Question

1. A new 75 m long concrete footpath is constructed down a Sydney street. Estimate how
many 2 cm thick expansion joints are required to accommodate the change in length of
the path from the coldest midwinter’s night to the hottest summer’s day.

Answer 1

QUESTION:

1. A new 75 m long concrete footpath is constructed down a Sydney street. Estimate how many 2 cm thick expansion joints are required to accommodate the change in length of the path from the coldest midwinter's night to the hottest summer's day.

SOLUTION:

The coefficient of thermal expansion of concrete is $\alpha_{\mathrm{con}} = 12\cdot 10^{-6}K^{-1}$.

(Ref: http://en.wikipedia.org/wiki/Thermal_expansion)

Record high temperature in Sydney was $T_{\max} = 45.8{}^{\circ}C$, and record low temperature was $T_{\min} = 2.1{}^{\circ}C$ (Ref: http://en.wikipedia.org/wiki/Climate_of_Sydney)

So, the change in the linear dimension of the footpath can be estimated to be

$$\Delta L = L _ {0} \alpha_ {\mathrm {c o n}} \Delta T$$

$L_{0} = 75\,m$ – the initial length of the footpath

$$\Delta T = T _ {\max } - T _ {\min } = 4 3. 7 \, K$$

Hence

$$\Delta L = 7 5 \cdot 1 2 \cdot 1 0 ^ {- 6} \cdot 4 3. 7 = 0. 0 3 9 3 3 \, m = 3. 9 3 \, cm$$

So, two 2 cm thick expansion joints are enough to accommodate the change in length of the path from the coldest midwinter's night to the hottest summer's day.

ANSWER: two 2 cm thick expansion joints.