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  3. you were asked to design a lightweight cantilever beam figure...

Question: you were asked to design a lightweight cantilever beam figure...

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You were asked to design a lightweight cantilever beam (Figure 2) of a given length L and shaped cross-section (ie. size is not given) uhat does not deflect more than a given value δ. F(force) Section F (Force) Without shape With shape Figure 2 (a) What are the function, objective, constrains and free variables in designing the beam? (2 marks) (b) Derive the materials performance index, M that includes the shape of the section. Use the 5 marks) Appendix B and C as references. (e) Derive the expression for the shape efficiency factorg for stiffness-limited design for the beanm (7 marks) with different sections as shown in Figure 3. Use the Appendix B and C as references. ha20r 2t Section A Section B Figure 3 (d) If the beem must have a strong structure to support load F without failure, make the same comparison of the two type of sections in Figure 3 for the strength limited design, o Discuss your answer. (6 marks) (e) There are few materials available as listed in Table 3 with different section as displayed in Figure 3. Determine the materials performance index for each design and select the best (5 marks) candidate materials for the stiffness-limited design beam in Figure 1. Discuss your answer
Youngs Modulus, E (Gpa- Density, p (Mg/mr- Section Design Materials A and B Steel Carbon fiber reinforced plastic Aluminium Alloy 198 69 68 8.1 1.5 2.5
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