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Beam Design Optimization

A rectangular beam column is a structural element that combines both the properties of a beam and a column. It has the ability to resist both bending and axial forces. It is typically made up of reinforced concrete, steel or timber and is used in the construction of buildings, bridges and other structures. Optimize a rectangular beam column to carry an axial (horizontal) load of 25 lb and a transverse (vertical) load of 10 lb. Design the beam column to be minimum weight while staying within the limits of material yield strength and buckling load. Assume that the beam can only bend in the horizontal (y) and vertical (x) directions and there is no bending in the other horizontal (z) dimension. The beam column is made of steel with a density (specific weight) of 0.3 lb/in3, a Young's modulus of 30x106 psi, and a yield stress of 3x104 psi. The beam must be at least 0.5 inches wide. The width (b) must be less than twice the depth (d).