HW#1b - Structural Optimization using Excel Consider the two-bar truss from the previous hw, subject to a concentrated load F = 20 kips. Assume the bars are made of the same material with elastic modulus E. **Note: Please name your Excel file: LastName_FirstName HWb. Submit only one excel file on the course website, with three different sheets for the three problems that require spreadsheet solutions. Do not print out your spreadsheet solutions. Turn in one sheet with a brief summary of your design for each problem (A and 8) and the weight or volume for each design. Also include your answer to problem #4 on the physical sheet. Problem #1 Both bars have the same cross-sectional area A2 = A2 = A with allowable tensile and compressive strengths of 20 ksi and 15 ksi respectively. As well, @z = 02 = 0, and the dimension L is constant. Determine the optimal design of this truss (A and 6) to obtain the minimum volume while satisfying the given stress constraints (this is the one we did in class). Use trial and error with an Excel spreadsheet and on your excel spreadsheet clearly indicate your design choice. Problem #2 Both bars have the same cross-sectional area Az = A2 = A with allowable tensile and compressive strengths of 20 ksi and 15 ksi respectively. As well, 0 = 02 = 0, and the dimension L is constant. Determine the optimal design of this truss (A and 6 ) to obtain the minimum volume while satisfying the given stress constraints as well as additional displacement constraints (Ux 5 50; Uy s 75). Use trial and error with an Excel spreadsheet and on your excel spreadsheet clearly indicate your design choice. Problem #3 The bars are not necessarily the same size A1 + A2 and 0, + 62. The allowable tension and compression strengths are still 20 ksi and 15 ksi respectively, and the dimension L is still constant. Determine the optimal design for this truss (A4, A3, 04, and 0,) to obtain the minimum volume while satisfying the given stress constraints. On your excel spreadsheet clearly indicate your design choice. Problem #4 (a) Compare the results of problem #1 and problem #2. What happened when you added new constraints? Was the weight higher or lower? Why? (b) Compare the results of problem #1 and problem #3. What happened when you added new design variables(A1, A2, 01, and 02)? Was the weight higher or lower? Why? AL Az L 01 O2 45 F