Analysis Of Pretension Deviation And Stiffness Of Cable-Strut Tensile Structures

The paper takes cable-strut tensile structures as the research object, focusing on the quantitative estimation and control of its pretension deviation, stiffness analysis problem. The main works include the following five aspects:(1) The most unfavorable structural pretension deviation (MUSPD) is studied. Adopting the quadratic sum of member's absolute and relative pretension deviations as the quantitative indices of structural pretension deviation, the MUSPD is proved to be bounded by means of the polarity of Rayleigh quotient of the quadratic matrix. By the spectral decomposition of the quadratic matrix and taking advantage of the steep attenuation of its eigenvalues, the method utilizing only its first-order eigenvalue and eigenvector to approximately solve the MUSPD as well as the corresponding distribution of cable length errors is established.(2) Aimed at controlling structural pretension deviation, the problem of choosing the optimal actively-stretched cables is discussed. The quadratic sum of elemental pretension deviations is adopted as an index to evaluate the pretension deviation of the whole structure, the reason is expounded that different stretch schemes lead to different control effect of structural pretension deviation from the perspective of eigenvalues. Adopting the first-order eigenvalue of the sensitivity matrix as the evaluating indicator, from the perspective of controlling the MUSPD, an optimization algorithm for choosing actively-stretched cables is put forward based on the Genetic Algorithm.(3) Combined with the crescent-shaped cable-truss tensile canopy structure of Yueqing Stadium, comparison of construction stretch schemes as well as measurement of structural pretension are carried out from the perspective of structural pretension deviation. The structural pretension deviations of different stretch-control schemes are analyzed and the feasible pretension construction scheme is proposed. The cable force monitoring scheme is introduced, the FBG and EM methods are applied to monitor cable forces and a long-term real-time monitoring system is established. In addition, the characteristics of structural pretension during the stretch process and the initial state are analyzed as well.(4) The research is focused on the relationship between element stiffness and structure demand stiffness. A new expression of structure tangent stiffness matrix is given, in which both element stiffness matrix and element geometric stiffness matrix can be expressed as the analytical form of its stiffness value and the corresponding direction vector. Two important structural freedom subspaces, demand stiffness subspace(DSS) and zero elastic stiffness subspace(ZESS) are discovered theoretically. The stiffness of ZESS is mainly offered by geometric stiffness while the stiffness of DSS is the structure stiffness in the direction of external load. The methods of quantifying the stiffness contribution of structural and elemental stiffness to DSS and ZESS are established, by which the key stiffness path of the structure can be found.(5) The dynamic stiffness characteristics of the structure are discussed preliminarily. The relationship between two basic structural modal parameters (frequency and mode) and element elastic stiffness and element geometric stiffness is established. The frequency spectrum of cable-strut tensile structure is found to have an obvious'partition phenomenon'depending on the contribution of geometric stiffness and elastic stiffness to frequencies, and a method is established to distinguish quantificationally the contribution of geometric stiffness and elastic stiffness to some frequency. Using the characteristics that the stiffness of zero elastic modal subspace mainly comes from the contribution of geometric stiffness, a method to find the key pretension elements is set up according to the contribution of element geometric stiffness. Finally, the analytical relationship of frequency, mode and pretension is established, with the help of which the structural pretension can be solved by the measured modal parameters.