Bolt connection with the limited external dimensions
In most cases, the simple bolt connections or connections with one bolt have such lean contours so that to the deformations of the compressed region corresponding body (called "influence body") exceeds its outside dimensions. Also, such joints behave strongly nonlinear. The connected parts deform under loading together with the screw creating with which the form of a bending bar.
For these joints, a specific calculation method was developed by the author, which was then introduced in the first versions of VDI guideline 2230 as a non-linear calculation approach.
In customary case of centrally located screw this relatively complicated method of calculation can be traced, to a simple equation for the calculation of the clamping force eccentricity
which after the s determination make possible to evaluate all forces in the connection with the aid of
The positive effect of the preloading height on the additional stresses in the bolt and the connected parts is already known, which is also likewise involved through the above-mentioned preload factor Φ by the calculation. Based on this, it could be expected that, with an eccentric position of the bolt near to the operating force, which also produces a pre-bending moment, similar effects occur. The results of the experiment that I have carried out have shown, however, that, contrary to the expectations, the i nterrelationships are much more complex. At the start of the loading, even much higher additional forces arise. This increase in the load remains until the compensation of the pre-bending moment, so that the expected positive effect of the pre-bending moment occurs only when the compensation is completed (compare figure).
This can be traced to the following causes: during the preload of the connection, that is, already during assembly, it comes from this, based on the bending of the connections bar, with the additional flexibility of the connected parts. When this initial bending is compensated by the external force and the stiffness reduction disappears (the bending deformations go to zero), produced is for the unchanged initial preload displacements a corresponding growth in the forces in the connection (see pre-stress diagram of the connector). This issue is even strengthened if the location of the screw (as in this experiment with Sv = -5 mm) is outside the core cross-section (for circular cross-section more than D/8) and the deformations of the bar are increased.
The corresponding transition is difficult to compute numerically because when the bending is zero, the bending radius is infinite and its direction changes.
The additional compliance during the preloading by the eccentric position (sV) corresponds
This results in the change of the forces in the connection of
For the data of the experiment set-up results the value of 660 N, which is in agreement with the test results (see picture).
The shift of the bolt in the opposite direction (compression part of the section) works exactly in reverse. The additional forces are even initially slightly reduced (Sv > D/8 compliance increases). Because the edge distance is smaller, however, in the following comes to a sharp increase of the additional loads. This placement of the screw is therefore very unfavorable.
In the event of the centric arrangement of the screw and the cylindrical form of the connection, the one-sided lifting in the connection falls out when the clamping force eccentricity has reached D/8. Inserting s = D/8 (to avoid this) in the above equation arises
This relationship can be simplified by taking into account that δs ≈ δ and last term << 1 so that then for the calculation of the necessary preload of the connection, the simplified relationship can be used:
The bolt additional force is then
Because of the very rapid increase in all stresses in the connection, further increase of the loading of the connection should be avoided. The evaluation of the stresses based on the so-called lever principle is not recommendable because the results are on the unsafe side.
Interested in more detail ? Konstruktion 27(1975) S.192-97
Return to top
Zurück zu den Schraubenverbindungen