Chapter 5 Elements of Seismic Design. CIE 619 Chapter 5 Seismic Design

Transcription

1 Chapter 5 Elements of Seismic Design 1

2 CONTENT 1. Force-Based Seismic Design Procedure 2. Seismic Design Criteria of ASCE Seismic Design Requirements of ASCE 7-05 for Building Structures t 4. Seismic Design Requirements of ASCE 7-05 for Nonstructural Components 5. Architectural Principles 6. Performance-Based Earthquake Engineering 7. Direct Displacement-Based Seismic Design Procedure 8. References 2

3 1. Force-Based Seismic Design Procedure Principles and Objectives Elastic spectral accelerations used to determine required lateral strength of equivalent elastic structure Elastic strength divided by a force reduction factor R representative of the inherent overstrength and global ductility capacity V V e R 3

4 1. Force-Based Seismic Design Procedure Concept of Ductility V E V y y max 4

5 1. Force-Based Seismic Design Procedure Lateral stiffness of a building determined in the early stages of design and depends on: Choice of materials (in our case wood) Choice of lateral load-resisting elements (diaphragms and shear walls) V E Position of the lateral load-resisting elements V y Changes in individual id strengths of structural ral elements has minor influence on lateral stiffness First goal of force-based seismic design: Select an adequate strength level so that structure can deform in the inelastic range without collapse y max 5

6 1. Force-Based Seismic Design Procedure Concept of Inelastic Response Spectra The fact that maximum lateral displacement of a nonlinear system is almost equal to the maximum displacement of the corresponding linear system allows us to define inelastic seismic response spectra from the elastic seismic response spectra discussed in Section 4.2. Here again, the equal displacement principle is used. For a given earthquake, the two systems have the same maximum lateral deflection. Using similar triangles, it yields the following equation : V max V max V y = y max = or V y = V y V max (5.8) y max 6

7 1. Force-Based Seismic Design Procedure Concept of Inelastic Response Spectra Equation 5.8 can be written as a function of seismic coefficients. or C (inelastic) W = C (elastic) W V max S A (inelastic) W g = S A (elastic) W g V y y max 7

8 1. Force-Based Seismic Design Procedure Concept of Inelastic Response Spectra The absolute inelastic acceleration response spectrum, SA (inelastic), can then be define as a function of the elastic acceleration response spectrum and of the ductility ratio. = S A(elastic) S A (inelastic) The relative inelastic displacement spectrum, SD (inelastic), can also be defined as the relative displacement of the structure when first yield is reached. V max y = S y D(inelastic) = max = S D (elastic) V y y max 8

9 1. Force-Based Seismic Design Procedure Concept of Inelastic Response Spectra Therefore, a tripartite graph can be used to construct an inelastic response spectrum for a certain level of ductility from an elastic response spectrum. On the top elastic curve, we can read: maximum absolute acceleration of the elastic system; maximum relative velocity of the elastic system; maximum relative displacement for the elastic and inelastic systems. On the bottom inelastic curve, we can read : maximum absolute acceleration of the inelastic system only. The bottom curve is really an absolute inelastic acceleration response spectrum. This spectrum can be used to determine the yield base shear, Vy, required to design the structure based on a given available ductility factor. 9

10 1. Force-Based Seismic Design Procedure Energy Criterion For Short Period Structures If a system is very stiff and has a much shorter natural period than the predominant period of the accelerogram, then the equal displacement principle cannot be used. In fact, for this specific case, the nonlinear dynamic analysis shows that, generally, the inelastic system produces more deformations than the corresponding elastic system. This phenomenon can be explained by the fact that when a system with iha short initial ii period yields, its period becomes longer and shifts toward the predominant period of the accelerogram. 10

11 1. Force-Based Seismic Design Procedure Energy Criterion For Short Period Structures For short systems, with short initial periods of vibration, an energy criterion seemed to better represent their bh behaviour. This criterion i states that the strain energy of an inelastic system and the strain energy of a corresponding elastic system are equal. From figure 6.8, the surfaces under the two curves are assumed to be equal. V e 2 max = Vy y 2 + V y max - y (5.13) Using similar triangles, the following relation is obtained: V e max = V y y or V e ( ) max y e = (5.15) Vy 11

12 1. Force-Based Seismic Design Procedure Energy Criterion For Short Period Structures Equation 6.15 is substituted into equation V max 2 V 2 y y = V y y 2 + max - y Simplifying, the following expression is obtained: 2 V y 2 2 max 2 = y 2-1 = y 2-1 V max The maximum base shear of the inelastic system can then be obtained from the base shear corresponding to the elastic system and from the available ductility ratio. V = V y V max

13 1. Force-Based Seismic Design Procedure Energy Criterion For Short Period Structures In general, the elastic acceleration spectrum is reduced as follows: S A inelastic = S Aelastic for T 05s 0,5s S A inelastic = SAelasticA 2-1 for T < 05s 0,5s 13

14 1. Force-Based Seismic Design Procedure Linear Static Analysis Method Typical Code Design Base Shear Equation, V: Seismic Design Force at Level i, F i i: F t F i Wi i h i 14

15 1. Force-Based Seismic Design Procedure Linear Dynamic Analysis Method For tall and/or irregular structures Linear modal superposition method Input motion defined by design acceleration response spectrum Statistical combination of modal maxima Peak dynamic base shear scaled to static design base shear Better evaluation of higher modes effects 15

16 1. Force-Based Seismic Design Procedure Nonlinear Dynamic Analysis Method For very tall and/or highly irregular important structures Time-integration of equations of motion Nonlinear structural model needed Cyclic behavior of structural elements deemed to respond in the inelastic range of the material needs to be included Realistic representation of limit states Ground motion input represented by an ensemble of acceleration time-histories Scaled historical ground acceleration time-histories Synthetic ti records Usually performed at the end of the design process for verification purposes 16

17 1. Force-Based Seismic Design Procedure Limitations of Force-Based Seismic Design Procedures Process uses estimate of elastic fundamental period Force reduction factor R based on judgment Deformation limit-states not directly addressed Equal displacement approximation inappropriate for short period structures No consensus on definition of yield and ultimate displacements 17

18 2. Seismic Design Criteria of ASCE 7-05 U.S. Building Code Seismic Requirements 18

19 2. Seismic Design Criteria of ASCE 7-05 NEHRP Seismic Provisions 19

20 2. Seismic Design Criteria of ASCE 7-05 Seismic Ground Motion Values Mapped Acceleration Parameters Parameters S S and S 1 determined from the mapped 0.2 and 1.0 s spectral response accelerations 20

21 2. Seismic Design Criteria of ASCE 7-05 Seismic Ground Motion Values Mapped Acceleration Parameters 21

22 2. Seismic Design Criteria of ASCE 7-05 Seismic Ground Motion Values Site Class Based on site soil properties, site classified as Site Class A, B, C, D, E, or F Where soil properties are not known in sufficient detail, Site Class D shall be used 22

23 2. Seismic Design Criteria of ASCE 7-05 Seismic Ground Motion Values Site Class 23

24 2. Seismic Design Criteria of ASCE 7-05 Si Seismic i Ground Motion Values Site Class for Rock Sites Upper 100 ft of rock considered Site Class A: Hard rock, generally east of the Rocky Mountains Site Class B: Competent rock sites with moderate fracturing Typically assigned to West Coast competent rock sites Site Class C: Soft or highly fractured rock sites If more than 10 ft of soil between rock surface and bottom of spread footing Site Class for Soil Sites Uper 100 ft of soil considered Site Class C: Very dense glacial tills, sands, and gravels Site Class D: Typical for buildings with shallow foundations Site Class E: Typical for buildings with deep foundations Site Class F: Liquefiable soils, quick and highly sensitive clays Requires site specific response spectrum analysis to assess ground amplification for T > 0.5 sec 24

25 2. Seismic Design Criteria of ASCE 7-05 Seismic Ground Motion Values Site Coefficients and Adjusted Maximum Considered Earthquake (MCE) Spectral Response se Acceleration e Parameters a MCE spectral response acceleration for short periods (S MS ) and at 1 s (S M1 ), adjusted for Site Class effects determined d by: 25

26 2. Seismic Design Criteria of ASCE 7-05 Seismic Ground Motion Values Site Coefficients and Adjusted Maximum Considered Earthquake (MCE) Spectral Response se Acceleration e Parameters a 26

27 2. Seismic Design Criteria of ASCE 7-05 Seismic Ground Motion Values Site Coefficients and Adjusted Maximum Considered Earthquake (MCE) Spectral Response se Acceleration e Parameters a 27

28 2. Seismic Design Criteria of ASCE 7-05 Seismic Ground Motion Values Design Spectral Acceleration Parameters Design Earthquake (DE) spectral response acceleration parameter at short period, S DS,, and at 1s period, S D1, determined by: 28

29 2. Seismic Design Criteria of ASCE 7-05 Seismic Ground Motion Values Design Response Spectrum (see Section 4.2) 29

30 2. Seismic Design Criteria of ASCE 7-05 Importance Factor and Occupancy Category Occupancy Category 30

31 2. Seismic Design Criteria of ASCE 7-05 Importance Factor and Occupancy Category Importance Factor Importance factor, I, assigned to each structure based on Occupancy Category 31

32 2. Seismic Design Criteria of ASCE 7-05 Seismic Design Category Buildings and structures assigned more severe Seismic Design Category in accordance with Table or Occupancy Category I, II, or III structures located where S 1 > 0.75 assigned Seismic Design Category E Occupancy Category IV structures located where S 1 > 0.75 assigned Seismic Design Category F. 32

33 3. Seismic Design Requirements of ASCE 7-05 for Building Structures Structural System Selection 33

34 Structural System Selection 34

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40 ATC-63 Quantification of Building System Performance and Response Parameters 40