The out-of-plane stability of the crane jib with two symmetric drawbars is studied. Differential equation with two non-conservative forces caused by the two symmetric drawbars is established in critical condition. According to the boundary conditions and proper parameter processing, the out-of-plane characteristic equation is obtained for the crane jib. Comparison with the ANSYS results verified the correctness of the method. And special cases are given to show the consistency of the method used in this paper and that with one drawbar given by the Chinese Design Rules for crane (GB3811-2008). The contribution of the angle between two symmetric drawbars to the out-of-plane stability of the crane jib is also discussed. The results show that, the crane jib with two symmetric drawbars has higher out-of-plane stability than that with one drawbar, and the increase of the angle between the two symmetric drawbars will lead to the significant increase of the out-of-plane stability of the crane jib.
To enhance the carrying capacity of the crane variable cross-section telescopic boom, the usual practice is using the cable at its top end, it makes the out-of-the-lifting plane stability problem of crane telescopic boom become solving the Euler critical force with follower force. This paper established the deflection differential equations of crane telescopic boom model which under actions of cable, with proper boundary conditions, the recurrence formula of buckling characteristic equations were presented, and some practical applications were given. The influence on buckling critical force of crane boom due to the ratio of the length of cable and crane boom was discussed. Took certain four-sectioned telescopic boom as example, the destabilizing critical force was calculated, the result showed that in comparison with the ANSYS method, the buckling characteristic equations in this paper is completely correct.
The tower cranes need constantly attaching to rise in the construction of high-rise buildings. The tower body which sets attached frames combined with the four-rod-type unilateral statically indeterminate attachment system is a common form. With the attachment height and distance increasing, the attachment rods become more delicate and flexible. It is necessary to check the overall and local stability of the attachment structure. When a single limb instability happens, the reduced-order variation structure brings about the redistribution of internal forces. The anti-buckling capability depends on the structure of variation. To the condition that the single limb instability occurrs on the component which has the weakest stiffness, an exact internal force expression of the structure under composite loads has been deduced in terms of the moment equilibrium method. At the same time, the decoupling support stiffnesses of the attachment device in each direction have been obtained by the unit load method. Based on the refined calculation model, the internal forces are further analyzed under the condition that the instability rod bears the fixed Euler critical force, and the structural strength and stability capacity has been judged. The calculation result proves that the whole structure has great bearing potential after a local buckling.
The exact stiffness matrix of a tapered Bernoulli-Euler beam is proposed, whose profile is assumed linear variation. Classical finite element method to get stiffness matrix through interpolation theory and the principle of virtual displacement is abandoned. Starting from the governing differential equation with second-order effect, the exact stiffness matrix of tapered beam can be obtained. In the formulation of finite element method, the stiffness matrix derived has the same accuracy with the solution of exact differential equation method. As is demonstrated in the numerical examples, the presented method can yield, in a very efficient way, accurate results for single tapered beam or structures consisting of tapered elements.
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