The member stiffness in a bolted connection has a direct influence upon safe design with regard to both static and fatigue loading, as well as in the prevention of separation in the connection This work provides a simple technique for computing the member stiffness in many types of bolted connections Finite element analyses are performed for joints having a range of materials and geometries, and the results are generalized by nondimensionalization An exponential expression for the stiffness is determined, and the results are compared with those of some of the techniques currently used

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Computation of Member Stiffness in Bolted Connections

Equivalent axial stiffness of various components in bolted joints subjected to axial loading

The use of pipe flange connections is standardized in the codes of JIS, ASME, DIN and so on. However, these codes are almost entirely dependent on experience, and subsequently some problems concerning pipe flange connections have been encountered. In the present paper, the distribution of contact stresses which governs the sealing performance is analyzed as a three-body contact problem, using an axisymmetrical three-dimensional theory of elasticity. The effects of the stiffness and the thickness of raised face metallic gaskets on the contact stresses and the effective gasket seating width are shown by numerical calculation. Moreover, stresses produced on the hub, the load factor (the relationship between an increment of bolt axial force and an internal pressure), and the maximum stress caused in bolts are analyzed. For verification, experiments are carried out. The analytical results are satisfactorily consistent with the experimental results.

A Stress Analysis of Pipe Flange Connections

Nonlinear Deformation Behavior of Clamped Bolted Joints Under a Separating Service Load

The stresses of a pipe flange connection with a spiral-wound gasket under internal pressure are analyzed taking account a nonlinearity and a hysteresis of the gasket by using an axisymmetric theory of elasticity and the finite element method (FEM) The leakage tests were also conducted using an actual pipe flange connection with a spiral-wound gasket Using the contact stress distribution of the pipe flange connection with 3-in nominal diameter under internal pressure and the tightness parameter, the values of the new gasket constants are obtained by taking into account the changes in the contact stress A difference in the new gasket constants between the estimated values obtained from the actual pipe flange connection and the values obtained by the PVRC procedure is small In addition, a method to determine the bolt preload for a given tightness parameter is demonstrated The obtained results of the bolt preload for the pipe flange connection are in a fairly good agreement with those obtained by the PVRC procedure under a lower pressure application However, a difference in the bolt preload is about 10% when an internal pressure is increased

Stress Analysis and Determination of Bolt Preload in Pipe Flange Connections With Gaskets Under Internal Pressure

An important point in designing a bolted joint is to know the increment of an axial force produced in a bolt, when a load is applied on an assembly. For this purpose, it is necessary to know the spring constant Kc for a connected part and Kt for the bolt with a nut. In the calculation of Kt, up to now, the deformations of bolt head and nut have not been taken into consideration. A purpose of this paper is to analyze the value of Kt, taking into account these deformation, and to rationalize the design of the bolted joint. Assuming that the bolt head is a finite cylinder and the nut is a finite hollow cylinder, these deformations are analyzed by using the three-dimensional theory of elasticity. Experiments on these deformations are carried out, and the theoretical value is compared with the experimental one. They show a fairly good agreement with each other. Taking into account these deformations, for example, the value of Kt for M24 (clamping length 50 mm) is calculated. It is found that this value is 20% smaller than that of Kt by the conventional method.

On the Deformation of the Bolt Head and Nut in a Bolted Joint

In designing a bolted joint, it is important to estimate the force ratio. But this force ratio is the factor to be considered in the case where a load is applied only in the axial direction, but it is not considered when an external bending moment is applied on an assembly. In the previous paper, in the case of T-flanges, a force ratio for the external bending moment, which is the ratio of the increment of bolt axial force to the external bending moment, is introduced. In this paper, the force ratio for the external bending moment is analyzed in the case of circular flanges. The effect of the circular pitch diameter on the force ratio for the external bending moment is discussed. In addition, the stresses produced in bolts are analyzed. Then, in order to verify these analyses, experiments are carried out. Comparing these results, they are in a fairly good agreement.

On the Characteristic of a Bolted Joint Subjected to an External Bending Moment : the case where clamped parts are circular flanges

In designing a bolted joint it is important find the ratio of the increment of an axial force produced in a bolt to a load applied to an assembly, that is, the force ratio. In the previous paper, the tensile spring constant Kpl 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 Kpl. In this paper, the similar method is applied to the force ratio of a connecting rod. The connecting rod is replaced by a circular ring and analysed by the two dimensional theory of elasticity. Moreover, the bending moment produced in the bolt corresponding to the applied load is analysed. In order to verify these theoretical analyses, an experiment is carried out. The obtained results are as follows: (1) The theoretical values show a fairly good agreement with experimental ones. (2) In the estimation of the maximum stress the influence of the bending ;moment should be taken into consideration.

The Force Ratio of Bolted Joints : The case where clamped parts are connecting rods

In designing a bolted joint it is important to find the ratio of an increment of an axial force produced in a bolt to a load applied to an assembly, that is the force ratio. In previous paper, 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. In this paper, the similar method is applied to calculation of the force ratio of flanged connections. Moreover, the bending moment produced in the bolt corresponding to the applied load is analysed. In order to verify these theoretical analyses, an experiment if carried out. The obtained results are as follows. (1) The theoretical values show a fairly good agreement with experimental ones. (2) In evaluation of sealing effect of flanged connections the raised face joints are more effective than the flat face joints.

The Force Ratio of Bolted Joints : The case where clamped parts are flanges

Gaskets have been usually used in bolted joints in mechanical structures such as pressure vessels and pipe flanged connections. But a design of bolted joints with gaskets almost depends on experience and the sealing performance is not theoretically clarified. In this paper, a bolted joint in which a metal flat gasket is interposed between two hollow cylinders is studied. At first, a contact stress, which governs the sealing performance is analyzed as a three body contact problem using the three-dimensional theory of elasticity. Effects of the stiffness and the thickness of gaskets on the sealing performance are shown by numerical analyses. Next, the force ratio of bolted joints with gaskets, that is a ratio of an increment of bolt axial force to an external load, is analyzed. Corresponding to this analysis, experiments are carried out. Analytical results fairly coincide with experimental ones.

Toshiyuki Sawa

Papers

On the Deformation of the Bolt Head and Nut in a Bolted Joint

On the Characteristic of a Bolted Joint Subjected to an External Bending Moment : the case where clamped parts are circular flanges

The Force Ratio of Bolted Joints : The case where clamped parts are connecting rods

The Force Ratio of Bolted Joints : The case where clamped parts are flanges

On the characteristics of bolted joints with gaskets: stress analysis of a metal flat gasket interposed between two hollow cylinders