CEE454

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CEE454

• Earthquake Load Formulation using ASCE7-05

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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 11-23 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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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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Chopra (2003)
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Chopra (2003)
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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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Chopra (2003)
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Definitions
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Effect of damping on free vibration Chopra (2003)
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How do we incorporate into ASCE7-05?
Ref Army Manual
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General model for design
Ref Army Manual
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ASCE7-05 Section 12.8, p. 129In 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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Equivalent Lateral Force Procedure
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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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Site Class Table 1613.5.2

• Appendix C, p. C.36 of Breyer text
• Site Class
• A, B, C, D, E, F
• Characterizes the soil properties
• Usually this information is provided

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Approximate fundamental period, Ta, p. 2.52-2.53
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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 0.75
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Mapped spectral response accelerationsFigures 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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Site coefficients adjusted max EQ spectral
response accelerations
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Site Coefficients Fa and Fv (pp.
C.36-C.37)Tables from ASCE7 are below These are
the same as Table 1613.5.391)
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Site Coefficients Fa and Fv The ASCE7 table is
given below. It is the same as Table 1613.5.3(2)
as shown below on p. C.37 of the text.
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Design Spectral Response Accelerations for
short and 1-second periods see p. 2.51 of the
text
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Seismic Design Category Short Period Design
SDSTable 11.6-1 in ASCE7-05 is the same as Table
1613.5.6 (3) p. C.38 in the text.
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Seismic Design Category 1-second Period Design
SD1Table 1613.5.6(2) p. C.38 of the text.
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Seismic Response Coefficient Cs
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Cs need not be greater than p. 2.50
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But shall not be taken less than p. 2.51
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Vertical distribution of base shear
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Overturning moment at level x, Mx
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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.