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

Equivalent stiffness of clamped plates should be prescribed not only to evaluate the strength of bolted joints by the scheme of “joint diagram” but also to make structural analyses for practical structures with many bolted joints. We estimated the axial stiffness and bending stiffness of clamped plates by using Finite Element (FE) analyses while taking the contact condition on bearing surfaces and between the plates into account. The FE models were constructed 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 (2003) code, in which the equivalent conical compressive stress field in the plate has been assumed. The code gives larger axial stiffness for 11% and larger bending stiffness for 22%, and it cannot apply to the clamped plates with different thickness. Thus the code shall give lower bolt stress (unsafe estimation). We modified the vertical angle tangent, tanφ, of the equivalent conical by adding a term of the logarithm of thickness ratio t1/t2 and by fitting to the analysis results. The modified tanφ can estimate the axial compliance with the error from −1.5% to 6.8% and the bending compliance with the error from −6.5% to 10%. Furthermore, the modified tanφ can take the thickness difference into consideration.