Nonlinear Bending Stiffness of Plates Clamped by Bolted Joints under Bending Moment

Abstract

Equivalent stiffness of plates clamped by bolted joints for designing should be evaluated according to not only the strength of bolted joints but also the deformation and vibration characteristics of the structures. When the applied external axial load or the bending moment is sufficiently small, the contact surfaces of the bolted joint are stuck together, and thus both the bolt and the clamped plates deform linearly. Although the sophisticated VDI 2230 code gives the appropriate stiffness of clamped plates for the infinitesimal deformation, the stiffness may vary nonlinearly with increasing the loading because of changing the contact state. Therefore, the present paper focuses on the nonlinear behaviour of the bending stiffness of clamped plates by using Finite Element (FE) analyses, taking the contact condition on bearing surfaces and between the plates into account. The FE models of the plates with thicknesses of 3.2, 4.5, 6.0 and 9.0 mm tightened with M8, 10, 12 and 16 bolts were constructed. The relation between bending moment and bending compliance of clamped plates is found to be categorized into three regions, namely, (i) constant compliance with fully stuck contact surfaces, (ii) transition showing the nonlinear compliance, and (iii) constant compliance with one-side contact surfaces. The mechanical models for these three regions are proposed and compared with FEM solutions. The prediction on the bounds of three regions is in a fairly good agreement except the case with smaller bolts and thicker plates.