For problems 1.1-1.8. identify the following problem components:
(a) decision variables;
(b) parameters;
(c) the objective function in words; and
(d) constraints in words.
Structures. A singly reinforced rectangular concrete beam must carry a known imposed moment and shear. The span length is also known, and the deflection of the beam must not exceed a certain value. The width and depth of the beam are to be determined, as is the area of steel to be placed in the bottom of the beam. The cost of concrete per-cubic-yard and the cost of steel per-pound is known, as is the compressive strength of the concrete and yield strength of the steel. The designer wants to design the least-cost beam. The code for such beams states that a certain minimum amount of steel, as a percent of the tot al effective cross sectional area, must be present in order to avoid excessive cracking on the bottom of the beam due to temperature fluctuations. The code also gives a limit on the maximum amount of steel, again expressed as a percentage of the total effective cross sectional area of the beam, that can be present to avoid sudden compressive failure in the concrete at the top of the beam.
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