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Earthquake Load Formulation using ASCE7-05
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 contains this information in a particular format. We will introduce the general concepts of dynamics before introducing the standard loading formulation of ASCE7-05. 11/13/2018 eqasce705.ppt
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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 11/13/2018 eqasce705.ppt
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Chopra (2003) 11/13/2018 eqasce705.ppt
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Chopra (2003) 11/13/2018 eqasce705.ppt
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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 11/13/2018 eqasce705.ppt
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Chopra (2003) 11/13/2018 eqasce705.ppt
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Definitions 11/13/2018 eqasce705.ppt
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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 11/13/2018 eqasce705.ppt
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General model for design
Ref: Army Manual 11/13/2018 eqasce705.ppt
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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 11/13/2018 eqasce705.ppt
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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 11/13/2018 eqasce705.ppt
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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 11/13/2018 eqasce705.ppt
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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 11/13/2018 eqasce705.ppt
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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 11/13/2018 eqasce705.ppt
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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
Site Coefficients Fa and Fv (pp. C.36-C.37) Tables from ASCE7 are below: These are the same as Table ) 11/13/2018 eqasce705.ppt
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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. 11/13/2018 eqasce705.ppt
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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 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. 11/13/2018 eqasce705.ppt
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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. 11/13/2018 eqasce705.ppt
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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. 11/13/2018 eqasce705.ppt
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