Two concrete spans of a 250-m-long bridge are placed end to end so that no room is allowed for expansion. If a temperature increase of 20.0C occurs, what is the height y to which the spans rise when they buckle?

y = 2.74 m

Explanation:

The linear thermal expansion processes are described by the expression

ΔL = α L ΔT

Where α the thermal dilation constant for concrete is 12 10⁻⁶ºC⁻¹, ΔL is the length variation and ΔT the temperature variation in this case 20ªc

If the bridge is 250 m long and is covered by two sections each of them must be L = 125 m, let's calculate the variation in length

ΔL = 12 10⁻⁶ 125 20

ΔL = 3.0 10⁻² m

Let's use trigonometry to find the height

The hypotenuse Lf = 125 + 0.03 = 125.03 m

Adjacent leg L₀ = 125 m

cos θ = L₀ / Lf

θ = cos⁻¹ (L₀ / Lf)

θ = cos⁻¹ (125 / 125.03)

θ = 1,255º

We calculate the height

tan 1,255 = y / x

y = x tan 1,255

y = 125 tan 1,255

y = 2.74 m