Damping Characteristics of Reinforced and Prestressed Normal- and High-Strength Concrete Beams

Abstract

In the last few decades there has been a significant increase in the design strength and performance of different building materials. In particular, new methods, materials and admixtures for the production of concrete have allowed for strengths as high as 100 MPa to be readily available. In addition, the standard manufactured yield strength of reinforcing steel in Australia has increased from 400 MPa to 500 MPa. A perceived design advantage of higher-strength materials is that structural elements can have longer spans and be more slender than previously possible. An emerging problem with slender concrete members is that they can be more vulnerable to loading induced vibration. The damping capacity is an inherent fundamental quantity of all structural concrete members that affects their vibrational response. It is defined as the rate at which a structural member can dissipate the vibrational energy imparted to it. Generally damping capacity measurements, to indicate the integrity of structural members, are taken once the structure is in service. This type of non-destructive testing has been the subject of much research. The published non-destructive testing research on damping capacity is conflicting and a unified method to describe the effect of damage on damping capacity has not yet been proposed. Significantly, there is not one method in the published literature or national design codes, including the Australian Standard AS 3600-2001, available to predict the damping capacity of concrete beam members at the design stage. Further, little research has implemented full-scale testing with a view to developing damping capacity design equations, which is the primary focus of this thesis. To examine the full-range damping behaviour of concrete beams, two categories of testing were proposed. The categories are the 'untested' and 'tested' beam states. These beam states have not been separately investigated in previous work and are considered a major shortcoming of previous research on the damping behaviour of concrete beams. An extensive experimental programme was undertaken to obtain residual deflection and damping capacity data for thirty-one reinforced and ten prestressed concrete beams. The concrete beams had compressive strengths ranging between 23.1 MPa and 90.7 MPa, reinforcement with yield strengths of 400 MPa or 500 MPa, and tensile reinforcement ratios between 0.76% and 2.90%. The full- and half-scale beams tested had lengths of 6.0 m and 2.4 m, respectively. The testing regime consisted of a series of on-off load increments, increasing until failure, designed to induce residual deflections with increasing amounts of internal damage at which damping capacity (logarithmic decrement) was measured. The inconsistencies that were found between the experimental damping capacity of the beams and previous research prompted an initial investigation into the data obtained. It was found that the discrepancies were due to the various interpretations of the method used to extract damping capacity from the free-vibration decay curve. Therefore, a logarithmic decrement calculation method was proposed to ensure consistency and accuracy of the extracted damping capacity data to be used in the subsequent analytical research phase. The experimental test data confirmed that the 'untested' damping capacity of reinforced concrete beams is dependent upon the beam reinforcement ratio and distribution. This quantity was termed the total longitudinal reinforcement distribution. For the prestressed concrete beams, the 'untested' damping capacity was shown to be proportional to the product of the prestressing force and prestressing eccentricity. Separate 'untested' damping capacity equations for reinforced and prestressed concrete beams were developed to reflect these quantities. To account for the variation in damping capacity due to damage in 'tested' beams, a residual deflection mechanism was utilised. The proposed residual deflection mechanism estimates the magnitude of permanent deformation in the beam and attempts to overcome traditional difficulties in calculating the damping capacity during low loading levels. Residual deflection equations, based on the instantaneous deflection data for the current experimental programme, were proposed for both the reinforced and prestressed concrete beams, which in turn were utilised with the proposed 'untested' damping equation to calculate the total damping capacity. The proposed 'untested' damping, residual deflection and total damping capacity equations were compared to published test data and an additional series of test beams. These verification investigations have shown that the proposed equations are reliable and applicable for a range of beam designs, test setups, constituent materials and loading regimes.