1. Earthquake Load Formulation using ASCE7-05
CEE454
Earthquake Load Formulation using ASCE7-05

2. Outline of lecture topics
In order to model seismic loadings, we must
examine the dynamic behavior of buildings and use mathematical models to predict behavior.
identify the seismic hazard in the region.
select framing systems to counter the lateral forces imposed.
ASCE7-05 sections contains this information in a particular format.
We will introduce the general concepts of dynamics before introducing the standard loading formulation of ASCE7-05.
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3. Dynamic behavior Design models based upon
Observation
Mathematics
Full-scale calibration
Start with simplest case of free vibration
Incorporate into loading formulation
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4. Chopra (2003)
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5. Chopra (2003)
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6. Damped Free Vibration
A damping force is added to the EOM. It is proportional to the velocity.
No forcing so the RHS is zero.
The EOM is
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7. Chopra (2003)
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8. Definitions
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9. Effect of damping on free vibration Chopra (2003)
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10. How do we incorporate into ASCE7-05?
Ref: Army Manual
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11. General model for design
Ref: Army Manual
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12. ASCE7-05 Section 12.8, p. 129 In the book, chapter 2 and Appendix C.
Model is of equivalent inertial forces applied to characterize the effect of base movement -- previous slide
Dynamic behavior of building considered
Soil conditions considered
Location in US considered
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13. Equivalent Lateral Force Procedure
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14. Importance Factors: ASCE7-05 Table 11.5-1 shown below
Occupancy Category I
I or II
1.0
III
1.25 IV
1.5
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15. Site Class: Table 1613.5.2 Appendix C, p. C.36 of Breyer text
A, B, C, D, E, F
Characterizes the soil properties
Usually this information is provided
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16. Approximate fundamental period, Ta, p. 2.52-2.53
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17. Table for Ta calculation p. 2.53 of the text
Structure Type Ct x
Steel moment resisting frames
0.028
0.8
Concrete moment resisting frames
0.016
0.9
Eccentrically braced steel frames
0.03
0.75
All other structural systems
0.02
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18. Mapped spectral response accelerations Figures on pages C.18-C.35
Are for Site B [soil condition]
Need to be modified for other site classes [soil conditions other than B]
Are used in the equations to find the Design spectral response accelerations such as SDS and SD1
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19. Site coefficients & adjusted max EQ spectral response accelerations
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20. Site Coefficients Fa and Fv (pp. C. 36-C
Site Coefficients Fa and Fv (pp. C.36-C.37) Tables from ASCE7 are below: These are the same as Table )
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21. Site Coefficients Fa and Fv The ASCE7 table is given below
Site Coefficients Fa and Fv The ASCE7 table is given below. It is the same as Table (2) as shown below on p. C.37 of the text.
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22. Design Spectral Response Accelerations: for short and 1-second periods: see p. 2.51 of the text
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23. Seismic Design Category: Short Period Design SDS Table 11
Seismic Design Category: Short Period Design SDS Table in ASCE7-05 is the same as Table (3) p. C.38 in the text.
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24. Seismic Design Category: 1-second Period Design SD1 Table 1613. 5
Seismic Design Category: 1-second Period Design SD1 Table (2) p. C.38 of the text.
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25. Seismic Response Coefficient Cs
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26. Cs need not be greater than [p. 2.50]
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27. But shall not be taken less than [p. 2.51]
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28. Vertical distribution of base shear
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29. Overturning moment at level x, Mx
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30. General Seismic Load Process
Determine occupancy, seismic use factor and site class.
Calculate W from dead load values.
Determine period T (or Ta) and building factor R.
Read SS and S1 from maps as needed for given location and modify via Fa and Fv as needed to convert from Site B.
Calculate SMS & SM1.
Calculate design values ( SDS and SD1).
Calculate Cs and base shear V.
Distribute V as necessary using the Fx equations.
If Mx is needed, calculate from applicable Fx.
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