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softening is by no means original. However, only a few researchers in the past have raised concerns about its suitability to represent concrete (Hughes, 1976), (Kotsovos, et al. 2005).
The author was able to report on both arguments and express his own reasoned opinion.
Finally, the initiative to deal with these types of problems at a macro/meso scale level has worked well and may be opening new horizons to practicing engineers and analysts and in particular those who are dealing with the simulation of large, civil engineering structures.
4.4.5 Value, Impact
It has been demonstrated by the author that the dedicated concrete element in ANSYS is not always the best option in modelling reinforced concrete and its performance under loading. However, the proposed combination of SOLID65 and LINK8 elements may be adequate to depict the full performance of RC terraces or, indeed other structures undergoing incremental loading. This is expected to be of value to researchers and practitioners who are interested on a relatively simple but rigorous solution of their problem. Also, the problem of transferring shear stresses from the main reinforcement to the concrete material was addressed by the author in an indirect and simplified manner and is expected to be utilised by others. It is relatively early to report any citations but both articles have enjoyed good comments from the Chairman of the editorial panel (Bothwick, 2009).
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and results collected from full size modal analyses tests on single and double terrace units were processed and utilised accordingly. These were compared with the corresponding natural frequencies and mode shapes predicted by the finite element models in order to obtain proficiency and validate the theoretical model. A good correlation was achieved and a series of conclusions and recommendations were drawn.
4.5.2 Contributions
The author was able to draw a series of general but useful comments as follows: He indicated that experimental modal analysis alone may not be adequate to provide a complete and accurate description of the performance of certain structures such as
grandstands undergoing complex modes of vibration. This is because some modes may be complex enough (coupled modes) not to be depicted by the available testing equipment. He pointed out that experimentation should be accompanied by finite element analysis, in an effort to understand and depict more accurately the resulting mode shapes, especially at higher modes of vibration.
There are conflicting messages in the engineering world regarding the influence of reinforcement in the dynamic performance of structures. Previous studies (Numayr. et al.
2003) and short term tests suggest that the amount of reinforcement has only very little effect on the dynamic properties of an uncracked reinforced concrete beam. However, the definition of an uncracked beam is rather conceptual as all RC beams would have hair-like cracks developing due to shrinkage. Also, no beam remains uncracked after a few load increments long before it reaches its ultimate load value.
Interim studies by Pandeli & Karadelis (2003) hinted towards the possibility that an increase in the amount of reinforcement is likely to force the structure into a different mode of vibration, hence altering the previously obtained dynamic properties. In the same studies it was shown that, introducing and gradually increasing the tension reinforcement resulted in a marginal increase of the first two natural frequencies associated with bending modes but had no effect on the next two, mainly torsional modes of vibration. A similar performance was also noted in the present study. He concluded that changes in the dynamic properties may not be detected by increasing the amount of one type of
reinforcement alone, because any significant change in the dynamic response of the system
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is bound to take place gradually and because there is not enough evidence to compare the different states obtained. The authors concluded that more work is needed for patterns to be formulated and benchmarks to be established.
In addition, he concluded that testing or modelling parts or elements of a structure only, does not necessarily provide a global understanding of the structure‟s dynamic
performance. Essentially, he noticed that, at certain modes of vibration, the two terrace units moved independently and the motion of one had the tendency to cancel the motion of the other. Therefore, one cannot generalise or conclude for the whole grandstand by simply studying one, or two, units alone. It has therefore been concluded that more methodical work is needed for patterns to emerge.
4.5.3 Benefits
The model developed established the basis for a further, more systematic modal parameter identification method, based on a continuously updated model that is demonstrated in the next paper. It was also shown that experimental modal analysis combined with a rigorous Finite Element approach can reduce uncertainties and produce reliable results. This has the potential to be a very accurate, generalised method of determining the dynamic properties of structures. By applying symmetric conditions the number of nodes and DOFs used in the model was reduced substantially. This has great benefits on the CPU time as well as the time and effort required by the analyst and in certain cases could even be obligatory due to limitations of the software itself.
Finally, it has been demonstrated that experimental techniques alone may not be accurate enough, and sometimes even misleading, in determining the dynamic properties of a structure. This may be particularly profound at the stage of results interpretation and therefore a combination of the latter with a finite element model can improve quality and reliability and become a valuable tool to specialist consultants, and a benchmark to academia for further research.
4.5.4 Originality
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The author was able to demonstrate that in the case of relatively complex reinforced concrete structures, experimental modal analysis alone may not be adequate to provide a complete and reliable account of its dynamic behaviour unless perhaps, a great deal of experience in interpreting results combined with state-of-the-art equipment is also
available. The author has recommended that laboratory or site tests are accompanied by the appropriate finite element model to provide higher accuracy and reliability, although it is accepted that it is not very often that a finite element model can be regarded by
professionals as comprehensive and reliable as real, full size tests.
Related studies and short term tests and results suggest that the amount of reinforcement has only very little effect on the dynamic properties of the uncracked reinforced concrete terrace units. Yet, our own studies hinted towards the possibility that an increase in the amount of reinforcement is likely to force the structure into a different mode of vibration, hence altering the previously obtained dynamic properties. The role of reinforcement in the dynamic properties of a structure should be the basis for more research.
Finally, It has been demonstrated that the dynamic properties of a RC terrace unit are very sensitive to the type of supports provided; the latter requiring as accurate modelling as possible. As mentioned earlier, symmetry was considered in order to reduce the number of nodes and DOFs used in the model and to optimise CPU-time and computer performance.
It was also stated that the application of symmetry may result in the exclusion of one or more mode shapes. It is recommended that if the analyst has reasons to believe that this is the case, the best solution may be to model the whole structure, using a coarse mesh in order to extract the mode shapes and then use symmetry and a dense mesh to obtain the natural frequencies. Nevertheless, it is likely that only higher order mode shapes and natural frequencies are lost, if any, with symmetry which in general, are of no importance to structural engineers.
4.5.5. Value, Impact
Paper No. V has been published recently and its value to the academic and practicing world is still untested. It has made a good impression and has received encouraging comments by academics and other professionals at the international conference where it was presented. It is hoped that the current article, as well as those to follow as an output of
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the grandstands research, will not only make a strong impression but they will also serve their purpose and make a constructive and positive contribution to this area of research.