Answer to Question #119107 in Molecular Physics | Thermodynamics for Thandeka

Question

Concrete sidewalks are always laid in sections, with gaps between each section. The drawing shows three identical 2.4-m sections. The outer two are against immovable walls. Two identical gaps between the three sections are provided so that thermal expansion will not create thermal stress that could lead to cracks. Calculate the minimum gap width necessary so that an increase in temperature of 32 C° will not cause cracking of the concrete sections.

Answer 1

Let us calculate the expansion in length of the three sections.

If the initial length of the section is $L_0$ then the final length will be (see https://x-engineer.org/undergraduate-engineering/physics/thermodynamics/calculate-thermal-expansion/)

$L=L_0(1+\alpha\Delta T)$ . The coefficient $\alpha$ of linear thermal expansion is $13\cdot10^{-6}\,\mathrm{/^\circ C}$ (see https://www.engineeringtoolbox.com/linear-expansion-coefficients-d_95.html), therefore the final length of one section will be

$2.4\,\mathrm{m}\cdot(1+13\cdot10^{-6}\cdot32^\circ\mathrm{C}) = 2.4\,\mathrm{m} + 1\,\mathrm{mm}.$ Therefore, the increase of length of one section is 1 mm. Three section will increase the total length by 3 mm, therefore the total length of two gaps should be equal or greater than 3 mm, so the every gap should be equal or greater than 1.5 mm.