A sensitivity study on the natural frequency of high-rise structures in the Netherlands

Abstract

As the world's population keeps increasing and the rate of urbanizations increases, The rate at which high-rise structures are being built is skyrocketing. In the Netherlands, this is no different. It is expected that the amount of high-rise structures taller than 70 meters will more than double in the coming 20 years. As these structures become taller and more slender, they also become more susceptible to wind-induced excitations. Where once the design of a structure was predominantly governed by the Ultimate Limit State (ULS) design criteria, for tall structures, the Serviceability Limit State (SLS) design criteria becomes as, if not more, important. Therefore, the accurate prediction of the dynamic characteristics are becoming increasingly important. One of these dynamic characteristics is the natural frequency, also called the eigen frequency, of the structure.

The natural frequency is a parameter which is largely influenced by the mass and the stiffness of the structure. One would think that after the completion of structure, that the magnitudes of parameters can be determined with a high level of certainty, and that the natural frequency can be calculated accurately, but this is not the case. When comparing the measured natural frequencies of several high-rise structures in the Netherlands, to their natural frequencies determined in the design phases, an underestimation of between 20\% to 50\% was seen. Although the likelihood that these underestimations will lead to structural failure are small, it does lead to larger design forces and higher peak accelerations, which are used in determining occupant comfort in the structures. The aim of this research is to find the reasons for the discrepancies between the measured and the calculated natural frequencies.

A literature study was performed to determine what the most common methods of determining the natural frequency are during the design phase. There are three main methods which are used throughout different stages of the design phase to approximate the natural frequencies. At the start of the design phase, when structural parameters have not yet been determined, the natural frequency is approximated using empirical formulae. These formulae mostly only depend on 1 or 2 spatial parameters.
As the design progresses and the structural parameters are specified, dynamic beam theory can be used to determine the natural frequency. These calculations take the stiffness of the super- and substructure, and the mass of the structure, into account. As the design nears completion, the structure is modelled in a FE software package. The natural frequency can then be calculated by the software to give a final impression of the natural frequency.

The main parameters influencing the natural frequency of a system are the stiffness and the mass. This is no different for high-rise structures, but how do these parameters affect the natural frequency, and which of these parameters has the greatest effect on the natural frequency? A sensitivity study, looking at 5 existing high-rise structures in the Netherlands, was performed. Each structure was represented by 5 different beam models. One structural parameter was added to each subsequent beam model as to be able to quantify the influence of the added parameter. Lower and upper bounds were determined for each structural parameter. By varying these parameters and calculating the natural frequencies, the effect this variation has on the natural frequency can be determined. It was found that there are 3 parameters which have significant influence on the natural frequencies, namely, the superstructure stiffness, the superstructure density and the rotational stiffness of the foundation.
For all cases with a flexible foundation, the measured natural frequencies could not be reached, even after determining the natural frequencies using the extreme parameter combination, the natural frequencies were still underestimated. The analyses were done for both uniform beam models and multibeam models. The general trend was that the multibeam model produced higher frequencies. This is due to more of the overall stiffness and mass of the structure being situated in the bottom sections of the structure. Using a multibeam can lead to an increase in natural frequency of up to 15\%. Although the natural frequencies were increased, they were still nowhere near the measured natural frequencies.

The underestimation of the natural frequencies using the beams models, led to the question if there are other factors which are not yet taken into account when determining the natural frequencies. In the calculation of the stiffness of the new Erasmus Medical Centre (NEMC), it was assumed that the beams, columns, non-structural elements and the low-rise structure have a negligible influence on the stiffness of the structure. The underestimation in the natural frequencies, led to the conclusion that the stiffness of the structure is underestimated. A complete model of the NEMC was modelled using the SCIA Engineer software. All the structural systems were added to the model. Modal analyses, including different combinations of structural systems and parameter magnitudes, were performed. It was found that for the NEMC the assumption that the beams and columns have a negligible contribution to the natural frequency, was correct. The main contributors to the stiffness of the superstructure were the outer tube and the central cores. The partition walls were added to the model using low stiffness wall elements, by added the walls, the natural frequency was increased by 8.5\%. Assumptions were made to include the influence of the low-rise structure. The determined natural frequency was increased past the measured natural frequency, however, this result might not be realistic.

The final conclusion of the thesis is that the stiffness of the superstructure is underestimated. This leads to the conclusion that there are certain elements which provide the structure with extra stiffness, which is not yet taken into account. At the end of the thesis several recommendations are made as to determine where this extra stiffness comes from.