Nonlinear Behaviour of Equivalent Stiffness of Plates Clamped by Bolted Joints Under Loading

Abstract

The equivalent stiffness of clamped plates is needed not only to evaluate the strength of bolted joints but also to estimate the deformation and vibration characteristics of practical structures with many bolted joints. The axial stiffness and bending stiffness of clamped plates were estimated using finite element (FE) analyses while taking the contact conditions on bearing surfaces and between plates into account. We constructed FE models with an M10 bolt and plate thicknesses of 3.2, 4.5, 6.0, or 9.0 mm, and subjected them to an axial load and a bending moment. The axial compliance was estimated using the load-displacement relation obtained from the FE results. When the axial load was lower than 110% of the clamping force, the load-displacement relation showed linear behaviour and the axial compliance was almost constant. When the axial load was higher than that, the axial compliance varied nonlinearly with changes in the contact conditions between clamped plates. The compliances of the clamped plates were compared with those specified in the German engineering society code VDI 2230 (2003), in which equivalent conical compressive stress fields in the plates had been assumed. When the load-displacement relation behaves linearly, the axial and bending compliances obtained in FE analysis can basically be expressed by the VDI 2230 (2003) code. However, this code gives the slightly large axial stiffness, and thus the internal force borne to the bolt is predicted in a little bit unsafe estimation. In addition, the code is not suitable for application in the case of clamped plates with different thicknesses due to the assumptions it makes with respect to models.