Our objective is to evaluate precisely a life-cycle of bolted joints under an eccentric load against a bolt axis. Many approaches to achieve the objective based on a lot of theories and practices have been proposed so far [1–12]. As we can refer from their approaches, the opening of the structural interface between clamped plates of bolted joints occurs by the eccentric load, which is over a bolt preload, and then the opening gradually propagates as the eccentric load increases. In the case, nonlinearity appears remarkably on the tensional and bending stress of bolts in the axial direction. In addition to the above, the axial bolt stress larger than expected occurs due to the principle of leverage depending on the load position and the bolted joints layout in the early phase of the pull-out action. Accordingly, the stress evaluation of bolted joints under the eccentric load is very important in order to ensure the safety of industrial machines.

If dimensionless quantities of the bolt stress are found out considering the influence of the structural opening and the load eccentricity, we can have a few advantages as follows. First, bolt stress evaluations can be conducted by easily converting the dimensionless quantities of the bolt stress to the physical dimension quantities in a lot of cases where the bolt preload and the load eccentricity are different. Second, the number of times of verification tests can be reduced.

We are developing a lot of industrial machines which have bolted joints used under eccentric load. In such development [13], bolt stress analyses are usually conducted under the combinations of the following conditions: (i) tapped thread joints, (ii) thin clamped plates than the bolt diameter, (iii) large eccentric loads, (iv) permitting the opening of the structural interface. Therefore, we propose a concept of a normalized bolt stress considering the effect of the structural opening and the load eccentricity. We validated this concept through theoretical studies, finite element analyses, and experiments under the direct load and the centrifugal load.

As a result, the dimensionless quantities of the bolt stress caused by the bolt preload and a lever ratio of bolted joints under combined conditions was determined in this study. We can easily evaluate the bolt stress by simple conversions in a lot of cases in which the bolt preload and the load eccentricity differ.

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