Deformation of a plane statically indeterminate frame system with buckling bars

Аuthors

Gnezdilov V. A.^1*, Grishanina T. V.^2**, Nagornov A. Y.^2***

1. ,
2. Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: gnezdilov_07@mail.ru
**e-mail: t.grishanina@mai.ru
***e-mail: andrey-nagornov@mail.ru

Abstract

Long frameworks (lattice beams) are often used in different building structures (cranes, masts, bridges, pylons of electric air-lines, etc.), as well as in space structures deployed or assembled on orbit. In some cases such structures can undergo to large elastic displacements with large angles of the bar turns. At the design it is usually required that there must not be any irreversible deformations and damages (cracks) in the structure at the maximum operational loads. Statically indeterminate frames allow elastic buckling of some compressed bars with moderate finite deflections limited by the relative longitudinal displacements (contaction) and the turn angles at the joints which connect the buckled bars with the others.

In this work the new approach is developed for solution of geometrically nonlinear problem of deformation for a plane frame system with large displacements and turn angles taking into account buckling of some bars with moderate elastic deflection.

Every bar of the system rigidly connected in the movable joints with the other bars and subjected to tension or compression and bending in considered as a beam finite element.

Large displacements and turns of bar in the structure are described by four unknown coordinates of the bar ends (the joints it connects) and by three supplementary generalized coordinates. Two of them represent the relative turn angles of the bar ends and the third — its deflection due to moderate elastic bending. Such representation of describes sufficiently exactly the possible instability of the bar with moderate buckling deflection.

The nonlinear equilibrium equations in displacements for the system loaded by the forces and moments applied in the joints are obtained by use of the virtual work principle. These equations are solved numerically. The example of calculation of the system behavior subjected to the increasing load with the successive buckling of some compressed bars is considered.

Keywords:

frame systems, geometrically nonlinear deformation, large displacements, buckling

References

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