A concrete highway is built of slabs 18.0 m long (at 25 °C). How wide should the expansion cracks be (at 25 °C) between the slabs to prevent buckling if the annual extreme temperatures are −32 °C and 52 °C?(the coefficient of linear expansion of concrete is 1.20 × 10 − 5 °C-1) g

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cjmejiab cjmejiab · Answer 1 · 2019-11-25T01:12:10+01:00

To solve the problem it is necessary to apply the concepts related to thermal expansion of solids. Thermodynamically the expansion is given by

[tex]\Delta L = L_0 \alpha \Delta T[/tex]

Where,

[tex]L_0 =[/tex] Original Length of the bar

[tex]\Delta T[/tex]= Change in temperature

[tex]\alpha[/tex]= Coefficient of thermal expansion

On the other hand our values are given as,

[tex]L_0 = 18m[/tex]

[tex]\alpha = 12*10^{-6}/\°C[/tex]

[tex]T_2 = 52\°C[/tex]

[tex]T_1= 25\°C[/tex]

Replacing we have,

[tex]\Delta L = L_0 \alpha (T_2-T_1)[/tex]

[tex]\Delta L = (18)(12*10^{-6})(52-25)[/tex]

[tex]\Delta L = 5.832*10^{-3}m[/tex]

The width of the expansion of the cracks between the slabs is 0.5832cm

samueladesida43 samueladesida43 · Answer 2 · 2022-04-07T12:40:08+02:00

The width of the expansion cracks between the slabs to prevent buckling should be 0.5832cm.

According to this question, the following information are given:

The values are given as follows:

∆L = Loα (T2 - T1)

∆L = 18 × 12 × 10-⁶ (27)

∆L = 3.24 × 10-⁴ × 18

∆L = 5.832 × 10-³m

Therefore, the width of the expansion of the cracks between the slabs is 0.5832cm.

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