Question

Use the Force Method to derive the slope-deflection relationship given in class (and provided in step 7 below) for Mab and Mba (as defined in the figure below) as functions of Theta_A. E and I are constant.

Assignment #11 Due: 11/26/2018 a 12pm Draw a free-body diagram for each problem clearly showing loads and reactions Summarize in one location all of your final answers together, with directions of displacements showrn You must show your work in order to receive full credit Follow the guidelines for homework assignments as given in the syllabus . Use the Force Method to derive the slope-deflection relationship given in class (and provided in Step 7 below) for MAB and MBA (as defined in the figure below) as functions of θΑ. E and I are constant. I used the following steps but you are welcome to use any approach 1. Select MBA as redundant. For the resulting primary system (actual system but with the redundant removed), solve for internal forces and compute θΒ using virtual work or moment-area. 2. Create the virtual system by applying a unit moment at B without any other external forces applied. Solve for internal forces and compute αвв using virtual work or moment-area. Remember that BB is simply the rotation at B due to a unit moment applied at B. Solve for MBA using the compatibility equation for rotation that we demonstrated in class: θΒ + MBA αΒΒ-0. If done correctly, MBA will be a function only of MAB 3. 4. Now that you have MBA and MAB, solve for Ay and By in terms of MaB and L 5. Draw your shear and moment diagrams for the real system (shown below) 6. Calculate θα for the real system using virtual work or moment-area (I found moment- area to be easier) 7. Compute MAB and MBA in terms of which should result in: 4EI 2EI BA AD 2

Answer 1