Equivalent Stiffness Evaluations of Clamped Plates in Bolted Joints under Loading

Abstract

The equivalent stiffness of clamped plates should be prescribed not only to evaluate the strength of bolted joints but also to evaluate deformation and vibration characteristics of practical structures with many bolted joints. The axial stiffness and bending stiffness of clamped plates were evaluated by using Finite Element (FE) analyses while taking the contact condition on bearing surfaces and between the plates into account. We constructed the FE models for bolted joints tightened with M8, 10, 12 and 16 bolts and plate thicknesses of 3.2, 4.5, 6.0 and 9.0 mm, and the axial and bending compliances were precisely evaluated. These compliances of clamped plates were compared with those from VDI 2230 codes (German Engineering Society), in which the equivalent cylindrical and conical compressive stress fields in the plate had been assumed. The compliances of the clamped plates for the preload states were estimated between the predictions as the cylindrical and the conical fields. Meanwhile, the axial and bending compliances of FE analysis can basically be expressed by the VDI 2230 (2003) with the conical field. However, the VDI 2230 (2003) gives the slightly large axial stiffness, and thus the internal force borne to the bolt is predicted in a little bit dangerous failure. Also, it cannot follow the case of clamped plates with different thickness due to assumption of its model.

Higher Accurate Estimation of Axial and Bending Stiffnesses of Plates Clamped by Bolts

“…The axial compliance δ c under the axial load could be calculated from the slope of the relationship between the compression force and the compression deformation. The axial compliance did not depend on the diameter at which the deformation of the clamped plates was estimated (11) . For example, the axial compliance δ c of analysis results and that calculated by Eq.…”

“…The analysis model of the previous study (11) was used in this study as well. We estimated the stiffness of the clamped plates under clamping force, axial external force, and bending moment by analysing something with a 3D FE model that took the contact conditions between the clamped plates into consideration.…”

“…The axial force and bending moment similar to those in the previous study (11) were supplied to the analysis models as shown in Figs. 2 and 3, and the axial and bending stiffness values of the clamped plates were estimated.…”

“…We previously calculated the stiffnesses of clamped plates under axial load and bending moment by using FE models taking contact condition between clamped plates into consideration (11) . The stiffnesses calculated by FE analyses agreed well with the German engineering society code, VDI 2230 (2003) (4) , in which equivalent conical compressive stress fields in the plates had been assumed.…”

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

“…However, little consideration has been given to the stiffness of the clamped plates, which is most important when evaluating the bolted-joint characteristics. We previously calculated the stiffnesses of clamped plates under an axial load and a bending moment by using FE models while taking the contact condition between clamped plates into consideration (10) . The equivalent stiffness model of the clamped plates in VDI 2230 (2003) was also improved to make it possible to precisely estimate the stiffness for clamped plates with different thicknesses (11) .…”