Problem 1 (20 points) The structure shown in the figure has length 3Z and a square cross- section with side a. The structure is made of a material with a modulus of elasticity E. The structure is simply supported at its ends. Using an appropriate finite-element formulation, show how you will determine the deflection and slope at the left end and at a distance of I from the left end. a. Write down the condensed equations. b. Show all boundary conditions. c. Solve for nodal unknowns (in terms of E, a and L) d. Assume that there is a spring of stiffness k is attached at the middle of the structure, as shown in the second image. How will your analysis and results change? Discuss and show the nodal unknowns F L

Fig: 1