by M.Y.I. Bulbul
Imperfections in geometric nonlinear reticulated space structures can have significant effects on their stiffness characteristics and load carrying capacity. These imperfections can be defined as deviations from the theoretical node geometry of the structure or imperfections within the length of the elements spanning between these nodes.
An analytical model is presented by which the spatial behaviour of a beam-column element with an initial sinusoidal profile supporting a lateral load of general triangular distribution along its length is described. Nonlinear force-deformation equations are developed in the natural coordinate system of the element based on the conventional beam-column theory. A tangent stiffness matrix consistent with the equilibrium equations is also derived. Using a Eulerian frame of reference, appropriate transformations are employed to express the derived quantities in the fixed global coordinate system allowing for large displacement and rotations in the structure.
The beam-column formulations are implemented in a geometric nonlinear analysis program, developed by the author, using an incremental iterative algorithm based on automatic load incrementation in a modified version of the arc-length method. A general stability analysis is incorporated in the program, based on a consistent tangent stiffness matrix formulated at each successive equilibrium state.
The numerical algorithm developed is applied to the analysis of four $1000mm$-span reticulated shallow domes tested by the author for various lateral load configurations. These included a uniform pressure loading designed to emulate the triangular distribution of lateral loading along the elements length expected in full size structures. Using the as-built geometry, good agreement between the numerical predictions and the experimental results was obtained for the cases of vertical nodal loading as well as the pressure loading.
[Cambridge University | CUED | Structures Group | Geotechnical Group]
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