# Expansion Due to Temperature

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The  Deformation Due to Temperature calculator computes the deformation caused by a change in temperature.1

INSTRUCTIONS: Choose units and enter the following:

• (α) Temperature Coefficient of Expansion (in units of 1E-6/oK) [see table]
• (L) Length of object
• (T0) Initial temperature
• (Tf) Final temperature

Change in Length (ΔL): The calculator returns the change in length in meters.  However, this can be automatically converted to compatible units via the pull-down menu.,

#### The Math / Science

The equation for change in length based on change in temperature is:

ΔL = α • L • ( T- T0)

where:

• ΔL = change in length (deformation)
• α = the temperature coefficient of expansion (in units of 1E-6/oK)
• L = the length of the object
• T0 = the initial temperature
• Tf = the final temperature.

### Usage

There are many uses for computing the expansion of a material in construction, in manufacturing, in physics experiments, in materials research, etc.  Here are some example applications:

Concrete -  When constructing a concrete floor surface -- let's say for a large storage building -- the temperature changes experienced by the concrete could be significant, depending on where the concrete is located.  Equally significant expansion and contraction can occur in the concrete pads.  To make certain that you have a properly-sized expansion joint between pads you can calculate the change in linear dimension of the concrete slab over a typical temperature range for your geographic region.

For Tulsa Oklahoma, as an example, the average high in July and August is 93.1 oF2.  The lowest of the monthly averages is January with 27.5 oF3 .  So, using this range for the temperature inputs to this equation, obtaining the coefficient for Concrete from the Temperature Coefficient of Expansion Lookup equation (which is 14.5*10^-6 m/(m*K) )as the material and assuming a 10 ft X 10 ft slab (the slab length or width being the expansion direction we want to check, this Deformation Due to Temperature equation would tell us that we would need to provide an expansion joint between the pads that would support a change in width or length of at least: 0.06 inches, which is a little more than a 20th of an inch.

Actually you could be even more precise and perform the calculation using the temperature on the date the concrete was poured and the average high temperature, since initial length will be that length at the temperature you initially cured the concrete.

Plumbing - just like the concrete example above, you might want to check the possible expansion of a run of copper pipe to determine a reasonable offset from the wall frame member where the pipe turns.  The length L would be the entire length of the pipe, including the bend in the pipe at both ends.  The temperatures inputs would be the extremes to which the pipe might be exposed and, of course, we can look-up the selected material,Copper, in the Temperature Coefficient of Expansion Lookup equation to find that the coefficient for Copper is 16.6*10^-6 m/(m*K) .

If we used the same average high and average low temperatures from the Tulsa Oklahoma temperature above, this equation tells us that a forty foot run of copper pipe could expand as much as 0.363 inches in Tulsa's temperature range. So, you would be safer to provide offsets of at least this much to accommodate possible expansion. You could of course, offset the pipe on both ends, first rounding the 0.363 inches up to a half inch and then your safe offset on either end would be approximately a quarter inch.

Manufacturing - fabrication processes may often require fairly stringent adherence to size specifications and thus estimating the expansion due to temperatures a component can experience during fabrication could play an important role in quality control.

An interesting example of the expansion requirements on an aircraft  can be observed in the extreme case of the SR-71.  The surface of this aircraft would exceed 500 oF at full velocity and the largest part of the aircraft was constructed of Titanium.  The aircraft actually leaked huge amounts of fuel on take-off until the surfaces could heat up enough to expand and seal the leaking of the fuel cell.4  The Titanium used for the SR-71's fuselage was an allow but if the fuselage had been constructed of pure Titanium, our equation tells us that a 25 foot panel of fuselage would subjected to a 430 oF temperature change would expand approximately 0.09245 inches (almost a tenth of an inch)