# Different materials - Elastic modulus

by flower76
Tags: elastic, materials, modulus
 P: 51 Hi This looks like an easy question but I'm stumped and would appreciate some help. A rod is made of two sections joined end to end. The sections are identical, except that one is steel and the other is brass. While one end is held fixed, the other is pulled to result in a change in length of 1.20 mm. By how much does the length of each section increase? Any ideas?
 Emeritus Sci Advisor PF Gold P: 9,772 What is the equation of young's modulus? ~H
 P: 51 I believe it to be: change in L = (1/E)(F/A)(Lo) I'm not sure what to do with the fact that you have two E values, add them together? Then do you ignore F and A, and is Lo actually 2Lo in this case? Thanks
 Admin P: 21,913 Different materials - Elastic modulus There would be a total length L, and one material has length x and the other one has length L-x. Think of Hooke's Law, and the relationship between stress and strain. See - http://en.wikipedia.org/wiki/Hooke%27s_law Stress is load (force)/area.
 P: 51 I'm sorry now I think i'm even more confused, there are no values for force or area and I can't see how you would get them. Am I overlooking something?
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,682 Do the two parts separately. How much does each increase separately?
 P: 51 The question is to figure them out separately and I don't know how to do it. I keep going around in circles and getting answers that don't make sense. Any other suggestions? Thanks
 P: 51 Ok I'm still trying to figure out this question and getting nowhere, does anyone have any other suggestions. It would be greatly greatly appreciated. Thanks
 Admin P: 21,913 flower76 - Sorry for the confusion, I seem to have made it more complicated than necessary. In series, i.e. with the two sections (rods/bars) end-to-end, they are subject to the 'same' force, and assuming they have the same cross-sectional area, each develops the same stress. However, the elastic (Young's) modulus of each is different, so the strain of each will be different. The strain is simply $\epsilon$ = $\sigma$/E, where $\epsilon$ is the strain, $\sigma$ is the axial stress, and E is the elastic modulus. If one section is length L1 and the other L2, then the initial length is simply L = L1 + L2. Now when the sections strain, one obtains a combined length given by (1+$\epsilon$1) L1 + (1+$\epsilon$2) L2.
 Quote by Astronuc flower76 - Sorry for the confusion, I seem to have made it more complicated than necessary. In series, i.e. with the two sections (rods/bars) end-to-end, they are subject to the 'same' force, and assuming they have the same cross-sectional area, each develops the same stress. However, the elastic (Young's) modulus of each is different, so the strain of each will be different. The strain is simply $\epsilon$ = $\sigma$/E, where $\epsilon$ is the strain, $\sigma$ is the axial stress, and E is the elastic modulus. If one section is length L1 and the other L2, then the initial length is simply L = L1 + L2. Now when the sections strain, one obtains a combined length given by (1+$\epsilon$1) L1 + (1+$\epsilon$2) L2.