Introduction to Building Structural Dynamics for Seismic

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Introduction to Building Structural Dynamics for Seismic Design

Geoff Bomba, SEForell/Elsesser Engineers, Inc.

San Francisco, CA

Learning Objectives

• Importance of dynamic analysis of structures

• Understand ground motion input for design

• IBC Code requirements for dynamic analysis

• Best practices for implementing building dynamic analysis

• Troubleshooting and debugging analysis models

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Scope

• Structural dynamics for practicing engineers

• Intended for new engineers or PM for QC

• Basic background in dynamics is assumed

• Covering seismic lateral forces

• Using IBC and ASCE 7‐10

• Notes on coming revisions to ASCE 7‐16 and FEMA P‐1050: NEHRP 2015

Focus

• Seismology for new building seismic design

• Buildings height less than 100 feet

• Linear Analysis

• Typical Structural Systems

– Not including energy dissipation devices and seismically isolated structures

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Structural Dynamics in Practice

• The Challenge:– Predicting and estimating response of buildings for design is difficult to quantify. Major sources of uncertainty and variability are present.

• We rely on codes and standards as discussed herein• Good engineering judgement is needed for design• Consider goals of the analysis early in design • Level of analysis equates to complexity of behavior:

– 1 story Moment Resisting Frame– 10 story irregular structure with plan offsets– 30 story (E) non‐ductile concrete structure with URM

Outline

• Ground Motions and Structures

• Modeling Characteristics and Structural Dynamics

• Dynamic Analysis, ELF, MRSA, LRHA

• Practical Considerations for Implementing Dynamic Analysis

• Conclusions and References

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GROUND MOTIONS AND STRUCTURES

Ground Motion Characteristics• Seismic “INPUT" for design is dependent on:

– Seismic hazard

– Magnitude

– Distance from fault

– Frequency content

– Duration

– Fault mechanism

– Soil at site

REF: USGS

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Ground Motion Time History

REF: PEER.BERKELEY.EDU

Ground Motion Response Spectrum

REF: strongmotioncenter.org

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Generating a Response Spectrum


ug..

ug..

m

k

1. SDOF, “Stick Model” at Ti2. Run “analysis” 3. Find max acc. for SDOF4. Plot max acc. at Ti

Ti

Max Acc @ Ti

Ti

Ground Motion Response Spectrum


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Design Response Spectrum

REF: ASCE 7‐10

Structural Dynamics Characteristics

• Seismic “RESPONSE” is dependent on:

– Structural System & Seismic Detailing

– Building configuration (i.e. regularities)

– Stiffness

– Mass

– Damping

– Also: material strengths, system ductility, reliability, foundations, SSI, construction....

} Building Period

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Historical EQ, Mexico City 1985

• Mw=8.0, approximately 5 min. of shaking

• Epicenter 250 mi away from Mexico City

• 9,500 killed, 400 buildings collapsed

• “Lake Zone” clay material, 6x amplification

• Period of maximum shaking was 2 ‐ 4 sec

• “Resonance” of medium to high‐rise structures, low rise unscathed even though unscathed

• Buildings 6 to 17 stories badly damagedREF: NIST NIBS Mexico Rpt

Historical EQ, Mexico City 1985

REF: USGS

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Mexico City 1985, Spectrum

REF: NIST NIBS Mexico Rpt

Comparison El Centro vs. Mexico City

REF: EERI.org

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MODELING CHARACTERISTICS AND STRUCTURAL DYNAMICS

Structural Modeling

• Most realistic structural model would:

– All sources of stiffness of structure and soil foundation system

– Includes P‐Delta, geometric nonlinearity

– Material inelastic behavior in superstructure and foundation

• In typical design practice, “realistic modeling”:

– Is time consuming, rarely warranted for typical buildings in scope of ASCE 7‐10, Use R and Cd

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Linear Elastic Structural Modeling

• Defining building mass

• Effective stiffness of elements

• Determining damping assumptions

• Evaluating building period assumptions

Defining Building Mass

• Effective Seismic Weight (12.7.2)– Self‐weight

– Partition loads, 10 psf

• Storage, 25% Live Load

• Equipment weights

• Snow loads if > 30 psf and/or green roof

• lumped mass ‐ lateral mass only

• Distributed mass over Lumped Mass

• Hand calculation to verify assumptions

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Stiffness of Elements

• 3d‐models commonplace

• Effective stiffness of elements

• Wall stiffness modifiers

• Frame stiffness, panel zones

• Beam‐column joints

• Boundary conditions

– Consider practical aspects at structural base condition

How does Damping affect Response?

5% critical damping

20% critical damping

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Damping Assumptions

• Viscous vs. hysteretic damping

• Inherent Damping input for linear analysis viscous: 0.5% to 5% maximum

• Raleigh Damping (mass stiffness proportional damping matrix specified at two periods)

• Energy Dissipation Systems (additional) 10% to 40%

Building Period

• ASCE 7 Code Equation (12.8‐7)

• Cap on Ta, Cu*Ta

• Approximation: T = 0.1N, for frames

• Rational AnalysisREF: ASCE 7‐10

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STRUCTURAL DYNAMIC ANALYSIS:ELF, MRSA, LRHA

Analysis Goals

• Is to develop an understanding of the design and building behavior

• Meet acceptance criteria and code requirements

• Determine specific response parameters:

– Maximum Inter‐story Drift Demands

– Peak Floor Accelerations

– Maximum Element Force Demands

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Equations of Motion

REF: FEMA 751

ASCE 7 Analysis Procedure Selection

• Requirements for analysis vary depending on:

– Seismic Design Category

– Structural system

– Dynamic properties

– Building height (typically 160’+)

– Regularity

• Rational approach

– Assess (de‐) coupling between lateral and torsional

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ASCE 7 Table of Analysis Requirements

REF: ASCE 7‐10

ASCE Table of Irregularities

REF: ASCE 7‐10

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Equivalent Lateral Force ‐ ELF

• Linear static method intended to represent inelastic dynamic response of structures

• Structure SDOF, 100% Modal Mass in 1st Mode• Used in the Code as static forces that represent fundamental mode induced seismic forces

• ELF is best for:– Regular structures and preliminary analysis

• ELF is needed for:– Torsion and redundancy check (12.8.4, 12.3)– P‐Delta (12.8.7)– Scaling of MRSA, LRHA

Modal Response Spectrum Analysis

• MRSA: Structure decomposed in a number of SDOF systems w/ individual mode shape/period.

• Number of modes equal to mass degrees of Freedom. e.g. rigid diaphragms 3 DOF per Floor

• In each direction displacement of each mode is determined from spectral acceleration, modal participation, and mode shape

• Results defined by combining each mode

– Assumes peak acceleration at each period all at once

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REF: csi.berekely.edu

= + + +..

Mode 1T1 = 0.3 sM1 = 0.83

Mode 2T2 = 0.5 sM2 = 0.11

Mode 3T3 = 0.1 sM3 = 0.04


• Eigen Vectors or Ritz Vectors, Ritz Vectors are preferred

• Number of modes to include should be studied

• Rigid diaphragm assumption reduces DOF

• Recommend semi‐rigid diaphragms where applicable

• ASCE 7‐10 Requirements:– Mass Participation, 90% min

– Damping, 5% max

– Combining results for each mode• SRSS, square root sum of squares

• CQC, complete quadratic combination

Base Shear

# of modes included

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• Design spectral ordinates x Ie/R• Calculated Drifts x Cd/Ie• Equilibrium is not satisfied in results• Possible lower component actions• Can not use MRSA for calculating torsional irregularity, use ELF

• Foundation design ‐ results are positive values• MRSA gives better results than ELF for stories with different heights, stiffness, masses, and irregularities

Linear Response History Analysis

• LRHA is Direct Analysis or Direct Integration:

– Solving Equation of Motion at each time step

• Signs preserved for Moments, Forces, etc.

• Equilibrium Satisfied

• ASCE 7‐10 Requirements:

– Number of records, Scaling of records

– Results are maximum for each record or average

– Damping is 5% max

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Dynamic Analysis Summary

PRACTICAL CONSIDERATIONS FORSTRUCTURAL DYNAMIC ANALYSIS

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Base Shear Scaling• Scaling may be needed if:

– Period in model is longer than used to calculate V– Response is not characterized by a single mode– ELF base shear assumes 100% in first mode, which is an overestimate

• MRSA (12.9)– Where calculated V MRSA < 85% VELF

– Scale forces up to 85% VELF

• LRHA (16.1.4)– Same scaling for forces as MRSA.

• Coming changes from FEMA P1050 & ASCE 7‐16: – Scaling to 100% VELF REF: ASCE 7‐10,

FEMA‐1050

Displacement Scaling

• Scaling of Drifts is required when – VMRSA < 85% CsW, where Cs is Eq. 12.8‐6

• Scaling required is 85% * CsW / VMRSA

• MRSA Displacements are otherwise, “not scaled because of an overly flexible model results in conservative estimate of displacement.”

• Coming changes from FEMA P1050 & ASCE 7‐16: Scaling to 100% CsW

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Debugging Models

• Elastic modes consistent with expectations– Checking for spurious modes, Periods make sense?

• Debugging Mass

• For LRHA, Run Vertical Response History compare with expected Linear Static “Self Weight”

• Center of Mass (CoM), Center of Rigidity (CoR)– Review, understand, and track changes

Debugging Models

• Review Participation Factors, Periods, and look for coupling UX, UY, and Rotation Z

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• Troubleshooting of spurious modes…

Debugging Models

• Use program summary tables.

– Modifiers:

– Center of mass:

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Debugging Models

• Review Boundary Conditions; pinned, fixed

• Review diaphragm assumptions

• Recommendations:– Parametric and sensitivity studies

– One model: gravity and lateral

– Revision numbers for model files

– Use an analysis log to track major changes

– Review elastic displacement spectra

– Build your understanding and confidence of software tools with increasing complex models

CONCLUSIONS & REFERENCES

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Conclusions

• Dynamic analysis is a useful tool for seismic design if used correctly

• Even ELF design method can use a dynamic analysis to troubleshoot models

• Use engineering judgement, calibrate yourself

• Know what you want to get from your analysis

• Consider level of analysis required based on presumed complexity of behavior

References

• ASCE 7 and Expanded Commentary

• Steel AISC 341, Concrete ACI 318, Wood AF&PA SDPWS

• http://www.nehrp.gov/library/guidance.htm– NIST / NEHRP / ATC GCR Reports

– NEHRP Tech Briefs

• FEMA 451 – Design Examples

• FEMA P‐1050 – NEHRP Provisions 2015

• SEAOC Blue Book and Seismic Design Manuals

• Chopra, Dynamics of Structures

• Wilson, 3d Static and Dynamic Analysis of Structures

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Thank You!

Send questions, comments, suggestions:

[email protected]

Documents

Introduction to Building Structural Dynamics for Seismic