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The interplay of forces in a bolted joint

Naturally, it is desirable for threaded joints to be reliable and without risk of loosening on their own. For a high degree of reliability, it is extremely important to have an understanding of the forces present in a bolt connection because every element in the connection influences the final result.
In simple terms, there are two possible types of static loads in a bolt connection:
  • Without a clamping force – the force is transmitted between the plates by upsetting forces and shearing forces in the body of the bolt or the thread. The plates that are to be connected move relative to each other until the bores bear against the body of the bolt or against the thread. In this case, the bolts are loaded on shearing (transverse loading); see figure 1.
  • With a high clamping force – this clamping force prevents the clamped parts from being displaced. The force is transferred by friction, and the bolts are loaded on extension (axial load); see figure 2.

Typically, mutual displacement of the parts to be connected is undesirable. Sufficient clamping force must therefore be applied in the bolt connection.
This force is the preload that is achieved after the nut or bolt has been tightened. If the forces on the structure regularly change direction or are not constant, then there is a dynamic load.
Below, it is shown that a dynamic load may be one of the reasons for bolt connections to loosen, or even for bolts to break. In order for a joint to fulfill its function, especially for a dynamic load, the clamping force must be maintained.
Transverse loading
Axial load

Elastic resilience of a threaded joint

When designing and making a threaded joint, it is very important to understand the following points:

  • The bolts and connected parts function as an elastically resilient unit. The clamped elements are compressed elastically, while the bolt stretches during assembly. If the bolt stretches further due to an external load, the clamped parts spring back. 
  • The tensile force in the bolts is also equal to the pressure force on the clamped elements, which is illustrated in figure 3.
The tensile force in the bolts is also equal to the pressure force on the clamped elements,
The interplay of forces and deformation is presented in a so-called force/deformation triangle, as shown in graph A below. Line 1 in the graph shows the deformation that a bolt undergoes due to tensile force. Line 2 relates to the clamped set that deforms under the influence of the pressure force due to the bolt.
Graph elongation of the bolt

From the graph above, it is evident that with a clamping force Fm, the elongation of the bolt is equal to fsm, and that the compression of the clamped parts is fpm. Because the materials used for the bolts and clamped parts are different, just like the design, fsm and fpm are usually not equal.

An external load Fa is applied to this bolt connection; see figure 4.

External tensile force FA graph
Bolt elongation graph
Compression curve clamped material

A more elastic bolt causes a smaller increase of the bold load.

On the one hand, Fa brings about a reduction in clamping force (Fpa), and on the other hand, it results in an increase in the load on the bolt (Fsa). 

It is desirable that the load increase is as minimal as possible, but not only to prevent the bolt from becoming overloaded. This preference is because if the external load is dynamic, then the bolt senses only the fluctuations in Fsa. A high amplitude of this force Fsa can soon cause fracturing due to fatigue. Moreover, the residual clamping force Fkr must never be zero. If this happens, the connection collapses.

The increase in bolt load Fsa can be limited as much as possible by using a very elastic bolt. As a result, the deformation curve of the bolt is less steep, as the external force is absorbed much more by a reduction in the clamping force; see graph C.

The same effect is reached by using very rigid clamped materials: as a result, the deformation curve of the clamped materials greatly steepens, and the external force is almost completely absorbed by a reduction in the clamping force; see graph D.

Graph D on clamped material

IN SHORT

Particularly with a dynamic load, it is extremely important to keep any additional load on the bolt as low as possible, as sudden fracture can occur due to fatigue.

With an external load, there are a few ways to limit the additional force on the bolt as much as possible:

  • The structural members must be maximally rigid.
  • The clamping force must be as great as possible and certainly greater than the external load.
  • Elastic bolts can be used, in which case (1) a high clamping length-to-diameter ratio (≥ 5xD) should be chosen, (2) a larger thread length should be selected and, if necessary, (3) a reduced shank diameter (reduced shank bolts) should be used.
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