If you could answer it to significant figures please Concrete sections 22 m long

Question

If you could answer it to significant figures please

Concrete sections 22 m long are laid at 15 degree C. What is the required gap if the highest temperature expected is 35 degree C? The coefficient of thermal expansion of concrete is 11 times 10-6 / degree C. What is the stress induced in the concrete if the temperature rises to 40 degree C? (Young's modulus for concrete is 26 GPa.) A copper wire is 25 m long on a winter day when temperature is -15 degree C. By how much does its length increase on a 30 degree C summer day? [The coefficient of thermal expansion of copper is 17 times 10-6 / degree C.] At 0 degree C, the hole in a steel washer is 9.52 mm in diameter. To what temperature must it be heated in order to fit over a 9.55 mm diameter bolt?

Explanation / Answer

(a)(i) linear expansion: the length change is proportional to initial length and temperature change. The constant of proportionality is called the "linear expansion coefficient). In a formula:
?L = ? L ?T
Just plug in the value of ? for concrete ( Here I will take ? = 11 x 10^(-6) /degree) to find the change in length of the 22 m long beam and a ?T = 35 C - 15 C = 20 C:

?L = 11 x 10^(-6) /C * 22 m * 15 C = 3.63 mm
Since each beam has room to expand both directions, the gap between the beam needs to be 3.63 mm

(ii) with a rise of 25 C, the length change can be calculated as in (a). Assuming that the gap used is 3.63 mm, you then know what the compression ?x is. Using p = E ?x/L, you will know the stress.

?x=11x10^-6*22*25= 6.05 mm

So p=26x10^9*6.05x10^-3/22= 7150000 Pa

3. ?L = 17 x 10^(-6) /C * 25 m * 45 C = 0.019125 m

4. linear expansion coefficient of steel at 20 C = 13 x 10^-6 /C

0.03 x10^-3 = 17x10^-6*9.52x10^-3*(T-0)

So T=185.4 C

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