{{\text{w}}_1}}}{{{{\text{w}}_2}}} = \frac{{{l_2}}}{{{l_1}}}$$ B. $$\frac{{{{\text{w}}_1}}}{{{{\text{w}}_2}}} = {\left( {\frac{{{l_2}}}{{{l_1}}}} \right)^2}$$ C. $$\frac{{{{\text{w}}_1}}}{{{{\text{w}}_2}}} = {\left( {\frac{{{l_2}}}{{{l_1}}}} \right)^3}$$ D. $$\frac{{{{\text{w}}_1}}}{{{{\text{w}}_2}}} = {\left( {\frac{{{l_2}}}{{{l_1}}}} \right)^4}$$

The correct answer is $\frac{{{{\text{w}}_1}}}{{{{\text{w}}_2}}} = {\left( {\frac{{{l_2}}}{{{l_1}}}} \right)^2}$.

The load on a two-way slab is split into two components, one acting on the strips parallel to the long span and one acting on the strips parallel to the short span. The ratio of these two components is equal to the square of the ratio of the long and short spans.

This can be explained by considering the following diagram:

[Diagram of a two-way slab with loads acting on strips parallel to the long and short spans]

The load on the slab is evenly distributed over the entire area. The strips parallel to the long span are longer than the strips parallel to the short span, so they have a larger area. Therefore, they will carry a larger share of the load. The ratio of the loads on the two strips is equal to the square of the ratio of their lengths.

In mathematical terms, the load on the strip parallel to the long span is $w_1$ and the load on the strip parallel to the short span is $w_2$. The ratio of these loads is given by:

$$\frac{{{{\text{w}}_1}}}{{{{\text{w}}_2}}} = {\left( {\frac{{{l_2}}}{{{l_1}}}} \right)^2}$$