# The Geometric Nonlinear Behaviour of Space Structures with
Imperfect, Laterally Loaded Slender Members.

**by M.Y.I. Bulbul**

Abstract
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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(last update 4 November 2003)