Question

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

Answer 1

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 = $12\times 10^{-6} /^{\circ} C$

Now,

⇒ $D_i\times (12\times 10^{-6}) \Delta \theta = \Delta D$

=  $25\times 12\times 10^{-6} \Delta \theta$

= $3\times 10^{-4} \Delta \theta$

= $3\times 10^{-2}$

hence,

The final diameter of hole will be:

$D_f=25.03 \ mm$