CEE 454 Earthquake Load Formulation using ASCE 7

CEE 454 Earthquake Load Formulation using ASCE 7 -05 eqasce 705. ppt

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. • ASCE 7 -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 ASCE 7 -05. 12/14/2021 eqasce 705. ppt 2

Dynamic behavior • Design models based upon – Observation – Mathematics – Full-scale calibration • Start with simplest case of free vibration • Incorporate into loading formulation 12/14/2021 eqasce 705. ppt 3

Chopra (2003) 12/14/2021 eqasce 705. ppt 4

Chopra (2003) 12/14/2021 eqasce 705. ppt 5

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 12/14/2021 eqasce 705. ppt 6

Chopra (2003) 12/14/2021 eqasce 705. ppt 7

Definitions 12/14/2021 eqasce 705. ppt 8

Effect of damping on free vibration Chopra (2003) 12/14/2021 eqasce 705. ppt 9

How do we incorporate into ASCE 7 -05? Ref: Army Manual 12/14/2021 eqasce 705. ppt 10

General model for design Ref: Army Manual 12/14/2021 eqasce 705. ppt 11

ASCE 7 -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 12/14/2021 eqasce 705. ppt 12

Equivalent Lateral Force Procedure 12/14/2021 eqasce 705. ppt 13

Importance Factors: ASCE 7 -05 Table 11. 5 -1 shown below 12/14/2021 Occupancy Category I I or II 1. 0 III 1. 25 IV 1. 5 eqasce 705. ppt 14

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 12/14/2021 eqasce 705. ppt 15

Approximate fundamental period, Ta, p. 2. 52 -2. 53 12/14/2021 eqasce 705. ppt 16

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 12/14/2021 eqasce 705. ppt 17

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 SD 1 12/14/2021 eqasce 705. ppt 18

Site coefficients & adjusted max EQ spectral response accelerations 12/14/2021 eqasce 705. ppt 19

Site Coefficients Fa and Fv (pp. C. 36 -C. 37) Tables from ASCE 7 are below: These are the same as Table 1613. 5. 391) 12/14/2021 eqasce 705. ppt 20

Site Coefficients Fa and Fv The ASCE 7 table is given below. It is the same as Table 1613. 5. 3(2) as shown below on p. C. 37 of the text. 12/14/2021 eqasce 705. ppt 21

Design Spectral Response Accelerations: for short and 1 second periods: see p. 2. 51 of the text 12/14/2021 eqasce 705. ppt 22

Seismic Design Category: Short Period Design SDS Table 11. 6 -1 in ASCE 7 -05 is the same as Table 1613. 5. 6 (3) p. C. 38 in the text. 12/14/2021 eqasce 705. ppt 23

Seismic Design Category: 1 -second Period Design SD 1 Table 1613. 5. 6(2) p. C. 38 of the text. 12/14/2021 eqasce 705. ppt 24

Seismic Response Coefficient Cs 12/14/2021 eqasce 705. ppt 25

Cs need not be greater than [p. 2. 50] 12/14/2021 eqasce 705. ppt 26

But shall not be taken less than [p. 2. 51] 12/14/2021 eqasce 705. ppt 27

Vertical distribution of base shear 12/14/2021 eqasce 705. ppt 28

Overturning moment at level x, Mx 12/14/2021 eqasce 705. ppt 29

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 S 1 from maps as needed for given location and modify via Fa and Fv as needed to convert from Site B. Calculate SMS & SM 1. Calculate design values ( SDS and SD 1). Calculate Cs and base shear V. Distribute V as necessary using the Fx equations. If Mx is needed, calculate from applicable Fx. 12/14/2021 eqasce 705. ppt 30