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Finding normal stress in composite bar

  • Thread starter newhere
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  • #1
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Homework Statement


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



Homework Equations


ε_x=σ_x/E

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.
 

Answers and Replies

  • #2
PhanthomJay
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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?
 
  • #3
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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?
So the stress would be the same in the steel piece?
 
  • #4
PhanthomJay
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Yes! and welcome to PF!
 
  • #5
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Yes! and welcome to PF!
A most excellent welcome indeed, thanks again!
 

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