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Mathematical Problems in Engineering
Volume 2014, Article ID 840937, 13 pages
Research Article

Prestress Force Identification for Externally Prestressed Concrete Beam Based on Frequency Equation and Measured Frequencies

Beijing Laboratory of Earthquake Engineering and Structure Retrofit, Beijing University of Technology, Beijing 100124, China

Received 29 March 2014; Accepted 14 May 2014; Published 29 May 2014

Academic Editor: Qingsong Xu

Copyright © 2014 Luning Shi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A prestress force identification method for externally prestressed concrete uniform beam based on the frequency equation and the measured frequencies is developed. For the purpose of the prestress force identification accuracy, we first look for the appropriate method to solve the free vibration equation of externally prestressed concrete beam and then combine the measured frequencies with frequency equation to identify the prestress force. To obtain the exact solution of the free vibration equation of multispan externally prestressed concrete beam, an analytical model of externally prestressed concrete beam is set up based on the Bernoulli-Euler beam theory and the function relation between prestress variation and vibration displacement is built. The multispan externally prestressed concrete beam is taken as the multiple single-span beams which must meet the bending moment and rotation angle boundary conditions, the free vibration equation is solved using sublevel simultaneous method and the semi-analytical solution of the free vibration equation which considered the influence of prestress on section rigidity and beam length is obtained. Taking simply supported concrete beam and two-span concrete beam with external tendons as examples, frequency function curves are obtained with the measured frequencies into it and the prestress force can be identified using the abscissa of the crosspoint of frequency functions. Identification value of the prestress force is in good agreement with the test results. The method can accurately identify prestress force of externally prestressed concrete beam and trace the trend of effective prestress force.