Friday, December 2, 2016

If you have ever driven on the roads in New York, you know they are horrible. Asides from potholes, often seen in the winter months, the roads experience a lot of warping. This is the result of having all four seasons: there is a large variation in temperature between winter and summer. In the summer when it is hot out, the concrete molecules of the road expand and  in the winter when temperatures drop below zero, the molecules contract.

figure 1: cracked highway

The behavior of the New York roads can be described by the 0th law of thermodynamics: thermal equilibrium. Thermal equilibrium is when two objects in contact have the same temperature. Objects in contact, of two different temperatures, will move towards thermal equilibrium.
To demonstrate how much the concrete road will expand as a result of a certain  temperature change, I will use the equation of liner thermal expansion:

The equation above solves for the change in length which is equal to the coefficient of linear expansion multiplied by the original length of the object multiplied by the change in temperature in celsius.
Assuming the original length (Lo) of the concrete is 200 m long, and our coefficient of linear expansion (α) is about 10.5 x 10-6 1/°C (source: Federal Highway Administration), we can calculate the expansion of the concrete (ΔL) as a result of a temperature change (ie. 5 °C). The calculated change in length would then be:

The concrete would expand 0.0105 meters which is equal to 0.413 inches.
To remedy the expansion, and subsequent destruction, of the concrete roads, engineers often put control joints into the concrete; you have most likely seen this in concrete sidewalks. Control joints are spaces carved into the concrete to allow expansion to occur in a controlled fashion.

figure 2: control joint in concrete

Sources:
https://en.wikipedia.org/wiki/Expansion_joint#/mediaFile:Saw_Cut_Control_Joint_in_ Concrete.jpg