AN APPROXIMATE ANALYTICAL METHOD FOR UNFAVORABLE PRETENSION DEVIATIONS OF CABLE-BAR TENSILE STRUCTURES

Cable-bar tensile structures require pretension to establish initial stiffness and stability. Hence, the pretension deviation resulted from such factors as the cable length errors cannot be ignored in engineering practice. Adopting the quadratic sum of the absolute and relative pretension deviations as the quantitative indices of structural pretension deviation, the analytical relationships between these two indices and the cable length errors are expressed in quadratic forms. By means of the polarity of the Rayleigh quotient of its quadratic matrix, the boundedness of unfavorable structural pretension deviation (MUSPD) is proved. Through a spectral decomposition, the MUSPD is expressed in the form of weighting quadratic summation, with the eigenvalues of the quadratic matrix being the weights and the projection of the cable length errors on eigenvectors being the factors. Due to the rapid attenuation of the eigenvalues, the MUSPD as well as the corresponding distribution of cable length errors can be approximated by adopting first-order eigenvalues and eigenvectors. The MUSPD of a practical cable-strut tensile structure is calculated using the proposed method, with its accuracy and validity investigated by comparing with two conventional optimization algorithms.