Seismic Analysis Concepts - Prof SH Lodi F = m a or F = Prof. Sarosh H Lodi

Seismic Analysis Concepts ? How to estimate internal forces due to seismic excitation F = m a or F =

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

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

mu(t) + cu(t) + ku(t) = -mug(t) Dynamic Concept Time History Analysis Mathematical Model .. . .. mu(t) + cu(t) + ku(t) = -mug(t) Two storied building

Response Spectrum Concept Dynamic Concept Response Spectrum Concept

Equivalent Force Method Base Shear Determination Base Shear, V = CsW where: Cs = seismic response coefficient W = the effective seismic weight, including applicable portions of other storage and snow loads Total ELASTIC earthquake force (in each direction): VEQ can be calculated

Equivalent Force Method Seismic 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

Equivalent Force Method Response 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.

Equivalent Force Method Fundamental 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 ASCE 7-05 Seismic Provisions - A Beginner's Guide to ASCE 7-05 10

Equivalent Force Method Approximate 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.

Equivalent Force Method Building Period Coefficient, CT

Equivalent Force Method Base Shear Summary V = CsW From Design Spectrum 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 map Numerical Analysis or Ta = CThnx or Ta = 0.1N R from Table 12.2-1 based on the Basic Seismic-Force-Resisting System CT = 0.028, 0.016, 0.030, or 0.020 hn = building height N = number of storys I from Table 11.5-1 based on Occupancy Category

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

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

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.

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.

Performance Levels Hazard Levels Occasional Incipient Collapse Rare 50% in 50 years Rare 10% in 50 years Very Rare 5% in 50 years Max Considered 2% in 50 years Incipient Collapse Life Safety Immediate Reoccupancy Fully Operational

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)

Development of Performance-based Seismic Design Standards and Criteria

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

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

Code Procedures Require buildings have complete structural systems Require systems have sufficient strength to resist specified forces Limit permissible drifts under specified forces Require members and connections be “detailed” prescriptively 2003

Building Codes Imply Performance 100 yrs 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 500 yrs 2003 2,500 yrs Performance is not guaranteed

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

First Generation Standards are Available Seismic Evaluation of Buildings 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 achieve desired 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 ASCE-31 Seismic Rehabilitation of Buildings ASCE-41

Selecting Performance Present Generation Bata BBQ! Food! Operational Operational – negligible impact on building Beer! Food! Joe’s BBQ! Bata Life Safety Life Safe – building is safe during event but possibly not afterward Collapse Prevention Collapse Prevention – building is on verge of collapse, probable total loss Beer! Food! Joe’s BBQ! Bata Immediate Occupancy Immediate Occupancy – building is safe to occupy but possibly not useful until cleanup and repair has occurred

Code-equivalent Performance Seismic Analysis Concepts - Prof SH Lodi Code-equivalent Performance Beer! Food! Joe’s BBQ! Bata Immediate Occupancy Frequent event (varying between 50- and 100- year return periods) Beer! Food! Joe’s BBQ! Bata Life Safety Collapse Prevention DBE MCE

Risk Assessment and Performance Based Design

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