# Mechanics and materials problem...

1. Aug 17, 2015

### aldo sebastian

• Thread moved from the technical Engineering forums, so no Homework Help Template has been used.
The problem is: A copper alloy having gauge length of 2 inches is subjected to strain of 0.4 inch/inch when the stress is 70 ksi. if yield stress is 45 ksi and yield strain is 0.0025 inch/inch, determine the distance between the gauge points when the load is released

So I tried to do this problem in the following way:
-I multiply the 0.4 strain with the initial gauge length to find the total elongation
-I added the total elongation to initial length to find new length, which is 2.8 inches

-I find the young's modulus by dividing yield stress with yield strain. I then made the stress strain graph and found out that the stress applied is in the plastic region (bigger than yield), so when load is released, the strain will not return to 0 point. However, the rate at which the beam gets thinner from that region is still young's modulus.
-So I used young's mod to find the plastic strain when stress is 0 by dividing 70 with young's mod, then subtracting 0.4 to the result (i.e. 0.4-result) to get this plastic strain
-and so, the new elongation/reduction in length is then the strain multiplied by original length (2.8 inch when load is applied).
-so the final length is 2.8-(new elongation) (minus because now the beam gets thinner)

I got the value of 1.7 inch, but the back of the book says its 2.792 inch. where was I wrong?

2. Aug 17, 2015

### paisiello2

How can the specimen possibly be shorter after the load is released?