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Vilka [71]
3 years ago
15

Two concrete spans of a 380 m long bridge are

Physics
1 answer:
Mazyrski [523]3 years ago
4 0

Answer:

4.163 m

Explanation:

Since the length of the bridge is

L = 380 m

And the bridge consists of 2 spans, the initial length of each span is

L_i = \frac{L}{2}=\frac{380}{2}=190 m

Due to the increase in temperature, the length of each span increases according to:

L_f = L_i(1+ \alpha \Delta T)

where

L_i = 190 m is the initial length of one span

\alpha =1.2\cdot 10^{-5} ^{\circ}C^{-1} is the temperature coefficient of thermal expansion

\Delta T=20^{\circ}C is the increase in temperature

Substituting,

L_f=(190)(1+(1.2\cdot 10^{-5})(20))=190.0456 m

By using Pythagorean's theorem, we can find by how much the height of each span rises due to this thermal expansion (in fact, the new length corresponds to the hypothenuse of a right triangle, in which the base is the original length of the spand, and the rise in heigth is the other side); so we find:

h=\sqrt{L_f^2-L_i^2}=\sqrt{(190.0456)^2-(190)^2}=4.163 m

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