Tutorial 10 edificio 4 plantas sap 2000 v15 wall footing warren truss design in sap2000 wind load. It is expressed in terms of the natural frequency and the amount of damping of. Damping models for structural vibration university of cambridge. Submitted to the department of civil and environmental engineering on may 12, 2006 in partial fulfillment of the. Sap2000 is a registered trademark of computers and structures, inc. I want to make sure i have no structural damping and no rayleigh damping. Modal damping in sap2000 modal damping in sap2000 easap civilenvironmental op 3 aug 17.
However, it seems that the procedure of the constant calculation is not clear. Computation of rayleigh damping coefficients for the seismic. Time history response analysis using extended rayleigh. The rayleigh s quotient represents a quick method to estimate the natural frequency of a multidegreeoffreedom vibration system, in which the mass and the stiffness matrices are known. Its shape is approximately that of a rayleigh distribution. Structural analysis for performancebased earthquake engineering. For each material, users specify a material modal damping ratio r, in which 0 damping ratio of each mode. Computation of rayleigh damping coefficients for large systems. In fact, setting the rayleigh damping to be both mass and stiffness proportional, as usually done in structural engineering practice, leads to a severe underestimation of the hysteretic damping of the soil, as shown in the example of fig. Rayleigh damping is the main form in direct integral method for structural nonlinear dynamic analysis. Then, the time history response analysis is performed to confirm the effectivity of the model.
It is evident that a damping value between %1 and %5 should be used. Rayleigh damping has been originally proposed and is suitable for single degree of freedom systems. On completion of this tutorial you should be able to do the following. The sap name has been synonymous with stateoftheart analytical methods since its introduction over 30 years ago. One is the internal or material damping which is inherently low 1 and the other one is the structural damping due to joints 2. A guide to linear dynamic analysis with damping this guide starts from applications of linear dynamic response and its role in fea simulation. Highquality data of modal damping ratios of 24 buildings, measured in 46 earthquakes, is presented. D f dy, 1 then the specific damping coefficient is. As such, rayleigh damping models can provide a clear.
It is shown that damping ratios increase approximately linearly with increasing modal frequency. Rayleigh damping rayleigh damping is a classical method to build easily the damping matrix c of a numerical model 5,7 under the following form. General topics sap2000 csibridge etabs safe perform3d csicol tutorials test. Modeling tuned mass dampers tmd in autodesk robot structural analysis professional description of example 1. Fedem, structural damping, rayleigh damping, frf, dynamic. Determination of the rayleigh damping coefficients of steel. Tutorial sap 2000, analysis of 2d truss, using sap 2000 youtube. Not that the rayleigh, energy, and lagrange methods are closely related. Modelling seismic isolation and viscous damping andreas schellenberg, ph. In abaqusstandard the operator used for implicit direct time integration contains artificial damping in addition to rayleigh damping. Thus, available software sap2000 applied for seismic analysis, design and the provisions of existing seismic codes. Obtained responses show that there is considerable effect of mode dependent damping on response of the system. Soil unit weight above phreatic level sat 19 knm3 rayleigh coef.
The type of damping described by equation 1 is known as rayleigh or proportional damping. Initialstiffness damping generally leads to faster convergence during analysis, but may overestimate damping and hence be unconservative. Overview key features of sap2000 modelling of elements analysis capabilities viewing results tutorial example. Rayleigh damping is not applied to any line segment whose unstretched length is actively varying because of line feeding. A presentation of the theory behind the rayleigh ritz rr method, as well as a discussion of the choice of admissible functions and the use of penalty methods, including recent developments such as using negative inertia and bipenalty terms. Then again modal damping is a viscus form of damping assumption. I can also put in a variable damping, but im just going to put in a constant damping. Rayleigh damping is proportional to the stiffness and mass of the structure.
Alpha and beta are constants used to set the amount of damping. Sap2000 follows in the same tradition featuring a very sophisticated, intuitive and versatile user interface powered by an unmatched analysis engine and design tools for engineers working on transportation, industrial, public works, sports, and other facilities. Then, the extended rayleigh damping model was proposed using the causal damping model 4. There are two optional, mutually exclusive parameters. This outcome could be used for investigations of noise, harshness and fatigue. Pdf computation of rayleigh damping coefficients for large.
Mass proportional damping in nonlinear timehistory. Rayleigh damping, mass proportional damping, elasticplastic, timehistory analysis. To reduce the calculation time, only onequarter of the overall geometry is modelled, using symmetry boundary conditions along the lines of symmetry. This is a good thing if these modes do not contribute to the response. Specify damping parameters for transient or frequency. For a frequency response model with damping, the results are complex. Tutorial sap 2000, analysis of two way slab, using sap2000. Pdf determination of rayleigh damping coefficient for. At nonlinear damping the hysteresis loop is peaked when damping is a result of friction figure 1b one possibility to quantify the level of damping is to determine the area captured within the hysteresis loop. Tutorial principles of earthquake engineering for bridges dameron principles of earthquake engineering of bridges part 2. It is shown that the use of rayleigh damping leads to an overestimation of the seismic response. For example, if a constant 5% modal damping is used for all modes, the equivalent hysteretic damping value is a constant d k.
Base isolation on sap2000, how do i determine the effective damping of a nllink. When a structure is subject to oscillatory deformations the state of the structure can be described by the combination of kinetic and potential. By applying the modal coordinate transformation, the modal damping matrix c becomes diagonal. Tutorial principles of earthquake engineering for bridges dameron nonlinear analysis of components example. Though earlier studies have identified issues with the use of this model in nonlinear seismic analysis, it still remains the popular choice for engineers as well as for software providers. Dynamic analysis of foundations for the effects of. We can use either percentage critical, we can use quality factor or we can use structural damping, so two percent, click ok and thats what were going to. Modal damping is used for responsespectrum and modal timehistory analyses. Fundamental concepts and principles will be introduced such as equation of motion, types of vibrations, role of damping in. The objective of this workshop is to understand the effect of damping on a mechanical structure, and how to apply damping.
The rayleighritz method for structural analysis civil. Both modal and rayleigh damping are used to avoid the need to form a damping matrix. Department between october 1997 and september 2000. Rayleigh damping came out of linear theory massspringdashpot systems where it is easy to view each mode independently. Material modal damping, also known as composite modal damping, is weighted according to element and modal stiffness. Finite element steadystate vibration analysis considering. Rayleigh damping does afford certain mathematical conveniences and is widely used to model internal structural damping. Sap90, sap2000, safe, floor and etabs are trademarks of.
Because of this, many researchers use viscous damping e. Rayleighs classical damping revisited sondipon adhikari1 university of bristol, bristol, united kingdom a. Influence of mode dependent rayleigh damping on transient. After the definition of rayleigh damping, we propose a rheological interpretation of rayleigh damping.
The generalized proportional damping expresses the damping matrix in terms of any nonlinear function involving specially arranged mass and stiffness matrices so that the system still posses classical normal modes. The problem is that for direct integration method, i do not know how to set a constant damping coefficient of 0. A simple model for implementing structural damping in an explicit simulation could be the one proposed by rayleigh in 1877, also studied in, for lamb wave simulations, that defines the critical damping ratio. In this tutorial the influence of a vibrating source on its surrounding soil is studied. This enables one to model practically any type of variations in the modal damping.
This tutorial focuses on rayleighs method, which yields the natural frequency. Export to pdf export to word copy with scaffolding xml pages. This form of c is orthogonal with respect to the system eigenvectors. To implement the damping im using rayleigh damping model following the documentation of 3. Learn about the sap2000 structural analysis and design program. Threedimensional static and dynamic analysis of structures. It considers a massproportional and a stiffnessproportional damping in order to achive the real damping lets say 5%.
Computation of rayleigh damping coefficients for the. To date, nonlinear dynamic analysis for seismic engineering predominantly employs the classical rayleigh damping model and its variations. Jun 22, 2014 damping, a property of the material and the structure, influences dynamic response. In this study, the extended rayleigh damping model is explained, first. It is also assumed that viscous damping can be modeled using a linear viscous damping term. Sep 04, 2010 hello everybody, im trying to simulate a silicon cantilever which with a quality factor of 50. If modaldirect is selected the user can specify the viscous damping factor for each mode separately. Equation 2 you can define rayleigh damping for linear and nonlinear dynamic studies. Rayleigh damping, mass proportional damping, elasticplastic, time history analysis. For mdof systems, rayleigh damping has the tendency to suppress the higher modes. A further idealization, also pointed out by rayleigh, is to assume the damping matrix to. The simplest form of damping is viscous damping, as it leads to linear equations of motion 15.
Absolute response statistics both the input and response time history had a sample rate of 5000 samples per. Modeling technique of material damping properties in ansys. This form of damping acts to decouple modal response. It can be a bad thing if these modes are important, such as. Outline of the rayleigh damping model and the extended model 2.
Rayleigh damping parameters estimation using hammer impact. In this type of damping, the damping force is proportional to the velocity of the body. Application of damping in highrise buildings by jeremiah c. The physical damping due to the viscous effects is taken into consideration via rayleigh damping. Damping, a property of the material and the structure, influences dynamic response. Rayleighs quotient in vibrations analysis wikipedia. Modal damping vs rayleigh damping solidworks forums. Jun 22, 2014 to approximate modal damping in terms of hysteretic damping, d m can be set to zero and d k can be calculated using the relation d k. Pdf computation of rayleigh damping coefficients for. The results show that the equivalent damping ratio changes with the height of the building and the kind of the structural system, but it is constant for all accelerations values. Jun 03, 2017 tutorial sap 2000, analysis of 2d truss, using sap 2000. The slide shows a physical interpretation for rayleigh damping. Determination of the rayleigh damping coefficients of. 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.
Sap user manual, university of california, berkeley. It introduces damping that grows with frequency and with the ratio of. So if were using modal methods, then its very convenient because it will decouple down into single degree of freedom equivalent problems. Damping faq technical knowledge base computers and. The probability density function of the absolute response peaks is given in figure 5. Others yield a governing equation of motion, from which the natural frequency may be determined. It is also called the halfpower point, or 3db point damping. Determine the natural frequency and periodic time for damped systems. For instance, a rayleigh damping model is widely used because of its excellent advantages 10. Srikantha phani2 university of cambridge, cambridge, united kingdom abstract proportional damping is a widely used approach to model dissipative forces in complex engineering. As such, rayleigh damping models can provide a clear physical meaning and present a convenient expression. Jun 03, 2017 tutorial sap 2000, analysis of two way slab, using sap2000. Modeling of material damping properties in ansys c.
Principles of earthquake engineering of bridges part 2. In the ansys software, only a value of each a di and b di can be input in a load step, regardless of the frequencies that are active in that load step. Hung defense systems division, institute of high performance computing 89c science park drive, singapore science park i, singapore 118261. Sap2000 allows users to either specify coefficients. The stiffness proportional term contributes damping that is linearly proportional to. The history of design has included the use of classical damping, rayleigh damping. Mass and stiffnessproportional damping, normally referred to as rayleigh damping, is commonly used in nonlineardynamic analysis.
Hi guys i have a problem with constant modal damping in sap2000. This form of damping is controlled by the value of the numerical damping control parameter, and is not the same as rayleigh damping. Within all load cases of a certain type, damping is applied consistently, though additional damping may be added to individual load cases. Base isolation on sap2000, how do i determine the effective. The function was calculated for the full 300 second duration. In linear dynaics, modal is easier to use, since all you must do is input the damping ratio by mode. Damping of structures is a very complex phenomenon, which refers to two basic reasons a material damping b friction damping at the connections. Structural damping in modal analysis published on apr 16, 2014 it is shown that among the various damping mechanisms that are generally encountered in a mechanical structure.
The damping ratio is related to the rayleigh damping coefficients by 26. Damping technical knowledge base computers and structures. The latter one offers an excellent source of energy release, thereby adequately compensating the low material damping of structures. In this paper a new approach to modelling damping is initiated by. Determination of rayleigh damping coefficient for natural damping rubber plate using finite element modal analysis. Sap2000 verification examples 6005, 6006, and 6007 examples.
But, this is only in case of metallic structures and not. Use the abs and angle functions to obtain realvalued magnitude and phase, respectively. They address a reader to the elbow bracket example smeug. In this paper a more general expression of the damping matrix is proposed while retaining the advantage of classical normal modes. Show that if the units of all terms in c are nmms, the units of.
This is because the rayleigh damping tends to work against the feeding and can cause the simulation to become unstable. An alternative assumption to modal damping is rayleigh damping. Damping is a function of velocity, so if there is no motion then there will be no damping. I have a problem with constant modal damping in sap2000. The eigenvalue problem for a general system of the form. A certain type of damping is available for each type of load case. Structural analysis for performance based earthquake. It can be safely assumed, at least in earths atmosphere, that the dominant damping mechanism for most structures is the viscous damping of the surrounding air. Some of these methods directly yield the natural frequency.
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