Question #119033

A straight aluminum wire 30m Long is subject to a tensile stress of 70MPa.

1. Determine the total elongation of the wire.

2. What temperature change would produce the same elongation

Take: Elastic modulus = 200GNM^-2 And temperature coefficient = 25 × 10^-6

1. Determine the total elongation of the wire.

2. What temperature change would produce the same elongation

Take: Elastic modulus = 200GNM^-2 And temperature coefficient = 25 × 10^-6

Expert's answer

l=30 m, "\\sigma_T=" 70 MPa,Y=200 GPa

we know that

stress= "Y\\times strain"

"\\sigma _T= Y \\times \\frac{\\Delta l}{l}"

here , "\\Delta l = elongation"

"\\Delta l= \\frac{70 \\times 30}{200}=10.5 mm"

(b) as per the concept of thermal stress

"\\Delta l= l\\alpha \\Delta T"

10.5"\\times 10^{-3}" = "30\\times 25\\times 10^{-6} \\Delta T"

"\\Delta T =" 13.33 "^oC" This is the temperature difference which will produce above elongation

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