Base Shear Terms
In this section, the various terms of the static base shear equation are examined in detail.
- Z = seismic zone factor.
- Effective peak ground accelerations with 10% probability of being exceeded in 50 yrs.
- Given as a percentage of acceleration due to gravity.
- For example, consider zone 4, where Z = .4 Þ lateral ground acceleration is predicted at .4g.
- Doesn't account for building dynamic properties or local soil conditions.
- '94 UBC Figure 16.2 Þ seismic zone map.
- Table 16.1 Þ Z values as given below:
Zone Z 0 0 1 .075 2A .15 2B .20 3 .30 4 .40
- I = importance factor.
- Classifying buildings according to use and importance.
- Essential facilities, hazardous facilities, special occupancy structures, standard occupancy structures, miscellaneous structures.
- Essential facilities mean that the building must remain functioning in a catastrophe.
- Essential facilities include: hospitals, communication centers, fire and police stations.
- Design for greater safety.
- '94 UBC Table 16-K.
- I = 1.25 for essential and hazardous facilities.
- I = 1.0 all others.
- Classifying buildings according to use and importance.
- C = dynamic response spectrum value.
- Accounts for how the building and soil can amplify the basic ground acceleration.
- Where T = building's fundamental period of vibration which influences the building's
response to motion.
- For most of the structures we will be studying, the default value of C = 2.75 applies because these structures are stiff.
- Period of vibration = time, in seconds, it takes a building to complete 1 cycle of
free vibration, recall:
- Period* of masonry structures:
*Estimated from T = .02 (h)3/4 ('94 UBC Eqn 28-3, see below)Height (ft) Period (seconds) 20 .19 40 .32 60 .43 120 .73 160 .90
- 2 methods to estimate building T
- Method A:
- Method B: (often not used in regular designs - its iterative)
- Method A:
- Where S = site coefficients:
- Listed in '94 UBC Table 16-J, 4 basic types:
Without a sufficient geotechnical investigation to determine soil profile at building location Þ use S3.Type Brief Description S S1 Rock 1.0 S2 Stiff soil > 200' 1.2 S3 Soft-to-medium 1.5 S4 > 40' soft clay 2.0
- Listed in '94 UBC Table 16-J, 4 basic types:
- Recalling that C = 1.25S / T2/3 which accounts for the interaction of soil and building, then the
following generalizations
about building response, given in terms of induced seismic forces, can be made.
Building Description Soil Description Induced Seismic Force Flexible (Large T's) Soft (big S) Higher Flexible Stiff Lower Stiff Soft Higher Flexible Stiff Lower
- Accounts for how the building and soil can amplify the basic ground acceleration.
- Rw = structural system coefficient.
- Judgement factor that accounts for building ductiltiy and damping.
- Ductility = ability to deform in the inelastic range prior to fracture:
- Damping = resistance to motion provided by internal material friction.
- Ductility = ability to deform in the inelastic range prior to fracture:
- Larger Rw = better seismic performance.
- '94 UBC Table 16-N: Rw range from 4 (light steel frame bearing walls with tension bracing) to 12 (special SMRFS of steel or concrete and some dual systems).
- For bearing wall systems that resist both lateral and vertical loads.
- Plywood shear panel buildings with 3 or less stories: Rw = 8
- Masonry shear walls: Rw = 6.
- Judgement factor that accounts for building ductiltiy and damping.
