MATHEMATIC MODEL OF A BEAM PARTIALLY SUPPORTED ON ELASTIC FOUNDATION

Abstract

The paper presents the methodic for analytical determining of stress-strain state of a beam partially supported on elastic foundation at sudden damage of foundation structure (partial failure). Bending equation for a beam is written using dimensional parameter and solved with the initial parameters method. Such approach al­lows to obtain dimensional analytical solution to static and dynamic problems for universal boundary conditions of a beam since it always leads to equations’ system of second order. Using numerical analysis for various values of generalized stiffness parameter of a system “beam - foundation”, we established affecting of the length of failure foundation part to stress-strain state of the beam for two supporting variants: partial supporting and sup­porting by two ends with foundation failure in the middle part of the beam.

Keywords

• system “beam - foundation”, accidental impact, sudden foundation failure, forces, deflections