Abstract
A method for analytical assessment of dynamic added stress in elastic loaded beam resting on elastic two-parameter Pasternak’s foundation due to sudden destruction a part of foundation is proposed. Equations of static bending, natural and forced oscillations are written in a matrix form using state vectors including deflection, rotational angles, bending moments, and shear forces at arbitrary cross section of a beam and also using the matrices of the initial parameters influence on the stress-strain state in arbitrary cross section. The influence of foundation failure on beam’s stress-strain state, taking into account a relation between the stiffness parameters of foundation, is analyzed. The condition of smallness for the shear stiffness parameter (Pasternak’s parameter) in comparison with the stretching-compressing stiffness parameter (Vinkler’s parameter) is accepted. It is shown that the accounting of Pasternak’s parameter reduces the level of dynamic added stress in a beam when sudden destructing of a foundation. The factor of sudden defect occurrence in the system “beam – foundation” increases considerably the internal forces in a beam in comparison with quasistatic formation of the same defect.
Highlights
In this work, a problem of construction a mathematical model for the dynamical process in a load-bearing beam resting on Pasternak’s two-parametrical foundation [1] during sudden occurrence a defect in the form of destruction a part of foundation
The sudden defect appearance leads to reduction in the overall construction stiffness
An analytical solution for the problem on determination of forces, modes, and frequencies of transversal oscillations for a beam resting on elastic twoparametrical foundation is obtained
Summary
A problem of construction a mathematical model for the dynamical process in a load-bearing beam resting on Pasternak’s two-parametrical foundation [1] during sudden occurrence a defect in the form of destruction a part of foundation. The stress-strain state of all the construction is determined by a static influence. The sudden defect appearance leads to reduction in the overall construction stiffness. This reduced stiffness does not already provide with static stability of all the system. The occurring inertial forces cause a dynamical response, the beam begins to move and this results in re-distribution and growth of strain and stress. Due to the dynamical added stress, violations in the established performance or loss of bearing capacity along with progressive destruction are possible. Note that a foundation was supposed to be Winkler’s one-parametrical in all the works
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