Buckling of a Timoshenko beam bonded to an elastic half-plane: Effects of sharp and smooth beam edges. (1st March 2020)

• Record Type: Journal Article
• Authors: Falope, F.O.; Lanzoni, L.; Radi, E.
• Is Part Of: International journal of solids and structures. Volume 185/186(2020)
• Page Start: 222
• Page End: 239
• Publication Date: 2020-03-01
• Subjects: Buckling load -- Elastic half-plane -- Edge effects -- Timoshenko beam -- Frictionless contact -- Chebyshev polynomials; Mechanics, Applied -- Periodicals; Structural analysis (Engineering) -- Periodicals; Elastic solids -- Periodicals; Mécanique appliquée -- Périodiques; Constructions, Théorie des -- Périodiques; Solides élastiques -- Périodiques; Elastic solids; Mechanics, Applied; Structural analysis (Engineering); Periodicals; 624.18
• DOI: 10.1016/j.ijsolstr.2019.08.034
• Languages: English
• ISSNs: 0020-7683

Abstract

Highlights: The buckling of a Timoshenko beam resting on an elastic half-plane is analytically investigated. The governing equation is solved by using Chebyshev polynomials and Galerkin method. The buckling loads and modes are assessed varying the governing parameters. Sharp and smooth beam edges have been investigated. Comparison with beams supported by a Winkler foundation is provided too. Abstract: The problem of a compressed Timoshenko beam of finite length in frictionless and bilateral contact with an elastic half-plane is investigated here. The problem formulation leads to an integro-differential equation which can be transformed into an algebraic system by expanding the rotation of the beam cross sections in series of Chebyshev polynomials. An eigenvalue problem is then obtained, whose solution provides the buckling loads of the beam and, in turn, the corresponding buckling mode shapes. Beams with sharp or smooth edges are considered in detail, founding relevant differences. In particular, it is shown that beams with smooth edges cannot exhibit a rigid-body buckling mode. A limit value of the soil compliance is found for beam with sharp edges, below which an analytic buckling load formula is provided without loss of reliability. Finally, in agreement with the Galin solution for the rigid flat punch on a half-plane, a simple relation between the half-plane elastic modulus and the Winkler soil constant is found. Thus, a straightforward formula predicting the buckling loads of stiff beams resting on compliant substrates is proposed.