# Math Help - a steel beam...

1. ## a steel beam...

A steel beam 10m long is installed in a structure at 20oC. What are the beam's changes in length at the temperature extremes of -30oC to 45oC?

2. Originally Posted by babygirl
A steel beam 10m long is installed in a structure at 20oC. What are the beam's changes in length at the temperature extremes of -30oC to 45oC?
Hello, babygirl,

let t be the temperature of a solid in °C. Then the length of it in m with respect to temperature in °C is
$l_t=l_{20}+(t-20)\cdot k \cdot l_{20}=l_{20}(1+(t-20)\cdot k)$

k is a constant, describing the change of length per Kelvin. For steel it is $k=11.7\cdot 10^{-6} \cdot \frac{1}{K}$.

$l_{-30}=10 m\left(1+(-50)K\cdot 11.7\cdot 10^{-6} \cdot \frac{1}{K}\right)=9.99415 m$

$l_{-45}=10 m\left(1+(25)K\cdot 11.7\cdot 10^{-6} \cdot \frac{1}{K}\right)=10.002925 m$

The total change of length at a length of 10 m is:

$\Delta l=l_{45}-l_{-30}=0.008775 m=8.775 mm$

Remark: The temperature of a railroad track in Middle Europe rates from -60°C up to 90°C)

Greetings

EB