Calculate Temperature for Closed Expansion Joint on Steel Bridge

[lilkrazyrae]

A 215.m steel bridge has an expansion joint of 18.0cm at one end at -15.0 degrees C. At what temperature would the joint be closed?

I would use the equation Change in L=L(alpha)T

But would the L equal zero since the joint is closed?

 

[Astronuc]

Is the length of the bridge 215 m?

If so, what temperature change could cause the bridge to go from 215 m to 215.18 m, or what what temperature change would cause length increase of 18 cm over 215 m of length.

http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thexp.html#c2

 

[lilkrazyrae]

Yes sorry I forgot the m. So are there two answers? And the bridge would have to move from 18cm to 215m for the second part that seems improbable.

 

[Astronuc]

No, the bridge has length of 215 m when its temperature is -15°C.

If the temperature of the bridge increases, the length will increase (thermal expansion).

One is asked to find the temperature at which the bridge will expand 18 cm to close the gap, in which case the bridge length will be 215.18 cm.

The thermal strain is the ratio of length after expansion to the length before expansion, i.e. 215.18/215 = 1 + $\epsilon$, where $\epsilon$ is the thermal strain.

Look at the link I provided - http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thexp.html#c2

Let L = 215 m and $\Delta{L}$ = 0.18 m (or 18 cm), and then find the temperature difference $\Delta{T}$ assuming you know the thermal expansion coefficient $\alpha$.

See also the plate below - http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/thexp.html#c3

 

[lilkrazyrae]

ok so .18=(215m)(12*10^-6)(T(f)-(-15)) and 69.767=T(f) +15 Finally T(f)=54.8 degrees C. Is this correct??

 

[Astronuc]

Correct.