# Design of Structures for Earthquake Resistance

Size: px
Start display at page:

Transcription

1 NATIONAL TECHNICAL UNIVERSITY OF ATHENS Design of Structures for Earthquake Resistance Basic principles Ioannis N. Psycharis Lecture 3

2 MDOF systems Equation of motion M u + C u + K u = M r x g(t) where: M = mass matrix C = damping matrix K = stiffness matrix r = earthquake direction vector

3 Natural modes Eigenfrequencies They are derived from the solution of the characteristic equation: K ω 2 M = 0 Eigenvectors They are derived from the solution of the system of equations: where: K ω 2 M φ i = 0 φ i = i th eigenvector φ ji = j th component of i th eigenvector

4 Properties Orthogonality φ Τ i M φ j = 0 for i j φ Τ i K φ j = 0 for i j Generalized mass m i = φ Τ i M φ i Generalized stiffness k i = φ Τ i K φ i It can be shown that k i = m i ω 2

5 Free vibrations For arbitrary initial displacements (From Chopra, AK, Dynamics of Structures, EERI)

6 Free vibrations For initial displacements according to 1 st mode (From Chopra, AK, Dynamics of Structures, EERI)

7 Free vibrations For initial displacements according to 2 nd mode (From Chopra, AK, Dynamics of Structures, EERI)

8 Free vibrations For initial displacements according to 3 rd mode (From Chopra, AK, Dynamics of Structures, EERI)

9 Modal analysis Displacement at the j th degree of freedom: u j (t) = N n=1 u jn (t) where u jn is the displacement of the j th degree of freedom that corresponds to the n th mode. Response of n th mode: u jn (t) = Y n t φ jn Yn + 2ζ n ω n Y n + ω n 2 Y n = Γ n x g where Γ n is the participation factor of the n th mode: Γ n = φ i Τ M r φ i Τ M φ i

10 Modal analysis x g(t) u jn (t) = Y n t φ jn Yn + 2ζ n ω n Y n + ω n 2 Y n = Γ n x g (From Chopra, AK, Dynamics of Structures, EERI)

11 Use of response spectra Maximum displacement of the n th mode at the j th degree of freedom: max u jn = Γ n S d T n, ζ n φ jn T n, ζ n is the spectral displacement that where S d corresponds to period T n and damping ζ n. Maximum seismic force of the n th mode at the j th degree of freedom: max F jn = Γ n S a,d T n, ζ n m j φ jn T n, ζ n is the design spectral acceleration where S a,d that corresponds to period T n and damping ζ n.

12 Combination of modal responses Significant modes k < N k n=1 M n 0.90 m tot where M n is the effective mass of the n th mode: M n = Γ n φ n Τ M r The effective mass of each mode depends on the direction of the seismic action.

13 Combination of modal responses Let A n, A m be the maximum value of a quantity A (internal force or displacement) of the n th and the m th mode respectively. SRSS k maxa = ± A n 2 CQC n=1 k k maxa = ± ε nm A n A m n=1 m=1 ε nm = 8 ζ 2 1+r r 3/2 1 r ζ 2 r 1+r 2 with r = T n T m

14 Simplified formulas For planar motion in the plane of the seismic action and for the n th mode: Γ n = N j=1 N j=1 m j φ jn 2 m j φ jn M n = Γ n N j=1 m j φ jn

15 Design procedure Define structural properties Compute mass and stiffness matrices M and K Estimate modal damping coefficients ζ n Solve the eigen-problem to determine the k lower natural frequencies ω n and modes φ n Compute the corresponding natural periods T n = 2π ω n For a given direction of the seismic action: Compute the participation factors Γ n Compute effective modal masses M n and check that their sum is larger than 90% of the total mass. If not, increase the value of k and repeat the procedure

16 Design procedure For a given direction of the seismic action, compute the maximum response for each mode n by repeating the following steps: On the design response spectrum read the spectral acceleration S a,d that corresponds to period T n and damping ζ n Compute the seismic force F j,n at each degree of freedom j Perform static analysis of the structure subjected to forces F j,n and determine internal forces and displacements Combine the modal responses using SRSS or CQC for each direction of the seismic action

17 Spatial combination Let A x, A y, A z be the estimated maximum values of a quantity A that correspond to two horizontal orthogonal directions x, y and the vertical direction z of the seismic action. The maximum value of A for simultaneous action of the earthquake in all directions x, y, z can be estimated as: 1 st Method A = ± A x 2 + A y 2 + A z 2 2 nd Method A = ±A x ± 0.3A y ± 0.3A z A = ±0.3A x ± A y ± 0.3A z or or A = ±0.3A x ± 0.3A y ± A z

18 Remarks For typical buildings, the vertical component of the seismic action can be neglected. Displacements If d E are the displacements from the above analysis, the actual displacements are calculated as d = q d E where q is the value of the behavior factor used in the design response spectrum. The elastic response of a structure to a specific earthquake can also be computed using the above procedure by substituting the design response spectrum with the elastic spectrum of the ground motion.

### Design of Earthquake-Resistant Structures

NATIONAL TECHNICAL UNIVERSITY OF ATHENS LABORATORY OF EARTHQUAKE ENGINEERING Design of Earthquake-Resistant Structures Basic principles Ioannis N. Psycharis Basic considerations Design earthquake: small

### Codal Provisions IS 1893 (Part 1) 2002

Abstract Codal Provisions IS 1893 (Part 1) 00 Paresh V. Patel Assistant Professor, Civil Engineering Department, Nirma Institute of Technology, Ahmedabad 38481 In this article codal provisions of IS 1893

### 3. MDOF Systems: Modal Spectral Analysis

3. MDOF Systems: Modal Spectral Analysis Lesson Objectives: 1) Construct response spectra for an arbitrarily varying excitation. 2) Compute the equivalent lateral force, base shear, and overturning moment

### Structural Dynamics Lecture 7. Outline of Lecture 7. Multi-Degree-of-Freedom Systems (cont.) System Reduction. Vibration due to Movable Supports.

Outline of Multi-Degree-of-Freedom Systems (cont.) System Reduction. Truncated Modal Expansion with Quasi-Static Correction. Guyan Reduction. Vibration due to Movable Supports. Earthquake Excitations.

### Chapter 4 Analysis of a cantilever

Chapter 4 Analysis of a cantilever Before a complex structure is studied performing a seismic analysis, the behaviour of simpler ones should be fully understood. To achieve this knowledge we will start

### FREE VIBRATION RESPONSE OF UNDAMPED SYSTEMS

Lecture Notes: STRUCTURAL DYNAMICS / FALL 2011 / Page: 1 FREE VIBRATION RESPONSE OF UNDAMPED SYSTEMS : : 0, 0 As demonstrated previously, the above Equation of Motion (free-vibration equation) has a solution

### RESPONSE SPECTRUM METHOD FOR ESTIMATION OF PEAK FLOOR ACCELERATION DEMAND

RESPONSE SPECTRUM METHOD FOR ESTIMATION OF PEAK FLOOR ACCELERATION DEMAND Shahram Taghavi 1 and Eduardo Miranda 2 1 Senior catastrophe risk modeler, Risk Management Solutions, CA, USA 2 Associate Professor,

University of California at Berkeley Structural Engineering Mechanics & Materials Department of Civil & Environmental Engineering Spring 2012 Student name : Doctoral Preliminary Examination in Dynamics

### STATIC NONLINEAR ANALYSIS. Advanced Earthquake Engineering CIVIL-706. Instructor: Lorenzo DIANA, PhD

STATIC NONLINEAR ANALYSIS Advanced Earthquake Engineering CIVIL-706 Instructor: Lorenzo DIANA, PhD 1 By the end of today s course You will be able to answer: What are NSA advantages over other structural

### Missing Mass in Dynamic Analysis

Missing Mass in Dynamic Analysis Introduction: The common practice of performing a dynamic analysis of a structure is to evaluate the response of a structure mode by mode and then combining the results

### Seismic Analysis of Structures Prof. T.K. Datta Department of Civil Engineering Indian Institute of Technology, Delhi

Seismic Analysis of Structures Prof. T.K. Datta Department of Civil Engineering Indian Institute of Technology, Delhi Lecture - 20 Response Spectrum Method of Analysis In the last few lecture, we discussed

### Dynamics of Structures

Dynamics of Structures Elements of structural dynamics Roberto Tomasi 11.05.2017 Roberto Tomasi Dynamics of Structures 11.05.2017 1 / 22 Overview 1 SDOF system SDOF system Equation of motion Response spectrum

### 1. Multiple Degree-of-Freedom (MDOF) Systems: Introduction

1. Multiple Degree-of-Freedom (MDOF) Systems: Introduction Lesson Objectives: 1) List examples of MDOF structural systems and state assumptions of the idealizations. 2) Formulate the equation of motion

### SHOCK RESPONSE OF MULTI-DEGREE-OF-FREEDOM SYSTEMS Revision F By Tom Irvine May 24, 2010

SHOCK RESPONSE OF MULTI-DEGREE-OF-FREEDOM SYSTEMS Revision F By Tom Irvine Email: tomirvine@aol.com May 4, 010 Introduction The primary purpose of this tutorial is to present the Modal Transient method

### Dr.Vinod Hosur, Professor, Civil Engg.Dept., Gogte Institute of Technology, Belgaum

STRUCTURAL DYNAMICS Dr.Vinod Hosur, Professor, Civil Engg.Dept., Gogte Institute of Technology, Belgaum Overview of Structural Dynamics Structure Members, joints, strength, stiffness, ductility Structure

### Control of Earthquake Induced Vibrations in Asymmetric Buildings Using Passive Damping

Control of Earthquake Induced Vibrations in Asymmetric Buildings Using Passive Damping Rakesh K. Goel, California Polytechnic State University, San Luis Obispo Abstract This paper summarizes the results

### BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE, Pilani Pilani Campus

First Semester 2017-2018 Instruction Division Course Handout (Part II) Date: 02/08/2017 In addition to Part I (General Handout for all courses appended to the Time Table), this portion gives further specific

### Problem 1: A simple 3-dof shear-building model has the following equation: =

MEEN 6 E: Normalization and Damped Response Fall 24 Problem : A simple -dof shear-building model has the following equation: m u k+ k2 k2 u p( t) m u k k k k + + u = p ( t) 2 2 2 2 2 2 m u k k u p( t)

### midas Civil Dynamic Analysis

Edgar De Los Santos Midas IT August 23 rd 2017 Contents: Introduction Eigen Value Analysis Response Spectrum Analysis Pushover Analysis Time History Analysis Seismic Analysis Seismic Analysis The seismic

Dynamic Analysis Using Response Spectrum Seismic Loading Paleti Teja M.Tech (Structural Engineering) Department of Civil Engineering Jogaiah Institute of Technology & Sciences College of Engineering Kalagampudi,

### DEPENDENCE OF ACCIDENTAL TORSION ON STRUCTURAL SYSTEM PROPERTIES

th World Conference on Earthquake Engineering Vancouver, B.C., Canada August -6, 4 Paper No. 6 DEPENDENCE OF ACCIDENTAL TORSION ON STRUCTURAL SYSTEM PROPERTIES Julio J. HERNÁNDEZ and Oscar A. LÓPEZ SUMMARY

### 3. Mathematical Properties of MDOF Systems

3. Mathematical Properties of MDOF Systems 3.1 The Generalized Eigenvalue Problem Recall that the natural frequencies ω and modes a are found from [ - ω 2 M + K ] a = 0 or K a = ω 2 M a Where M and K are

### Structural Dynamics Lecture 4. Outline of Lecture 4. Multi-Degree-of-Freedom Systems. Formulation of Equations of Motions. Undamped Eigenvibrations.

Outline of Multi-Degree-of-Freedom Systems Formulation of Equations of Motions. Newton s 2 nd Law Applied to Free Masses. D Alembert s Principle. Basic Equations of Motion for Forced Vibrations of Linear

### ANALYSIS OF HIGHRISE BUILDING STRUCTURE WITH SETBACK SUBJECT TO EARTHQUAKE GROUND MOTIONS

ANALYSIS OF HIGHRISE BUILDING SRUCURE WIH SEBACK SUBJEC O EARHQUAKE GROUND MOIONS 157 Xiaojun ZHANG 1 And John L MEEK SUMMARY he earthquake response behaviour of unframed highrise buildings with setbacks

### Introduction to structural dynamics

Introduction to structural dynamics p n m n u n p n-1 p 3... m n-1 m 3... u n-1 u 3 k 1 c 1 u 1 u 2 k 2 m p 1 1 c 2 m2 p 2 k n c n m n u n p n m 2 p 2 u 2 m 1 p 1 u 1 Static vs dynamic analysis Static

### Preliminary Examination in Dynamics

Fall Semester 2017 Problem 1 The simple structure shown below weighs 1,000 kips and has a period of 1.25 sec. It has no viscous damping. It is subjected to the impulsive load shown in the figure. If the

### Preliminary Examination - Dynamics

Name: University of California, Berkeley Fall Semester, 2018 Problem 1 (30% weight) Preliminary Examination - Dynamics An undamped SDOF system with mass m and stiffness k is initially at rest and is then

### Seismic Design of Tall and Slender Structures Including Rotational Components of the Ground Motion: EN Approach

Seismic Design of Tall and Slender Structures Including Rotational Components of the Ground Motion: EN 1998-6 6 Approach 1 Chimneys Masts Towers EN 1998-6: 005 TOWERS, CHIMNEYS and MASTS NUMERICAL MODELS

### Stochastic Dynamics of SDOF Systems (cont.).

Outline of Stochastic Dynamics of SDOF Systems (cont.). Weakly Stationary Response Processes. Equivalent White Noise Approximations. Gaussian Response Processes as Conditional Normal Distributions. Stochastic

### Response Analysis for Multi Support Earthquake Excitation

Chapter 5 Response Analysis for Multi Support Earthquake Excitation 5.1 Introduction It is very important to perform the dynamic analysis for the structure subjected to random/dynamic loadings. The dynamic

### Seismic design of bridges

NAIONAL ECHNICAL UNIVERSIY OF AHENS LABORAORY FOR EARHQUAKE ENGINEERING Seismic design of bridges Lecture 4 Ioannis N. Psycharis Seismic isolation of bridges I. N. Psycharis Seismic design of bridges 2

### Secondary Response Spectra

Task NA 3.6 Preparatory Course on Seismic Qualification Bristol, 11-12 January 2011 Secondary Response Spectra Prof. Colin Taylor, University of Bristol Paul Johnston, Atkins Scope Response spectra Modelling

### on the figure. Someone has suggested that, in terms of the degrees of freedom x1 and M. Note that if you think the given 1.2

1) A two-story building frame is shown below. The mass of the frame is assumed to be lumped at the floor levels and the floor slabs are considered rigid. The floor masses and the story stiffnesses are

### INELASTIC SEISMIC DISPLACEMENT RESPONSE PREDICTION OF MDOF SYSTEMS BY EQUIVALENT LINEARIZATION

INEASTIC SEISMIC DISPACEMENT RESPONSE PREDICTION OF MDOF SYSTEMS BY EQUIVAENT INEARIZATION M. S. Günay 1 and H. Sucuoğlu 1 Research Assistant, Dept. of Civil Engineering, Middle East Technical University,

### Reduction in number of dofs

Reduction in number of dofs Reduction in the number of dof to represent a structure reduces the size of matrices and, hence, computational cost. Because a subset of the original dof represent the whole

### Selection of Rayleigh Damping Coefficients for Seismic Response Analysis of Soil Layers

Selection of Rayleigh Damping Coefficients for Seismic Response Analysis of Soil Layers Huai-Feng Wang, Meng-Lin Lou, Ru-Lin Zhang Abstract One good analysis method in seismic response analysis is direct

### Effects of Damping Ratio of Restoring force Device on Response of a Structure Resting on Sliding Supports with Restoring Force Device

Effects of Damping Ratio of Restoring force Device on Response of a Structure Resting on Sliding Supports with Restoring Force Device A. Krishnamoorthy Professor, Department of Civil Engineering Manipal

### Lecture 4 Dynamic Analysis of Buildings

1 Lecture 4 Dynamic Analysis of Buildings Course Instructor: Dr. Carlos E. Ventura, P.Eng. Department of Civil Engineering The University of British Columbia ventura@civil.ubc.ca Short Course for CSCE

### Chapter 2: Rigid Bar Supported by Two Buckled Struts under Axial, Harmonic, Displacement Excitation..14

Table of Contents Chapter 1: Research Objectives and Literature Review..1 1.1 Introduction...1 1.2 Literature Review......3 1.2.1 Describing Vibration......3 1.2.2 Vibration Isolation.....6 1.2.2.1 Overview.

### CHAPTER 7 EARTHQUAKE RESPONSE OF INELASTIC SYSTEMS. Base shear force in a linearly elastic system due to ground excitation is Vb

CHAPTER 7 EARTHQUAKE RESPONSE OF INELASTIC SYSTEMS Base shear force in a linearl elastic sstem due to ground excitation is Vb = ( A/ g) w where A is the pseudo-acceleration corresponding to natural period

### In-Structure Response Spectra Development Using Complex Frequency Analysis Method

Transactions, SMiRT-22 In-Structure Response Spectra Development Using Complex Frequency Analysis Method Hadi Razavi 1,2, Ram Srinivasan 1 1 AREVA, Inc., Civil and Layout Department, Mountain View, CA

### Multi Degrees of Freedom Systems

Multi Degrees of Freedom Systems MDOF s http://intranet.dica.polimi.it/people/boffi-giacomo Dipartimento di Ingegneria Civile Ambientale e Territoriale Politecnico di Milano March 9, 07 Outline, a System

### International Journal of Advance Engineering and Research Development

Scientific Journal of Impact Factor (SJIF): 4.72 International Journal of Advance Engineering and Research Development Volume 4, Issue 11, November -2017 e-issn (O): 2348-4470 p-issn (P): 2348-6406 Study

### ANALYSIS OF ORDINARY BRIDGES CROSSING FAULT-RUPTURE ZONES

ANALYSIS OF ORDINARY BRIDGES CROSSING FAULT-RUPTURE ZONES R.K. Goel and A.K. Chopra 2 Professor, Dept. of Civil & Environmental Engineering, California Polytechnic State University, San Luis Obispo, California,

### Damping Matrix. Donkey2Ft

1 Damping Matrix DonkeyFt Damping in a single-degree-of-freedom (SDOF) system is well studied. Whether the system is under-damped, over-damped, or critically damped is well known. For an under-damped system,

### Effects of damping matrix in the response of structures with added linear viscous dampers

Effects of damping matrix in the response of structures with added linear viscous dampers J.R. Arroyo', J. Marte2 l Department of General Engineering, University of Puerto Rico, Mayagiiez Campus 'Department

### Alireza Mehdipanah BEHAVIOUR OF BUILDINGS FEATURING TRANSFER BEAMS IN THE REGIONS OF LOW TO MODERATE SEISMICITY

BEHAVIOUR OF BUILDINGS FEATURING TRANSFER BEAMS IN THE REGIONS OF LOW TO MODERATE SEISMICITY Alireza Mehdipanah PhD Candidate at The University of Melbourne SUPERVISORS: A/PROF. NELSON LAM DR. ELISA LUMANTARNA

### Stochastic Structural Dynamics Prof. Dr. C. S. Manohar Department of Civil Engineering Indian Institute of Science, Bangalore

Stochastic Structural Dynamics Prof. Dr. C. S. Manohar Department of Civil Engineering Indian Institute of Science, Bangalore Lecture No. # 33 Probabilistic methods in earthquake engineering-2 So, we have

### THREE-DIMENSIONAL CRITICAL SEISMIC GROUND ACCELERATION TIME HISTORIES FOR HIGH-TECH FACILITIES

4th International Conference on Earthquake Engineering Taipei, Taiwan October 2-3, 26 Paper No. 79 THREE-DIMENSIONAL CRITICAL SEISMIC GROUND ACCELERATION TIME HISTORIES FOR HIGH-TECH FACILITIES You-Lin

### Earthquake design for controlled structures

Focussed on Recent advances in Experimental Mechanics of Materials in Greece Earthquake design for controlled structures Nikos G. Pnevmatikos Technological Educational Institution of Athens, Greece pnevma@teiath.gr

### Advanced Vibrations. Elements of Analytical Dynamics. By: H. Ahmadian Lecture One

Advanced Vibrations Lecture One Elements of Analytical Dynamics By: H. Ahmadian ahmadian@iust.ac.ir Elements of Analytical Dynamics Newton's laws were formulated for a single particle Can be extended to

### 2C9 Design for seismic and climate changes. Jiří Máca

2C9 Design for seismic and climate changes Jiří Máca List of lectures 1. Elements of seismology and seismicity I 2. Elements of seismology and seismicity II 3. Dynamic analysis of single-degree-of-freedom

### Static & Dynamic. Analysis of Structures. Edward L.Wilson. University of California, Berkeley. Fourth Edition. Professor Emeritus of Civil Engineering

Static & Dynamic Analysis of Structures A Physical Approach With Emphasis on Earthquake Engineering Edward LWilson Professor Emeritus of Civil Engineering University of California, Berkeley Fourth Edition

### MODAL ANALYSIS OF PLANE FRAMES

MODAL ANALYSIS OF PLANE FRAMES Mr. Mohammed Siraj Professor, Department of Civil Engineering, Deogiri Institute of Engineering and Management Studies Aurangabad, M.S, India. ABSTRACT In the modal analysis

### Contents i. Contents

Contents i Contents 7 SEISMIC LOADS Commentary 7. Estimation of Seismic Loads.............................. 7.. Seismic load and design earthquake motion.................. 4 7..2 Idealization of building

### Numerical Solution of Equation of Motion

Class Notes: Earthquake Engineering, Ahmed Elgamal, September 25, 2001 (DRAFT) Numerical Solution of Equation of Motion Average Acceleration Method (Trapezoidal method) m a + c v + k d = f (t) In the above

### Modal analysis of shear buildings

Modal analysis of shear buildings A comprehensive modal analysis of an arbitrary multistory shear building having rigid beams and lumped masses at floor levels is obtained. Angular frequencies (rad/sec),

### Seismic Performance of RC Building Using Spectrum Response and Pushover Analyses

Seismic Performance of RC Building Using Spectrum Response and Pushover Analyses Mehani Youcef (&), Kibboua Abderrahmane, and Chikh Benazouz National Earthquake Engineering Research Center (CGS), Algiers,

### Seismic design of bridges

NATIONAL TECHNICAL UNIVERSITY OF ATHENS LABORATORY FOR EARTHQUAKE ENGINEERING Seismic design of bridges Lecture 3 Ioannis N. Psycharis Capacity design Purpose To design structures of ductile behaviour

### A MODIFIED RESPONSE SPECTRUM METHOD FOR ESTIMATING PEAK FLOOR ACCELERATION DEMANDS IN ELASTIC REGULAR FRAME STRUCTURES

A MODIFIED RESPONSE SPECRUM MEHOD FOR ESIMAING PEAK FLOOR ACCELERAION DEMANDS IN ELASIC REGULAR FRAME SRUCURES Lukas MOSCHEN 1, Dimitrios VAMVASIKOS 2 and Christoph ADAM 3 ABSRAC In this paper an extended

### DYNAMIC RESPONSE OF EARTHQUAKE EXCITED INELASTIC PRIMARY- SECONDARY SYSTEMS

DYNAMIC RESPONSE OF EARTHQUAKE EXCITED INELASTIC PRIMARY- SECONDARY SYSTEMS Christoph ADAM 1 And Peter A FOTIU 2 SUMMARY The objective of the paper is to investigate numerically the effect of ductile material

CE 543 Structural Dynamics Introduction Dynamic Loads Dynamic loads are time-varying loads. (But time-varying loads may not require dynamic analysis.) Dynamics loads can be grouped in one of the following

### Structural Dynamics Lecture Eleven: Dynamic Response of MDOF Systems: (Chapter 11) By: H. Ahmadian

Structural Dynamics Lecture Eleven: Dynamic Response of MDOF Systems: (Chapter 11) By: H. Ahmadian ahmadian@iust.ac.ir Dynamic Response of MDOF Systems: Mode-Superposition Method Mode-Superposition Method:

### Dynamic Response of Structures With Frequency Dependent Damping

Dynamic Response of Structures With Frequency Dependent Damping Blanca Pascual & S Adhikari School of Engineering, Swansea University, Swansea, UK Email: S.Adhikari@swansea.ac.uk URL: http://engweb.swan.ac.uk/

### CAPACITY SPECTRUM FOR STRUCTURES ASYMMETRIC IN PLAN

13 th World Conference on Earthquake Engineering Vancouver, B.C., Canada August 1-6, 004 Paper No. 653 CAPACITY SPECTRUM FOR STRUCTURES ASYMMETRIC IN PLAN B. K. Raghu Prasad 1, A. Seetha Ramaiah and A.

### Application of Capacity Spectrum Method to timber houses considering shear deformation of horizontal frames

Application of Capacity Spectrum Method to timber houses considering shear deformation of horizontal frames Kawai, N. 1 ABSTRACT Relating to the revision of Building Standard Law of Japan, the application

### Dynamics of Structures: Theory and Analysis

1. Free vibrations 2. Forced vibrations 3. Transient response 4. Damping mechanisms Dynamics of Structures: Theory and Analysis Steen Krenk Technical University of Denmark 5. Modal analysis I: Basic idea

### Finite Element Analysis Lecture 1. Dr./ Ahmed Nagib

Finite Element Analysis Lecture 1 Dr./ Ahmed Nagib April 30, 2016 Research and Development Mathematical Model Mathematical Model Mathematical Model Finite Element Analysis The linear equation of motion

### Design Spectra. Reading Assignment Course Information Lecture Notes Pp Kramer Appendix B7 Kramer

Design Spectra Page 1 Design Spectra Reading Assignment Course Information Lecture Notes Pp. 73-75 Kramer Appendix B7 Kramer Other Materials Responsespectra.pdf (Chopra) ASCE 7-05.pdf Sakaria time history

### Identification Methods for Structural Systems. Prof. Dr. Eleni Chatzi Lecture March, 2016

Prof. Dr. Eleni Chatzi Lecture 4-09. March, 2016 Fundamentals Overview Multiple DOF Systems State-space Formulation Eigenvalue Analysis The Mode Superposition Method The effect of Damping on Structural

### SEISMIC PERFORMANCE ESTIMATION OF ASYMMETRIC BUILDINGS BASED ON THE CAPACITY SPECTRUM METHOD

SEISMIC PERFORMACE ESTIMATIO OF ASYMMETRIC BUILDIGS BASED O THE CAPACITY SPECTRUM METHOD Tatsuya AZUHATA, Taiki SAITO, Masaharu TAKAYAMA And Katsumi AGAHARA 4 SUMMARY This paper presents the procedure

### Seismic Design of Slender Structures Including Rotational Components of the Ground Acceleration Eurocode 8 Approach

Seismic Design of Slender Structures Including Rotational Components of the Ground Acceleration Eurocode 8 Approach Z. Bonev E. Vaseva D. Blagov K. Mladenov 1 Chimneys Masts Towers 2 EN 1998-6: 2005 TOWERS,

### COMPARATIVE STUDIES ON SEISMIC INCOHERENT SSI ANALYSIS METHODOLOGIES

Transactions, SMiRT-22 COMPARATIVE STUDIES ON SEISMIC INCOHERENT SSI ANALYSIS METHODOLOGIES Dan M. Ghiocel 1 1 Ghiocel Predictive Technologies, Inc., Rochester, New Yor, USA (dan.ghiocel@ghiocel-tech.com)

### Pushover Seismic Analysis of Bridge Structures

Pushover Seismic Analysis of Bridge Structures Bernardo Frère Departamento de Engenharia Civil, Arquitectura e Georrecursos, Instituto Superior Técnico, Technical University of Lisbon, Portugal October

### EVALUATION OF SEISMIC ACTION IN SWEDEN USING THE EUROPEAN SEISMIC HAZARD MODEL. Structural Mechanics. Master s Dissertation

EVALUATION OF SEISMIC ACTION IN SWEDEN USING THE EUROPEAN SEISMIC HAZARD MODEL ERIK LARSSON and LUCAS MAGNUSSON Structural Mechanics Master s Dissertation DEPARTMENT OF CONSTRUCTION SCIENCES DIVISION

### CE6701 STRUCTURAL DYNAMICS AND EARTHQUAKE ENGINEERING QUESTION BANK UNIT I THEORY OF VIBRATIONS PART A

CE6701 STRUCTURAL DYNAMICS AND EARTHQUAKE ENGINEERING QUESTION BANK UNIT I THEORY OF VIBRATIONS PART A 1. What is mean by Frequency? 2. Write a short note on Amplitude. 3. What are the effects of vibration?

### NATURAL MODES OF VIBRATION OF BUILDING STRUCTURES CE 131 Matrix Structural Analysis Henri Gavin Fall, 2006

NATURAL MODES OF VIBRATION OF BUILDING STRUCTURES CE 131 Matrix Structural Analysis Henri Gavin Fall, 006 1 Mass and Stiffness Matrices Consider a building frame modeled by a set of rigid, massive flos

### VERIFYING THE LOCATION OF THE OPTIMUM TORSION AXIS OF MULTI-STORY BUILDINGS USING DYNAMIC ANALYSIS

13 th World Conference on Earthquake Engineering Vancouver, B.C., Canada August 1-6, 004 Paper No. 833 VERIFYING THE LOCATION OF THE OPTIMUM TORSION AXIS OF MULTI-STORY BUILDINGS USING DYNAMIC ANALYSIS

### Response Spectrum Analysis Shock and Seismic. FEMAP & NX Nastran

Response Spectrum Analysis Shock and Seismic FEMAP & NX Nastran Table of Contents 1. INTRODUCTION... 3 2. THE ACCELEROGRAM... 4 3. CREATING A RESPONSE SPECTRUM... 5 4. NX NASTRAN METHOD... 8 5. RESPONSE

### The Comparative Analysis of Methods for Calculation of Buildings With Rubber Bearings

The Comparative Analysis of Methods for Calculation of Buildings With Rubber Bearings Andrey Y. Yun, Earthquake Engineering Research Center, TsNIISK, Moscow Alexander A. Bubis Earthquake Engineering Research

### SEISMIC RESPONSE EVALUATION OF AN RC BEARING WALL BY DISPLACEMENT-BASED APPROACH

3 th World Conference on Earthquake Engineering Vancouver, B.C., Canada August -, 4 Paper No. 49 SEISMIC RESPONSE EVALUATION OF AN RC BEARING WALL BY DISPLACEMENT-BASED APPROACH Chang-Hun HYUN, Sanghyun

### Nonlinear static analysis PUSHOVER

Nonlinear static analysis PUSHOVER Adrian DOGARIU European Erasmus Mundus Master Course Sustainable Constructions under Natural Hazards and Catastrophic Events 520121-1-2011-1-CZ-ERA MUNDUS-EMMC Structural

### APPLICATION OF RESPONSE SPECTRUM METHOD TO PASSIVELY DAMPED DOME STRUCTURE WITH HIGH DAMPING AND HIGH FREQUENCY MODES

3 th World Conference on Earthquake Engineering Vancouver, B.C., Canada August -6, 4 Paper No. 5 APPLICATION OF RESPONSE SPECTRUM METHOD TO PASSIVELY DAMPED DOME STRUCTURE WITH HIGH DAMPING AND HIGH FREQUENCY

### Structural Dynamics A Graduate Course in Aerospace Engineering

Structural Dynamics A Graduate Course in Aerospace Engineering By: H. Ahmadian ahmadian@iust.ac.ir The Science and Art of Structural Dynamics What do all the followings have in common? > A sport-utility

### Session 2: MDOF systems

BRUFACE Vibrations and Acoustics MA Academic year 7-8 Cédric Dumoulin (cedumoul@ulb.ac.be) Arnaud Deraemaeker (aderaema@ulb.ac.be) Session : MDOF systems Exercise : Multiple DOFs System Consider the following

### BI-DIRECTIONAL SEISMIC ANALYSIS AND DESIGN OF BRIDGE STEEL TRUSS PIERS ALLOWING A CONTROLLED ROCKING RESPONSE

Proceedings of the 8 th U.S. National Conference on Earthquake Engineering April 18-22, 2006, San Francisco, California, USA Paper No. 1954 BI-DIRECTIONAL SEISMIC ANALYSIS AND DESIGN OF BRIDGE STEEL TRUSS

### A STUDY ON IMPROVEMENT OF PUSHOVER ANALYSIS

A SUDY ON IMPROVEMEN OF PUSHOVER ANALYSIS Pu YANG And Yayong WANG SUMMARY he static pushover analysis, POA, is becoming popular as a simplified computer method for seismic performance evaluation of structures.

### SPECIAL DYNAMIC SOIL- STRUCTURE ANALYSIS PROCEDURES DEMONSTATED FOR TWO TOWER-LIKE STRUCTURES

2010/2 PAGES 1 8 RECEIVED 21. 9. 2009 ACCEPTED 20. 1. 2010 Y. KOLEKOVÁ, M. PETRONIJEVIĆ, G. SCHMID SPECIAL DYNAMIC SOIL- STRUCTURE ANALYSIS PROCEDURES DEMONSTATED FOR TWO TOWER-LIKE STRUCTURES ABSTRACT

### EXAMPLE OF PILED FOUNDATIONS

EXAMPLE OF PILED FOUNDATIONS The example developed below is intended to illustrate the various steps involved in the determination of the seismic forces developed in piles during earthquake shaking. The

### Structural Matrices in MDOF Systems

in MDOF Systems http://intranet.dica.polimi.it/people/boffi-giacomo Dipartimento di Ingegneria Civile Ambientale e Territoriale Politecnico di Milano April 9, 2016 Outline Additional Static Condensation

### 2C09 Design for seismic and climate changes

2C09 Design for seismic and climate changes Lecture 08: Seismic response of SDOF systems Aurel Stratan, Politehnica University of Timisoara 13/03/2014 European Erasmus Mundus Master Course Sustainable

### Geotechnical Earthquake Engineering

Geotechnical Earthquake Engineering by Dr. Deepankar Choudhury Professor Department of Civil Engineering IIT Bombay, Powai, Mumbai 400 076, India. Email: dc@civil.iitb.ac.in URL: http://www.civil.iitb.ac.in/~dc/

### A Nonlinear Static (Pushover) Procedure Consistent with New Zealand Standards

A Nonlinear Static (Pushover) Procedure Consistent with New Zealand Standards B. J. Davidson Compusoft Engineering Ltd, Auckland, New Zealand. 010 NZSEE Conference ABSTRACT: The Nonlinear Static Procedure,

### EQ Ground Motions. Strong Ground Motion and Concept of Response Spectrum. March Sudhir K Jain, IIT Gandhinagar. Low Amplitude Vibrations

Amplitude Strong Ground Motion and Concept of Response Spectrum March 2013 Sudhir K Jain, IIT Gandhinagar Sudhir K. Jain March 2013 1 EQ Ground Motions Low Amplitude Vibrations Long distance events Usually

### Comparative study between the push-over analysis and the method proposed by the RPA for the evaluation of seismic reduction coefficient

33, Issue (27) 5-23 Journal of Advanced Research in Materials Science Journal homepage: www.akademiabaru.com/arms.html ISSN: 2289-7992 Comparative study between the push-over analysis and the method proposed

### AA242B: MECHANICAL VIBRATIONS

AA242B: MECHANICAL VIBRATIONS 1 / 50 AA242B: MECHANICAL VIBRATIONS Undamped Vibrations of n-dof Systems These slides are based on the recommended textbook: M. Géradin and D. Rixen, Mechanical Vibrations:

### NON-ITERATIVE EQUIVALENT LINEAR METHOD FOR DISPLACEMENT-BASED DESIGN

13 th World Conference on Earthquae Engineering Vancouver, B.C., Canada August 1-6, 24 Per No. 3422 NON-ITERATIVE EQUIVALENT LINEAR METHOD FOR DISPLACEMENT-BASED DESIGN Eduardo MIRANDA 1, Yu-Yuan LIN 2