On Fri, 4 Aug 2017 12:38:34 -0700 (PDT), Harrison Hill
Post by Harrison HillPost by Tak ToPost by J. J. LodderPost by Tak ToPost by Athel Cornish-BowdenPost by J. J. LodderPost by Paul CarmichaelPost by J. J. LodderPost by Athel Cornish-BowdenThe floor tiles in our kitchen were installed about 45 years ago
without any spacers between them, whether mortar or air or anything
else. Big mistake.
Don't think so. Mortar wouldn't have helped,
since sand doesn't compress very well.
This is why we have flexible grout.
Yes, but Athel's floor is 45 years old,
What about railway lines? When I were a lad we were told that the
characteristic sound of the wheels going over the gaps was due to the
need to allow expansion, but modern rails don't seem to have any gaps.
The force is great but apparently not unmanageable.
<gross simplification>
The Young's modulus (E) of steel is about 200GPa[1]. The
coefficient of linear thermal expansion (?) is ~<= 13E-6/K[2].
The rail's linear density (?_r) is ~<= 70Kg/m[3]. The density
of steel (?) is~<= 7800Kg/m^3[4]. Assuming a temperature
differential (?T) of 60K, the thermal stress in the longitudinal
direction of the 2 rail beams is
horizontal stress (F_h) = E * ? * ?_r/? * ?T * 2 ~= 2.85E+5 Kg-wt
This is to be countered by frictional forces, the weakest of which
is assumed to be that between the concrete sleepers the gravel
below. The coefficient of friction (?) in this case being
~>= 0.55[5], the required normal force is
normal force (F_n) = F_h/? = 5.2E+5 Kg-wt
I don't know much about concrete sleepers so I just picked
a type randomly from the web[6]. Each of this has a mass (M_c)
of 620 lb (281Kg) and the spacing distance (?s) is <= 28" (0.71m).
Together with the mass of the rails themselves, the total
linear density (rail and sleepers) is
track linear density (?_ttl) = M_c/?s + ?_r*2 = 515 Kg/m
Thus, any *straight* continuously welded track that is slightly
longer than 1 Km and is securely attached to concrete sleepers
should have enough frictional force to resist thermal expansion
or contraction in the longitudinal direction.
Curves, OTOH, ...
[1] https://en.wikipedia.org/wiki/Young%27s_modulus
[2] https://en.wikipedia.org/wiki/Thermal_expansion
[3] https://en.wikipedia.org/wiki/Rail_profile
[4] http://www.engineeringtoolbox.com/metal-alloys-densities-d_50.html
[5] http://usacetechnicalletters.tpub.com/ETL-1110-3-446/ETL-1110-3-4460006.ht
m
Post by Tak To[6] http://www.roclatie.com/rocla-products/concrete-rail-ties/yard-tie-101y/
</gross simplification>
Indeed, quite wrong even.
The problem with hot rails is not material strength,
it is instability against suddenly bending out.
With cold rails it is rails breaking, not friction,
Who said anything about the problem being material strength
or friction? It is not clear if you have read my analysis
but did not understand it, or have not read it all.
Moreover, you failed to answer what Athel asked, namely how
continuously welded tracks handle thermal expansion and
contraction.
I'm not an engineer, but as far as I know the answer is
very simple. The gap is still there, but it is a diagonal
gap. The rails are there bearing the weight - but there
is no "clickety-clack".
The discussion is about gap-less rails, aka "Continuous welded rail".
Stretches of CWR can be linked with expansion joints with diagonal gaps
<https://en.wikipedia.org/wiki/Track_(rail_transport)#Continuous_welded_rail>
Most modern railways use continuous welded rail (CWR), sometimes
referred to as ribbon rails. In this form of track, the rails are
welded together by utilising flash butt welding to form one
continuous rail that may be several kilometres long. Because there
are few joints, this form of track is very strong, gives a smooth
ride, and needs less maintenance; trains can travel on it at higher
speeds and with less friction. Welded rails are more expensive to
lay than jointed tracks, but have much lower maintenance costs. The
first welded track was used in Germany in 1924 and the US in
1930[12] and has become common on main lines since the 1950s.
The preferred process of flash butt welding involves an automated
track-laying machine running a strong electrical current through the
touching ends of two unjoined pieces of rail. The ends become white
hot due to electrical resistance and are then pressed together
forming a strong weld. Thermite welding is used to repair or splice
together existing CWR segments. This is a manual process requiring a
reaction crucible and form to contain the molten iron.
Thermite-bonded joints are seen as less reliable and more prone to
fracture or break.[citation needed]
North American practice is to weld 1/4 mile long segments of rail at
a rail facility and load it on a special train to carry it to the
job site. This train is designed to carry many segments of rail
which are placed so they can slide off their racks to the rear of
the train and be attached to the ties (sleepers) in a continuous
operation.[13]
If not restrained, rails would lengthen in hot weather and shrink in
cold weather. To provide this restraint, the rail is prevented from
moving in relation to the sleeper by use of clips or anchors.
Attention needs to be paid to compacting the ballast effectively,
including under, between, and at the ends of the sleepers, to
prevent the sleepers from moving. Anchors are more common for wooden
sleepers, whereas most concrete or steel sleepers are fastened to
the rail by special clips that resist longitudinal movement of the
rail. There is no theoretical limit to how long a welded rail can
be. However, if longitudinal and lateral restraint are insufficient,
the track could become distorted in hot weather and cause a
derailment. Distortion due to heat expansion is known in North
America as sun kink, and elsewhere as buckling. In extreme hot
weather special inspections are required to monitor sections of
track known to be problematic. In North American practice extreme
temperature conditions will trigger slow orders to allow for crews
to react to buckling or "sun kinks" if encountered.[14]
After new segments of rail are laid, or defective rails replaced
(welded-in), the rails can be artificially stressed if the
temperature of the rail during laying is cooler than what is
desired. The stressing process involves either heating the rails,
causing them to expand,[15] or stretching the rails with hydraulic
equipment. They are then fastened (clipped) to the sleepers in their
expanded form. This process ensures that the rail will not expand
much further in subsequent hot weather. In cold weather the rails
try to contract, but because they are firmly fastened, cannot do so.
In effect, stressed rails are a bit like a piece of stretched
elastic firmly fastened down.
CWR rail is laid (including fastening) at a temperature roughly
midway between the extremes experienced at that location. (This is
known as the "rail neutral temperature"). This installation
procedure is intended to prevent tracks from buckling in summer heat
or pulling apart in winter cold. In North America, because broken
rails (known as a pull-apart) are typically detected by interruption
of the current in the signaling system, they are seen as less of a
potential hazard than undetected heat kinks.
Joints are used in continuous welded rail when necessary, usually
for signal circuit gaps. Instead of a joint that passes straight
across the rail, the two rail ends are sometimes cut at an angle to
give a smoother transition. In extreme cases, such as at the end of
long bridges, a breather switch (referred to in North America and
Britain as an expansion joint) gives a smooth path for the wheels
while allowing the end of one rail to expand relative to the next
rail.
This shows a welded joint:
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and this, an expansion joint with diagonal gap:
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--
Peter Duncanson, UK
(in alt.usage.english)
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>#/media/File:Geschweisster_schienenstoss.jpeg)
#/media/File:Expansion_joint,_Hayle.jpg)
