An unconstrained 10mm thick plate of steel 100mm on a side with a 25mm diameter hole in the center is heated from 20 degrees C to 120 degrees C. The linear CTE is 12x10-6/⁰C. What is the final diameter of the hole

Respuesta :

Answer:

The correct answer is "25.03 mm".

Explanation:

Given:

Thickness of plate,

= 10 mm

On a side,

= 100 mm

Diameter hole,

= 25 mm

Coefficient of thermal expansion,

CTE = [tex]12\times 10^{-6} /^{\circ} C[/tex]

Now,

⇒ [tex]D_i\times (12\times 10^{-6}) \Delta \theta = \Delta D[/tex]

=  [tex]25\times 12\times 10^{-6} \Delta \theta[/tex]

= [tex]3\times 10^{-4} \Delta \theta[/tex]

= [tex]3\times 10^{-2}[/tex]

hence,

The final diameter of hole will be:

[tex]D_f=25.03 \ mm[/tex]