[Part 2] Step by Step Analysis Procedure of Seismic Loads Based on IBC2012/ASCE7-10
After the huge response of the first article of [Part 1] Step by Step Analysis Procedure of Seismic Loads Based on IBC2012/ASCE7-10 , here we go with the second part of the article .
In the first part of the article, we have elaborated the following topics:
1-Determination of maximum considered earthquake and design spectral response accelerations.
2-Determination of seismic design category and Importance factor.
3-Determination of the Seismic Base Shear.
3.1-Equivalent Lateral Force Analysis.
Before continuing this article, it may be useful to have a check on the following posts:
- IBC/ASCE 7 Seismic Provisions for Seismic Design Category A Structures
- ASCE 7 Drift Check for Seismic and Wind Loading
- When does a mezzanine need to be considered a story for seismic design ?
- Live Load on Parking Structures: To Reduce or Not To Reduce
- Rigid or Flexible Diaphragm ?
- Why the Lateral Loads Factors Differs in ASD Load Combinations ?
… And here we go:
3.2- Vertical Distribution of Seismic Forces
Fx = Lateral force at level x
Cvx = Vertical distribution factor
V = total design lateral force or shear at the base of the building
Wx and Wi = the portions of W assigned to levels x and i
hx and hi = heights to levels x and i
k = a distribution exponent related to the building period as follows:
k = 1 for buildings with T less than or equal to 0.5 seconds
k = 2 for buildings with T more than or equal to 2.5 seconds
Interpolate between k = 1 and k = 2 for buildings with T between 0.5 and 2.5
3.3-Horizontal Distribution of Forces and Torsion
Horizontally distribute the shear Vx
Fi = portion of the seismic base shear, V , introduced at level i
Accidental Torsion, Mta
Mta = Vx * (0.05B)
Total Torsion, MT , MT= Mt + Mta
3.4- Story Drift
The story drift, Δ , is defined as the difference between the deflection of the center of mass at the top and bottom of the story being considered.
Cd = deflection amplification factor, given in Table 12.2-1
δxe = deflection determined by elastic analysis
4- Seismic Load Effects and Combinations
4.1 Seismic Load Effect
Use E = ρ QE + 0.2 SDS*D for these combinations
Use E = ρ QE − 0.2SDS*D for these combinations
The vertical seismic load effect, SDS , is permitted to be taken as zero when SDS is equal to or less than 0.125.
4.2 Load Effect with Over-strength Factor
- The value of ρ is permitted to equal 1.0 for the following:
1. Structures assigned to Seismic Design Category B or C.
2. Drift calculation and P-delta effects.
3. Design of collector elements.
4. Design of members or connections where the seismic load effects including overstrength factor are required for design.
5. Diaphragm loads.
- For structures assigned to Seismic Design Category D, E, or F, ρ shall equal 1.3 unless one of the following two conditions is met, whereby ρ is permitted to be taken as 1.0:
a. Each story resisting more than 35 percent of the base shear in the direction of interest shall comply with Table 12.3-3.
b. Structures that are regular in plan at all levels provided that the seismic force-resisting systems consist of at least two bays of seismic force-resisting perimeter framing on each side of the structure in each orthogonal direction at each story resisting more than 35 percent of the base shear. The number of bays for a shear wall shall be calculated as the length of shear wall divided by the story height or two times the length of shear wall divided by the story height, hsx , for light-frame construction.
For a given building site, the risk-targeted maximum considered earthquake spectral response accelerations Ss, at short periods, and S1, at a 1-second period, are given by the acceleration contour maps in Chapter 22 in Figures 22-1 through 22-6. This example illustrates the general procedure for determining the design spectral response acceleration parameters SDS and SD1 from the mapped values of SS and S1. The parameters SDS and SD1 are used to calculate the design response spectrum in Section 11.4.5 and the design base shear in Section 12.8. The easiest and most accurate way to obtain the spectral values is to use the “U.S. Seismic Design Maps” application from the USGS website (http://geohazards.usgs.gov/designmaps/us/application.php). The USGS application allows for values of SS and S1 to be provided based on the address or the longitude and latitude of the site being entered.
A building site in California is located at 38.123° North (Latitude 38.123°) and 121.123° West (Longitude -121.123°). The soil profile is Site Class D.
We will determine the following:
1. Mapped risk-targeted maximum considered earthquake (MCER) spectral response acceleration parameters Ss and S1.
2. Site coefficients Fa and Fv and MCER spectral response acceleration parameters SMS and SM1 adjusted for Site Class effects.
3. Design spectral response acceleration parameters SDS and SD1.
1. Mapped MCER Spectral Response Acceleration Parameters Ss and S1
For the given site at 38.123° North (Latitude 38.123°) and 121.123° West (Longitude -121.123°), the USGS “U.S. Seismic Design Maps” application provides the values of
SS = 0.634g
S1 = 0.272g.
2. Site Coefficients Fa and Fv and MCER Spectral Response Acceleration Parameters SMS and SM1 Adjusted for Site Class Effects ( §11.4.3 )
For the given Site Class D and the values of SS and S1 determined above, the site coefficients are
Fa = 1.293 T11.4-1
Fv = 1.856. T11.4-2
The MCER spectral response acceleration parameters adjusted for Site Class effects are
SMS = Fa* SS = 1.292(0.634g) = 0.819g Eq 11.4-1
SM1 = Fv* S1 = 1.857(0.272g) = 0.505g Eq 11.4-2
3. Design Spectral Response Acceleration Parameters SDS and SD1 ( §11.4.4 )
SDS = (2/3) SMS = (2/3)(0.819g) = 0.546g Eq 11.4-3
SD1 = (2/3) SM1 = (2/3)(0.505g) = 0.337g Eq 11.4-4
The USGS application “U.S. Seismic Design Maps” requires the risk category to be specified, even though that category is not necessary for determining SDS and SD1.