The correct answer is $\boxed{\text{A. }0.207}$.
The maximum bending moment in a simply supported beam with two equal overhangs occurs at the support, and is equal to $wL^2/8$, where $w$ is the uniform load per unit length and $L$ is the total length of the beam. The ratio of the length of the overhang to the total length of the beam is $a/L$.
To minimize the maximum bending moment, we need to minimize $a/L$. The minimum value of $a/L$ is 0.207, which occurs when $a=0.207L$.
Here is a diagram of a simply supported beam with two equal overhangs:
[Diagram of a simply supported beam with two equal overhangs]
The maximum bending moment occurs at the support, and is equal to $wL^2/8$. The ratio of the length of the overhang to the total length of the beam is $a/L$.
The following are brief explanations of each option:
- Option A: $a/L=0.207$. This is the minimum value of $a/L$, and it minimizes the maximum bending moment.
- Option B: $a/L=0.307$. This is a larger value of $a/L$ than Option A, and it will result in a larger maximum bending moment.
- Option C: $a/L=0.407$. This is an even larger value of $a/L$ than Option B, and it will result in an even larger maximum bending moment.
- Option D: $a/L=0.508$. This is the largest value of $a/L$, and it will result in the largest maximum bending moment.