Answer to Question #104963 in Physics for Nyx

Question

Two concrete spans of a 170 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.

Answer 1

$$L_i=0.5L=0.5(170)=85\ m$$

After expansion, the length of one span is

$$L_f=L_i(1 +αΔT)=85(1 +(1.2 \cdot10^{−5})(20))=\\=85.0204\ m$$

From the Pythagorean theorem,

$$h=\sqrt{L_f^2-L_i^2}$$

$$h=\sqrt{85.0204^2-85^2}=1.86\ m$$