Earthquake is an interesting natural phenomenon. If you live in the west coast of United States or in a seismic zone anywhere and are a civil structural engineer, I am sure you have designed or will be asked to design structures for seismic loads. For others who don’t deal with seismic loads on a regular basis this would be an interesting read.
Before we get into the detailed part of the post, lets see why and what types of waves of earthquakes cause such devastation. Earthquake is propagated by moving of the tectonic plates and thereby the release of energy that accompanies the movement of the tectonic plates. The following map courtesy of NASA shows the tectonic plates. As you can see, it is not a simple map with certain types of fault lines. If you look into the Legend at the bottom right of the image below, you can see what the different colored jagged lines represent. Some are Normal faults, some are reverse faults, some are strike slip faults and some are combinations.
The plates are always moving (very very slowly) either towards one another, away from one another or slide past one another. This movement of the plates against each other causes a build up of energy and when the faults finally slip it cause tremendous release of this energy that travels through the earth and produces the earthquakes. There are several websites that go in detail about the types of faults and how they work.
There are basically 4 different types of waves that are produced by the earthquake under 2 main categories:
The 2 main categories are Body waves and Surface waves.
Body waves: P and S waves
Surface waves: Rayleigh and Love waves
When an earthquake occurs, P waves occur first followed by S waves and then the Surface waves. The following seismograph shows the distinctions between the waves and the order in which they occur (courtesy of Mary Washington Geography)
Body waves are waves that travel through the body of the earth. Surface waves as the name implicates are the waves that only travel along the surface of the earth.
Under the Body waves are two types of waves: P waves (compression waves) and S waves (shear waves). P waves travel in a straight line back and forth and can travel through solids and liquids. S waves are transverse waves and can only travel through solids.
Here is an animation of P and S waves courtesy of Atkinson Physics (check out Youtube)
If you are curious as to why S waves can’t travel through liquids see an interesting presentation by Kieth Miller
Under the Surface waves are again two types of waves: Rayleigh’s waves (that cause backward rotations) and Love waves (that are side to side waves). Of these type of waves, Rayleigh waves causes the most destruction to structures.
Here is a good animation of the Rayleigh waves courtesy of Wolfram Research.
Here is a good animation of the Love wave courtesy of Myungsunn Ryu (Youtube). The Love waves is basically ripping the earth from under the structures side to side.
Structures do not like Rayleigh waves. From the seismograph at the top of this post you can see that these Surface waves are pretty big in amplitude which means they can cause heavy destruction. Watch this interesting animation posted by Ben Turkson. You will see why structures do not take kindly to these violent Rayleigh Waves. The backward rolling motion of the earth violently shakes every part of the structure.
When you design buildings or any anchorage to seismic forces, you are designing against the forces that we just discussed. Let’s not kid ourselves, the codes suggest designing the structures to these perceived forces but designing per code does not mean your structure will stand undamaged in a seismic event. Codes are designed to protect human lives.
The main purpose of Building Codes is to protect human lives not necessarily to protect the structures. Please refer to the intent of the code in Section 101.3 of 2015 International Building Code.
You can see the purpose of the code is to provide a “reasonable” level of safety. This reasonable level of safety would include protecting means of egress so people inside the structure have enough time to get out of it. This would also include protection from fire and other hazards that may follow after a seismic event. Through years of practice and lessons learned from other natural hazards, some type of structures have been analyzed enough in real life situations to incorporate modifications in order to make them withstand some of these realistic hazardous forces. Hence the building codes get updated to incorporate the latest and greatest of real world experiences for future building design.
According to commentary C11.4, “Probabilistic MCE (Maximum Considered Earthquake) ground motion are based on assumption that buildings designed with ASCE have a collapse probability of not more than 10% on average if MCE ground motion occur at the building site. While stronger shaking could occur it was judged that economically it is impractical to design for such ground motion and that MCE ground motions based on a 1% probability of collapse in 50 years provides an acceptable level of seismic safety”.
So how do you know where your structure is and what forces you design your building to? I will take you through a step by step process of how to find the seismic force. First of all, you have to locate where your structure is. Find the latitude and longitude of the structure (where it will be built). There are several websites that can give you latitude and longitude of a place for free. USGS (US Geological Society has an application online here. You can also click on the image below for the link.
Lets say for example we have a structure in the City of San Jose with Latitude: 37.3382° N, and Longitude 121.8863° W
We enter this information in the above screen under Site Latitude and Site Longitude. From experience I know that most often Site Soil classification in San Jose area is Site Class D-Stiff soil. You should actually check with your Geotech to know for sure what the Site Soil Classification is before you enter it here because this can make a huge difference in the results you get.
The next slide shows all the inputs.
Here is the result from USGS: NOTE: Make sure that you allow pop ups in your browser for this application to work.
So lets decipher the results:
What is Ss and S1? Ss and S1 are defined in Section 11.4 of ASCE 7-10.
Ss is the Mapped MCE (Maximum Considered Earthquake) spectral response acceleration parameter at short periods (ie, 0.2 sec)
S1 is the Mapped MCE spectral response acceleration parameter at a period of 1 sec.
What is SMS and SM1?
SMS = Fa x SS where Fa = short-period site coefficient (at 0.2 s)
SM1 = Fv x S1 where Fv = long-period site coefficient (at 1 s)
In previous editions of the code, one has to determine manually what Fa and Fv are at a site, but new USGS application calculates the values automatically based on site location.
What is SDS and SD1?
According to code, structural design is performed for earthquake demands that are 2/3 of the Maximum considered Earthquake response spectra. SDS (Design spectral response acceleration at short period 0.2s) and SD1 (Design spectral response acceleration at 1 sec) can be directly obtained from USGS application.
SDS = 2/3 SMS
SD1 = 2/3 SM1
Once you have calculated the SDS and SD1, then according to Section 12.8 of ASCE 7, Equivalent Lateral Force Procedure, the base shear V=CsW
Where Cs=Seismic response coefficient
where R=Response modification factor given in Table 12.2-1 and Ie=the importance factor determined in accordance with section 11.5.1
what is a Response modification factor?
Per ASCE 7, Response modification factor is a factor that is based on considerable judgement based on knowledge of actual earthquake performance and research studies. The values of R are given in Table 12.2-1. These factors have been continually revised in each edition of code and have been refined based on recent earthquakes.
Ie is the Importance factor based on Table 1.5-2 of ASCE 7, note that importance factor for seismic design is different than wind, ice and snow and also different based on Risk category.
In our example problem, lets assume that our structure that is supposed to be built has Special reinforced concrete shear wall to resist the seismic lateral loads, then R=5 from Table 12.2-1 and lets assume that the importance factor will be 1.25, then
Cs =1.0g/(5/1.25) = 0.25g
Base shear V=0.25W (where W is the effective seismic weight of the building)
NOTE: The base shear coefficient shown here is for the “special reinforced” concrete shear walls of the building. Building codes further dissect and analyze the diaphragms, collectors, connections differently. Non structural components and anchorage of electrical and mechanical components are analyzed differently based on Chapter 13 of ASCE 7. The above calculation is just a simple example of how to calculate the base shear.
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