Chapter 5 Elements of Seismic Design

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CONTENT 1. Force-Based Seismic Design g Procedure 2. Seismic Design Criteria of ASCE 7-05 3. Seismic Design Requirements of ASCE 7-05 for B ildi Structures Building St t 4. Seismic Design Requirements of ASCE 7-05 for Nonstructural Components p 5. Architectural Principles 6. Performance-Based Earthquake Engineering 7. Direct Displacement-Based Seismic Design Procedure 8. References CIE 619 Chapter 5 – Seismic Design

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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 p of the inherent overstrength and global ductility capacity

Ve V R CIE 619 Chapter 5 – Seismic Design

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1. Force-Based Seismic Design Procedure • Concept of Ductility VE

Vy

y

max

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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 h walls) ll ) V – Position of the lateral load-resisting elements E

Vy

• Changes in indi individual id al strengths of structural str ct ral elements has minor influence on lateral stiffness • First goal of force-based force based seismic design:

y

– Select an adequate strength level so that structure can deform in the inelastic range without collapse CIE 619 Chapter 5 – Seismic Design

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max

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 y have the same maximum lateral deflection. Using g similar triangles, g it two systems yields the following equation : Vmax

V max  max = = Vy y or



Vy

V y= y

max

V max



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(5.8)

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1. Force-Based Seismic Design Procedure • Concept of Inelastic Response Spectra Equation 5.8 5 8 can be written as a function of seismic coefficients coefficients.

C (inelastic) W = C (elastic)

W

 Vmax

or

S A(inelastic)

W W = S A(elastic) g g



Vy

y

CIE 619 Chapter 5 – Seismic Design

max

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1. Force-Based Seismic Design Procedure • Concept of Inelastic Response Spectra The absolute inelastic acceleration response spectrum spectrum, SA (inelastic), (inelastic) can then be define as a function of the elastic acceleration response spectrum and of the ductility ratio.

S A(inelastic) =

S A((elastic))



The relative inelastic displacement spectrum, SD (inelastic), can also be defined as the relative displacement of the structure when first yield is reached. Vmax

 y= SD

= (inelastic)

 max = S D  

(elastic)



Vy

CIE 619 Chapter 5 – Seismic Design

y

max

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1. Force-Based Seismic Design Procedure • Concept of Inelastic Response Spectra Therefore,, a tripartite p graph g p can be used to construct an inelastic response p spectrum p 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 i relative l ti velocity l it off the th elastic l ti system; t 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 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.

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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 hi phenomenon h can be b explained l i d by b the h fact f that h when h a system with i h a short h initial i ii l period yields, its period becomes longer and shifts toward the predominant period of the accelerogram.

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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 b better represent their h i behaviour. b h i This Thi criterion i i states that h the h strain i energy off 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 max  e V y  y = + V y   max -  y 2 2



(5.13)

Using similar triangles, the following relation is obtained:

V max

e

=

Vy

y

or

 e=

V max  y Vy

CIE 619 Chapter 5 – Seismic Design

((5.15)) 11

1. Force-Based Seismic Design Procedure • Energy Criterion For Short Period Structures Equation 6.15 is substituted into equation 6.13.

 V max 2  y 2 Vy

 y  = Vy  +   max -  y    2 

Simplifying, the following expression is obtained:





 V max 2 =  V y 2  2  max - 1  =  V y 2  2  - 1  

y



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 y=

V max 2  -1

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1. Force-Based Seismic Design Procedure • Energy Criterion For Short Period Structures In general, the elastic acceleration spectrum is reduced as follows:

S Ainelastic =

SAinelastic =

S Aelastic



for T  0,5 0 5s

SAelastic for T < 0,5 0 5s 2  -1

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1. Force-Based Seismic Design Procedure • Linear Static Analysis Method

– Typical Code Design Base Shear Equation, V:

– Se Seismic s c Design es g Force o ce at Level eve i,, Fi: Ft Fi CIE 619 Chapter 5 – Seismic Design

hi

Wi 14

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 CIE 619 Chapter 5 – Seismic Design

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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 S th ti records d

– Usually performed at the end of the design process for verification purposes CIE 619 Chapter 5 – Seismic Design

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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 limit-states states not directly addressed – Equal displacement approximation inappropriate for short period structures – No consensus on definition of yield and ultimate displacements p CIE 619 Chapter 5 – Seismic Design

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

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

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2. Seismic Design Criteria of ASCE 7-05 • Seismic Ground Motion Values – Mapped Acceleration Parameters • Parameters SS and S1 determined from the mapped 0.2 and 1.0 s spectral p response p accelerations

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

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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

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

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2. Seismic Design Criteria of ASCE 7-05 •

S i i Ground Seismic G d Motion i Values l – 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 Sit Class Cl C: 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 CIE 619 Chapter 5 – Seismic Design

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2. Seismic Design Criteria of ASCE 7-05 • Seismic Ground Motion Values – Site Coefficients and Adjusted Maximum Considered Earthquake (MCE) Spectral Response espo se Acceleration cce e at o Parameters a a ete s • MCE spectral response acceleration for short periods (SMS) and at 1 s (SM1), adjusted for Site Cl effects Class ff determined d i d by: b

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2. Seismic Design Criteria of ASCE 7-05 • Seismic Ground Motion Values – Site Coefficients and Adjusted Maximum Considered Earthquake (MCE) Spectral Response espo se Acceleration cce e at o Parameters a a ete s

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2. Seismic Design Criteria of ASCE 7-05 • Seismic Ground Motion Values – Site Coefficients and Adjusted Maximum Considered Earthquake (MCE) Spectral Response espo se Acceleration cce e at o Parameters a a ete s

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2. Seismic Design Criteria of ASCE 7-05 • Seismic Ground Motion Values – Design Spectral Acceleration Parameters • Design Earthquake (DE) spectral response acceleration pparameter at short pperiod,, SDS, and at 1s period, SD1, determined by:

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2. Seismic Design Criteria of ASCE 7-05 • Seismic Ground Motion Values – Design Response Spectrum (see Section 4.2) 4 2)

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

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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 p y Category g y

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2. Seismic Design Criteria of ASCE 7-05 • Seismic Design Category – Buildings and structures assigned more severe Seismic Design Category in accordance with Table 11.6-1 or 11.6-2

– Occupancy Category I, II, or III structures located where S1 > 0.75 assigned g Seismic Design g Category g yE – Occupancy Category IV structures located where S1 > 0.75 assigned Seismic Design Category F. CIE 619 Chapter 5 – Seismic Design

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

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• Structural System Selection

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ATC-63 Quantification of Building System Performance and Response Parameters

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