A flexibility approach for geometric nonlinear static analysis of guyed masts

The present study proposes a novel flexibility-based approach for the large displacement analysis of guyed masts. The guyed mast is modeled as an equivalent beam-column supported by catenary cables, and the exact force-displacement relations of sagging cables and slender beam-column are accounted for with sufficient rigor. The proposed method starts with formulating two mutually exclusive sets of second-order force- displacement equations, one for the mast and the other for the cables. Flexibility matrices are derived in an incremental form for an Euler-Bernoulli beam-column using the well-known Variational Iteration Method (VIM). Since an exact Lagrangian multiplier is used in the correction functional, the displacements obtained from this numerical method are also exact. The cable behavior is studied using Irvine's model, which is the most accurate and realistic one since it represents the equilibrium configuration of the cable using a catenary curve. But, the model is non-algebraic and is unsuitable for complex structures. Hence, Irvine's equations are recast into an incremental form to obtain exact incremental flexibility matrices. Then, displacement compatibility is re-established between the mast and the cables at their interfaces. This method can effectively address the eccentric compression on the mast shaft from the supporting guy cables, stay slackening, postbuckling of the mast, and trace the mast's nonlinear response for large displacements. A multi-level guyed mast is analyzed to demonstrate the practical application of the proposed method. Classic examples of single-level guyed towers are used to illustrate the behavior in the postbuckling and post-slackening region. The sensitivity of a guyed mast to cable prestress levels, as well as mast shaft imperfections, are also discussed. The solved examples are also analyzed using commercial finite element software packages, and comparisons are drawn regarding their accuracy in capturing the load-deflection response under large displacements.