Your objective is to design the cheapest possible bridge to span a highway. The total span of the bridge (across both halves of the highway) must be L = 30 meters, and it must support its own weight a

Your objective is to design the cheapest possible bridge to span a highway. The total span of the bridge (across both halves of the highway) must be L = 30 meters, and it must support its own weight and a load q = 33 × 10^4 N/m along its span (a total load of about 1 × 10^6 N plus its own weight). The bridge span will be supported by between one and four I-beams. In the figure above.

The I-beams would be parallel to each other going into the page, for example it could be one Ibeam in the middle of the bridge, or one I-beam on both sides of the bridge, etc. and this will be represented by the design variable, nIbeams. The shape of the I-beams will be represented by three continuous design variables, the height, h, the flange width, b, and thickness, t. The middle support will be rectangular (when viewed from above), and will have two design variables, the width, w, and depth, d. Let, ρIbeams be the density of the material used for the I-beams.