This paper presents a new method for generating inelastic response spectra that allows for various structural behavior models. The method is implemented in a computer program called INSPECT. Example inelastic response spectra are generated and compared to elastic spectra for the 1940 El Centro earthquake. The results show that the equal displacement concept does not apply, as displacements diverge significantly from the elastic case at longer periods. Force reduction factors also vary substantially with period and ductility. The paper concludes that assumptions used in current seismic codes for deriving inelastic design spectra are not valid and should be re-examined given advances in analysis methods over the past 40 years.
The dynamic behavior of structures is an important topic in many fields. Aerospace engineers must understand dynamics to simulate space vehicles and airplanes, while mechanical engineers must understand dynamics to isolate or control the vibration of machinery. In civil engineering, an understanding of structural dynamics is important in the design and retrofit of structures to withstand severe dynamic loading from earthquakes, hurricanes, and strong winds, or to identify the occurrence and location of damage within an existing structure.
The Equation Based on the Rotational and Orbital Motion of the PlanetsIJERA Editor
Equations of dependence of rotational and orbital motions of planets are given, their rotation angles are calculated. Wave principles of direct and reverse rotation of planets are established. The established dependencies are demonstrated at different scale levels of structural interactions, in biosystems as well. The accuracy of calculations corresponds to the accuracy of experimental data
The dynamic behavior of structures is an important topic in many fields. Aerospace engineers must understand dynamics to simulate space vehicles and airplanes, while mechanical engineers must understand dynamics to isolate or control the vibration of machinery. In civil engineering, an understanding of structural dynamics is important in the design and retrofit of structures to withstand severe dynamic loading from earthquakes, hurricanes, and strong winds, or to identify the occurrence and location of damage within an existing structure.
The Equation Based on the Rotational and Orbital Motion of the PlanetsIJERA Editor
Equations of dependence of rotational and orbital motions of planets are given, their rotation angles are calculated. Wave principles of direct and reverse rotation of planets are established. The established dependencies are demonstrated at different scale levels of structural interactions, in biosystems as well. The accuracy of calculations corresponds to the accuracy of experimental data
Structure Properties of Yrast Superdeformed Bands
in the Mass Region Around Gd-144
A. M. Khalaf, M. Kotb, Asmaa AbdElSalam* and G.S.M. Ahmed
Physics Department, Faculty of Science, Al-Azhar University, Cairo, Egypt.
*Physics Department, Faculty of Science (Girls), Al-Azhar University, Cairo, Egypt.
This is an Introductory material for those who want to understand the basic difference between linear and nonlinear analysis in the context of civil and structural engineering.
The presentation presents to the reader an understanding of Scalar and Vector Spherical Harmonics, it's origin and application to various engineering fields.
Gravitational field and potential, escape velocity, universal gravitational l...lovizabasharat
What is Escape Velocity-its derivation-examples-applications
Universal Gravitational Law-Derivation and Examples
Gravitational Field And Gravitational Potential-Derivation, Realation and numericals
Radial Velocity and acceleration-derivation and examples
Transverse Velocity and acceleration and examples
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability.
Estimating damping in structure made of different m aterials (steel,brass,aluminum) and processes sti ll remains as one of the biggest challengers. All mate rials posses certain amount of internal damping,wh ich manifested as dissipation of energy from the system . This energy in a vibratory system is either dissipated into heat or radiated away from the syst em. Material damping or internal damping contribute s to about 10-15% of total system damping. Cantilever beams of required size & shape are prepared for experimental purpose & damping ratio is investigate d. Damping ratio is determined by half-power bandwidth method. It is observed that damping ratio is higher for steel than brass than aluminum.
Structure Properties of Yrast Superdeformed Bands
in the Mass Region Around Gd-144
A. M. Khalaf, M. Kotb, Asmaa AbdElSalam* and G.S.M. Ahmed
Physics Department, Faculty of Science, Al-Azhar University, Cairo, Egypt.
*Physics Department, Faculty of Science (Girls), Al-Azhar University, Cairo, Egypt.
This is an Introductory material for those who want to understand the basic difference between linear and nonlinear analysis in the context of civil and structural engineering.
The presentation presents to the reader an understanding of Scalar and Vector Spherical Harmonics, it's origin and application to various engineering fields.
Gravitational field and potential, escape velocity, universal gravitational l...lovizabasharat
What is Escape Velocity-its derivation-examples-applications
Universal Gravitational Law-Derivation and Examples
Gravitational Field And Gravitational Potential-Derivation, Realation and numericals
Radial Velocity and acceleration-derivation and examples
Transverse Velocity and acceleration and examples
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
The papers for publication in The International Journal of Engineering& Science are selected through rigorous peer reviews to ensure originality, timeliness, relevance, and readability.
Estimating damping in structure made of different m aterials (steel,brass,aluminum) and processes sti ll remains as one of the biggest challengers. All mate rials posses certain amount of internal damping,wh ich manifested as dissipation of energy from the system . This energy in a vibratory system is either dissipated into heat or radiated away from the syst em. Material damping or internal damping contribute s to about 10-15% of total system damping. Cantilever beams of required size & shape are prepared for experimental purpose & damping ratio is investigate d. Damping ratio is determined by half-power bandwidth method. It is observed that damping ratio is higher for steel than brass than aluminum.
1 February 28, 2016 Dr. Samuel Daniels Associate.docxoswald1horne84988
1
February 28, 2016
Dr. Samuel Daniels
Associate Professor of Mechanical, Civil and Environmental Engineering
University of New Haven Tagliatela College of Engineering
1124 Campbell Ave., Room 102
West Haven, CT 06516
Dear Dr. Daniels,
This report outlines the procedures and results of the MECH 3315 Impact Force Lab. The lab includes a
concise description of the lab setup, the results and analysis of the results, and description of anything
that went wrong as well as future recommendations. With the numerical values of the data, error
propagation and uncertainties are included so that the error of the equipment and the calculations are
already taken into account. The purpose behind this information is to determine how different distances
impact the force on a beam through the deformation of the beam.
Although the calculations were the majority of the report there is a strong emphasis on the theory behind
the calculations and the data is explained as well so that it can be converted into knowledge for everyday
use. Data tables with paired graphs were created as the visual portions of the analysis. The raw data will
be included in the appendix as well so that there is proof of where the data originated from and with that,
pictures of the lab setup to create an actual picture of what the lab consisted of. It is our hope that from
this document, the theory of impact force will be clarified, as well as make recommendations to improve
the project for future students performing the same lab.
Kind Regards,
xxxxxxxxxxxxxxxx
University of New Haven Tagliatela College of Engineering
Mechanical Engineering
2
University of New Haven
Tagliatela College of Engineering
The Effect of Impact on a Beam
xxxxxxxxxxxxxx
Performed February 24, 2016
Due March 27, 2016
3
Abstract
The objective of this experiment was to describe how a small rotating steel hammer impacts an
aluminum cantilever beam at different angles. When the hammer hits the beam, it creates a dynamic
point load which then is converted into a strain. An accelerometer was used measure the different
angels, while a strain gauge measured the beam deflection. From the strain, the force which was
imposed on the beam was calculated using the equation for strain and then plotted against the angles.
From that plot the conclusion was made that as the angle increases so does the force on the beam and
with analysis grouped into a specific function (e.g linear, exponential, logarithmic, and sinusoidal). The
conclusion was drawn that values of the theoretical were very similar to the experimental.
4
Contents
Abstract ......................................................................................................................................................... 3
Executive Summary ........................................................................................
Fatigue Iife analysis of Aluminum Alloy Sheet Underrandom VibrationIJRESJOURNAL
ABSTRACT: Based on the analysis method of structural vibration fatigue life, the fatigue failure of an aluminum alloy sheet subjected to random vibration load is studied by using finite element analysis software. By using the finite element software of sheet strength and the first six modes are analyzed, which shows that the model meets the engineering requirements; secondly, the vibration fatigue life in frequency domain method Dirlik rain flow distribution model based on the Dirlik formula of fatigue damage and fatigue life of the plates is studied and estimated. The results show that the thin plate satisfies the demand of life under random vibration.
The SpaceDrive Project - First Results on EMDrive and Mach-Effect ThrustersSérgio Sacani
Propellantless propulsion is believed to be the best option for interstellar travel. However, photon rockets or solar sails have thrusts so low that maybe only nano-scaled spacecraft may reach the next star within our lifetime using very high-power laser beams. Following into the footsteps of earlier breakthrough propulsion programs, we are investigating different concepts based on non-classical/revolutionary propulsion ideas that claim to be at least an order of magnitude more efficient in producing thrust compared to photon rockets. Our intention is to develop an excellent research infrastructure to test new ideas and measure thrusts and/or artefacts with high confidence to determine if a concept works and if it does how to scale it up. At present, we are focusing on two possible revolutionary concepts: The EMDrive and the Mach-Effect Thruster. The first concept uses microwaves in a truncated cone-shaped cavity that is claimed to produce thrust. Although it is not clear on which theoretical basis this can work, several experimental tests have been reported in the literature, which warrants a closer examination. The second concept is believed to generate mass fluctuations in a piezo-crystal stack that creates non-zero time-averaged thrusts. Here we are reporting first results of our improved thrust balance as well as EMDrive and Mach-Effect thruster models. Special attention is given to the investigation and identification of error sources that cause false thrust signals. Our results show that the magnetic interaction from not sufficiently shielded cables or thrusters are a major factor that needs to be taken into account for proper μN thrust measurements for these type of devices.
Comparison of symmetric and asymmetric steel diagrid structures by non linear...eSAT Journals
Abstract Diagonalized grid structures – “diagrids” - have emerged as one of the most innovative and adaptable approaches to structuring buildings in this millennium. Diagrid is a particular form of space truss, it consists of perimeter grid made up of a series of triangulated truss system. Diagrid is formed by intersecting the diagonal and horizontal components. Construction of multi‐storey building is rapidly increasing throughout the world. Advance in construction technology, materials, structural systems, various analysis and design software have facilitated the growth of various kinds of buildings. Diagrid buildings are emerging as structurally efficient as well as architecturally and aesthetically significant assemblies for tall buildings. Recently these diagrid structural systems have been widely used for tall buildings due to the structural efficiency and aesthetic potential provided by the unique geometric configuration of the system. This paper presents a 12 storey steel diagrid structure which is 36m in height. Symmetric and asymmetric structural configurations of diagrid structures were modelled and analyzed using SAP 2000 by considering Dead load, Live load and Seismic Loads (IS 1893-Part-1, 2002). Then FEMA 356 hinges (auto hinges) are assigned to the same structure and Nonlinear Static (Pushover) analysis is carried out by using seismic load as the pushover load case to find out the performance points that is Immediate Occupancy, Life Safety, and Collapse Prevention of diagrid elements using static pushover curve. At the same time spectral displacement demand & spectral displacement capacity as well as spectral acceleration demand and spectral acceleration capacity is compared to know the adequacy of the design by using ATC capacity spectrum method. Keywords: Diagrid, Pushover analysis, Spectral displacement demand, Spectral displacement capacity, Spectral acceleration demand, Spectral acceleration capacity
Directional Spreading Effect on a Wave Energy ConverterElliot Song
The results demonstrate the importance of tuning the WEC system for specific wave environments to harvest most energy and to avoid potential capsize due to hurricanes etc.
Higher-Order Squeezing of a Generic Quadratically-Coupled Optomechanical SystemIOSRJAP
Using short-time dynamics and analytical solution of Heisenberg equation of motion for the Hamiltonian of quadratically-coupled optomechanical system for different field modes, we have investigated the existence of higher-order single mode squeezing, sum squeezing and difference squeezing in absence of driving and dissipation. Depth of squeezing increases with order number for higher-order single mode squeezing. Squeezing factor exhibits a series of revival-collapse phenomena for single mode, which becomes more pronounced as order number increases. In case of sum squeezing amounts of squeezing is greater than single mode higher-order squeezing (n = 2). It is also greater than from difference squeezing for same set of interaction parameters. Sum squeezing is prominently better for extracting information regarding squeezing.
The need for high pump performance and efficiency continue to encourage the study of flow between two parallel co-rotating discs in multiple discs pump or turbine. Therefore, this study entails the design, construction and CFD simulation of a 3D Tesla pump model axisymmetric swirling flow in order to enhance the understanding of Tesla pump for future development.
Method of solution entails designing and construction of a small prototype tesla pump and then using the design geometry and parameters to design and perform numerical simulation. The results of the numerical simulation were then analyzed.
The result obtained indicates static pressure to have minimum value of -4.7791Pa at the outlet and 13.777Pa at the pump inlet and with velocity magnitude having minimum velocity of 0.00m/s and maximum velocity of 4.12m/s. The strength of the velocity was seen to be very high at the pump outlet. The analysis radial velocity showed minimum value of -0.508m/s and maximum value of 3.981m/s with the radial velocity vector being concentrated at the discs periphery and outlet.
Model simulation results exhibited smooth pressure and velocity profiles. With the 3D simulation all flow variables are able to be predicted.
The need for high pump performance and efficiency continue to encourage the study of flow between two parallel co-rotating discs in multiple discs pump or turbine. Therefore, this study entails the design, construction and CFD simulation of a 3D Tesla pump model axisymmetric swirling flow in order to enhance the understanding of Tesla pump for future development.
Method of solution entails designing and construction of a small prototype tesla pump and then using the design geometry and parameters to design and perform numerical simulation. The results of the numerical simulation were then analyzed.
The result obtained indicates static pressure to have minimum value of -4.7791Pa at the outlet and 13.777Pa at the pump inlet and with velocity magnitude having minimum velocity of 0.00m/s and maximum velocity of 4.12m/s. The strength of the velocity was seen to be very high at the pump outlet. The analysis radial velocity showed minimum value of -0.508m/s and maximum value of 3.981m/s with the radial velocity vector being concentrated at the discs periphery and outlet.
Model simulation results exhibited smooth pressure and velocity profiles. With the 3D simulation all flow variables are able to be predicted.
Identification of coulomb, viscous and particle damping parameters from the r...ijiert bestjournal
This paper deals with Theoretical and Experimental methods for identification of coulomb ,Viscous and Particle
damping parameters from the response of Single degree of freedom harmonically forced linear oscillator when
system damped with more than one type of damping ,which parameter is responsible for the control of resonant
response of vibrating systems, in experimental method setup have been presented to investigate steady state
response amplitude xi for SDOF system for different values of amplitude Yi of the base excitation from this
relationship of (Xi ,Yi) the values of viscous damping coefficient „c‟ and coulomb friction force F0 ,also
equivalent viscous damping ratios ,have been calculated from frequency response analysis for the systems with
viscous damping ,Viscous and Coulomb friction damping, coulomb friction damping and particle damping by
using half power band-width method and in theoretical studies expression for steady state amplitude X0
obtained is used to study the effect of frequency ratio and coulomb friction parameters on phase angle and
amplitude ratio.
Vibrational Analysis Of Cracked Rod Having Circumferential Crack IDES Editor
The frequency ratio of torsional vibration of a rod without crack and of rod with crack subjected to torque at the free end for various crack depth and varying crack location is investigated. It is found that even a cracked of small depth is
dangerous at the fixed end, also as the crack depth is increases more than 50% of diameter of rod there is a considerable drop in natural frequency of the rod .
NO1 Uk best vashikaran specialist in delhi vashikaran baba near me online vas...Amil Baba Dawood bangali
Contact with Dawood Bhai Just call on +92322-6382012 and we'll help you. We'll solve all your problems within 12 to 24 hours and with 101% guarantee and with astrology systematic. If you want to take any personal or professional advice then also you can call us on +92322-6382012 , ONLINE LOVE PROBLEM & Other all types of Daily Life Problem's.Then CALL or WHATSAPP us on +92322-6382012 and Get all these problems solutions here by Amil Baba DAWOOD BANGALI
#vashikaranspecialist #astrologer #palmistry #amliyaat #taweez #manpasandshadi #horoscope #spiritual #lovelife #lovespell #marriagespell#aamilbabainpakistan #amilbabainkarachi #powerfullblackmagicspell #kalajadumantarspecialist #realamilbaba #AmilbabainPakistan #astrologerincanada #astrologerindubai #lovespellsmaster #kalajaduspecialist #lovespellsthatwork #aamilbabainlahore#blackmagicformarriage #aamilbaba #kalajadu #kalailam #taweez #wazifaexpert #jadumantar #vashikaranspecialist #astrologer #palmistry #amliyaat #taweez #manpasandshadi #horoscope #spiritual #lovelife #lovespell #marriagespell#aamilbabainpakistan #amilbabainkarachi #powerfullblackmagicspell #kalajadumantarspecialist #realamilbaba #AmilbabainPakistan #astrologerincanada #astrologerindubai #lovespellsmaster #kalajaduspecialist #lovespellsthatwork #aamilbabainlahore #blackmagicforlove #blackmagicformarriage #aamilbaba #kalajadu #kalailam #taweez #wazifaexpert #jadumantar #vashikaranspecialist #astrologer #palmistry #amliyaat #taweez #manpasandshadi #horoscope #spiritual #lovelife #lovespell #marriagespell#aamilbabainpakistan #amilbabainkarachi #powerfullblackmagicspell #kalajadumantarspecialist #realamilbaba #AmilbabainPakistan #astrologerincanada #astrologerindubai #lovespellsmaster #kalajaduspecialist #lovespellsthatwork #aamilbabainlahore #Amilbabainuk #amilbabainspain #amilbabaindubai #Amilbabainnorway #amilbabainkrachi #amilbabainlahore #amilbabaingujranwalan #amilbabainislamabad
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
ML for identifying fraud using open blockchain data.pptx
Paper carr
1. Paper Number 076
The generation of in-elastic response spectra for earthquake
acceleration records
Athol J. Carr
University of Canterbury, Christchurch, New Zealand.
ABSTRACT: In 1960 Newmark showed that the displacements of inelastic structures
subjected to earthquake excitation were similar to those of the same structure when it
behaved elastically. Code writers have taken this to develop the equal displacement
concept that has been the mainstay of seismic design codes for the past 40 years.
Modifications have been made to the approach for structures with short natural periods of
free vibration, to use the equal energy and equal acceleration concepts when deriving the
inelastic design spectra. It will be shown in this paper that many of these assumptions are
not particularly true even for the earthquake accelerograms used by Newmark. With all
the advances in the analysis methods and design philosophies, such as capacity design
and performance based design, made over the past 40 years that it is appropriate than the
basic assumptions used in deriving the inelastic design spectra need to be re-appraised.
This paper will outline a method of deriving the inelastic design spectra for any
earthquake excitation allowing for almost any stiffness and strength degradation models
to be used to represent the structural behaviour.
1 INTRODUCTION
The current method of producing the inelastic design spectra used in many building codes including
the New Zealand Loadings Code [NZ4203:1992] is to use the equal displacement concept of
[Newmark, 1960] which implies that the inelastic structure will have the same displacement as the
elastic structure and this implies [Carr, 1994] that if the structure has a design ductility of 4 then the
yield force will be a ¼ of the elastic design force. This means that the inelastic acceleration design
spectrum will be the elastic acceleration spectrum divided by the ductility factor. For shorter natural
period structures the equal energy concept is used. As the natural period tends to zero the inelastic
acceleration spectrum will tend to the elastic acceleration spectrum, the equal acceleration concept. In
the NZ Loadings Code a linear interpolation of the reduction factor is used between the equal
displacement method at natural periods greater than 0.7 seconds and the equal acceleration concept as
the natural period tends to zero. In many inelastic analyses carried out over the past 30 years there
have been many instances where the equal displacement concept was observed to have been
inapplicable. As a result, a combination of the inelastic capabilities of the analysis program
Ruaumoko [Carr, 2001] and the response spectra methods to produce a program, INSPECT [Carr,
2002] to produce inelastic response spectra for any earthquake accelerogram using almost any of the
44 hysteretic stiffness degradation rules and for any of the 5 strength degradation rules used in
Ruaumoko.
2 INELASTIC SPECTRA FOR A SPECIFIED DUCTILITY FACTOR
The method used for computing the inelastic response spectra follows the methods used for computing
an elastic response spectrum with the addition of an iterative approach to achieve the target ductility
factor and provision to allow for the hysteretic and strength degradation behaviour of the system. As
the behaviour of the structure is non-linear the Constant Average Acceleration method [Carr, 2002] is
2. 2
used to integrate the equations of motion as the linear elastic methods used in most elastic response
spectra programs are inapplicable. The first step is to compute the elastic acceleration and
displacement response spectra for the earthquake accelerogram for the specified level of viscous
damping. The initial yield force for the target ductility uses the reduction ratios derived for the current
inelastic design acceleration response spectra, i.e. for long period structures where the natural period
of free-vibration T is greater than 0.7 seconds, the acceleration spectrum is divided by the ductility
ratio. For natural periods less than 0.1 seconds the yield force is taken as being equal to the
acceleration spectrum. For intermediate natural periods a linear interpolation is made between the
reduction factor at a free-vibration period of 0.7 seconds and the value of 1.0 at a free-vibration period
of 0.1 seconds.
The next step is to compute the displacement for each natural period of free-vibration and to compare
the computed ductility with the target ductility. The strength is then adjusted using a logarithmic
relationship between the required strength and the ductility ratio between the target ductility and the
computed ductility. The displacement is then re-computed and the strength is again adjusted until the
computed displacement is within one percent of the target ductility, or if the iteration number exceeds
200. The relationship between the yield strength Y and the ductility Mu is given by
Y = Y0 MuC
where Y0 is the elastic spectral acceleration and C is the least squares slope of the relationship between
log(Yi/Y0) and log(Di) where Yi and Di are the Yield force and Displacement at each iteration i. Most
computation requires of the order of 6 to 20 cycles and experience has shown that increasing the
maximum number of cycles to greater than 200 does not improve the computed ductility which means
that at some frequencies the relationship between strength and computed ductility is not strongly
related.
Once convergence to the target ductility is achieved then the displacement of the oscillator gives the
Spectral Displacement, the Yield Strength provides the equivalent of the current Strength
(Acceleration) Design Spectra, the maximum total acceleration recorded provides the Spectral
Acceleration and the program also computes the amount of plastic work done during the response and,
provided a duration of free-vibration is allowed to occur following the duration of the earthquake
excitation an estimate can be made of the residual displacement of the oscillator. The last piece of
information is becoming of interest to designers as it gives an estimate of the permanent displacement
that may result in the structure following the earthquake.
The elastic natural period of free-vibration is then incremented and the whole procedure is repeated.
Once the whole range of natural periods of free-vibration has been covered the spectra for that target
ductility is complete. The procedure can now be repeated for the next target ductility.
If the displacements computed for the target ductility are the same as the elastic displacements then the
equal displacement concept espoused by Newmark would apply. However, as will be seen in the
presented results this does not appear to apply even for the El Centro may 1940 earthquake which was
supposed to be an earthquake that justified the Equal Displacement concept.
3 INELASTIC RESPONSE SPECTRA.
The El Centro May 1949 North-South component will be used to generate examples of the inelastic
spectra to show both the capabilities of the INSPECT program and also to show the differences in the
results from those that have been assumed by designers over the past 40 years. In this paper only two
of the available hysteresis rules are used, the Elasto-plastic rule which is the same as the Bi-linear rule
with the post elastic stiffness r = 0.0 and the Modified Takeda rule where the bi-linear factor r = 0.05
and Alpha and Beta are 0.4 and 0.5 respectively. These two hysteresis loops are illustrated in Figure
1. The examples in this paper have no strength degradation with either ductility or number of in-elastic
cycles.
3. 3
Figure 1. Bi-linear and Modified Takeda Hysteresis Loops.
Figures 2 and 3 show the Displacement Spectra for the El Centro accelerogram for both hysteresis
loops and for the elastic system (ductility 1) and for ductility 2 and ductility 4. It is evident that the
Equal Displacement Concept of Newmark does not hold for if it did then all three lines would follow a
similar relationship. The current New Zealand code (NZ4203:1992) assumes that the concept holds
for natural periods of free vibration greater than 0.7 seconds where it is evident from the plots that the
spectra show a fairly large divergence at the longer natural periods. This implies that the current
methods of reducing the inelastic design acceleration spectra from the elastic acceleration spectra by
dividing by the structure ductility factor are not appropriate. It is also obvious that the shape of the
hysteresis loop also has an effect on the spectral displacements for the inelastic structure. This effect
of the loop shape has been observed by the author in dynamic analyses over many years and is
contrary to the belief that the shape of the loop does not have a great effect on the inelastic
displacements.
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Natural Period (Seconds)
Displacement
(m)
Elastic
Ductility 2
Ductility 4
Figure 2. Spectral Displacement – Elasto-plastic
4. 4
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Natural Period (Seconds)
Spectral
Displacement
(m)
Elastic
Ductility2
Ductility4
Figure 3. Spectral Displacement – Takeda
The next two plots, Figures 4 and 5, show the Spectral Accelerations and the Yield Forces for the El
Centro earthquake for ductilities 1, 2 and 4 using the Elasto-plastic hysteresis. Again, if the equal
displacement concept was true then for the longer natural periods the spectral values for ductility 2
would be half the elastic response and for ductility 4 a quarter of the elastic response. The Yield Force
Spectra for the elastic case is the same as the Spectral Acceleration but the other lines show the
reduced yield forces required to give the target structure ductility. For longer period structures, the
shape of the Yield Spectra and the Acceleration Spectra are similar but for the shorter natural period
structures they are very different. Figures 6 and 7 show similar results using the Modified Takeda
hysteresis loop. For both hystersis loops the yield force distributions are similar to the acceration
spectra but both the magnitudes and the shapes of the curves are not the same. The spike seen in the
Spectral Acceleration plot for ductility 4 is the result of not achieving the target ductility (about a 2%
error from the target ductility of 4.0) at the 0.1 second natural period. It must be noted that at large
ductilities, i.e. greater than about 2.0 it appears to be quite common to have spectral accelerations than
exceed the elastic accelerations at these short natural periods of free vibration. Such an effect is also
observable in Figure 4 for the Elasto-plastic hysteresis.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Natural Period (Seconds)
Acceleration
(g)
Elastic
Ductility 2
Ductility 4
Figure 4. Spectral Acceleration – Elasto-plastic
6. 6
0
1
2
3
4
5
6
7
8
9
10
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Natural Period (Seconds)
Yield
Force
(x
10g)
Elastic
Ductility 2
Ductility 4
Figure 7. Spectral Yield Force – Takeda
The analysis is also able to compute the residual displacement in the structure that is associated with
the inelastic displacement. Some designers are now regarding the residual displacements an important
design parameter. It does represent, in a way, the state of the structure at the end of the earthquake, a
large residual displacement implying that considerable effort may be required to restore the structure
to a fully operational state as it is a measure of the permanent deformation in the structure. In the
example shown in Figure 8 it is achieved by continuing the analysis for a further 10 seconds of free
vibration following the 20 seconds of earthquake excitation. For the elastic structure this is sufficient
to return the structure to its at rest position. For the ductile structures the inelastic displacements have
left the structure with the permanent deformation shown. The effect is very dependant on the choice
of hysteresis loop which the more pronounced effects being shown with loops such as the Elasto-
plastic loop while the loops showing a degree of stiffness degradation do not exhibit the same
sideways ratcheting effect during their inelastic excursions.
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Natural Period (Seconds)
Displacement
(m)
Elastic
Ductility 2
Ductility 4
Figure 8. Residual Displacement – Elasto-plastic
7. 7
Figure 9 shows the achieved ductility spectra where the targets were ductility 1, ductility 2 and
ductility 4. It can be seen that the agreement is very good, for the Elasto-plastic hysteresis the
agreement was to within 1% of the target for all but 1 natural period of free vibration. There were
about 3 natural periods that did not achieve the target for the Modified Takeda hysteresis.
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Natural Period (Seconds)
Obtained
Ductility
Elastic
Ductility 2
Ductility 4
Figure 9. Ductility – Elasto-plastic
Figures 10 and 11 show the Force Reduction factors required for different ductility ratios for the
various natural periods of free vibration. The equal displacement concept would imply that the
reduction factors would be 2 and 4 for ductilities 2 and 4 for natural periods greater than about 0.7
seconds.
0
1
2
3
4
5
6
7
8
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Natural Period (Seconds)
Ratio
R
Elastic
Ductility 2
Ductility 4
Figure 10. Force Reduction Ratio – Elasto-plastic
The Inspect program has been in use by Ph.D students in the Civil Engineering Department at the
University of Canterbury for the past 2 years during which time it has undergone a fairly rigorous
testing program. In future it is intended that it will be included as part of the Ruaumoko suite of
programs.
8. 8
0
1
2
3
4
5
6
7
8
9
10
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Natural Period (Seconds)
Reduction
Factor
R
Elastic
Ductility 2
Ductility 4
Figure 11. Force Reduction Ratio - Takeda
4 CONCLUSIONS
This paper has shown that the assumptions made in the selection of inelastic design spectra are not
valid. The equal displacement concept of Newmark does not appear to hold even for the earthquake
which was always described as one which Newmark used as part of the analyses from which he drew
his similar displacement observation. Possibly, the real problem has been the code writers who
interpreted Newmark’s similar displacement to give them their equal displacement. This may have
served a useful purpose in the days of limited computational capabilities but it seems appropriate, forty
years on, to revisit the basis of the inelastic design force spectra. This analysis program could be one
of the tools that may be helpful in developing a more rational basis for the design. It also shows that
the inelastic displacement spectra are also a function of the ductility levels and of the shape of the
hysteresis rule. This will have implications for those designers using the newer displacement based
design.
REFERENCES:
Newmark, N.M. 1960. A development in the modeling of far-field intensities for New Zealand earthquakes.
Bulletin of the New Zealand Society for Earthquake Engineering. 28 (3). 196-217.
Standards New Zealand, NZS 4203:1992, Code of Practice for General Structural design and Design Loadings
for Buildings. Standards New Zealand, Wellington, New Zealand, 1994.
Carr, Athol J., Dynamic Analysis of Structures, Bulletin of the New Zealand National Society for Earthquake
Engineering, 27 (2), June 1994, 129-146
Carr, A.J. 2001. Ruaumoko3D Users Guide. Department of Civil Engineering, University of Canterbury, New
Zealand. 242p.
Carr, A.J. 2002. Inspect Users Guide. Department of Civil Engineering, University of Canterbury, New Zealand.
12p.