Modeling Forces
- 1997 UBC static lateral method considers both horizontal movement
and vertical ground movement.
- The vertical component may be taken as zero, however, when using the allowable stress design procedure.
- We statically model the inertial effects using Newton's 2nd
law of motion:
Rewrite equation (1) as:
Compare (2) to UBC base shear design equations, as given below, where each equation is a function of the building weight and some form of an acceleration factor.- Each acceleration factor is somewhat equivalent to a/g, except
they account for factors like underlying soil, the structural system,
and building occupancy.
- Each acceleration factor is somewhat equivalent to a/g, except
they account for factors like underlying soil, the structural system,
and building occupancy.
- Where:
- V= base shear force. The horizontal seismic force acting at the base of the structure as modeled by the "yank" of the paper in the previous cereal box example. It is important to note that this force was developed for the strength design methodology and not the allowable stress approach.
- W = the dead weight of the building plus a percentage of the live load that is thought to be present during a seismic event. See UBC '97 1630.1.1 for details about this live load addition.
- (Cv I / R T) = acceleration factor (also known as a seismic base shear coefficient). This coefficient will govern V for buildings with medium to long fundamental period of vibrations. The forces in these buildings are induced by the velocity component of the bedrock motion. Hence the "v" subscript.
- (2.5 Ca I/R) = this coefficient is independent of the period of vibration. It will govern V for buildings with short fundamental periods of vibrations, like the buildings being studied in this class. The forces in these stiff buildings are generated by the acceleration component of the bedrock motion. Hence the "a" subscript.
- (0.11 Ca I) = this coefficient is also independent of the period of vibration. It is a lower bound value, keeping V at some minimum value.
- (0.82 N v I / R) = this lower bound coefficient is only applicable to structures located in seismic zone 4 and within 9.3 miles (15 km) of a known seismic fault.
- The difference in building response can be simply demonstrated
by "shaking" the base of two different "structures".
- It is common practice to express the base shear design force as a
percentage of W; calculating only the coefficient term.
- The following are some typical base shear coefficient values for
a regular, single-story masonry building not located near a fault.
In addition, we conservatively assumed that a geotechnical site
investigation was not completed. Because this type of building is
so stiff, the (2.5 Ca I / R) coefficient governs V.
Zone Coefficient 1 V = .067W 2a V = .122W 2b V = .156W 3 V = .200W 4 V = .244W
- The following are some typical base shear coefficient values for
a regular, single-story masonry building not located near a fault.
In addition, we conservatively assumed that a geotechnical site
investigation was not completed. Because this type of building is
so stiff, the (2.5 Ca I / R) coefficient governs V.
