1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Finding normal stress in composite bar

  1. Sep 7, 2012 #1
    1. The problem statement, all variables and given/known data
    The 2000 mm long composite bar shown in Fig. 1 consists of an aluminum bar having
    a modulus of elasticity EAl = 70 GPa and length LAl = 500 mm, which is securely fastened
    to a steel bar having modulus of elasticity ESt = 210 GPa and length LSt = 1500 mm. After
    the force P is applied, a tensile normal strain of εAl = 1000 × 10-6 is measured in the
    aluminum bar. Find the tensile normal stress in each bar and the total elongation of the
    composite bar.

    ba1mD.png


    2. Relevant equations
    ε_x=σ_x/E

    3. The attempt at a solution

    So I first took the equation and rearranged it, such that ε_x*E=σ_x and got σ_AL=0.07 GPa. Then for the changed in distance of the aluminum bar, dl=ε*l_0 = (1000*10^-6)(500mm) = 0.5mm change for Al bar.

    Assuming that's correct, I'm stuck on how to find the stress for the steel bar and the length it changed.
     
  2. jcsd
  3. Sep 7, 2012 #2

    PhanthomJay

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    The cross section area of each section is the same. If you know the stress in the alum piece, what must be the stress in the steel piece? Hint: what is the force in each piece as a function of P?
     
  4. Sep 7, 2012 #3
    So the stress would be the same in the steel piece?
     
  5. Sep 7, 2012 #4

    PhanthomJay

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Yes! and welcome to PF!
     
  6. Sep 7, 2012 #5
    A most excellent welcome indeed, thanks again!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook