The author‟s experience in non-linear analysis has made him aware that sometimes it may be difficult to detect and recognise problems involving large deformation effects and allow for the latter in numerical representations. He demonstrated that the quality of the results obtained from such an analysis will not be affected if one has the large deformations option open, even if the latter do not, finally, take place. This option is highly recommended by the author when similar work (analysis of plates, struts, thin walled structures) takes place and especially when design optimisation procedures are sought. The author has pointed out that this technique should be particularly useful when revising existing, old design
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methods, or when design optimisation procedures take place, or when drafting or amending design guidelines, or even when a complete assessment of the strength of a particular type of structure or structural element is needed. The author‟s contribution due to this study is:
1. Improving the knowledge of the performance and accuracy of results of certain structures (plates, shells, beams) by introducing material and geometric non- linearities in the numerical analysis process.
2. Providing clear and rigorous guidelines for the optimum design of a family of structural connections.
3. Endow other researchers and practitioners facing similar problems, with useful ideas such as the large deformation effects, to be integrated in the analysis procedure.
5.3 Paper III, Grandstand Terraces, Part 1. Experimental Investigation.
This is an original example of experimental research as no other in-depth, full size
laboratory investigation on grandstand terraces has been reported so far. The significance, value and benefits from full size, laboratory controlled tests compared to tests on scaled down, small specimens has always been well appreciated by researchers. Findings from the specific tests can be used directly to assist in drafting design guidelines and
recommendations. They can be useful to other researchers and practitioners who have an interest and would like to make a comparison with similar structures of their own.
The author was able to enhance the understanding of the behaviour of these structures under different loading regimes. He used the experience gained to develop and „fine-tune‟ a series of successful computational models. He is confident that his recently published results will be utilised by a number of researchers who would like to build upon existing strengths. A summary of the author‟s contribution based on this research is as follows:
1. A novel experimental investigation of a family of grandstand terraces under loading-unloading regimes and the acquisition of good quality data for the designers of these precast units to revise their design philosophies.
2. Extracting stiffness values for the uncracked and cracked sections and using them to calibrate a finite element model as shown in the next article.
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3. Underpinning established theories and use of the findings as a benchmark for further work by the author and other researchers on similar fields.
5.4 Paper IV, Grandstand Terraces, Part 2. Numerical Modelling
The author‟s general elasto-plastic, constitutive, meso-macro scale level approach, featuring cracking and crushing options of reinforced concrete has captured successfully the non-linear flexural behaviour of grandstand terraces, to failure. This model is useful to analysts who seek to look at reinforced concrete beyond the conventional codes of practice.
It may epitomise an aid for the design of nuclear power installations, or offshore structures, or, in general, structures for specialised use such as silos or cooling towers. The author was able to diverge from the disputed area of strain softening and present a model based on more realistic failure criteria, that of cracking and crushing, treating concrete as a brittle material. In brief, he has made the following contributions:
1. A general elasto-plastic, constitutive, meso-macro scale level numerical model of a reinforced concrete structure, featuring cracking and crushing options for concrete failure and yielding for steel. This can be particularly useful to practicing engineers involved in the design of RC structures beyond the conventional codes of practice.
2. The same model was used to demonstrate and caution the engineering community that Crisfield‟s (1983) method developed specifically to replace Newton-Raphson‟s solution algorithm in special cases of non-linear analysis, does not always produce accurate results. In fact, it has been demonstrated that there is no such algorithm to- date that can be used to capture successfully the descending part of the stress-strain curve of any material.
3. Finally, the author suggested a simple but effective way to overcome the problem of contribution to shear resistance of the main reinforcement, by attributing it to the surrounding aggregate interlocking ability.
5.5 Paper V, „Grandstand Terraces. Experimental and Computational Modal Analysis‟.
It was stated by the author that sometimes, carefully conducted computational modal analysis may produce more comprehensive results than the experimental one. He
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demonstrated that some complex modes of vibration, especially those associated with a relatively complex structure, may not be depicted by the available testing hardware and software. He suggested that complex experimentation should be accompanied by a rigorous finite element analysis in an effort to identify fully the resulting dynamic behaviour of a structure.
Opinions have been divided regarding the influence of reinforcement in the dynamic properties of concrete structures. Interim studies by the author hinted towards the
possibility that the introduction of, or an increase in, the amount of reinforcement is likely to force the structure into a different mode of vibration, hence altering the previously obtained properties. The author has suggested that the above needs more dedicated work so that possible boundaries can be established and the general behaviour can be postulated.
Changes in dynamic properties may not always be detected when increasing the amount of reinforcement in a structure alone, because any change in the dynamic response of the system takes place gradually and because there is nothing to be used as a benchmark and therefore distinguish and compare the different modes obtained by the change in
reinforcement. Nevertheless, the author has made the engineering community aware of the possible effects of the reinforcement in the dynamic properties of a structure.
The author is aware that testing or modelling parts of a structure alone, does not
necessarily provide a global understanding of its dynamic performance. He has noticed that at certain modes of vibration, the system of two terrace units under observation responded independently and the motion of one unit had the tendency to damp the motion of the other. Currently, his efforts are headed towards developing a suitable pattern to predict the performance of the entire structure by studying certain key parts of the latter. The main arguments of his contribution are:
1. It is highly recommended that experimental modal analysis is always accompanied by FEA for a better understanding of the dynamic properties of a structure.
2. The influence of reinforcement in the dynamic performance of RC structures has been sending out conflicting signals. The author has indicated that the
reinforcement can change the dynamic performance of a structure by reverting from one mode of vibration to another.
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3. The author has cautioned the engineering community that by studying parts of a large structure such as a grandstand, one cannot draw reliable conclusions regarding the dynamic performance of the whole structure itself.
5.6 Paper VI, Reliability Pointers for Modal Parameter Identification of Grandstand