Finding normal stress in composite bar

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Discussion Overview

The discussion revolves around calculating the normal stress in a composite bar consisting of aluminum and steel sections under tensile load. Participants are exploring the relationships between strain, stress, and elongation in the context of this composite material system.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant presents the problem statement and initial calculations for the tensile normal stress in the aluminum bar, arriving at σ_AL = 0.07 GPa.
  • Another participant suggests that knowing the stress in the aluminum piece allows for determining the stress in the steel piece, hinting at a relationship involving the applied force P.
  • There is a question about whether the stress would be the same in the steel piece as in the aluminum piece, indicating a potential exploration of stress distribution in the composite bar.
  • A later reply confirms that the stress is indeed the same in both sections of the composite bar, reinforcing the idea of uniform stress across the cross-section.

Areas of Agreement / Disagreement

Participants generally agree that the stress in the aluminum and steel sections is related, but the specifics of how to calculate the stress in the steel bar remain under discussion. There is no consensus on the complete solution as further calculations are needed.

Contextual Notes

The discussion does not resolve how to find the stress in the steel bar or the total elongation of the composite bar, leaving these aspects open for further exploration.

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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.
 
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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?
 
PhanthomJay said:
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?
 
PhanthomJay said:
Yes! and welcome to PF!

A most excellent welcome indeed, thanks again!
 

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