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:

T₂ = 18.65 °C (For Steel)

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

Explanation:

The formula for stress due to temperature difference in a member is given as follows:

Stress = αEΔT

where,

Stress = 12 MPa = 12 x 10⁶ Pa

α = co-efficient of linear expansion of the material

E = Young's Modulus of the Material

ΔT = Temperature Difference = Final Temperature - Initial Temperature

12 x 10⁶ Pa = αE(T₂ - 15°C)

FOR MAGNESIUM:

α = 25.2 x 10⁻⁶ /°C

E = 45 x 10⁹ Pa

Therefore,

12 x 10⁶ Pa = (25.2 x 10⁻⁶/°C)(45 x 10⁹ Pa)(T₂ - 15°C)

T₂ - 15°C = (12 x 10⁶ Pa)/(1.134 x 10⁶ Pa/°C)

T₂ = 15°C + 10.58°C

T₂ = 25.58 °C (For Magnesium)

FOR STEEL:

α = 17.3 x 10⁻⁶ /°C

E = 190 x 10⁹ Pa

Therefore,

12 x 10⁶ Pa = (17.3 x 10⁻⁶/°C)(190 x 10⁹ Pa)(T₂ - 15°C)

T₂ - 15°C = (12 x 10⁶ Pa)/(3.287 x 10⁶ Pa/°C)

T₂ = 15°C + 3.65°C

T₂ = 18.65 °C (For Steel)

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