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New formulas are developed for the torque-tension relationship, various torque components, and breakaway torque values in threaded fastener applications. The three-dimensional aspects of the lead helix and thread profile angles and the kinetic and static friction coefficients are all taken into account. Two scenarios of the contact pressure between threads and under the turning fastener head are considered, namely, uniformly distributed and linearly distributed contact pressure scenarios. The effect of thread pitch, lead helix and thread profile angles, friction coefficients, and fastener geometry is discussed. Results from the new formulas are compared with the approximate torque-tension relationship provided in the literature. A percentage difference analysis indicates that the new formulas provide a significant improvement that would enhance the reliability and safety of bolted connections, especially in critical applications.

The nonlinear deformation behavior of clamped bolted joints under a separating service load is investigated using finite element and experimental techniques. Although the materials for the bolted joint remain in the linear elastic range, the interface contact area between the clamped plates is sensitive to both the magnitude and the location of the separating force. This often causes nonlinear deformation behavior of the bolted joint. This finite element analysis study investigates the variation in the tension of a tightened bolt and the corresponding change in the joint clamp load due to a separating service load that is placed at various distances from the bolt center. The separating force is symmetrically placed at locations (from the bolt center) that are equal to 3–5 times the nominal diameter of the bolt. Experimental verification of the finite element results is provided.

A mathematical model is proposed for studying the vibration induced loosening of threaded fasteners that are subjected to harmonic transverse excitation, which often causes slippage between the contact surfaces between engaged threads and under the bolt head. Integral equations are derived for the cyclic shear forces as well as the bearing and thread friction torque components. They depend on the ratio of the relative rotational to translational velocities. The relationship between the dynamic thread shear force and bending moment is developed. When the external transverse excitation is large enough, it causes the threaded fasteners to loosen. Numerical results show that the dynamic transverse shear forces on the underhead contact surface, and between the engaged threads, decrease the bearing, and thread friction torque components. The effect of bolt preload, bearing and thread friction coefficients, the amplitude of the harmonic transverse excitation, and the bolt underhead bending on the bolt loosening are investigated. Experimental verification of the analytical model results of the bolt twisting torque is provided.

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