please do all 16 question and input the results in the form below

Design a cantilevered beam of Length L with a square cross-section, with side dimension b. A transverse point load F is applied to its free end which causes a deflection at its free end, . Your goal is to use the materials below (the 3 provided and any additional 2 you choose), and determine the square cross-section dimension b, that are required to meet the constraints below: F=2.5kN L=1.5m 8mm Using the information above and the next page: 1. Using the equation above and "l" (from Statics), provide the equation to solve for b, the beam's cross-sectional dimension. Write this equation in Box 1. 2. Using the Granta software, determine the average values for the E and of the materials below. Then, fill in columns 1 and 2. 3. Using the equation from 1. above, calculate b for each material and fill in column 3 (note the units). 4. Remembering that you found the density of the material, write the equation for mass (m) in Box 2. 5. Calculate the total mass of each beam and fill in column 4 . 6. Using the Granta software, fill in column 5 for each material. 7. Calculate the total cost of each beam and fill in column 6 . 8. Combine the equations from 1. and 4. above and provide an expression for b in terms of the given values (F,L,) and the material values (E,). Write this equation in Box 3 as follows: m= (constants)*(material properties). a. The material properties arrangement, which is shown in column 7, is known as the Material Index for this design problem. 9. In Box 4, comment on which material you would choose for this cantilevered beam. a. If the M.I. was the criteria, which material would you choose? Why? b. If cost was the criteria, which material would you choose? Why? c. If mass was the criteria, which material would you choose? Why? d. Overall, which material would you recommend? Why? 10. Create and place in Box 5 the appropriate density ( y-axis) v. Young's Modulus ( x-axis) graph and label the materials on the graph. Be sure to include the appropriate M.I. line and indicate its slope. 11. Finally, choose any two materials of your liking from the Granta software, and complete the table for those. a. Also, in Box 6, comment on whether your chosen materials are better or worse candidates for this beam. 12. Print PAGE 2 ONLY (the table and boxes), make it a PDF, and submit it as your Grant Design Festival 1