NON-LINEAR TIME HISTORY ANALYSIS: AN ADVANCE ANALYSIS
Non-linear Time History Analysis ( NLTHA) ,Sometimes called Non-linear Dynamic Analysis is mostly affected by geometry effects,in analysis which are considered by using stability functions and the geometry stiffness matrix.The inelasticity of material is considered by the gradual yielding of plastic hinges.A space zero-length multi-spring element is proposed to simulate the non-linear cyclic behavior of steel connections through the independent hardening model.In the Non-linear Time History Analysis(NLTHA),an incremental-iterative scheme based on the hilbert-Huges-Taylor method and the Newton-Raphson method which was developed for solving the non-linear equations of motions.
Considerable factors for Beam-Column element:- -
1) Stability functions accounted for second order effects.
2) Refined plastic hinge models accounting for inelastic effect.
3) Shear deformation effect.
4) Element stiffness matrix accounting for P-Delta effect.
Non-Linear time history analysis algorithm:-- Three main resources of damping of steel frame structures taken into account in the proposal program are---
1) Hysteretic damping due to inelastic material.
2) Structural viscous damping employing Rayleigh damping.
3) Hysteretic damping due to non-linear beam to column connections ,An effective Non-linear force deformation behavior.
The structural systems which have linear inetia,damping and restoring forces are analyzed by linear methods.Whenever,the structural system has any or all of the three reactive forces having non-linear variations with the response parameters namely displacement,velocity and accelerations,a set of non-linear differential equations is evolved.To obtain,the these equations need be solved .The most common non-linearity is the stiffness and the damping non-linearity comprices of two types namely the geometric non-linearity and the material non-linearity.
The structural systems which have linear inetia,damping and restoring forces are analyzed by linear methods.Whenever,the structural system has any or all of the three reactive forces having non-linear variations with the response parameters namely displacement,velocity and accelerations,a set of non-linear differential equations is evolved.To obtain,the these equations need be solved .The most common non-linearity is the stiffness and the damping non-linearity comprices of two types namely the geometric non-linearity and the material non-linearity.
For the material non-linearity ,restoring action shows a hysteretic behavior under cyclic loading .In order to understand the complete behavior of structures ,time history analysis of different Single Degree of Freedom (SDOF) and Multi-Degree of Freedom(MDOF) structures having non-linear characteristics is required to be performed.The results of time history analysis,i.e non-linear analysis of these structures will help in understanding their true behavior.From the results,it can be predicted ,whether the structure will not collapse / partially collapse or totally collapse.
The structural systems which have linear inertia,damping and restoring forces are analysed by linear methods .Whenever ,the structural system has any or all of the three reaction forces.(i.e , inertia,damping and stiffness) having non-linear variation with the response parameters ,namely displacement,velocity and acceleration a set of non-linear differential equations is evolved .To obtain the response ,these equations need be solved.The most common non-linearity is the stiffness and the damping non-linearity.The stiffness non-linearity comprises of two types namely the geometric non-linearity and the material non-linearity.Damping non-linearity may be encountered in dynamic problems associated with structural control ,offshore structural aerodynamics of structures.Most of the type damping non-linearity are of non-hysteretic type.Most structures under earthquake excitation undergo yielding.Hence,it is necessary to discuss material non-linearity exhibiting hysteretic behavior .
Consideration to design steel structure:
Design of steel structures usually is done based on strong column and weak beams ,therefore the plastic hinges form at the beams before the columns fails.Also, in the partially restrained steel frames the moment capacity of the connections is usually less than the moment capacity of the beam.Then the plastic hinges form at the beam-column connections.First,consequently it can be assumed that in the partially restrained steel frames the non-linear rotational springs attached at the end of each beam and non-linear behavior of these connections can be modeled in the finite element analysis of the structures by using moment rotation diagram
The accurate estimation of the peak demand and response of the bridge structure under dynamic excitation requires the use of a suite of ground motions ,and will therefore further increase the complexity of the analysis process and size of the output data.Therefore,these important considerations arise in non-linear analysis in addition to parameter selection.
1) Understanding the balance between model complexities and the corresponding gain in accuracy of the result ,and
2) Making both input and output readily accessible and understandable ,and
3) Ensuring that the element and material formulations in a given software are understood relative to the linear and non-linear response.
*** Some important factors considered as "Knowledge Gap " in NLTHA :
While the current state of research in NLTHA of highway bridges encompasses a wide range of modeling approaches element and constitutive model formulations and solution strategies,significant knowledge gaps may remain :
- - - The difference in simulated response when using similar bridges models in separate software packages.
- - - The effect of cyclic degredation of structural components on the dynamic response of bridges.
- - - Modeling errors associated with the choice of non-linear constitutive/element models and errors with respect to known benchmark solution.
- - - Ranking and prioritization of the modeling parameters that have the most significant influence on bridge response during earthquake loadings.
- - - Numerical integators and non-linear algorithms including accuracy and stability ,for solving non-linear time history equations of motions.
- - - The sensitivity of response to the choice of damping model and the corresponding need for more information on other non-classical damping models.
- - - Lack of information to relate predictions from NLTHA to useful acceptance criteria based on the performance of the bridge system as a whole.
- - - Effect of ground motion uncertainty on NLTHA response predictions.
- - - Propagation of ground motion uncertainty ,model uncertainty and parameter uncertainty through NLTHA.
*** PERFORMANCE ASSESMENT THROUGH NLTHA--
*** Some important factors considered as "Knowledge Gap " in NLTHA :
While the current state of research in NLTHA of highway bridges encompasses a wide range of modeling approaches element and constitutive model formulations and solution strategies,significant knowledge gaps may remain :
- - - The difference in simulated response when using similar bridges models in separate software packages.
- - - The effect of cyclic degredation of structural components on the dynamic response of bridges.
- - - Modeling errors associated with the choice of non-linear constitutive/element models and errors with respect to known benchmark solution.
- - - Ranking and prioritization of the modeling parameters that have the most significant influence on bridge response during earthquake loadings.
- - - Numerical integators and non-linear algorithms including accuracy and stability ,for solving non-linear time history equations of motions.
- - - The sensitivity of response to the choice of damping model and the corresponding need for more information on other non-classical damping models.
- - - Lack of information to relate predictions from NLTHA to useful acceptance criteria based on the performance of the bridge system as a whole.
- - - Effect of ground motion uncertainty on NLTHA response predictions.
- - - Propagation of ground motion uncertainty ,model uncertainty and parameter uncertainty through NLTHA.
*** PERFORMANCE ASSESMENT THROUGH NLTHA--
*** ASSESMENT USING IMPROVED NLTHA- - -
- - - Non-linear component and system modeling.
- - - FEMA356 concepts with NLTHA.
- - - Preview of comprehensive collapse simulation.
*** CONCLUSION:
- - -Design & assesment methods based on non-linear analysis should be used for masonry structures .Linear elastic analysis methods (applications of "equivalent" static forces and modal superposition) are questionable.
- - - Adequate models and commercial software based on pushover analysis are available for masonry with box behavior.
- - - It was shown that pushover analysis do not simulate correctly the failure mode of masonry structures without box behavior,meaning that higher vibration modes have a significant contribution.
- - - Pushover analysis proportional to the mass are probably the best solution is global structural analysis models are used.
- - - For design purposes ,particularly for strengthening design ,macro-block limit analysis is probably the best analysis tool for practitioners.
- - - More research needs to be done in the field of masonry structures without box behavior and earthquake.
- - - FEMA356 concepts with NLTHA.
- - - Preview of comprehensive collapse simulation.
*** CONCLUSION:
- - -Design & assesment methods based on non-linear analysis should be used for masonry structures .Linear elastic analysis methods (applications of "equivalent" static forces and modal superposition) are questionable.
- - - Adequate models and commercial software based on pushover analysis are available for masonry with box behavior.
- - - It was shown that pushover analysis do not simulate correctly the failure mode of masonry structures without box behavior,meaning that higher vibration modes have a significant contribution.
- - - Pushover analysis proportional to the mass are probably the best solution is global structural analysis models are used.
- - - For design purposes ,particularly for strengthening design ,macro-block limit analysis is probably the best analysis tool for practitioners.
- - - More research needs to be done in the field of masonry structures without box behavior and earthquake.
( THANKS TO EVERYONE)
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