Question

The 50-mm-diameter cylinder is made from Am 1004-T61 magnesium and is placed in the clamp when the temperature is T1 = 15°C. If the two 304-stainless-steel carriage bolts of the clamp each have a diameter of 10 mm, and they hold the cylinder snug with negligible force against the rigid jaws, determine the temperature at which the average normal stress in either the magnesium or the steel first becomes 12 MPa.

Answer 1

Answer:

The temperature of steel first becomes 12 MPa at a temperature of 18.65°C

Explanation:

Given that,

Diameter = 50 mm

Temperature = 15°C

Diameter = 10 mm

Stress = 12 MPa

We need to calculate the temperature of steel

Using formula of stress

$stress=\alpha Y\Delta T$

Where, Y = young modulus

T = temperature

$\alpha$= coefficient of linear expansion of the material

Put the value into the formula

$12\times10^{6}=17.3\times10^{-6}\times190\times10^{9}\times(T_{2}-15)$

$(T_{2}-15)=\dfrac{12\times10^{6}}{17.3\times10^{-6}\times190\times10^{9}}$

$T_{2}=3.650+15$

$T_{2}=18.65^{\circ}$

We need to calculate the temperature of magnesium

Using formula of  stress

$stress=\alpha Y\Delta T$

Put the value into the formula

$12\times10^{6}=25.2\times10^{-6}\times45\times10^{9}\times(T_{2}-15)$

$(T_{2}-15)=\dfrac{12\times10^{6}}{25.2\times10^{-6}\times45\times10^{9}}$

$T_{2}=10.5+15$

$T_{2}=25.58^{\circ}$

Hence, The temperature of steel first becomes 12 MPa at a temperature of 18.65°C