# CWR stress transition zone

(prelude to a new PWI Journal article)

A stress transition zone is any section of continuous welded rails (CWR) where the thermal force is variable, the longitudinal resistance (p) is active and rail movement occurs due to rail temperature variations. The most common (and well known) location of the stress transition zone is at the end sections of the CWR track, where the rail thermal force varies from the constant value in the central fixed zone (see the definition of CWR) to null (or close to null) at the end of the continuous welded rails.

Here is presented the development of the transition zone at the end of a CWR section provided with an adjustment switch.

The CWR is presumed installed naturally, at a suitable stress-free temperature T0. During the night, the temperature falls to a minimum T1 and in the central fixed zone of CWR a constant tension force is developed, since no rail contraction can occur.

The rail contracts at the ends of the CWR, gradually activating the track longitudinal resistance (p – illustrated by the horizontal arrows drawn in the diagrams), and a stress transition zone LT1 is developed. In this zone the tension force varies linearly from the tensile force developed in the constant fixed value to null, at the adjustment switch: This length can be theoretically calculated using the equation: The next day the rail temperature is presumed to return to the stress-free temperature (T2 = T= SFT). On the central zone the thermal force returns to zero. On the stress transition zone the rail will tend to expand, the longitudinal resistance (p) is activated to oppose this tendency and will retain a variable compression force induced by the increase in temperature from T1 to T2. Even though the rail has now returned to the original installation temperature and on the central fixed zone there is no thermal force present (N2 = 0), there is a thermal compression force on the stress transition length developed over night due to the temperature increase from T1 to T2. This might sound strange – the rail temperature has not yet increased above the installation (stress free) temperature, however, in the rail there is already a compression force. After several days of rail temperature variations, the stress transition zone (LT) develops further and its length can no longer be accurately evaluated. The rail thermal force variation over this zone becomes irregular and will never again be null, at least not until a new natural re-stressing is undertaken. Within its length, it can contain higher thermal forces than the ones in the central zone and even have a combination of both compression and tension force sections at one and the same time. In time, the length of this zone grows further reaching a maximum value (LTmax) , specific for each railway network. Within this maximum stress transition zone the thermal force is irregular and unknown. However, it is theoretically accepted to be contained within a range (between a maximal and minimal envelope) defined, among other factors, by the average value of the track longitudinal resistance. This complex behaviour is not prevented by the presence of an adjustment switch at the end of the CWR section. What  it does is to avoid the transfer of the thermal forces to the adjacent section of track by reducing the rail thermal force to null at the end of the CWR section (as shown in the drawings above). If at the end of the CWR a normal joint would be installed instead (as some railway administration are doing), part of the thermal force will be transferred to the adjacent section of  (jointed?) track which, at least on a certain length, is required to have similar structure/components/stability as the CWR.

The thermal force diagrams shown here and in other articles of this blog, should be accompanied by force equilibrium diagrams, showing the longitudinal resistance force (p) distribution along the rail, balancing the (axial) thermal force N, constant in the fixed zone of CWR – as shown in the example below. The longitudinal resistance directions are highlighted also in colour:

• brown if it opposes the rail expansion and increases the compression force in the rail – noted pcompression in the equilibrium equation and considered distributed on sections of the stress transfer zone noted LT compression
• dark blue if it opposes the rail contraction and increases the tension force in the rail – noted ptension in the equilibrium equation and considered distributed on sections of the stress transfer zone noted LT tension

The (vectorial) sum of forces is defined by this equilibrium equation:

∑ (pcompression * LT compression) + ∑ (ptension * LT tension) = Nn

I will try in future to provide them in this way, however, I hope the way they were presented up until now have not created any confusion. The diagrams which show the thermal force (axial, longitudinal in nature) as a vertical variation – above the axis/brown for compression and below the axis/blue for tension should not have the longitudinal resistance, p, shown as horizontal arrows. A better and clearer illustration is the one in the last drawing above, with a separate equilibrium force diagram. I apologise if the previous illustrations have created any confusion.

## 2 thoughts on “CWR stress transition zone”

1. Constantin says:

A. I was expecting you to comment that p should not be shown as horizontal arrows on a diagram where the axial force variation is illustrated vertically – I know this is not entirely correct and p should be shown on an equilibrium axial diagram, where also the force N should be shown also. But I hope the reader will excuse me and understand the way p is illustrated in the drawings above (and in the other articles here) . However, I added a short note in the text.

B. Yes, that phrase requires more explanations – some of them provided in thearticle presenting the definition of CWR.

C. Indeed, this last diagram requires also more explanations. I will leave that for later.

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2. Valentin-Vasile UNGUREANU says:

For prelude is good with some coments:

A. Add p under arrows in figure with step 1 Night. T1=To-deltaT1!

B. The phrase ,,In time, the length of this zone grows further reaching a maximum value (LTmax) , specific for each railway network” must be explained more, in my opinion! In fact LT max depend by the tipe of rail, track longitudinal resistance and maximum range of temperature differences between SFT and extremal temperatures of rail.

C. It is questionable if is accurately ,,the average value of the track longitudinal resistance” in the phrase ,,Within this maximum stress transition zone the thermal force is irregular and unknown, it is however contained within a theoretical range (between a maximal and minimal envelope) defined by the average value of the track longitudinal resistance.”

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