Bridge span length of 10 [m] supporting a total load of 450,000 [N] uniformly distributed over the beam length. This total load includes the bridge operating load and the other bridge–related equipment and structure, but does not include the self–weight of the supporting beam itself. A solid rectangular beam cross–section with dimensions of base b and height h are specified for this beam design. Required:
a. Determine optimum values of the beam, b, and h, for a simply supported beam, i. e., pinned support at one end and roller support at the other end.
b. Provide drawings and detailed list of final design details, i. e., dimensions, materials, etc.