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Seismic Analysis Concepts

Prof. Sarosh H Lodi

0 5 10 15 20 25 30 35 40 45 50 55

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F = m a

or

F =

2

Acceleration vs Time, File ELCENTRO

Time (SECONDS)

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Tra

nsla

tio

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cce

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^2

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?How to estimate internal forces due to seismic excitation

F = m a

or

F =

Seismic Analysis Concepts

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Earthquake Protective Design Philosophical Issues

High probability of “Failure”

“Failure” redefined to permit behavior (yielding) that would be considered failure under other loads.

High Uncertainty Importance of

Details

“In dealing with earthquakes we must contend with appreciable probabilities that failure will occur in the near future. Otherwise, all the wealth of the world would prove insufficient… We must also face uncertainty on a large scale… In a way, earthquake engineering is a cartoon… Earthquakes systematically bring out the mistakes made in design and construction, even the minutest mistakes.” Newmark & Rosenblueth

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Elastic vs Inelastic Response

The red line shows the force and displacement that would be reached if the structure responded elastically.

The green line shows the actual force vs. displacement response of the structure

The pink line indicates the minimum strength required to hold everything together during inelastic behavior

The blue line is the force level that we design for.

We rely on the ductility of the system to prevent collapse.

From 1997 NEHRP Provisions

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Dynamic ConceptTime History Analysis

Mathematical Model

Two storied building

mu(t) + cu(t) + ku(t) = -mug(t).. . ..

Acceleration vs Time, File ELCENTRO

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Acceleration vs Time, File ELCENTRO

Time (SEC)

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Dynamic ConceptResponse Spectrum Concept

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where:Cs = seismic response coefficient

W = the effective seismic weight, including applicable portions of other storage and snow loads

Base Shear, V = CsW

Total ELASTIC earthquake force (in each direction): VEQ can be calculated

Equivalent Force MethodBase Shear Determination

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Equivalent Force MethodSeismic Response Coefficient, Cs

Cs = SDS /(R/I)

Cs need not exceed

SD1/(T(R/I)) for T < TL

SD1TL/(T2(R/I)) for T > TL

Cs shall not be taken less than

Max[0.044SDSI, 0.01] for S1 < 0.6g

0.5S1/(R/I) for S1 > 0.6g

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Equivalent Force MethodResponse Modification Coefficient, R

The response modification factor, R, accounts for the dynamic characteristics, lateral force resistance, and energy dissipation capacity of the structural system.

Can be different for different directions.

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Equivalent Force MethodFundamental Period, T

May be computed by analytical means May be computed by approximate means, Ta

Where analysis is used to compute T:

T < Cu Ta

May also use Ta in place of actual T

10ASCE 7-05 Seismic Provisions - A Beginner's Guide to ASCE 7-05

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Equivalent Force MethodApproximate Fundamental Period, Ta

An approximate means may be used.

Ta = CThnx

Where:

CT = Building period coefficient.

hn = height above the base to the highest level of the building

for moment frames not exceeding 12 stories and having a minimum story height of 10 ft, Ta may be taken as 0.1N, where N = number of stories.

For masonry or concrete shear wall buildings use eq 12.8-9 Ta may be different in each direction.

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Equivalent Force Method Building Period Coefficient, CT

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Equivalent Force Method Base Shear Summary

V = CsW

W = Building Seismic Weight

Max[0.044SDSI,0.01] or 0.5S1/(R/I) < SDS/(R/I) < SD1/(T(R/I)) or TLSD1/(T2(R/I))

From Design Spectrum

From map

R from Table 12.2-1 based on the Basic Seismic-Force-

Resisting System

Numerical Analysis or Ta = CThn

x or Ta = 0.1N

CT = 0.028, 0.016, 0.030, or 0.020

hn = building heightN = number of storys

I from Table 11.5-1 based on Occupancy Category

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Equivalent Force Method Vertical Distribution of Base Shear

For short period buildings the vertical distribution follows generally follows the first mode of vibration in which the force increases linearly with height for evenly distributed mass.

For long period buildings the force is shifted upwards to account for the whipping action associated with increased flexibility

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Equivalent Force Method Story Force, Fx

Fx = CvxV

Where Cvx = Vertical Distribution Factor

Wx = Weight at level x

hx = elevation of level x above the base

k = exponent related to structure period When T < 0.5 s, k =1, When T > 2.5 s, k =2,

Linearly interpolate when 0.5 < T < 2.5 s

Cvx

Wx

hx

k

1

n

i

Wi

hi

k

=

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Equivalent Force Method Story Shear, Vx

Story shear, Vx, is the shear force at a given story level

Vx is the sum of all the forces above that level.

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Equivalent Force Method Horizontal Distribution

Being an inertial force, the Story Force, Fx, is distributed in accordance with the distribution of the mass at each level.

The Story Shear, Vx, is distributed to the vertical lateral force resisting elements based on the relative lateral stiffnesses of the vertical resisting elements and the diaphragm.

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Hazard Levels

Incipient Collapse Life Safety Immediate

Reoccupancy Fully Operational

Occasional 50% in 50 years

Rare 10% in 50 years

Very Rare 5% in 50 years

Max Considered 2% in 50 years

Performance Levels

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Design Objective Defined

A specific performance level given a specific earthquake hazard level

Stated basis of current codes: Life safety (+some damage control) at 10% in

50 year event (nominally)

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Development of Performance-based Seismic Design Standards and Criteria

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Advantages of Performance-Based Approach

Specifically Addresses: Unique Building Features Client Needs Building Use Considerations Proposed Alternatives

Assessment of Code Requirements Increased Engineering Rigor / Peer Review Comprehensive Systems Overview

Integration of Systems Cost Effectiveness

Improved Knowledge of Loss Potential

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Disadvantages of Performance-Based Approach

Reluctance to Approve PB Approach Unfamiliar with Methodology Lack of Knowledge of Science Creates Tendency to

Disagree with or be Skeptical of: Approach, Objectives, Certainty

Perception that Anything Less than Code is not “Safe” Qualifications of Designer / Reviewer More Design/Engineering Time Occupancy Changes May Require Re-analysis

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• Limit permissible drifts under specified forces

• Require buildings have complete structural systems

Code Procedures

• Require systems have sufficient strength to resist specified forces

• Require members and connections be “detailed” prescriptively

2003

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Building Codes Imply Performance

• Ability to resist frequent, minor earthquakes without damage

• Ability to resist infrequent, moderate earthquakes with limited structural and nonstructural damage

• Ability to resist worst earthquakes ever likely to occur without collapse or major life safety endangerment

100 yrs

500 yrs

2,500 yrs

Performance is not guaranteed

2003

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Building Codes & Performance Warranties

• If a building is affected by an extreme event and performs poorly:– There is an expectation of how the building

should have performed but no implied warranty• The only warranty is that the engineer complied

with the standard of care– For most buildings, demonstration that a design

was performed in accordance with the building code will provide adequate proof of conformance to the standard of care

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First Generation Standards are Available

• ASCE/SEI has standardized FEMA guideline documents on::

• Seismic Evaluation– Predict types of damage a building would

experience in future events (based on FEMA178)

• Rehabilitation– Procedures to design building upgrades to

achievedesired performance (based on FEMA 356)

• Though not directly recognized by the building codes, these standards are being used as the basis for Performance-based design of new buildings and seismic retrofit

SeismicEvaluation ofBuildings

ASCE-31

SeismicRehabilitation ofBuildings

ASCE-41

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Selecting PerformancePresent Generation

Bata

BBQ!Food!Food!

Operational

Operational – negligible impact on building

Beer!Beer!Food!Food!

Joe’s

Beer!Beer!Food!Food!BBQ!Food!Food!

Joe’sBata

ImmediateOccupancy

Immediate Occupancy – building is safe to occupy butpossibly not useful until cleanup and repair has occurred

Beer!Beer!Food!Food!

Joe’s

Beer!Beer!Food!Food!BBQ!Food!Food!

Bata

LifeSafety

Life Safe – building is safe during event but possibly notafterward

CollapsePrevention

Collapse Prevention – building is on verge of collapse, probable total loss

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Code-equivalent Performance

Beer!Beer!Food!Food!

Joe’s

Beer!Beer!Food!Food!BBQ!Food!Food!

Joe’sBata

ImmediateOccupancy

Frequent event (varying between 50- and 100- year return periods)

Beer!Beer!Food!Food!

Joe’s

Beer!Beer!Food!Food!BBQ!Food!Food!

Bata

LifeSafety

DBE

CollapsePrevention

MCE

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Risk Assessment and Performance Based Design

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Thank you