Two concrete spans of a 380 m long bridge are
placed end to end so that no room is allowed
for expansion. If the temperature increases by 20◦C, what
is the height to which the spans rise when
they buckle? Assume the thermal coefficient
of expansion is 1.2 × 10^−5(◦C)^−1
Answer in units of m.

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

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

where

is the initial length of one span

is the temperature coefficient of thermal expansion

is the increase in temperature

Substituting,

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:

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