Chapter 8

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Chapter 8: Final Conclusions

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Chapter 8 Final Conclusions

As final step of the thesis the more interesting conclusions have been collected in the final chapter, in order to have an overall summary of the work as well as a base point for future related studies.

 DETERIORATION MODEL IN SIMULATED ANALYSIS

To understand the overall behavior of a structure is necessary to push the analysis beyond its elastic limit. Once plasticity occurs, this behavior become strongly conditioned by the deterioration characteristics of structure’s sections. Therefore, in order to obtain reasonable results from the simulated analysis, it’s necessary to input deterioration in the numerical model. This has to include both degradation in stiffness and strength. In this work both degrading and not degrading modeling have been taken into consideration and the results have been compared.

 MODIFIED IMK DETERIORATION MODELS

According to the previous point, all modified Ibarra-Medina-Krawinkler models can be considered as the state of the art as deterioration models, as they are able to capture all the previously mentioned degradation. These last are controlled by several parameters that have to be input in the model definition. The empirical relations, provided by the authors to determine the deterioration parameters, are characterized by a general validity. Therefore it’s important, for an accurate definition and specially for modeling semi-compact and slender steel section, to compare them with the value obtained from the wide provided database of tests or, if available, from laboratory cyclic tests. In some case it’s helpful to change the results obtained with the application of the previous mentioned relations. For example the reduction the value of yield Moment of the springs, together with the increase of the pre-capping stiffness, allow to obtain a better and more reasonable evaluation of the dissipated energy within a cyclic displacement pattern.

 CALIBRATION OF THE MODEL

In order to validate and calibrate the IMK deterioration model several analysis have been performed at different levels of specificity. At first both static and dynamic analysis have been realized on a cantilever column and on a beam-to-column connection by neglecting deterioration in stiffness and strength. That allowed to take confidence with the possibilities provided by the program and to define the parameters of the backbone curve of plastic sections. After that deterioration has been taken into consideration and the parameters related to that have been calibrated. This has been realized by subjecting the beam-to-column connection to several simulated cyclic displacement-controlled tests and by comparing the results obtained with the ones obtained by real laboratory tests, performed by RWTH Aachen University within the PLASTOTOUGH project. The comparison, expressed in terms of moment-rotation curves has been very satisfactory, as all diagrams of simulated analysis fix pretty well the ones of real tests. This part of the work has been crucial, as the definition of deterioration is the key point to model the realistic behavior of steel frame and connection subjected to cyclic stresses.

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 ANALYSIS OF STEEL FRAMES

The analysis of the results of a complex structure as a plane frame focus the importance of what discussed in the previous points. The model definition, in all its characteristics, is crucial to obtain reasonable results. In this work a plane frame has been extrapolated from a 3D Opus building and modeled. By using the relations provided by the authors and the experience previously matured with the IMK model, deterioration has been implemented in the model behavior. Besides this, a non deteriorating fiber-section model has been considered in order to have a comparison and to better understand the effects of degradation in the behavior of the structure. At first a Eigen analysis has been performed on the two models, to have basic indications about the behavior. The results, in terms of mode shapes and fundamental periods, are satisfactory and the differences are smaller than 7%.

Then a monotonic lateral displacement-controlled pushover analysis has been realize. The results, in terms of capacity curve, show that the two model has the same behavior within the elastic range of deformation. When plastic deformation occurs the two curves strongly diverge and a softening branch appears in the deteriorating model.

A ground motion simulation analysis has been performed by subjecting the model to a ground acceleration pattern, provided by RWTH. The behavior of the two models, in terms of maximum absolute displacement of the stories and corresponding time in the analysis, has been very similar. The reason is that the amplitude of the used ground motion is at the border line between the elastic branch and the plastic one. Therefore the two different behaviors cannot show up.

For that reason the aforementioned amplitude has been related to a ground motion

scaling factor of 1,0. This value has been increased up to 8,0 and an incremental

dynamic analysis (IDA) has been realized, in order to have an overall comprehension of the behavior of the response of the model under different levels of earthquake severity. The result of that is presented as the IDA curve, which is a plot of a damage measure versus one or more intensity measure. These lasts can be divided in three parts. In the first one, within the elastic branch of the structure behavior, the two curves have approximately the same values. In the central one, as ground motion intensity increases and plasticity occurs in the members, the different behavior of the two models appears and the value of deformation are often distant. The remarkable differences, however, are in the third one. In fact, whilst the model without deterioration is able to bear the increase of the ground motion intensity until the last value, the IDA curve of deteriorating model is characterized by an upper limit. Trying to push the analysis over this limit, this stops before the theoretical ends. It’s not immediate to connect the forced end of the simulation with the structural reason that could have caused it. Anyway the computational reasons of the numerical collapse have to be searched in the definition of the IMK deterioration model [see Par. 2.5]. In fact the rates of cyclic deterioration are controlled by theoretical rules, based on the hysteretic energy dissipated when the component is subjected to cyclic loading. Every component is characterized by a reference hysteretic energy capacity, which is a function of the yield moment, the pre-capping rotation and a deterioration parameter. After any excursion a rate of energy is dissipated, until the moment in which the cumulative dissipated energy reached the dissipation capacity.

While the plastic deformation are focused in the hinges of the beams, the solver of the program is still able to find a soluction in the equations. Increasing value of the GMfactor of the analysis determines the plastification of the base-column hinges. For that reason the horizontal displacements increase, as well as the second order effects and the stresses. When the base-column hinges reach the dissipation capacity the

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solver is not able to find a numerical solution to the system of equations and consequently it’s forced to break the analysis, as actually happens for GMfactor bigger than .

The increasing of the GMfactor from to , thus of the intensity of the ground motion energy, determines that the achievement of the aforementioned energy equivalent appears gradually before.

 OPENSEES SOFTWARE

OpenSees, the Open System for Earthquake Engineering Simulation, is a powerful finite element computer applications for simulating the response of structural and geotechnical systems. As open source, the software is steadily under development. Despite this, many different combinations of materials, sections and element are already provided, including or neglecting deterioration in the model definition. Every typology of analysis is executable, both static and dynamic, both load or displacement-controlled.