# Linear Expansion

1. Dec 11, 2005

### 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?

Last edited: Dec 11, 2005
2. Dec 11, 2005

### Astronuc

Staff Emeritus
3. Dec 11, 2005

### 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.

4. Dec 11, 2005

### Astronuc

Staff Emeritus
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 $\alpha$.

5. Dec 11, 2005

### 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??

6. Dec 11, 2005

### Astronuc

Staff Emeritus
Correct.