Question

Steel train rails on LRT2 are laid in 10.0-m-long segments placed end to end. The rails are laid on a day when their temperature is 28.0°C. (a) How much space must be left between adjacent rails if they are just to touch on a summer day when their temperature is 39.0°C? (b) If the rails are

originally laid in contact, what is the stress in them on a summer day when their temperature is

39.0°C?

Answer 1

Given:

$l_0=10\rm \: m$

$t_0=28.0^\circ \rm C$

$t=39.0^\circ \rm C$

$\alpha= 11.5*10^{−6}\:\rm1/°C$

$E=200\:\rm GPa$

(a) the linear exspansion equation says

$$l=l_0(1+\alpha (t-t_0))$$

So

$$\Delta l=l_0\alpha (t-t_0)\\ =10*11.5*10^{−6}(39.0-28.0)=\rm 0.0077\: m$$

(b) the stress is given by

$$\sigma=\epsilon E=\frac{\Delta l}{l_0}E\\ =\frac{0.0077}{10}*200*10^9=1.54*10^8\:\rm Pa$$