British Columbia Institute of Technology
A significant portion of this section has been developed based on the paper by Christopher Arnold; the students are advised to refer to this paper or to a book by the same author referred to in the Resources section for a more detailed coverage on the subject. A couple of important terms related to building reaction to earthquakes, inertial forces and fundamental period of vibration, will be covered in this unit.
When earthquake shaking occurs, a building gets thrown from side to side and/or up and down. That is, while the ground is violently moving from side to side, the building tends to stand at rest, similar to a passenger standing on a bus that accelerates quickly. Once the building starts moving, it tends to continue in the same direction, but by this time the ground is moving back in the opposite direction (as if the bus driver first accelerated quickly, then suddenly braked). Internal forces in a building caused by vibration of the building's mass during earthquake shaking are called inertial forces. The building's mass, size, and shape - its configuration - partially determine these forces and also partially determine how well they will be resisted.
Inertial forces are equal to the product of mass and acceleration per the Newton's Second Law
Acceleration a is the change of velocity (or speed in a certain direction) over time and is a function of the nature of the earthquake; mass m is an attribute of the building. Since the forces are inertial, an increase in the mass generally results in an increase in the force.
Hence the immediate virtue of the use of lightweight construction as a seismic design approach.
The other detrimental aspect of mass, besides its role in increasing the lateral loads, is that failure of vertical elements such as columns and walls can occur by buckling when the mass pushing down due to gravity exerts its force on a member bent or moved out of plumb by the lateral forces. This phenomenon is known as the P-e, or P-Delta effect. The greater the vertical force, the greater the moment due to the product of the force, P, and the eccentricity, e (or Delta).
Although buildings generally have large vertical load-carrying reserves due to code gravity load requirements, this safety factor does not necessarily mitigate the P-e problem, which can induce bending in columns.
Earthquakes shake the ground in a variety of directions - including up and down components. Historically, codes generally treated these vertical earthquake forces lightly, although they may be two-thirds as great as the lateral earthquake forces, and "seismic design" and "design for lateral forces" are not really synonymous terms. It is vertical loads that almost always cause buildings to collapse in earthquakes; however, in earthquakes buildings generally fall down, not over. The lateral forces use up the strength of the structure by bending and shearing columns, beams, and walls, and then gravity pulls the weakened and distorted structure down.
It is important to note that the main difference between the nature of earthquake and wind loading is due to the fact that the earthquake ground motion induces internally generated inertial forces caused by vibration of the building's mass, whereas wind loading acts in the form of externally applied pressure.
Fundamental Period of Vibration
If one shook a flag pole with a heavy weight on top in the attempt to break it, one would quickly learn to synchronize one's pushes and pulls with the pole's natural tendency to vibrate back and forth at a certain rate - its fundamental period. If it tends to swing back and forth one complete cycle once a second when "plucked" and allowed to vibrate, it has a fundamental period of one second. If we can predict approximately the rate at which the ground will shake, which is similar to controlling the rate at which one shakes the base of the pole by hand, we could adjust the rate at which the pole will naturally vibrate so that the two either will or will not coincide. If they coincide, then the dimensions of the swing will start to increase, the pole will be said to resonate, and the loads on it will increase.
Ground motion will impart vibrations to a building of a similar nature to our shaking of the flag pole. The fundamental periods of structures may range from about 0.05 second for a well anchored piece of equipment, 0.1 second for a one story simple bent or frame, 0.5 second for a low structure up to about 4 stories, and between 1-2 seconds for a tall building from 10-20 stories. A water tank on an offshore drilling rig will be between 2.5 and 6 seconds, and a large suspension bridge may have a period of about 6 seconds.
An illustrative animation of vibrations of a braced frame steel structure is presented below. This animation file has been developed using SAP2000, a structural analysis software package taught at the the BCIT Civil Engineering Department.
Natural periods of soil are usually in the range of 0.5 to 1 second, so that it is possible for the building and ground to have the same fundamental period and therefore there is a high probability for the building to approach a state of partial resonance (quasi-resonance). Hence in developing a design strategy for a building, it is desirable to estimate the fundamental periods both of the building and of the site so that a comparison can be made to see if the probability of quasi-resonance exists. If the initial study shows this to be the case, then it would be advisable to change the resonance characteristics of the building (for the site characteristics are fixed).
In this unit you have been introduced to the effects of earthquakes and the associated human and economic losses. We have explained the characteristics of earthquakes and identified some of the typical earthquake representations used in earthquake engineering studies and design. Further on, we have identified the four main types of damaging effects of earthquakes, and we have concluded that, out of all these damaging effects, structural engineers are most involved in dealing with the effects of ground shaking to building structures. Finally, we have explained two important terms related to building reaction to earthquakes i.e. inertial forces and fundamental period of vibration. We have explained how inertial forces are developed during an earthquake and what affects the size of these forces. We have defined what is the fundamental period of vibration and what are typical values of this period for various types of structures.
The remaining part of the seismic design course on Internet is under construction
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