Length of the bridge(L) : 280 m
There are 2 spans, so: initial lenght of each span
Li = L/2 = 280 /2 = 140 m
The increase in temperature makes the lengths increase:
Lf = Li ( 1 + ∝ΔT)
Li = initial lenght of each span = 140m
∝= thermal coefficient of expansion = 1.2 × 10^−5(◦C)^−1
ΔT= change in temperature = 20°C
Replacing:
Lf = (140) ( 1 + (1.2 × 10^−5) (20) )) = 140.0336 m
Apply the Pythagorean theorem to find the height that each span rises due to thermal expansion.
h = √Lf^2 - Li^2 = √ (140.0336 ^2 - 140 ^2 ) = 3.067 m