Question

A long steel I-beam used in bridge construction has a length of 15.0 m. The beam may be exposed to temperatures as low as −23°C in the winter and as high as 32°C in the summer. What is the difference in length of the beam between these two temperature extremes? (Give the absolute value of the difference. Enter your answer in mm.)

Answer 1

To solve this problem it is necessary to apply the concepts of thermal expansion. Thermal expansion can be expressed in longitudinal terms such as

$\Delta L = L_0 \alpha \Delta T$

Where,

$\alpha =$ Thermal Expanssion Coefficient

$L_0 =$ Initial Length

$\Delta T =$ Change in Temperature

Our values are given as

$\alpha = 11*10^{-6}/\°C \rightarrow$ from Steel

$L_0 = 15m$

$T_1 = -23\°C$

$T_2 = 32\°C$

Replacing we have that,

$\Delta L = L_0 \alpha \Delta T$

$\Delta L = (17)(11*10^{-6})(32-(-21))$

$\Delta L = 0.009911m$

$\Delta L = 9.911mm$

Therefore the difference in length of the beam between these two temperature extremes is 9.911mm