The Force Ratio of Booted Joints : The case where clamped parts are hollow cylinders

In designing a bolted joint, it is important to find the ratio of the increment of an axial force produced in a bolt to a load applied on an assembly, that is, the force ratio. For the force ratio, up to today, the formula proposed by Thum has been used. Recently it has been found that the value of the force ratio varies with the position of the load application on the assembly, and the method to compensate Thum's formula was proposed by Junker. But this compensation is based on experience and the theoretical basis is not made clear. In this paper, the concept of the tensile spring constant Kpt for the clamped part is introduced when a load is applied on the outer circumference of clamped parts and the force ratio is calculated by using Kpt. The value of Kpt is analysed by the three dimensional theory of elasticity. In order to verify this theory, an experiment is carried out and the theoretical results are compared with the experimental ones. They show a fairly good agreement. In the case where a part of the interface of clamped parts causes a separation with an increase of the load, theoretical and experimental results show a fairly good agreement, too.