An additive manufacturing process has been developed that can 3D print with carbon fiber yarns infused with a high-temperature polymer to form high-strength composite structures. An aircraft is being designed using state-of-the-art optimization software to take advantage of the complex, pseudo-organic structures that this process can manufacture. However, their analysis only considered rectangular cross-section beams in regions subjected to bending. You are being asked to analyze the benefit of non-rectangular crosssections. The improved shape under consideration is the so-called hourglass section, as shown below. The process has an unknown limitation in how steep a slope/angle it can print, and so you must analyze the effectiveness of the section for a range of possible printable angles. The figure shows the rectangular section, and a 20, 30, and 45 degree angle hourglass. Your job is to calculate the dimensions of the hourglass for overhang angle 20-60 degrees, such that the section modulus is identical to that of the nominal rectangle (as shown, W=16mm,H=50mm ). The height of each section is to remain 50mm, and the minimum web thickness is Wmin=5.25mm. Hint: the width of the hourglass W is a variable, as is the height of the web, C, and both must be non-negative for the analysis to make sense. Note that we are concerned with bending about the horizontal neutral plane. We are currently only considering doubly symmetric sections. Find: a) Dimensions W,C, and H for hourglass overhang angles 1060 degrees (in at most 5 degree increments) such that the section modulus is the same as the nominal 1650mm rectangular section given. Design constraints (e.g., H and Wmin) are described above. Use a computer for this (see part C). b) Draw a simple figure (like given below) with labeled accurate dimensions of a low-angle, a mediumangle, and a high-angle design from the analysis, where each satisfies the given constraints. c) Generate a plot of the weight ratio of each section, compared to the nominal rectangular section (A/Ae). d) Comment on the maximum stress state in bending for each of these sections, compared to the nominal rectangular section. Comment on the effectiveness of the use of hourglass specimens. Figure 1. Rectangular nominal section, and example hourglass specimen designs with equivalent seetion modulus to the nominal design and a minimum web thickness Wa