Rayleigh damping mass and stiffness proportional damping and ground motion analysis, stressed load, geometric nonlinearity, load combination hysteresis type with proportion damping in. Mass at restrained degrees of freedom is set to zero. Mini sap 2000 tutorial for an example beam hands on exercise. This manual describes the theoretical concepts behind the modeling and analysis features offered by the sap2000 analysis engine that underlies the sap2000, etabs and safe structural analysis and design software packages. It considers a massproportional and a stiffnessproportional damping in order to achive the real damping lets say 5%. See if you can come up with something that behaves a bit more realistically.
If the system is lightly damped, authors propose a simple and ef. Effects of damping on mode shapes, volume 1 see other formats. From the main menu select file import sap2000v6, v7 file. However, the question fielded concerns modal damping. The field is the domain of interest and most often represents a. Seconds illustration of mass proportional component in classical damping. Measurement of stiffness of standing trees and felled logs. It doesnt seem to have an effect on the response when i change the damping, even if i set it to 0,99 has anyone encountered this problem. An outline is given of the properties of wood and how these are related to stiffness and acoustic velocity throughout the tree. One of the main limitation of the mass and stiffness proportional damping approximation comes from the fact that the arbitrary variation of damping factors with. Evaluation of assumptions used in engineering practice to. Effect of supplemental viscous damping on the seismic response of structural systems with metallic dampers ramiro vargas1 and michel bruneau2 abstract. Viscous proportional damping is used for directintegration timehistory analysis. All bridges are threedimensional and their dynamic behavior is governed by the mass and stiffness properties of the structure.
The finite element method fem, or finite element analysis fea, is a computational technique used to obtain approximate solutions of boundary value problems in engineering. The stiffness matrix, usually called the k matrix, is assembled using data such as member and element lengths, member and element properties, modules of elasticity, poisons ratio, member and element release, member offsets, support information, etc. Were upgrading the acm dl, and would like your input. I understand stiffness as the extent to which an object e. How can i determine the stiffness and damping coefficient of viscoelastic damper which is to be installed in a building. Nonlinear analysis sap 2000 1 nonlinear static analysis using sap 2000 mitesh surana research scholar, department of earthquake engineering, iit roorkee for queries please mail to. Structural dynamics department of civil and environmental engineering duke university henri p. As stated in the sap2000 analysis reference manual, for steadystate and powerspectraldensity cases, the hysteretic damping matrix is calculated as a linear combination of the stiffness matrix, scaled by coefficient d k, and the mass matrix, scaled by coefficient d m. Proportional damping matrix a proportional damping matrix is assumed to be a linear combination of the mass and stiffness matrices. In vortex, spring refers to the entire springdamper system.
The damping ratio provides a mathematical means of expressing the level of damping in a system relative to critical damping. Wilson department of civil engineering, university of california, berkeley. Its found in hookes law f kx where f is the force the spring is exerting and x is the distance from the equilibrium point. The mass and stiffness proportional damping equivalent to 5% of critical damping was assumed during this analysis. Damping coefficients technical knowledge base computers.
Dec 17, 2008 the critical damping ratio of a system is often used to compare system damping to that which would result in a critically damped case i. Import import mct files as well as other types of files. Rayleigh damping is proportional to the stiffness and mass of the structure. Implementation of configuration dependent stiffness. Stiffness and damping parameters for dynamic analysis of. Drain lewis research center summary the longitudinal dynamic characteristics of a linear structure may be approximated by a lumpedparameter model, which usually includes only the stiffness and mass distri bution of the system.
Damping devices may also be modeled as a structural subsystem, as described. Once a set of modal data has been measured for a vibrating structure, it is possible to compute the full mass, stiffness and damping matrices for the structure by using. When the materials, vibration control devices or vibration isolators in a structure have different damping ratios, elements with different damping ratios can be. The masses are always referred to the local axes of the joint. Mass, stiffness, and damping matrix estimates from structural measurements by ken shye and mark richardson structural measurement systems, inc. Dynamic analyses of 1story moment frame with viscous. Model of a tuned mass damper on a simple structure youtube. In this paper, new procedures are proposed for the damping modeling and its numerical implementation in distinct element analysis of rigid multiblock systems. Changing the effective mass to control resonance problems richard smith, rl smith engineering, newmarket, new hampshire. Gavin fall 2018 1 preliminaries this document describes the formulation of sti.
Dont you have some equations relating the frequency of the oscillations of the spring mass system and the spring constant of the spring. Experimental results, however, suggest that damping factors can vary with frequency. So the trick is to find a nice balance between spring stiffness and damping. So now the damping is proportional to the undamped natural. Derivation of mass, stiffness and damping parameters from. A uniform excitation option is selected with application of ground acceleration history as the imposed motion. New user manual new html based help quality assurance program new qa program in place. For classically damped structures, modal mass, stiffness and damping can be defined directly from formulas that relate the full mass, stiffness and damping matrices to the transfer function matrix. Easily share your publications and get them in front of issuus. During simulation, it is important that dynamic rigid bodies accurately behave and interact with the environment as they would in the realworld. Compute the damping value for two masses in a harmonic oscillator.
Damping faq technical knowledge base computers and. Effect of supplemental viscous damping on the seismic. Results simulation results for the 50% jr takatori record. Method of relating modal damping to local dampers in lumpedparameter systems by harry j. Effect of mass and springs on the damping of mass spring.
Jun 22, 2014 viscous proportional damping is used for directintegration timehistory analysis. Area added mass assignments area auto mesh assignments area bridge object flags. Nonlinear static analysis using sap 2000 mitesh surana. Mass and stiffnessproportional damping, normally referred to as rayleigh damping, is commonly used in nonlineardynamic analysis. The distinct element method dem has been used successfully for the dynamic analysis of rigid block systems. Judul buku ini nantinya sama seperti judul sebelumnya, hanya ditambah kata edisi baru di bawah judul utama sama seperti judul yg bapak. For a damped harmonic oscillator with mass m, damping coefficient c, and spring constant k, it can be defined as the ratio of the damping coefficient in the systems differential equation to the critical damping coefficient. Hysteretic proportional damping, also mass and stiffnessproportional, is used for steadystate and powerspectraldensity analyses. Mass and stiffness proportional damping, normally referred to as rayleigh damping, is commonly used in nonlineardynamic analysis. From the main menu select file import midas civil mct file. The damping force of the damper is proportional to the pressure difference across the piston head and is expressed as a function of velocity of the piston as follows. The method involves 2 matrices the stiffness matrix and the mass matrix. How can i determine the stiffness and damping coefficient of. Modelling and analysis of base isolated structures with.
Modeling inherent damping using rayleigh proportional damping note. Any modal damping specified as additional material damping will also be included in linear and nonlinear directintegration time history load cases. Paper 15 mass, stiffness, and damping matrix estimates from. Materialbased damping is now available for steadystate and psd analysis. Sap 2000 reference manual cartesian coordinate system. Suitability for an incremental approach to numerical solution merits its use. From the main menu select file import autocad dxf file. For the research purpose, analyses have been carried out with and without considering the terms which represents the hardening effects in the model due to the uplift of the mass in the pendulum model. All mass assigned to the elements is apportioned to the connected joints, so that this table represents the total unrestrained mass of the structure. And i understand damping as the energy dissipative properties of an objectsystem e. Materialbased damping is now available for linear and nonlinear directintegration timehistory analysis. Stiffness and damping video simulation khan academy. The new procedure is more consistent, requires less iteration, is more likely to converge, and produces better results. Structural analysis for performance based earthquake engineering.
Prells department of mechanical engineering, university of wales swansea, swansea sa2 8pp, uk email. Is 18932002 is used to carryout the seismic analysis of multistorey building. Building on over 30 years of research and experience, the company provides worldclass software products and services in the field of. Method of relating modal damping to local dampers in lumped. Simple numerical algorithms for the mode superposition. The modal mass, stiffness, and damping definitions are derived in a previous paper 1, and are restated here for convenience. Diana fea bv previously tno diana bv was established in 2003 as a spinoff company from the computational mechanics department of tno building and construction research institute in delft, the netherlands. I have a problem with constant modal damping in sap2000. During formulation, the damping matrix is assumed to be proportional to the mass and stiffness matrices as follows. Metallic dampers can enhance structural performance by reducing seismically induced lateral displacements, and by reducing inelastic behavior of beams and columns. That is, the viscous damping forces are assumed to be proportional to the inertial and restoring forces, as represented in the following equation. Nonlinear analysissap 2000 1 nonlinear static analysis using sap 2000 mitesh surana research scholar, department of earthquake engineering, iit roorkee for queries please mail to.
Classical rayleigh damping is viscous damping which is proportional to a linear combination of mass and stiffness. One of many difficulties associated with dem is modeling of damping. While it is easy to calculate the theoretical values for optimal mass, damping and stiffness for an stmd, making one that meets the requirement is a challenge. The film may be applied directly to the mechanical system or an. The main parameters of the seismic analysis of structures are load carrying capacity, ductility, stiffness, damping and mass. The newmark integration scheme is selected for integration of the equations of motion with a time step dt 0. K is the initial stiffness of the system in drain and most other nonlinear dynamic analysis programs the inherent damping is represented as rayleigh damping, which produces a damping matrix that is proportional to mass and stiffness. Sap 2000 reference manual free ebook download as pdf file.
Worldwide rights of ownership rest with computers and structures, inc. For interactions that are not completely rigid, vortex allows modeling soft interactions as springdamper systems. Nonlinear static pushover analysis has been improved to reduce the. Seismic assessment of wsdot bridges with prestressed. Energy dissipation in the superstructure was represented by rayleigh damping calibrated to 2.
Overwrites aluminum design aaasd 2000 overwrites aluminum design aalrfd 2000 overwrites auto wave loads cable. Response spectrum of irregular and multistory building was very tedious. The artificial stiffness that was being used to prevent instability when the stiffness of an element became zero or negative has now been reduced. One of the main limitation of the mass and stiffness proportional damping approximation comes from the fact that the arbitrary variation of damping factors with respect to vibration frequency cannot be modelled accurately by using this approach. Summary of modal mass, stiffness, and damping given the three equations 20, 24, and 28 for diagonalizing the mass, stiffness and damping matrices, it is now a straightforward task to define. Csi analysis reference the computer programs sap2000, etabs, safe, and csibridge and all associated documentation are proprietary and ed products.
Here you can control damping of each spring, number of hairs, number of springs per hair, and spring stiffness. Mass proportional damping in nonlinear timehistory analysis. Factors are described that influence the speed of sound in wood, including the different types of acoustic waves which propagate in tree stems and lumber. Damping effect of spring mass system or is this elasticease. Hysteretic proportional damping, also mass and stiffness proportional, is used for steadystate and powerspectraldensity analyses. Although only a minimum mathematical and programming background is required to completely understand the book, a thorough understanding of the physical behavior of real structures is essential. Stiffnessproportional damping now uses initial stiffness instead of tangent stiffness to improve the consistency of results and convergence behavior. The stiffness proportional damping is constructed for the. Case response spectrum 4 proportional damping case response spectrum 5 damping overrides case static 1 load assignments. Orthogonality, mass stiffness, damping matrix mit opencourseware. Modal analysis of mdof systems with proportional damping.
Manual and sap result of story displacement, base reaction of equivalent static method were approximately same. Voltage of proper amplitude and phase is fed across the piezoelectric film to induce strain in the film of appropriate phase, amplitude and frequency to dampen beam vibrations of the mechanical system. Nov 16, 2012 by stiffness im assuming you mean the spring constant, often known as k. Us4565940a method and apparatus using a piezoelectric. Changing the effective mass to control resonance problems. Boundary value problems are also called field problems. Derivation of mass, stiffness and damping parameters from experimental modal data. The added mass and damping data represent the fluid loads on the vessel due to wave radiation effects. Damping technical knowledge base computers and structures.
Damping modelling using generalized proportional damping. The bounds unconditionally guarantee a stable system. Seismic assessment of wsdot bridges with prestressed hollow core piles part ii. Sap2000 tutorials training videos, manuals and model files 38 gb civil engineering community from. Non linear sttic analysis sap2000 linkedin slideshare. Section 2 describes the derivation, sections 3 and 4 outline our experiments and their results respectively. From the main menu select file import sap2000v8 file. Manual and sap result of story displacement, base reaction of equivalent static. Summarizes the theoretical development of the finite elements and numerical methods used in the latest versions of the sap and etabs programs.
Both stiffness and damping depend upon strain and this results in nonlinear behavior of soils, which must be considered in any realistic analysis. This property is proportional to mass and stiffness. Bounds for damping that guarantee stability in massspring. Select an existing sap 2000 model of a ordinary standard bridge with several different spans both straight and curved. Other readers will always be interested in your opinion of the books youve read. Mass proportional damping is linearly proportional to period. Introduction to finite element analysis fea or finite. Stiffness proportional damping now uses initial stiffness instead of tangent stiffness to improve the consistency of results and convergence behavior.
There are many ways to compute a classical damping matrix from mass and stiffness matrices. In these models damping must be introduced to account for energy dissipation during motion. In the meantime, rayleigh damping, mass and stiffness proportional damping, was used in the seismic analysis 28,29,30. Proportional damping is the most common approach to model dissipative forces in complex engineering structures and it has been used in various dynamic problems for more than 10 decades. Stiffness and mass proportional damping control over selective execution of analysis cases nonlinear buckling analysis steadystate analysis with damping.
Both modal and rayleigh damping are used to avoid the need to form a damping matrix. A method and apparatus is disclosed in which a piezoelectric film is used to control or dampen vibrations in a mechanical system. This energy dissipation may depend on velocity general viscous damping, displacement hysteresis damping or a combination of both. Extract the sap2000 stiffness matrix for a twostory frame and compare it to the manual solution. Whether youve loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them.
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