There will be a differential of temperature between the parts. Assuming the spikes won't relatively move, you can assume there fixity points. In simplified way all else is to translate the elongation of the rail between a pair of ties under temperature increment or the shortening under cooling -for the wanted temeperature increment- to locked compressive and tensile stresses, what is readily made through the coefficient of elongation of the steel under temperature.

It might appear that the eccentrical spikes might induce moment, but it is not to be forgotten that the rail is precisely continuous and will oppose entire and equal reaction at the ends. The stresses locked from temperature should remain relatively small, for the rails have to sustain the heavy loads of the wheels and braking.

There will be no longitudinal thermal expansion, but there will be longitudinal thermal stresses instead.  Hence the clips that connect the rail to the sleeper ("tie") do not transfer large eccentric longitudinal loads.

An irrelevant aside.  To lessen the risk of buckling, continuously welded rail is pre-tensioned so that it will be in tension over the majority of its expected operating temperature range.  A railway I was involved with recently has to cope with temperatures between about -8 and +60 degrees centigrade (18F to 140F):  the rail was pre-tensioned so that its stress-free temperature was 40 degrees (104F).

Dear ishvaaag,

I believe that I understand your reply but I just want to clarify thru the following:

Are you saying that all expansion stresses are being accommodated by the rail material itself?  In other words, is the rail possibly seeing a very very slight non-axial  deformation due to the buildup of stresses at the local area in between the points of fixity (a so called wall stress build-up)?

Also, is the spike restraining all forces by the friction action between it's head and the rail surface ?  What happens if you get slippage at this location?????  Will the next consecutive spike fail in a domino effect or could the rail possibly fail in a non-axial direction ????

How is the friction effect of the spike on the rail enhanced so that risk of either failure (slip or rail material)is reduced ?   

Can this theory be found in a publication, article or text book anywhere along with an example?  If so, where?

I'm no rail expert, but i have seen bolted splice plates on the webs of rails spaced regularly.  I never measured the distance between, but I'd guess maybe 200 to 300 feet apart.  I think these splice plates have slotted holes to allow for thermal expansion and contraction.
I also think if there were no joints for expansion, more rails would buckle during the hottest summer days then already do (you occasionally hear of a derailment during heat-waves).

Well, I understood a case in which there was fixation downwards at the ties. The same only would be the case with friction clips if able to overcome all resulting slippage forces from temperature (and if so available and locked initial stresses such the prestress Denial refers to).

Of course if the expansion forces (or shortining ones) overcome friction you have one rail that is able to expand, in the extent that the standing restrictions allow. If such elongations were big, joints also need be -a problem-, or else what one needs to make is control expansion or shortening at the tie level, rather than for whole rails between joints.