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