Answer
$228\ kg$
Work Step by Step
Step 1. Assume $L\ (kg)$ is the maximum load of such a horizontal beam that is supported at both ends.
Step 2. Assume $w\ (cm)$ is the width of the beam, $h\ (cm)$ is the height and $x\ (m)$ the length between supports.
Step 3. From the given conditions, we have $L=kwh^2/x$ and $400=k(12)(15)^2/8$, thus $k=\frac{1600}{675}\approx1.185$
Step 4. For $w=24\ (cm)$, $h=8\ (cm)$, $x=16\ (m)$, we have $L=(\frac{1600}{675})(24)(8)^2/(16)\approx227.56\approx228\ kg$
