Assembling the PB.

A one story PB is created by assembling four frames. The assembling procedure is described in the next section. The following plan dimensions are adopted:

b = lin ... length of the side parallel to X axis

d = in ... length of the side parallel to Y axis

For the purpose of this chapter, a doubly symmetric building is defined. The four frames are identical, and based on a modified prototype frame. The K and factors are f_u factors are used to modify the prototype frame. The prototype frame is modified to obtain the target natural period, T = 0.22 sec. The 1/2 factor is introduced to consider that the lateral stiffness is supplied by two parallel frames in each orthogonal direction. The f_u = 10000 is used to have a linear elastic response for the set of seismic records used in this research. By trial and error, this value was found to be appropriate. No ductility demand is induced at any element. Dissertation Methodology

4.4 Maximum Elastic Demand and Evaluation of Strength Factor (f_u).

The next step is to find the maximum elastic demand, induced by the action of the set of ten seismic events used for this research. The possibility that any of the seismic events attack the building from random directions is considered. The evaluated incidence angles (directions of attack) go from 0° to 180°, at each 15°, measured respect to the positive X axis.

The time-history analysis lead to a maximum base shear force demand, Ve = 720.749kip, for each one of the four frames. With this result and the procedure prescribed by the ASCE 7-05 code, the reduced inelastic base shear force is evaluated as:

The strength factor for one frame is:

Using these results, the f_u factors are changed to the value: f_u = 0.23777.

Verification of Developed Plastic Mechanism

The last stage of the procedure is to verify that the defined prototype building can develop the SCWB plastic mechanism, for all the seismic events in the set and all the evaluated incidence angles.

On the other hand, the ductility demand for columns is about 1.2. The expectation is that this value should be smaller than one, indicating no ductility demand in the columns. These results indicate that the Q factor needs to be a little bit larger than Q0 = 3, value specified by the code. Anyway, the ductility demand is just above the desired upper limit (one). Another implication of these results is that for any future seismic event, that could be larger than the ones used here, the building would respond with a weak column-weak beam plastic mechanism for the peak demands of the unexpected event. And this is against the original spirit of the Capacity Design philosophy. As stated by Park and Paulay in their work. It is important to visualize that this observation emerges from the analysis of the effect of a swept of seismic events and incidence angles. When only one seismic event is considered, the observation could be different. The author is convinced that conclusions base only on one seismic event are fundamentally wrong. Dissertation Methodology

In conclusion, the designed prototype building satisfies the criteria (approximately) of withstanding the set of seismic actions developing SCWB plastic mechanisms.