The effect of prestress force magnitude and eccentricity on natural bending frequencies of prestressed concrete structures - Noble, Darragh (Trinity College (Dublin, Ireland). Department of Civil, Structural and Environmental Engineering, 2016)
The effect of prestress force magnitude on the natural bending frequencies of prestressed concrete structures is something widely debated in literature to date. It has major implications for the dynamic design and accurate analysis of such structures, as accurate knowledge of the modal properties of structures is a vital part of accurate prediction modelling and safe dynamic design. This Ph.D. thesis outlines the work carried out between September 2012 and August 2015 on a research project investigating how the application of a prestress force affects the dynamic properties of prestressed concrete structures. Steel and concrete test specimens have been tested both statically and dynamically to determine the change in their flexural/bending stiffness according to the application of both external axial loads and posttensioning loads to the sections. A new simple linear mathematical model predicting changes in natural frequency with increasing post-tensioning load magnitude has also been proposed. Dynamic impact testing has been conducted on four rectangular steel hollow sections. Two sections with different slenderness ratios have been externally axially loaded by jacking them against abutments in a large load frame. Dynamic impact tests were conducted at incremental values of external axial load, and the natural frequencies and damping ratios were determined by analysing the response signals obtained from an accelerometer affixed to the beams during vibration. As such, the migration of the modal properties with increasing external axial load could be determined. Similar testing was repeated on two identical rectangular hollow sections that instead of being externally axially loaded by jacking them against external abutments, were post-tensioned by threading a post-tensioning strand through their hollow. The migration of the fundamental frequencies with increasing post-tensioning load was determined and compared with the results for the externally axially loaded sections. The purpose of this research was to determine under what conditions the “compression-softening” effect is valid. A new simple linear mathematical model predicting changes in natural frequency with increasing post-tensioning force for post-tensioned concrete beams has been proposed. The model predicts linear changes in Young's Modulus, second moment of area, span length and mass per unit length with increasing post-tensioning load magnitude, and subsequently calculates the resulting changes in the natural frequency as a result of the changes in the aforementioned parameters affecting natural frequency. Static and dynamic testing was also conducted on nine different reinforced, post-tensioned concrete beams. Each beam had a different straight-profiled post-tensioning strand eccentricity. The magnitude of the post-tensioning force was increased incrementally and accelerometer impact response signals were obtained at different post-tensioning load levels, from which the natural frequency and damping ratios were obtained. A signal processing algorithm was applied to each of the signals in order to eliminate noise and isolate the correct bending frequency. The Fast Fourier Transform (FFT) was used to convert the obtained response signals from the time domain to the frequency domain, from which the natural frequencies were determined by a peak-peaking algorithm, and the damping ratios were calculated via the half-power bandwidth method. Static three-point bending testing was also conducted at incremental values of post-tensioning force. The mid-span deflection was measured for a given applied force, at each value of post-tensioning load, and subsequently the flexural rigidity of the section at different post-tensioning load levels could be determined. The beams were then cracked by loading them in four-point bending. Following cracking of each of the beam sections the dynamic impact tests were repeated, determining the fundamental bending frequency and damping ratio at different post-tensioning load levels. The migration of the bending frequency with increasing post-tensioning force magnitude was compared for the cracked and uncracked cases. Conclusions are subsequently drawn as to the effect of post-tensioning force magnitude on the natural frequencies of post-tensioned concrete structures and the implication any effect may have on design and analysis of these structures.
Keywords: Civil, Structural and Environmental Engineering, Ph.D.; Ph.D. Trinity College Dublin