An analytical model for torque-tension relationship of bolted joints based on quadratic bearing pressure distribution and its validation

The torque-tension relationship is fundamental to evaluating the performance of bolted joints. Inaccurate estimation of this relationship can result in insufficient clamping force or excessive tightening, thereby impairing the integrity and reliability of bolted joints. Although numerous analytical models have been developed for conventional threads, their applicability to diverse thread geometries is often restricted by oversimplified assumptions regarding the distribution of bearing contact pressure. In practical applications, the mechanical response of bolted joints is further complicated by frictional variability, evolving contact conditions, and service-induced effects, making accurate preload prediction challenging. Although these factors affect long-term behavior, the torque-tension relationship is primarily established during the tightening stage, where the initial contact conditions govern the subsequent mechanical behavior. To address these limitations, an analytical model is proposed wherein the bearing contact pressure is characterized by a quadratic distribution. This assumption offers a more realistic representation compared with conventional uniform or linear assumptions, while explicitly incorporating its interplay with thread geometry and friction behavior. The model is validated through three-dimensional elastic-plastic finite element analysis and controlled bolt-tightening experiments. Results show that the model achieves prediction accuracies of 98.59% for standard threads and 97.90% for arc-locking self-locking threads, showing good agreement with both numerical and experimental data. The consistent prediction performance across different thread configurations demonstrates the robustness of the quadratic pressure distribution assumption. The proposed model provides a more accurate and practically viable method for predicting the torque-tension behavior of bolted joints.