Structures - Design Response Spectrum

The IBC Design Response Spectrum correlate time period T and Spectral Acceleration, defining three zones.  Two critical zones are:  

T < TS          governs low-rise structures of short periods
T > TS          governs tall structures of long periods

where

T = time period of structure (T ~ 0.1 sec. per story - or per ASCE 7 table 1615.1.1)
TS = SDS/SD1  (See the following graphs for SDS and SD1)

Seismic Design

Earthquakes are caused primarily by release of shear stress in seismic faults, such as the San Andreas fault, that separates the Pacific plate from the North American plate, two of the plates that make up the earth’s crust according to the plate tectonics theory.  Plates move with respect to each other at rates of about 2-5 cm per year, building up stress in the process.  When stress exceeds the soil’s shear capacity, the plates slip and cause earthquakes.  The point of slippage is called the hypocenter or focus, the point on the surface above is called the epicenter.  Ground waves propagate in radial pattern from the focus.  The radial waves cause shaking somewhat more vertical above the focus and more horizontal far away; yet irregular rock formations may deflect the ground waves in random patterns.  The Northridge earthquake of January 17, 1994 caused unusually strong vertical acceleration because it occurred under the city.

Occasionally earthquakes may occur within plates rather than at the edges.  This was the case with a series of strong earthquakes in New Madrid, along the Mississippi River in Missouri in 1811-1812.  Earthquakes are also caused by volcanic eruptions, underground explosions, or similar man-made events.

Buildings are shaken by ground waves, but their inertia tends to resists the movement which causes lateral forces.  The building mass (dead weight) and acceleration effects these forces.  In response, structure height and stiffness, as well as soil type effect the response of buildings to the acceleration.  For example, seismic forces for concrete shear walls (which are very stiff) are considered twice that of more flexible moment frames.  As an analogy, the resilience of grass blades  will prevent them from breaking in an earthquake; but when frozen in winter they would break because of increased stiffness.

The cyclical nature of earthquakes causes dynamic forces that are best determined by dynamic analysis.  However, given the complexity of dynamic analysis, many buildings of regular shape and height limits, as defined by codes, may be analyzed by a static force method, adapted from Newton’s law F= ma (Force = mass x acceleration).

1  Seismic wave propagation and fault rupture
2  Lateral slip fault
3 Thrust fault
4 Building overturn
5 Building shear
6  Bending of building (first mode)
7  Bending of building (higher mode)
E Epicenter
H Hypocenter