This project  analyzed  a 12-story one-bay building constructed using a beam-hinging frame and 12 distributions of lateral forces for uniform floor masses when subjected to earth movements equivalent to the Loma Prieta, Saratoga earthquake.  Three variations of this building were analyzed.  These included building A, the basic building constructed according to the uniform building code, building B, in which the strength of the lowest support column was reduced to simulated a weak-story response, and building C, similar to building B, but in which the columns in the first floor were inclined by 0.5, 1.0, 1.5, and 2.0 m from the base, making a total of six variations on the building.

When viewing the data, it is clear that in terms of roof displacement response, building C, with the 1.0 m incline both had the sharpest initial roof displacement and the highest initial acceleration, but that displacement rapidly dies off within 20 sec with substantially damped displacement thereafter compared to other forms.  Building A had a strong initial response, but that response was also strong for a longer period, with substantial roof displacement (i.e., >0.5 m) lasting for approximately 40 sec.

The elastic response data show that T (sec), G, and α vary to different degrees among th six exemplar buildings. The variations in T for the six building variations were fairly small.  For the first mode, the period varied only a little, across all six, from 2.16 sec (building A) to 2.44 sec (building C, 2.0 m. incline). That fairly small variation increased for the other two modes, however,  ranging from 0.774 sec (building A) to 0.842 sec (building C, 0.5 m. incline) for the second vibration mode. In the third vibration mode, all six buildings had periods within 0.027 sec with building A having the shortest T (0.445 sec) and building B the longest (0.472 sec.)  It is of interest to note that in general, for the four variations of C (with inclined lower story) , the greater the inclination, the shorter the period in the 2^nd and third mode, but the longer the period in the first vibration mode.

In other results, G for the first vibration mode varies little for all six variations.  Second vibration mode, however varies considerably among the buildings, with A and B having the lowest magnitudes (-5.90E-01 and -5.68E-01 respectively). The four C variations have substantially larger magnitudes, with the magnitude of G increasing as the incline at the base increases, from -6.26E-01 for the 0.5m.  incline to -7.10E-01 for the 2.0 m. incline. In the third mode, the differences among the six variations were even greater, ranging from    3.19E-01 for building A to -4.78E-01 for building C (2.0 m. inclination at the base).

In determining  α, in the first vibration mode, Building B had a larger α than A, but all the variations of C had α significantly less than building A.  In the second mode, while A and  B α were nearly the same, the various building C forms all had significantly larger α than A and B. In the third mode, the values of α across all buildings varied considerably.  Building B α was only about two-thirds the value of building A, while the various building C versions had α values substantially larger than building A.

These data demonstrate that the six forms of the building analyzed would have substantially different responses to a Loma Prieta, Saratoga seismic event.  While the reponses of each to first mode vibrations are quite similar, the second and third mode vibration responses are significantly different.  While α decreased significantly from mode 1 to mode 2 and from  mode 2 to mode 3 in all buildings, the C buildings typically had substantially larger values of α than either building A or B. The same can be said in general for G across the various modes and building types.  These data indicate that the longer period of the C buildings provides more security during a seismic event than the design of building A. Inclining the lower supports changes the seismic response of the buildings, and provides greater stability in a Loma Prieta, Saratoga type of seismic event.

…