**Extra Credit Opportunity SA Fall 2020**

**WORTH 90PTS AND CAN ADD UP TO 10PTS TO YOUR OVERALL GRADE**

1. This problem has two parts. Part a. is manual work and part b can be done on the computer using SAP2000.

a. Compute the reactions for the beam below. E and I are constant unless noted otherwise. The force method is to be used. Select RBy as the redundant. (Ans: RBy = 43.9 k) (10pts)

b. Model the beam shown and take E = 4000 ksi. For the middle 35 ft of the beam, set I equal to the values 200 in4, 600 in4, 1000 in4, 1400 in4, 1700 in4, 2000 in4, and 2300 in4 and find the reaction at B. Generate a plot of Imiddle/Iouter versus reaction at B. What happens to the reaction at B as the moment of inertia increases for the middle portion relative to the outer sections? Now, set the I for the entire length to be 1800 in4, set I for the entire beam to be 1000 in4, and find the reaction at B for both cases. What conclusion can you draw about the influence of I? (20pts)

2. This problem has two parts. Part a. is manual work and part b can be done on the computer using SAP2000.

a. Use the force method to find the value of the redundant force indicated for each truss. E is constant for all members. Find redundant NCD. Bar areas given in in2 are AD = 3, BD = 6, and CD = 4. (Ans: NCD = 12.93 k) (10pts)

b. Model the truss shown using SAP2000 and find the bar forces. Do this multiple times while changing the cross-sectional area of bar BD. Areas are given as (in2) 0.2, 0.5, 0.8, 1.0, 1.5, 2.0, 4.0, 6.0, 10.0, and 20.0. Create a plot of the cross-sectional area versus the force in bar BD. Create another plot of the cross-sectional area of BD versus the force in bar DC. Make an observation of the trend observed in both plots. (20pts)

3. This problem has two parts. Part a. is manual work and part b can be done on the computer using SAP2000.

a. Determine the vertical deflection at joint B and the rotation at joint C. I = 900 in4 and kR = 500,000 (k·in.)/rad. (Ans: ΔBy = 0.2289 in. ↓, θC = 0.00325 rad ↺) (10pts)

b. Model the beam of shown in SAP2000 and find the vertical displacement at point B. Change the rotational spring stiffness and repeat the analysis. Do the analysis for the following stiffness values (units of (k·in.)/rad): (500; 5000; 50,000; 500,000; and 5,000,000). Generate a plot of spring stiffness versus displacement. (Use a logarithmic scale for the plot of spring stiffness.) What impact does the spring stiffness play in the displacement? Is it a linear relationship? (20pts)