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PROCEEDINGS OF THE FOURTH INTERNATIONAL CONFERENCE ON CIVIL AND STRUCTURAL ENGINEERING COMPUTING
Edited by: B.H.V. Topping
Stability and Dynamics of Piles Subjected to Nonconservative Loads
M.A. de Rosa
Istituto di Scienza e Technica delle construzioni, Universita di Basilicata, Potenza, Italy
M.A. de Rosa, "Stability and Dynamics of Piles Subjected to Nonconservative Loads", in B.H.V. Topping, (Editor), "Proceedings of the Fourth International Conference on Civil and Structural Engineering Computing", Civil-Comp Press, Edinburgh, UK, pp 213-221, 1989. doi:10.4203/ccp.9.18.2
The influence of the follower distributed forces on the instability behaviour of a foundation pile is an intriguing field, because of the non self-adjont nature of the eigenvalue problem.
In this Paper, we derive the equation of motion of a foundation pile in a Winkler soil, subjected to an arbitrary distribution of follower forces along the axis. The modulus of subgrade reaction of the soil is assumed to increase with the depth, as usually happens. The boundary conditions are quite generic, the pile can be assumed to be free, clamped, simply supported and supported by a roller. This last kind of constraint seems to be particularly important in soil analysis, even if it is rarely encountered in classical stability textbooks.
The structure is discretized according to the 'cell discretization method', which has already been used to analyse girder bridges, foundation beams on a general Winkler soil and foundation beams on an uniform Boussinesq soil. The influence of nonconservative forces on the instability behaviour of beams on Green soil was also studied, according to the same method. The structure is reduced to a discrete number of elastic cells, linked together by means of rigid bars. The resulting finite-degree-of-freedom system can be analyzed with the aid of well established theorems.
The emphasis is here placed on the influence of the nonconservative forces on the critical loads of the system. Therefore, a complete solution is given for piles with uniform cross section, subjected t o an uniform load distribution (Leipholz rod) and to a linearly varying load distribution (Hauger rod) . It is shown that some pseudo-conservative structures are changed to truly nonconservative systems by the presence of the Winkler soil. From the computational point of view, the critical loads cannot be detected with any statical Euler-type method, but it is necessary to draw the entire frequency-load relationship, so signalling both divergence and flutter. An eigenvalue problem must be solved, in which the matrix is not symmetrizable, and a general QR routine has to be used. Fortunately, the proposed discretisation method leads t o small eigenproblems, so that the solution can be obtained in a few seconds.
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