Our firm has been selected to design a new mixed-use building. The lower two levels will be retail and offices, while the upper four floors will be residential. Our team leader has determined that flat-slab concrete construction will be the most cost effective. Based on previous experience, the team leader also wants us to design the columns to be the same size at each column line all the way up the structure; that will reduce the cost of formwork during construction. The geotechnical engineers think we will be able to use shallow foundations, thus saving even more expense. As a result, we should idealize the supports at the bottom of the columns as pins. In order to begin designing the foundations, the geotechnical engineers need preliminary estimates of only the vertical support reactions that the foundations must provide. We have been tasked with finding those reactions for one column line due to static equivalent seismic load.
a. Guess which column will have the largest vertical force due to seismic loading (can be up or down).
b. What is the most appropriate method for approximate analysis of this frame? Why is that method most appropriate?
c. For the desired results, vertical reactions, what is the most efficient approximate analysis method? Use this method regardless of your answer to part (b).
d. List the assumptions you make in order to perform an approximate analysis of the frame.
e. Use approximate analysis to find the vertical reaction at the base of each column.
F. To demonstrate the effectiveness of approximate analysis, use structural analysis software to find the reactions at the base of each column. The experienced member's preliminary calculations were based on a slab thickness of 7.5 inches and an effective beam width of 5 ft (A = 450 in. Z, l = 2110 in 4). That team member also anticipates that we will use 16-inch-square columns (A = 256 in.2,1 = 5460 in.4). The modulus of elasticity of the concrete will be about 3600 ksi.
g. Submit a printout of the displaced shape. Identify at least four features that suggest the displaced shape is reasonable.
h. Verify equilibrium of the computer aided analysis results.
i. Are the results of your computer aided analysis reasonable? Make a comprehensive argument to justify your answer.
j. Comment on why your guess in part (a) was or was not close to the solution in part (e).
