Chapter 13, Problem 8P

To determine

The required width of the expansion cracks between the concrete slabs

Answer to Problem 8P

Solution:

The width of the expansion cracks is 0.504 cm

Explanation of Solution

Given:

Length of the concrete slab at 15°C,1₀=12 m

Temperature range is -30°C to + 50°C

Formula used:

$\text{Δl=l×α×ΔT}$, where α is the coefficient of linear expansion of a material.

Calculation:

The width of the expansion cracks needs to take into account the expansion of the concrete slabs when the temperature rises above 15°C.

The relation between change in length of a substance and change in temperature is given by,

$\text{Δl=l×α×ΔT}$, where ΔT is the change in temperature and α is the coefficient of linear expansion of a material.

For concrete, ${\text{α= 12 × 10}}^{\text{-6}}\text{/°C}$

Based on the given information, ${\text{ΔT=T}}_{\text{f}}{}_{{}^{\text{-}}}{\text{–T}}_{\text{0}}\text{= 50°C – 15°C = 35°C}$

Therefore, $\text{Δl= }\left(\text{12 m}\right)\text{ × }\left({\text{12 × 10}}^{\text{-6}}\text{/°C}\right)\text{ × }\left(\text{35°C}\right)$

$\text{= 5}{\text{.04 x 10}}^{\text{-3}}\text{m }\left(\text{or 0}\text{.504 cm}\right)$