Question

You are given the job of designing a bridge that is to be made of concrete slabs that rest on a steel support frame. The total length of the bridge is 304 m, and you want to be sure that the expansion joints are sufficiently large. If the temperature increases by 28°C, what is the difference in the new lengths of the concrete and steel components of the bridge?

concrete _____m

steel ______m

Which of these components will have the largest increase in length? (The two components are considered expanded by the same amount if their expansions are within 5% of each other.)

a)concrete b)steel c)they both expand by the same amount

Answer 1

from the definition of coefficient of linear expansion

Alpha = Change of length/(0riginal length * change of temp)

Alpha = (dL)/(L0* dT)

here

Alpha of conrete = 1.35 *10^-5 per deg k

alpha of Steel = 12 *10^-6 per deg K

so dL of concrete = Alpha * Lo* dT

dL = 1.35 *10^-6 * 304 * (28)

dL = 0.011 m or 1.1 cm for concrete.

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so dL of steel = Alpha * Lo* dT

dL = 12 *10^-6 * 304 * (28)

dL = 0.102 m or 10.2 cm for steel

so steel have largest expansion (option B)

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