Work all problems completely and show your work. Provide electronic copies as appropriate. Make sure to clearly indicate your final solution.
1. Use the portal method to determine the approximate vertical reactions. Circles represent pinned connections. Note the pins on the horizontal beam are just to the right/left of the columns.
2. A steel 2" x 3" rectangular bar is 9' long (E = 29,000ksi) and is used in a truss. Write the appropriate local stiffness matrix.
3. Determine the internal moments and reactions at each support using Visual Analysis. Make sure you submit your .vap file along with your solution. Ignore the self-weight of the beam, and assume the E and I of the beam are constant about the length.
4. Determine the column loads at the base of the interior (highlighted) column in this office building, which is situated in a large open building lot. Include dead loads, roof live loads, floor (interior) live loads, and snow loads. The dead weight of the roof decking is 20psf, 18psf for the interior floors, and 12psf for the wall cladding. The ground snow load is 40psf, and you may ignore drifting and assume Ct=1.0.
5. Using the direct stiffness method, determine the following:
a. The global stiffness matrix [K]
Apply a point load P at node 3 pointing rightward, and determine:
b. The displacements at nodes 2, 3, and 4.
c. The reactions at nodes 1 and 5.
Note: Do not substitute values for P and k. Leave the solutions as variables. You must show your work to get full credit.
6. Calculate the global structure stiffness matrix for the truss structure shown, which is made from pieces of 2x6 Douglas fir lumber (1.5" x 5.5" in cross-section, modulus of elasticity of 1,600,000psi)
Do not solve for any displacements or reactions, and make sure you assign node numbers to facilitate partitioning.
