Young's modulus, stretching question.

lundi 2 septembre 2013

1. The problem statement, all variables and given/known data

Three separate members of steel, copper and brass are of identical dimensions and are

equally loaded axially.Young’s moduli for the materials are:

steel, 210,000 N/mm^2

copper, 100,000 N/mm^2

brass, 95,000 N/mm^2

If the steel member stretches 0.13mm,

calculate the amount of elongation in the copper and brass members.

2. Relevant equations

The equation i believe to be relevant;

Young's modulus=Stress/Strain

3. The attempt at a solution

I am confused how to approach this question at first i believed i had to find the stress by using the elongation of 0.13mm, and because all the members would be under the same stress i could then input that information into a youngs modulus equation for the other two members. However the young's modulus equation requires strain not just the elongation and i don't know the original length.

The only way I can think of solving this question would to assume that the strain = 0.13 and solve the question like so

Steel young's modulus= stress/strain

210=stress/0.13

stress=210*0.13=27.3

Starting with brass as an example

Young's modulus = stress/strain

strain= stress/young modulus

Strain= 27.3/95 =0.29 mm

and Copper =0.27mm

Is this assumption correct, if not any hints on how i could go about solving this problem?

Thank you very much.