# What is the stress in steel train rails if the segments are laid in contact?

I have this problem from University Physics (13th edition):

Steel train rails are laid in $12.0-m-long$ segments placed end to end. The rails are laid on a winter day when their temperature is $-2°C$. a) How much space must be left between adjacent rails if they are just to touch on a summer day when their temperature is $33.0°C$? b) If the rails are originally laid in contact, what is the stress in them on a summer day when their temperature is $33.0°C$?

I have solved the a) part as follows:

Expansion coefficient for steel: $1.2\cdot 10^{-5}/°C$

With the formula for lineal expansion

$$\Delta L=\alpha\Delta T L_{0}$$

I just replace with the given values:

$$\Delta L=\frac{1.2\cdot 10^{-5}}{°C}(33.0°C-(-2.0°C))12.0m$$ $$\Delta L=5.04\cdot 10^{-3}m$$

But, for the second part -b)- I have not been able to understand how to approach the problem... What stress means in the context? What concept I need to take into account to solve this problem?

• The word 'stress' means exactly what it usually means in a technical context. It might help you to look up the relevant section to know that it is usually paired with 'strain' when discussing the 'elastic modulus'. – dmckee Jan 30 '17 at 1:53
• Suppose that, after you allowed them to freely expand thermally, you then applied compressive forces at their ends to squeeze them back down to their original lengths. How high would the compressive stress have to be to do this? – Chet Miller Jan 30 '17 at 3:30