Question

Two concrete spans of a 280 m long bridge areplaced end to end so that no room is allowedfor expansion. If the temperature increases by 20◦C, whatis the height to which the spans rise whenthey buckle? Assume the thermal coefficientof expansion is 1.2 × 10^−5(◦C)^−1Answer in units of m.

Answer 1

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