Question

A steel ring is 50mm diameter and 2mm thick. it must be fitted onto a shaft 50.04 mm diameter. calculate the temperature to which it must be heated in order to fit the shaft. the initial temperature is 20 deg C and the coefficient of linear expansion is 15x10^-6 per degrees celcius. calculate the stress and forced induced in the ring
okay so the stress and forced induced I can do that but the first part is confusing me because there is no final temperature.

Answer 1

The temperature to which it must be heated in order to fit the shaft is 73.33 ⁰C.

Linear expansivity

The temperature to which it must be heated in order to fit the shaft is calculated as follows;

$\frac{\Delta L}{L} = \alpha \Delta T\\\\\Delta T = \frac{\Delta L}{\alpha L}$

where;

• ΔT is change in temperature
• ΔL is change in length = 50.04 mm - 50 mm = 0.04 mm
• α is coefficient of linear expansion
• L is original length

ΔT = (0.04)/(50 x 15 x 10⁻⁶)

ΔT = 53.3 ⁰C

Final temperature

T₂ - T₁ = ΔT

T₂ = ΔT + T₁

where;

• T₂ is final temperature
• T₁ is initial temperature

T₂ = 53.3 + 20

T₂ = 73.33 ⁰C

Learn more about linear expansivity here: brainly.com/question/14325928

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