In Matlab

A reinforced concrete column is proposed for an elegant urban shopping mall. The column is 40 feet tall, and its radius as a function of height is described by the following equation: Equation1 where r is the column radius in feet, and y is the column height in feet. We wish to know the axial deformation for a 100,000 lb. axial load As you may (or may not) know, the axial deformation o of a column can be calculated from the formula Not to Scale where P is the load, L is the length, A is the cross-sectional area, and E is the modulus of elasticity. Note that the equation cannot be used for the proposed column because the cross-sectional area varies with height. However, we can approximate a solution by discretizing the column into a series of uniform diameter columns of length dL, with radii that correspond to the appropriate vertical position in the curved column. We can take the diameter to be constant over that length, and thus use the given formula. The total deformation is the sum of the deformations of the short columns segments In our analysis, we wish to do what is known as a convergence study. It should be apparent that the accuracy of our calculation will be dependent on how we break up our column into discrete segments. Presumably more (and therefore shorter) segments will mean a more accurate calculation For this lab assignment, write a function that will return the deformation of the column given the number of segments in the discretized column. The radius of the discrete segment should be taken at its mid-height. Once this function is complete, write a script to run the function using 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024 and 2048 segments. Create a plot of the calculated deformation as a function of the number of segments, using a log scale for the number of segments. (Hint: semilogx function.) 1For this problem use E 4,000,000 psi