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What is the height to which the spans rise when they buckle

What is the height to which the spans rise when they buckle-example-1
User Derek Organ
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1 Answer

11 votes
11 votes

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

What is the height to which the spans rise when they buckle-example-1
User Marshalee
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2.4k points