Damping Characteristics of Reinforced and Partially Prestressed Concrete Beams

Abstract

Advances in construction materials and computational methods have made it possible to design and construct taller masts, buildings with increasingly slender frames, and bridges (and roof structures) with ever larger spans. In addition, masts, towers and new forms of construction such as offshore structures are being built in more hostile environments than previously contemplated. These evolving structures which keep extending the boundary of 'normal' designs require that the designers take into account vibration of structures at the design stage to a much greater extent than they have done in the past.

The slenderness of modern structures and the large magnitude of the loads that many of them must carry also make it imperative that such structures be designed for stresses induced by dynamic disturbances. The response of a structure to a dynamically applied load may be many times greater than its response to the same load applied statically. The relationship between a structure's static and dynamic responses depends primarily on its damping characteristics and on its natural periods of vibration. In fact, damping is one of the most significant contributors to the dynamic response of high-rise buildings, bridges, tall chimneys and other slender structures considered to be significantly affected by dynamic forces.

Under a severe lateral dynamic loading condition, the structure that is likely to survive is one whose members are sufficiently ductile to absorb and dissipate energy by elastic and/or inelastic deformation. This requires the designer to realistically assess the possible levels of strength in flexural and shear elements. Thus, in designing such a concrete structure, it is important to understand and determine the ability of the structure to absorb energy under an external impulsive force. At this stage, information in this regard is lacking in published literature and the ability of the constituent elements of the structure to absorb energy is not well understood. This, for example, is true for reinforced and partially prestressed concrete beam, especially the cracked ones. In particular, no simple and accurate formulae are available to evaluate the damping ratios of reinforced and partially prestressed concrete beams cracked or otherwise, for use in the dynamic design of civil engineering structures. It is this area which forms the primary focus of this research.

In this research, an extensive test programme has been carried out to study the cracking and damping behaviour of reinforced and partially prestressed concrete beams. The tests were carried out in two stages and involved a total of 30 reinforced and partially prestressed beams. Nine reinforced and 12 partially prestressed simply supported full-size box beams were tested at the first stage. Tested at the second stage were 2 simply supported and 3 two-equal span continuous reinforced full-size box beams and 4 solid rectangular full-size simply supported reinforced beams. For all the beams, at each level of loading, measurements were made of instantaneous and residual crack widths, instantaneous and residual concrete strains, and mid-span deflections. Each beam was also subjected to free vibration tests to measure its logarithmic decrement of damping corresponding to each load level.

Based on the experimental results, two empirical formulae have been developed for predicting logarithmic decrement of damping separately in reinforced and partially prestressed concrete beams. These formulae predict damping from the residual crack widths of the beams. For these formulae to be of practical use, a formula relating the residual crack widths of concrete beams to the instantaneous average crack widths was developed. In addition, a unified formula was derived for the prediction of the instantaneous average crack widths based on the general beam parameters. As an alternative, separate formulae are also presented for predicting residual crack widths using mid-span deflections of reinforced and partially prestressed beams. These further enhance the practicability of the proposed damping formulae.

In an effort to verify the accuracy and reliability of the proposed formulae, comparative studies are carried out based on the author's own laboratory test results as well as those available in published literature. In total, 104 full-size reinforced and prestressed concrete solid and box beams are involved in the comparative study. In general, good correlations are obtained for instantaneous and residual average crack widths and for logarithmic decrement of damping values. These are true for both reinforced and partially prestressed concrete beams.