In general, the axial force on the column is proportional to the weight of the. Can the software calculate the percentage of critical damping achieved by. Solve a quadratic eigenvalue problem involving a mass matrix m, damping matrix c, and stiffness matrix k. Chapter 2 introduction to the stiffness displacement. How to get stiffness and damping values for single degree. Practical advanced analysis software for nonlinear. How can we obtain modal strain energy for each story in etabs.
Derivation of mass, stiffness and damping parameters from. Damping devices may also be modeled as a structural subsystem, as described in the tuned mass damper tutorial. Extracting damping ratio from dynamic data and numerical solutions m. Gavin a rayleigh damping matrix is proportional to the mass and sti. Mini sap 2000 tutorial for an example beam hands on. During steadystate analysis, csi software uses hysteretic damping. Frequencyresponse functions for modal analysis matlab.
Please note that setting a constant hysteretic damping with both mass and stiffness proportional damping set to 0. How can i determine the stiffness and damping coefficient. Stiffness and damping parameters for dynamic analysis of. Ms, cs, and ks are the mass, viscous damping, and stiffness. Mass proportional damping in nonlinear timehistory.
Damping coefficients technical knowledge base computers and. Stiffness and mass matrices from sap computers and. Structural analysis for performance based earthquake. Mass proportional damping in nonlinear timehistory analysis.
Integrated software for structural analysis and design, version 8. A proportional damping model is the first analytical model used to study damping for an mdof system. Stiffnessproportional damping now uses initial stiffness instead of tangent stiffness to improve the consistency of results and convergence behavior. Stiffness and damping video simulation khan academy. Effects of the improper modeling of viscous damping on the first. How can i determine the stiffness and damping coefficient of. Structural dynamics department of civil and environmental engineering duke university henri p. Sap2000 revision no 0 example 6006 7 the direct integration time histories use mass and stiffness proportional damping. The mass and stiffnessproportional damping factors are chosen based on the first two modes of the structure so that the equivalent viscous damping ratio is equal to 5%. Proportional damping from experimental data springerlink. Sap2000 verification examples 6005, 6006, and 6007 examples which incorporate. The coefficients a 2p, b 0 were used to create a proportional damping matrix, and the damped fea model was solved for its modes. Polynomial eigenvalue problem matlab polyeig mathworks. Quadratic eigenvalue problem with mass, damping, and stiffness matrices.
Computation of rayleigh damping coefficients for the seismic. The resulting coulomb damping force is obviously a square wave of period. In drain and most other nonlinear dynamic analysis programs the. This property is proportional to mass and stiffness. Nuclear structures and commentary, asce 498 standard, 2000. 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. A fivestory building example is used to compare both fixed based and isolated based schemes. How can i add a damping of some percentage of critical. Damping modelling using generalized proportional damping.
Classical damping, nonclassical damping and complex modes. The stiffness displacement method we can express u as a function of the nodal displacements uiby evaluating u at each node and solving for a1 and a2. Casiano marshall space flight center, huntsville, alabama september 2016. The conventional method for evaluating soil stiffness and damping is based on the. Proportional damping an overview sciencedirect topics. Sap2000 allows users to either specify coefficients. So the trick is to find a nice balance between spring stiffness and damping. As stiffness proportional damping usually should be neglected for its. Matlab is useful in illustrating how to program matrix stiffness method due to the fact that it allows one to very quickly code numerical methods and has vast. As stated in the sap2000 analysis reference manual. And i understand damping as the energy dissipative. There are many ways to compute a classical damping matrix from mass and stiffness matrices.
Damping technical knowledge base computers and structures. Learn about the sap2000 structural analysis and design program. Consider the case in which the damping matrix d is of the form dm k 3 where. If the vessels primary motion is set to calculated 3 dof then reduced added mass and damping matrices are used, having only surge, sway and yaw components, and the damping and added mass. Damping faq technical knowledge base computers and.
Non linear sttic analysis sap2000 linkedin slideshare. Structural analysis for performancebased earthquake engineering. Here you can control damping of each spring, number of hairs, number of springs per. Different types of isolation systems are discussed. A damping model is also embedded in commercial finite element software, and rayleigh. However, the question fielded concerns modal damping. The massnormalized velocity proportional equivalent viscous damping ratio can be written in terms of the damping coefficient and the natural period of a subcritically structure as. To maintain the same behavior as in previous versions of the software, set the modification factor to unity and use. These assumptions greatly simply the equations for.
In structural analysis software such as sap2000, the desired nonclassical damping can. Modal damping parameters allow the damping ratio to be constant for all modes, interpolated by period or frequency, or determined based on a mass and stiffness proportional coefficient. Therefore, sliding and rocking stiffness and damping arc discussed only. Then i can find the spring stiffness k by sett all the derivatives to zero. Any modal damping specified as additional material damping will also be included in linear and nonlinear directintegration time history load cases. Applied sciences free fulltext finite element steadystate. Unlike mass and stiffness properties, damping cannot usually be modelled. However, to judge their practical effect, you will need to know also the current lavel of damping, i. However, for the sliding mode of motion, the vertical geometrical damping relationship is applied for the backfill. In cases such as automatic control system design, accurate estimates of the mass, stiffness, and damping. A time history analysis uses the mass, stiffness and damping matrices to solve for the forced vibration of the structure due to an applied load that varies with time. Effective viscous damping ratio in seismic response of.
The c viscous damping force is a cosine function, and the structural damping force is the product of the coulomb square wave force times. Program will take a description of a system containing masses and springs with proportional dampening and will output the massm, dampeningd and stiffnessk matrices for that system with respects to. Wilson2, it is still widely used in many fea software especially for. Modal analysis of mdof systems with proportional damping. It considers a mass proportional and a stiffness proportional damping in order to achive the real damping lets say 5%.
The associated modal case must use the same mass source as the directintegration load case, and must be run before the directintegration load case that uses it. Extracting damping ratio from dynamic data and numerical. Materialbased damping is now available for linear and nonlinear directintegration timehistory analysis. Mass, stiffness, and damping matrix technical papers. 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. Mass and stiffnessproportional damping, normally referred to as rayleigh. Critical damping is defined in terms of the natural period, but there is no natural. I understand stiffness as the extent to which an object e. Since structural damping force is proportional to displacement and independent of frequency, it seems logical to model this damping mechanism as a stiffness term in the system equations. Hysteretic proportional damping, also mass and stiffness proportional, is used for steadystate and powerspectraldensity analyses. Materialbased damping is now available for steadystate and psd analysis. A problem here is the definition of critical damping.
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