If K is a constant depending upon the ratio of the width of the slab to its effective span $$l$$, x is the distance of the concentrated load from the nearer support, bw is the width of the area of contact of the concentrated load measured parallel to the supported edge, the effective width of the slab be is A. $$\frac{{\text{K}}}{{\text{x}}}\left( {1 + \frac{{\text{x}}}{{\text{d}}}} \right) + {\text{bw}}$$ B. $${\text{Kx}}\left( {1 – \frac{{\text{x}}}{l}} \right) + {\text{bw}}$$ C. $${\text{Kx}}\left( {1 + \frac{{\text{x}}}{l}} \right) + {\text{bw}}$$ D. All the above

The correct answer is $\boxed{\text{A}}$.

The effective width of a slab is the width of the slab that is considered to be carrying the load. It is always less than the actual width of the slab, and it depends on the distance of the concentrated load from the nearer support, the width of the area of contact of the concentrated load measured parallel to the supported edge, and a constant depending upon the ratio of the width of the slab to its effective span.

The equation for the effective width of a slab is given by:

$$\text{effective width} = \frac{{\text{K}}}{{\text{x}}}\left( {1 + \frac{{\text{x}}}{{\text{d}}}} \right) + {\text{bw}}$$

where:

• $K$ is a constant depending upon the ratio of the width of the slab to its effective span
• $x$ is the distance of the concentrated load from the nearer support
• $d$ is the effective depth of the slab
• $bw$ is the width of the area of contact of the concentrated load measured parallel to the supported edge

Option A is the correct equation for the effective width of a slab. Option B is incorrect because it does not include the term $\frac{{K}}{{x}}$. Option C is incorrect because it does not include the term $\frac{{\text{x}}}{{\text{d}}}$. Option D is incorrect because it includes all three options, but only option A is correct.