Calculate the change in length of this concrete deck: 40' long 20° winter 100° summer.

• A. 0.21 inches
• B. 0.18 inches
• C. 0.25 inches
• D. 0.30 inches

Answer: (A)

When concrete heats up, it expands in length. The amount it lengthens is given by ΔL = α L ΔT, where α is the coefficient of linear expansion for concrete (roughly 10 × 10^-6 per °C in many practice problems), L is the original length, and ΔT is the temperature rise in degrees Celsius.

Temperatures are given in Fahrenheit, so convert the temperature change to Celsius: the outdoor temperature rises from 20°F to 100°F, a difference of 80°F. This is 80 × 5/9 ≈ 44.4°C.

The deck is 40 feet long, which is 480 inches. Using α = 10 × 10^-6 per °C, the change in length is:

ΔL = (10 × 10^-6) × 480 × 44.4 ≈ 0.213 inches.

So the deck expands by about 0.21 inches from winter to summer, which matches the given answer.