Base Shear Terms
In this section, the various terms of the static base shear equation are examined in more 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 = 0.4g horizontal ground acceleration is predicted at 0.4g at bedrock.
- Doesn't account for building dynamic properties or local soil conditions.
- '97 UBC Figure 16.2? seismic zone map.
- Table 16.1? Z values as given below:
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.
- '97 UBC Table 16-K.
- I = 1.25 for essential and hazardous facilities.
- I = 1.0 all others.
T : building's fundamental period of vibration.
Fundamental period of vibration is the length of time, in seconds, it takes a structure to move through one complete cycle of free vibration in the first mode.
There are two methods to estimate T:
- Method A:
- Method B: (an iterative approach not generally used in regular structures)
Using Method A, the fundamental period of vibrations for masonry buildings is estimated at:
Height (ft) Period (seconds)
- Ca and Cv : seismic dynamic response spectrum values.
- Accounts for how the building and soil can amplify the basic ground acceleration or velocity.
- Ca and Cv are determined from respectively '97 UBC tables 16-Q and 16-R as a function of Z, underlying soil conditions, and proximity to a fault.
- Using method A,
- Soil profile type:
- The soil layers beneath a structure effects the way that structure responds to the earthquake motion.
When the period of vibration of the building is close to the period of vibration of the underlying soil, the bedrock motion is amplified. The building experiences larger motions than that predicted by Z alone. The following are generalizations about building response as a function of building flexibility and underlying soil stiffness.
- Building Description Soil Description Induced Seismic Force
- Flexible (Large T's) Soft (big S) Higher
- Flexible Stiff Lower
- Stiff Soft Higher
- Flexible Stiff Lower
- The soil profile types are:
- Description Type
- Hard Rock SA
- Rock SB
- Very dense soil and soft rock SC
- Stiff soil SD
- Soft soil SE
- See '97 UBC 1629.3.1 SF
Specific details about each type can be found in '97 UBC Table 16-J and '97 UBC 1629.3.1.
- In the absence of a Geo-technical site investigation, use SD. This is in accordance with '97 UBC 1629.3
- Do not confuse this requirement with the one stated in '97 UBC 16220.127.116.11 which applies ONLY when using the simplified design base shear procedures of '97 UBC 1630.2.3. This web site is NOT using these simplified procedures, but is using 1630.2.1.
- R = response modification factor.
- A judgement factor that accounts for building ductility, damping, and over-strength.
- Ductility = ability to deform in the inelastic range prior to fracture:
- Over-strength : the extra or reserve strength in the structural system. It comes from the practice of designing every member in a group according to the forces in the most critical member of that group.
- Structural systems with larger R = better seismic performance.
- In '97 UBC Table 16-N, R range from 2.8 (light steel frame bearing walls with tension bracing) to 8.5 (special SMRFS of steel or concrete and some dual systems).
- For bearing wall systems where the wall elements resist both lateral and vertical loads:
- Wood shear panel buildings with 3 or less stories: R = 5.5
- Masonry shear walls: R = 4.5.
- Nv and Na : near source factors that are applicable in only seismic zone 4. They account for the very large ground accelerations that occur near the seismic source (the fault).
- Nv is generally used with Cv for structures located < 9.3 miles (15km) from the fault.
- Nv is found in '97 UBC Table 16-T
- Na is used with Ca for structures located < 6.2 miles (10 km) from the fault.
- Na is found in '97 UBC Table 16-S.
- Both Na and Nv are based upon the type of seismic source, A-C. This source type, and location of fault, must be established using approved geotechnical data like a current USGS survey.