# Joint Resistance Force

All the railway track fishplates for mechanical joints are designed to provide a gap to the rail web. This gap, together with the wedge shape of the fishplate section ensure, by tightening the joint bolts, the correct alignment of the rail head between the two jointed rails.

The bolt tightening torque is developing in the bolt a tensile force, A. This tensile force is causing a set of  normal forces N at the contact areas between the fishplates and the rail head and foot.  These normal forces can be found by decomposing the vector of the force A onto the two contact areas between the fishplate and the rail – one on the rail head and the other on the rail foot.

If the rail will tends to move in the joint, these normal forces will cause a set of friction forces between the fishplate and the rail. Any such force will be Nf – where N is the value of the normal force and f is the steel on steel friction coefficient.
Theoretically, for each bolt there will be four such friction forces which will oppose the rail tendency of movement.

The resultant R of these friction forces is called the joint resistance force. This can be defined as:

R = 4n Nf

where n is the number of bolts per rail, N is the normal force caused by the tensile force of the bolt and f is the steel on steel friction coefficient.

The rails will move in the joint only if this resultant force R will be overcome. Only then the joint gap will tend to close or open.
For a normal 4 bolt mechanical joint, designed for constrained thermal expansion track superstructure, the joint resistance force R is usually around 50 kN but might depend significantly dependant on the joint bolts used.

Great Western Railway – heritage rail joint with normal fishplate. Source of the image http://www.oldpway.info/index.html

The joints for free thermal expansion superstructure, usually old type of joints, don’t have a well defined tightening torque for installation and also are lacking essential components to keep this torque constant throughout the normal usage of the joint. In such cases the joint resistance force is ignored in rail thermal expansion calculations, even though the joint bolts have a certain tensile force and, consequently, will develop a joint resistance force. This joint resistance is not continuous, constant and above a well defined limit value and it cannot be used to define in a safe way the thermal behaviour of the track. This, together with the absence of a constant and continuous track longitudinal resistance, commented in a previous post, is modelled in the track behaviour described in the article: When a rail can be called long?, presuming free thermal expansion/contraction of the rail.

Joint gap expansion diagram for free thermal expansion (FTE) track superstructure

#### References

• Hila, V. Radu, C. Ungureanu, C. Stoicescu, G. (1975) Cai Ferate. Partea II. Suprastructura caii. (Railway Track. Part II. Track superstructure). Institutul de Constructii Bucuresti.
• Radu, C. (1999). Cai Ferate – Suprastructura Caii (Railway – Track Superstructure) – Course notes, Faculty of Railways, Roads and Bridges – Technical University of Civil Engineering Bucharest
• http://www.oldpway.info/index.html

## 4 thoughts on “Joint Resistance Force”

1. Hi Bob. Thank you for your comment.
Yes, most of the old fishplated joints are not able to provide a reliable and continuous joint resistance. A certain resistance nevertheless exists but that will only provide a safety factor, delaying slightly the reaction of the rail due to temperature variation.
But for modern joints – it might be for all – NR recommends 475 Nm tightening torque.
That would create a significant joint resistance which should not be ignored. Such a track becomes, by this at least, a “constrained thermal expansion track superstructure” .

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2. Bob Crease MSc CEng FICE FCIArb FPWI says:

Hi Constantin,

Thanks for an interesting paper which added to my understanding of rail joint behaviour. In the UK, the traditional use of jointed track was in “free thermal expansion superstructure”. Normal plain joints were designed to support the differential vertical and transverse loads experienced by each rail end as a wheel passed over the joint. As far as I’m aware, fishplates (known as junction plates) that enabled the jointing of rails of different cross-sections were designed on a similar, empirical basis, in the light of experience. As you say, except in the case of insulated block joints, the frictional resistance of the joint was ignored in considering the resistance to longitudinal movement of the rails.

Indeed, I would suggest that the traditional approach went further and relied upon there being insignificant longitudinal resistance so as to permit the joint to “breathe”. The intention was to allow the gap width between the rail ends to vary depending on the temperature, thereby permitting rail expansion (and contraction) and reducing the propensity of the track to buckle. To that end, a range of gap widths was specified for the installation of jointed track at various rail temperatures. Furthermore, there was a range of annual track maintenance activities known as “spring fettling”, to prepare the track in the spring-time to withstand the effects of summer heat and of temperature variations between day and night. This included the critical activity of plate-oiling, when fishplates were loosened in turn and a lubricant was applied to the inner surfaces before re-tightening the bolts. The purpose was not only to reduce component wear but also to avoid the fishplates seizing, thereby preventing rail expansion and raising the risk of buckles. Traditional practice was not to check the torque of every fishplate bolt, but rather to look for looseness with reference to signs of differential movement and wear, rust marks etc., and to tighten loose bolts during regular track patrols.

Even after the initial development of continuous welded rail, jointed track used to be laid over long structures so as to allow for the differential expansion between the structure and the track. It’s interesting to see the development of models which permit the assessment of the forces involved.

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3. The joint bolts should be tightened according to the specifications of the joint manufacturer and are, I presume, dependant (at least) on the allowed ultimate tensile loads of the bolt threads.
The final torque and the lubrication should be based on the manufacturer recommendation. It should also recommend the maintenance regime – torque check and re-tightening.
I don’t have such details about the products used in UK but I presume the joint resistance force to be similar to the one generally found on the railway networks in Europe.

A thing I forgot to mention here is that the (normal) fishplated joints are using normal grade bolts to allow the gap variation. The insulated block joints are using high strength grade bolts and joint glue to lock the joint and not allow any joint gap “breathing”.

Joint seizing – as in joints between different size of rails?
That’s an interesting subject – I don’t know too much details about this but I expect the joint components to be in such way designed to allow a similar behaviour as for the normal fishplated joints.

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4. Hello Constantin.

Interesting article.

How do you determine the applied torque?

How do you determine the coefficient of friction?

Do you lubricate the interface to permit a reliable coefficient of friction?

Are the bolts regularly checked for torque?

Have you experienced the joints seizing?

Best regards,

Stephen Sharp sharp@stress-test.co.uk

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