Loading plane factor (n)

The basis of the procedure concerning the determination of the so-called Loading Plane Factor (n) is controversial. Usually, during assembly of the connection, the both forces, bolt preload F_V and the reaction force in the separation surface F_K, act along the bolt axis (see Fig., a). The clamped parts are pressed together where the counting compliance is . Under the external load this effect separates (Fig. b), so that the compliance of connected parts is divided to the effect based on the bolt force and effect based on the force in the separation surface.

Clearly then, the corresponding effect manifests differently and, evidently, has nothing to do with the position of the force application of the external force. Moreover, based on the VDI explanation in the case of the larger eccentricity the designer had to come to the conclusion that he should neglect any of these effects, although the impact stays very strong.

Mounting uncertainty value for connection with several screws

For complex structures it is common to treat the possible deviation of scattering parameters statistically. In addition, the multy-bolted connections are dominated by the Fail-safe case where the failure of one fastener is compensate by the carrying capacity of the neighbourhoods' one.

This means for the consideration of the variation of preloading force it is necessary to consider the number of bolts in the connection and the conditions of loads. The difference in this respect for one rotating flange and statistic pipe flange is obvious.

Influence of the preloading force level

Analytical studies have clearly shown that the stress conditions in a connection are determined, not only by ratio of stiffness in the joint, but also much more by the ratio between preloading and working force. Consequently, the level of the preload is very important parameter for the integrity of the structures with bolted joints.

In the practice, the bill becomes this fact already for a long time, through the over elastic preloading. Paradoxally, especially with the dynamically loaded connections in the engine construction, since through it the level of the mean stress increases strongly. Obviously is the cut of the tension-amplitude in this case more important. With the materials that respond very strongly to mean stress must, however, this situation should be more exactly examined.

Additional embedding

Through eccentric outer loads the clamping-force transfers itself with increased loading from the connection-axis. With it the new contact areas were enclosed that also leads to the additional embedding, and consequently leads to the effective reduction of the preloading force in the connection that must be taken into account additionally.

Determination of the eccentricity of the external force "a"

The determination of the eccentricity, "a" is tainted with large risk, because the bolt connection could not be considered fully disconnected from the rest of the structure (plate, flange, etc.). Usually, at the place of clamping of the connection to the remaining structure in addition to the force, there is also the moment , that must be considered and the stiffness ratios in the connection are not independent of the remaining structure. The determination in this respect, which is not at all easy, has been leaved to the user, by which of course the potential pitfalls are enormous. By less accurate determination of the relevant parameter of the load, the results of the calculation will be called into question.

Connection with limited external dimensions

Individual connections, in which the so-called deformation cone has been cut on all sides, present the typical case of the connections with the limited external dimensions. Such slender cylindrical compounds behave strongly non-linear. For the treatment of such compounds, the method has been developed by author [Konstruktion 27(1976) S. 192-97)], which is taken out, unfortunately, from the latest edition of VDI 2230.

Less important for the analysis but necessary for understanding is the explanation for the Compression Cone Half Angle. This angle is the fictive one limiting the effect zone (Cone) based on equal pressure distribution for the purposes of calculations. Separation to the Cone and Sleeve based on this fictive angle is not accurate.

Some general comments

Adequate function of a bolted connection is dependent on all parts in the assembly that are loaded by each other. Therefore, with the calculation of the connection not only the joint part but also the clamped parts are at stake. This means that the parts can not be constructed independently. The parts such as flange, cover, etc., weakened by the screw holes, are also exposed by the eccentric loading of the connection to the increased bending loads. How then will they be calculated?

Perhaps the most significant shortcoming of the known models is that the function of this connection is reduced to only two control parameters: compliance of the parts in the direction of the screw axis and the guarantee of the sufficient preloading minimal force. All other influencing variables, such as the bending stiffness of the connected parts (plates, cylinders, etc.), actual position (eccentricity) of the external force, level of preloading force and preloading bending moment, inserting of increased stressing (Prying) remained virtually ignored.

In contrast, the safe and conservative methods, based on the beam model are available for the design of screw connections. By the author, based on the fundamental relationships of solid mechanics, the firstly proposed beam model has been developed. Using this model, the bolted joint can be modelled by considering the nonlinear behaviour and the conditions for adequate function in a more general manner.

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