Question Analysis:
We are given a simply supported beam of length L and a concentrated load W at the center. We need to determine the collapse load for this beam. The collapse load is the load at which the beam fails or collapses. We can find this load using the moment-curvature relationship for beams.

Answer Explanation:
To find the collapse load for the simply supported beam, we need to determine the moment and curvature at the center of the beam. The collapse load can be related to the moment and curvature using the equation:

Wu = 4Mp/L

where Wu is the collapse load, Mp is the moment at the center of the beam, and L is the length of the beam.

Moment at the Center of the Beam:
The moment at the center of the beam can be calculated using the formula:

Mp = W * L / 4

where W is the concentrated load at the center and L is the length of the beam.

Curvature at the Center of the Beam:
The curvature at the center of the beam can be calculated using the formula:

curvature = 1 / R

where R is the radius of curvature. For a simply supported beam with a concentrated load at the center, the radius of curvature can be calculated using the formula:

R = L / 2

Substituting Values:
We can now substitute the values of Mp and L into the equation for the collapse load:

Wu = 4 * (W * L / 4) / L

Simplifying the equation:

Wu = 4 * W / 4

Wu = W

Therefore, the collapse load for a simply supported beam of length L with a concentrated load W at the center is given by:

Wu = W

Conclusion:
The collapse load for a simply supported beam of length L with a concentrated load W at the center is Wu = W. Therefore, the correct answer is option A) Wu = 4Mp/L.