Engineering >> Civil & Environmental EngineeringOptimization of a Wall Built on a Slopeby John Hanna
Submitted : Spring 2011 A wall is to be built on a slope as shown below by placing rows of identical wall segments.The thickness of the wall (in and out of the paper in the drawing) is .01 m. The slope is at an angle θ = 25° from the horizontal and distance L is 30 m. The apparent height of the wall h above the slope is fixed at 2 m. The goal of this problem is to find the dimension x of each segment that will minimize the total cost of building the wall and the resulting minimum cost. Cost data are given below: C_{b0}= is the cost per unit volume of each segment = $500.00 / m^{3} C_{f0 }= is the fixed cost per row = $200.00 / row C_{e0}= is the excavation cost = $150.00 / m^{3} This project is about building a wall with identical wall segments on a slope. Faced with certain cost limitations that vary and others that are fixed, one can find the width of a segment that will minimize the cost to produce identical wall segments. The answer returned by calculus may not be an integer, so certain adjustments are required to produce a sensible solution. Finally, the lowest cost was determined to come from 11 segments of width 2.727272727 m. This made the most sense based on the valuations below.
