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A concrete highway is built of slabs 12 m long .How wide should be the expansion cracks between the slabs at 15 Celsius to prevent buckling if the range of temperature is -30 to 50 Celsius?

Respuesta :

Answer:

[tex]x=4.2\ mm[/tex]

Explanation:

Given:

  • length of the concrete slab, [tex]l=12\ m[/tex]
  • temperature of observation, [tex]T_o=15^{\circ}C[/tex]
  • we've the coefficient of linear expansion for concrete, [tex]\alpha=10^{-5}\ ^{\circ}C^{-1}[/tex]
  • lower temperature limit, [tex]T_l=-30^{\circ}C[/tex]
  • upper temperature limit, [tex]T_u=50^{\circ}C[/tex]

Change in length due to temperature can be  given as:

[tex]\Delta l=l.\alpha.(T_u-T_l)[/tex]

[tex]\Delta l=12\times 10^{-5}\times (50-(-30))[/tex]

[tex]\Delta l=0.0096\ m=9.6\ mm[/tex]

Now at temperature 15°C:

[tex]\Delta l'=12\times 10^{-5}\times (15-(-30))[/tex]

[tex]\Delta l'=0.0054\ m=5.4\ mm[/tex]

Hence the expansion crack between the slabs at this temperature must be:

[tex]x=\Delta l-\Delta l'[/tex]

[tex]x=9.6-5.4[/tex]

[tex]x=4.2\ mm[/tex]

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