Assuming each concrete span is half the length of the bridge, so 195 m
ΔL = αLΔT,
where,
ΔL: change in length
α: coeff. of thermal expansion
L: current original length
ΔT: change in temperature
We need to look at each span individually.
Let's fill in the variables we know:
L = 195 m
α = 1.2*10^-5 /C
ΔT = 20 C
ΔL = (1.2*10^-5)(195)(20)
ΔL = 0.0468 m, this is how much each span expands.
Now, we can form a triangle with the original length of each span, the new length of each span, and the rise due to buckling.
L0 = 195
Ln = 195 + 0.0468 = 195.0468
Now that we have two of the three sides of the triangle, we can solve for the last side, h.
Pythagorean theorem:
195^2 + h^2 = 195.0468^2
Solving for h,
h = 4.272 m