Dynamic Analysis of Structures reflects the latest application of structural dynamics theory to produce more optimal and economical structural designs. Written by an author with over 37 years of researching, teaching and writing experience, this reference introduces complex structural dynamics concepts in a user-friendly manner. The author includes carefully worked-out examples which are solved utilizing more recent numerical methods. These examples pave the way to more accurately simulate the behavior of various types of structures. The essential topics covered include principles of structural dynamics applied to particles, rigid and deformable bodies, thus enabling the formulation of equations for the motion of any structure.
Preface
General concepts and principles of structural dynamics
Chapter outline
Introduction
Types of dynamic loads
Dynamic degrees of freedom
Dynamic model and formulation of the equation of motion of SDOF systems
Derivation of the equations of motion using dAlemberts principle
Principle of virtual displacements
Hamiltons principle
Lagranges equations
Derivation of Lagranges equations
Lagrange multipliers
Small displacements
Potential energy and stiffness matrix
Kinetic energy and mass matrix
Raleighs dissipation function
Influence of the gravity loads
Problems
References and further reading
Single-degree-of-freedom systems: Free vibrations
Chapter outline
Introduction
Free undamped vibrations
Free damped vibrations
Critically damped system
Underdamped system
Overdamped system
Conservation of energy in an undamped system
Problems
References and further reading
Chapter 3: Single-degree-of-freedom systems: Forced vibrations
3.1. Introduction
3.2. Response to harmonic loading
3.2.1. Response of undamped systems to harmonic loading
3.2.2. Response of damped systems to harmonic loading
3.3. Response to arbitrary dynamic loading-Duhamels integral
3.3.1. Undamped vibrations
3.3.2. Damped vibrations
3.4. Analytical evaluation of the Duhamel integral-applications
3.4.1. Response to step function load
3.4.2. Response to ramp function load
3.4.3. Response to step function load with finite rise time. Static load
3.5. Response to impulsive loads
3.5.1. Rectangular pulse load
3.5.2. Triangular pulse load
3.5.3. Asymmetrical triangular pulse load
3.5.4. Response to piecewise linear loading
3.6. Response to a periodic loading
3.6.1. Periodic loads
3.6.2. Fourier series
3.6.3. Response of the SDOF system to periodic excitation
3.7. Response to unit impulse
3.7.1. The delta function or Diracs delta function
3.7.2. Response to unit impulse
3.7.3. Response to arbitrary loading
3.7.4. The reciprocal theorem in dynamics
3.8. Problems
References and further reading
Numerical integration of the equation of motion
Chapter outline
Introduction
The central difference method
The average acceleration method
The analog equation method
Stability of the numerical integration methods
Errors in the numerical integration
Difference equations
Difference equations and stability of the numerical integration methods
Stability of the central difference method
Stability of the average acceleration method
Stability of the analog equation method
Accuracy of the numerical integration
Problems
References and further reading
Chapter 5: Nonlinear response: Single-degree-of-freedom systems
Chapter outline
5.1. Introduction
5.2. The central difference method
5.3. The average acceleration method
5.4. The analog equation method
5.5. Problems
References and further reading
Response to ground motion and vibration isolation
Chapter outline
Introduction
Equation of motion: Relative displacement
Response spectra
Equation of motion in terms of the total displacement
Vibration isolation
Transmission of force
Transmission of motion
Problems
References and further reading
Damping in structures
Chapter outline
Introduction
Loss of energy due to damping
Equivalent viscous damping
Hysteretic damping
Coulomb damping
Free vibrations with Coulomb damping
Forced vibrations with Coulomb damping
Damping modeling via fractional derivatives
Introduction
The fractional derivative
Measurement of damping
Free vibration decay method
Resonance amplitude method
Width of response curve method
Problems
References and further reading
Generalized single-degree-of-freedom systems-Continuous systems
Chapter outline
Introduction
Generalized single-degree-of-freedom systems
Continuous systems
Introduction
Solution of the beam equation of motion
Free vibrations of beams
The simply supported beam
The cantilever beam
Orthogonality of the free-vibration modes
Forced vibrations of beams
Problems
References and further reading
Analysis in the frequency domain
Chapter outline
Introduction
Complex form of the Fourier series
Complex dynamic response to periodic load
Fourier integral representation of a nonperiodic load
Response to a nonperiodic load
Discrete Fourier transform
Application of the discrete Fourier transform to dynamic analysis
Fast Fourier transform
The Sande-Tukey algorithm
Problems
References and further reading
Multi-degree-of-freedom systems: Models and equations of motion
Introduction
Systems with localized mass and localized stiffness
Systems with distributed mass and localized stiffness
Systems with localized mass and distributed stiffness
The method of influence coefficients
Elastic forces
Damping forces
Inertial forces
Systems with distributed mass and distributed stiffness
The method of global shape functions
Mixed systems
Transformations of the equations of motion
Problems
References and further reading
The finite element method
Introduction
The finite element method for the plane truss
Properties of the plane truss element
The method of the Lagrange equations
The method of virtual work
Transformation of the nodal coordinates of the truss element
Equation of motion of the plane truss
Steps to formulate the equations of motion for a plane truss by the finite element method
Modification of the equations of motion due to the supports of the structure
The finite element method for the plane frame
Properties of the plane frame element
The method of the Lagrange equations
The method of virtual work
Transformation of the nodal coordinates of the plane frame element
Static condensation: Guyans reduction
Flexural vibrations of a plane frame
Reduction of the degrees of freedom due to constraints
Axial constraints in the plane frame
The finite element method for the plane grid
Properties of the plane grid element
Transformation of the nodal coordinates of the plane grid element
The finite element method for the space frame
Properties of the space frame element
Transformation of the nodal coordinates of the space frame element
The finite element method for the space truss
Properties of the space truss element
Transformation of the nodal coordinates of the space truss element
Rigid bodies within flexible skeletal structures
Rigid bodies in spaces frames
Rigid bodies in spaces trusses, plane grids, plane frames, and plane trusses
Problems
References and further reading
Multi-degree-of-freedom systems: Free vibrations
Chapter outline
Introduction
Free vibrations without damping
Orthogonality of eigenmodes
Eigenmodes of systems with multiple eigenfrequencies
The linear eigenvalue problem
The standard eigenvalue problem of linear algebra
Properties of the eigenvalues and eigenvectors
The generalized eigenvalue problem
The Rayleigh quotient
Properties of eigenfrequencies and modes of MDOF systems without damping: A summary
Solution of the vibration problem without damping
The method of mode superposition
Solution of the vibration problem with damping
Direct solution of the differential equation
Linearization of the quadratic eigenvalue problem
The use of a proportional viscous damping matrix
Construction of a proportional damping matrix
Rayleigh damping
Additional orthogonality conditions: Caughey damping matrix
Construction of the proportional damping matrix using the modal matrix
Problems
References and further reading
Numerical evaluation of the eigenfrequencies and eigenmodes
Chapter outline
Introduction
The vector iteration method
The inverse vector iteration method
Convergence of the inverse vector iteration method
Computation of higher-order eigenpairs
The vector purification method
The inverse vector iteration method with shifts
Free or partially supported structure
Problems
References and further reading
Multi-degree-of-freedom systems: Forced vibrations
Introduction
The mode superposition method
Modal contribution in the mode superposition method
Modal participation
Static correction method
Error in mode superposition method due to truncation of higher modes
Reduction of the dynamic degrees of freedom
Static condensation
Kinematic constraints
Rayleigh-Ritz method
Ritz transformation
Approximation using Ritz vectors
Selection of Ritz vectors
Method of natural mode shapes
The method of derived Ritz vectors
Support excitation
Multiple support excitation
Uniform support excitation
The response spectrum method
Comparison of mode superposition method and Rayleigh-Ritz method
Numerical integration of the equations of motions-Linear MDOF systems
The central difference method (CDM)-Linear equations
The average acceleration method (AAM)-Linear equations
The analog equation method (AEM)-Linear equations
Numerical integration of the equations of motions-Nonlinear MDOF systems
The average acceleration method (AAM)-Nonlinear equations
The analog equation method (AEM)-Nonlinear equations
Problems
References and further reading
Dynamic analysis of multistory buildings
Chapter outline
Introduction
The multistory building
The concept of the multistory element
Nodal displacement matrix, nodal force matrix, transformation matrix, and stiffness matrix of the MSE
Mass matrix of the MSE and multistory building
Equation of motion of the multistory building
Dynamic response of multistory buildings due to ground motion
Problems
References and further reading
Base isolation
Chapter outline
Introduction
Analysis of the one-story building with base isolation
Linear response of the isolation systems
Modeling of nonlinear response of isolation systems
Linear springs or laminated rubber bearings with flat sliders
Linear springs or rubber bearings and nonlinear dampers
Friction pendulum bearing
High damping rubber bearing or lead rubber bearing-Bilinear model
Hysteretic isolators-Bouc-Wen model
The multistory building with base isolation
The equation of motion of the multistory building with base isolation
Reduction of the DOF of the superstructure using mode shapes
Reduction of the superstructure DOF using Ritz vectors
Linear response of the isolation system
Nonlinear response of the isolation system
Problems
References and further reading
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Science is for those who learn; poetry for those who know. ―Joseph Roux This book is a continuation of my previous book, Dynamics and Control of Structures [44]. The expanded book includes three additional chapters and an additional appendix: Chapter 3, “Special Models”; Chapter 8, “Modal Actuators and Sensors”; and Chapter 9, “System Identification. ” Other chapters have been significantly revised and supplemented with new topics, including discrete-time models of structures, limited-time and -frequency grammians and reduction, almo- balanced modal models, simultaneous placement of sensors and actuators, and structural damage detection. The appendices have also been updated and expanded. Appendix A consists of thirteen new Matlab programs. Appendix B is a new addition and includes eleven Matlab programs that solve examples from each chapter. In Appendix C model data are given. Several books on structural dynamics and control have been published. Meirovitch’s textbook [108] covers methods of structural dynamics (virtual work, d’Alambert’s principle, Hamilton’s principle, Lagrange’s and Hamilton’s equations, and modal analysis of structures) and control (pole placement methods, LQG design, and modal control). Ewins’s book [33] presents methods of modal testing of structures. Natke’s book [111] on structural identification also contains excellent material on structural dynamics. Fuller, Elliot, and Nelson [40] cover problems of structural active control and structural acoustic control.
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The book introduces the basic concepts of the finite element method in the static and dynamic analysis of beam, plate, shell and solid structures, discussing how the method works, the characteristics of a finite element approximation and how to avoid the pitfalls of finite element modeling. Presenting the finite element theory as simply as possible, the book allows readers to gain the knowledge required when applying powerful FEA software tools. Further, it describes modeling procedures, especially for reinforced concrete structures, as well as structural dynamics methods, with a particular focus on the seismic analysis of buildings, and explores the modeling of dynamic systems. Featuring numerous illustrative examples, the book allows readers to easily grasp the fundamentals of the finite element theory and to apply the finite element method proficiently.
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he Guide to Meeting the Challenges of Tall Buildings Tall buildings present unique and formidable challenges to architects and engineers because of their size, location in major urban areas, and the multiple, complex occupancies they often contain. ASHRAE Design Guide for Tall, Supertall, and Megatall Building Systems is a unique reference for owners; architects; and mechanical, structural, and electrical engineers as well as other specialized consultants involved in designing systems for these buildings. Expanded since ASHRAE's previous guide on the topic in 2004, this new design guide covers not only tall buildings (taller than 300 ft [91m]) but now also addresses supertall (taller than 984 ft [300 m]) and megatall (taller than 1968 ft [600 m]) buildings, with a broadened scope and updated content that reflects current standards and industry practices. This guide not only focuses on the efforts of designers of the HVAC systems but also addresses the importance of the design team and their collective efforts and concerns that are the critical elements in determining the ultimate solutions to the project needs of a tall building. This guide addresses design issues for tall commercial buildings, which are very often mixed use, with low-level retail, office floors, residential floors, and hotel floors. Also included are appendices with examples of stack effect and wind pressure for four representative climates, energy analysis examples, and HVAC design criteria and a systems description for a multiple-tenant office building.....
all, supertall, and megatall buildings present unique challenges because of their size, urban location and complex occupancies.
Expanded since the first edition published in 2015, ASHRAE Design Guide for Tall, Supertall and Megatall Building Systems, Second Edition has a broadened scope and updated content that reflects current standards and industry practices, including major sections on:
architectural design
indoor air quality (IAQ) and thermal comfort
vertical transportation
life safety
residential occupancy needs
intelligent buildings and controls
Each chapter refers to different parts of the building design phase, from initial concepts through specific calculations. It's ASHRAE's only reference that encompasses the entirety of tall building design.
The second edition contains all-new case studies of real-world buildings and supplemental files throughout, plus new information on stack effect, controls, Smart Grid, and high-rise residential.
It's an ideal companion text for owners, architects, engineers, and other specialized consultants involved in designing systems for these formidable projects.
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The 4th International Conference on Performance-based Design in Earthquake Geotechnical Engineering (PBD-IV) is held in Beijing, China. The PBD-IV Conference is organized under the auspices of the International Society of Soil Mechanics and Geotechnical Engineering - Technical Committee TC203 on Earthquake Geotechnical Engineering and Associated Problems (ISSMGE-TC203). The PBD-I, PBD-II, and PBD-III events in Japan (2009), Italy (2012), and Canada (2017) respectively, were highly successful events for the international earthquake geotechnical engineering community. The PBD events have been excellent companions to the International Conference on Earthquake Geotechnical Engineering (ICEGE) series that TC203 has held in Japan (1995), Portugal (1999), USA (2004), Greece (2007), Chile (2011), New Zealand (2015), and Italy (2019). The goal of PBD-IV is to provide an open forum for delegates to interact with their international colleagues and advance performance-based design research and practices for earthquake geotechnical engineering.
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This book critically assesses Christchurch, New Zealand as an evolving post-earthquake city. It examines the impact of the 2010–13 Canterbury earthquake sequence, employing a chronological structure to consider 'damage and displacement', 'recovery and renewal' and 'the city in transition'.
It offers a framework for understanding the multiple experiences and realities of post-earthquake recovery. It details how the rebuilding of the city has occurred and examines what has arisen in the context of an unprecedented opportunity to refashion land uses and social experience from the ground up. A recurring tension is observed between the desire and tendency of some to reproduce previous urban orthodoxies and the experimental efforts of others to fashion new cultures of progressive place-making and attention to the more-than-human city. The book offers several lessons for understanding disaster recovery in cities. It illuminates the opportunities disasters create for both the reassertion of the familiar and the emergence of the new; highlights the divergence of lived experience during recovery; and considers the extent to which a post-disaster city is prepared for likely climate futures.
The book will be valuable reading for critical disaster researchers as well as geographers, sociologists, urban planners and policy makers interested in disaster recovery.
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Autodesk Structural Bridge Design 2024 is the leading 3D designing application for creating bridges and testing the design under several loads and situations. It is a complete and full-featured suite which provides engineers with all the basic tools and features they need to deal with real-life bridge design scenarios. It can accurately evaluate different types of bridges for any dynamic and non-linear behavior. The latest version offers advanced and effective simulation tools to help you make your design projects more natural and realistic than ever before. It has the ability to design bridge designs of any complexity.
System Requirements for Autodesk Structural Bridge Design 2024.
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Leading 3D designing application for creating bridges and testing the design under several loads and situations.
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Ability to design bridge designs of any complexity.
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Uses robust analysis tools that can handle small and big project bridge designs.
Enables engineers to intelligently perform analysis, design, and load-rating all in one environment.
Allows users to directly exchange project information to improve decision making during design and construction.
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Advances in Civil Engineering: Structural Seismic Resistance, Monitoring and Detectio
Author(s)/Editor(s): Mohd Johari Mohd Yusof Faculty of Design and Architecture, Universiti Putra Malaysia Junwen Zhang China University of Mining & Technology, Beijin | Size: 30.9 MB| Format:PDF| Publisher: CRC PRESS| Year: 2022 | ISBN: ISBN: 978-1-032-31491-4 (hbk) ISBN: 978-1-032-31684-0 (pbk) ISBN: 978-1-003-31088-4 (ebk)
Advances in Civil Engineering: Structural Seismic Resistance, Monitoring and Detection is a
collection of papers resulting from the conference on Structural Seismic Resistance, Monitoring
and Detection (SSRMD 2022), Harbin, China, 21–23 January, 2022. According to the development
of many new seismic theories, technologies and products, the primary goal of this conference is
to promote research and developmental activities in structural seismic resistance, monitoring and
detection. Moreover, another goal is to promote scientific information interchange between scholars
from the top universities, business associations, research centers and high-tech enterprises working
all around the world.
The conference conducted in-depth exchanges and discussions on relevant topics such as
structural seismic resistance, monitoring and detection, aiming to provide an academic and technical communication platform for scholars and engineers engaged in scientific research and
engineering practice in the field of civil engineering, seismic resistance and engineering entity
structure testing. By sharing the research status of scientific research achievements and cutting-edge
technologies, it helps scholars and engineers all over the world to comprehend the academic development trend and broaden research ideas. So as to strengthen international academic research,
academic topics exchange and discussion, and promoting the industrialization cooperation of
academic achievements.
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The monograph entitled “Dynamics of Structure and Foundation -– A Unified
Approach” consists of two volumes. While in Volume 1 we dealt with background theories and formulations that constitute the above subject, this second volume deals with application of these theories to various aspects of civil engineering problems constituting topics related to dynamic soil-structure interaction, machine foundation and
earthquake engineering. If we have managed to stir the wrath of the professionals in Volume 1 with mazes of tensors, differential and integral equations, it is our strong conviction that in this
present volume we will be able to considerably appease this fraternity for it constitutes of a number of applications that are innovative, easy to apply and solutions to many practical problems that puts an engineer into considerable difficulty and uncertainties in a design office. We start Volume 2 with the topic of Dynamic Soil Structure Interaction (DSSI). We
believe this topic would play a key role in future and more so with the distinct possibility of construction of Nuclear power plants (especially in India) globally. A clear concept on this topic would surely be essential for designing such plants. Though we have dealt this topic only in terms of fundamental concepts, yet we feel that we have given sufficient details to eradicate the misnomer from which many engineers suffer that “DSSI is nothing but adding some springs to the boundary of a structure and then
doing the analysis through a computer”.The geotechnical aspects that play an extremely important role in selecting the soilspring value, (that are highly influenced by the strain range) have been dealt in quite
detail. We hope that this section will do away with some of the major blunders that we make in DSSI analysis, and appreciate how the results thus obtained become unrealistic and questionable. We sincerely hope that engineers performing DSSI analysis, would start paying sufficient attention to some of the key engineering parameters as furnished in the soil report – that are being habitually ignored in design offices.
Second chapter consists of design and analysis of machine foundations (both block and frame type). In our collective experience as a consultant and academician we have seen significant confusion on this topic as to who is responsible for this hapless orphan, structural or geotechnical engineers? While people from classical soil mechanics disowns it, as it involves the evaluation of eigen-values and vectors that are far away their traditional failure theories of foundation, structural engineers on the other hand
are equally reluctant to shoulder the guardianship for their inherent apathy towards ‘what lies beneath the machine foundation’. As such, a design involving machine foundation throws the most challenging and interesting task in the domain of civil engineering that requires multi-discipline knowledge and should be equally interesting to an engineer having structural or geotechnical background. The matrix analysis
concept that we have introduced herein is quite easy to follow and we hope wouldB bridge the gap that is still prevalent in academics and practice alike. We would be looking forward to have some feedback from hardened professionals who are working in this area, as to how they feel about our representation which we believe is quite novel and has tried to answer a number of problems that often become burning issues on which they have spent significant time on clarifying either to their Clients or Project Management Consultants.
The last chapter of this volume deals with the most fearful force Mother Nature has created – “Earthquake”. Earthquake engineering as a topic is so vast, complex and diverse (and ever changing) that we concede that it did give us some uncomfortable moments as to what should justifiably constitute this chapter? Majority of the books that address this topic are far too focused on buildings and there are hardly any book
around, that has addressed other specialized structures like chimneys, dams, retaining walls, water tanks etc (except some very specialized literature). It should be realized that some of these structures are expensive, important and cannot be ignored while building an earthquake resistant infrastructure.
Buildings, we concede are the biggest casualties during an earthquake and are directly related to human life but damages to other structures as mentioned above can also create havoc especially in the post earthquake relief scenario. The major focus being still thrust on buildings, we were also quite surprised to find that there is still much room for improvement in many of these structures, where technologies which are as old as 60 years are still in use (for instance earthquake response of retaining walls). We tried to improve upon many of them and believe that we have brought about
a number of innovative solutions that can be adapted in a design office environment and can also be used as a basis for further research.
While presenting the topic no demarcation is made between geotechnical and structural earthquake engineering. For, as a seismic specialist our job is to minimize the destruction of property and save human lives. Thus doing a structural design we can perform the most sophisticated analysis and provide the most expensive detailing and our building still fails due to liquefaction killing people__“no medals for doing an excellent structural design!”, so if you do something do it in totality and not in isolation and this has been our major endeavour- that we have tried to communicate to you through this book.
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