Use The Engineering Toolbox's Coefficients of Linear Expansion table to determine the rate of expansion for a material per inch, per change in temperature. For example, steel's rate is 7.3 times 10 to the minus 6 inches per degree Fahrenheit. To convert from scientific notation into real numbers, a cube of steel 1 inch on a side expands .0000073 of an inch when the temperature rises 1 degree Fahrenheit. This is about 1/50 the thickness of a hair.
You may think that expanding 1/50 the thickness of a hair for steel is not much, but expansion coefficients add up. For example, the Mackinaw bridge in Michigan is 5 miles in length. This converts to 316,800 inches. In the winter, temperatures in Michigan can dip to minus 20 degrees Fahrenheit, and in the summer can reach 90 degrees Fahrenheit. This is a temperature difference of 110 degrees. Multiplying .0000073 by 316,800 by 120 yields 254 inches, or about 21 feet of expansion or contraction.
The Mackinaw bridge problem is one small example of the millions of expansion and contraction problems engineers overcome every day. Engineers design special movable joints, called expansion joints, to allow some "give" for the expansion/contraction problem. If the Mackinaw bridge did not have expansion joints, it would tear itself off its supports when expanding. The Mackinaw bridge has 31 strategically placed expansion joints. These joints interlock like fingers, and slide over each other when the bridge moves. Concrete also expands and contracts. Driveways have black strips at preset intervals -- these are expansion joints for concrete. If they were not there, the concrete would crack, due to internal stresses built up by expansion.
Dissimilar materials placed next to each other pose their own problems. Many automotive engines have cast iron blocks, but aluminum heads. Aluminum's coefficient of linear expansion is greater that iron's. When the engine reaches operating temperature, if the heads expand too much, the head bolts may break. When cooled, the head bolts may loosen. Engineers solved the problem by developing a special head bolt, called a stretch bolt. Stretch bolts are made of a special steel compound, and literally stretch when heated. When the aluminum head expands, the bolt stretches, so it won't break. When the head cools, it retracts. A stretch bolt is almost like a spring, able to expand and contract.