Small amplitude elastic buckling of a beam under monotonic axial loading, with frictionless contact against movable rigid surfaces

Abstract

The elastic buckling of planar beams in the presence of frictionless unilateral contact against rigid surfaces is reconsidered, taking also into account a possible elastic translation of the rigid surfaces with respect to each other.Exclusive reference is made to the case of small amplitude deflections, such as it is expected to occur in the engineering application of buckling-restrained braces, where the gap between the brace itself and the external containment structure is normally extremely small.Even though this case precludes the occurrence of several deformed shapes possible for the general case of large displacement (to be treated like Euler's elastica), already described in the literature, a significant variety of behaviors is still possible.Only monotonic loading is considered.The main variables under investigation are (i) the wavelength of the buckled beam for a given value of the axial shortening and (ii) the total thrust exerted by the buckled beam against the rigid constraints.It is found that both variables can assume several possible values under the same load; in some cases, their values can be bounded analytically.It appears that, even in the extremely simplified case considered here, the actual behavior is dominated by the existing imperfections, both mechanical and geometrical, thus being quite difficult to be predicted with accuracy.