Stress strain laboratory question

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Discussion Overview

The discussion revolves around establishing the constitutive relationship for the material of a cantilever beam, specifically focusing on the empirical formula relating stress and strain, and generating a corresponding plot. The context is a laboratory exercise involving beam bending theory, data collection from a rosette gauge, and analysis of material properties.

Discussion Character

  • Homework-related
  • Technical explanation

Main Points Raised

  • One participant expresses confusion about the question and the equation, questioning whether stress would cancel out and suggesting that strain might equal one.
  • Another participant clarifies that the notation σxx(εxx) indicates finding stress as a function of strain, providing an example of a linear relationship in uniaxial tension.
  • A participant reports having figured out the problem using the provided formula and seeks information on identifying the material based on their graph.
  • A later reply suggests that the participant should be able to determine the elastic modulus from their graph and recommends consulting tables to identify the material with that modulus.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the initial confusion regarding the question. However, there is agreement on the approach to finding the elastic modulus and identifying the material based on the graph.

Contextual Notes

The discussion includes assumptions about the relationship between stress and strain, and the need for additional resources to identify materials based on elastic modulus. There may be limitations in the data or definitions used in the analysis.

xzibition8612
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Homework Statement


Establish the constitutive relationship for the cantilever beam material, i.e., provide an empirical formula for the relationship σxxxxxx) and generate a plot of this relationship. What is the cantilever beam material?

Homework Equations


This is a pure beam bending theory lab, rosette gauge on beam with loads and displacements from a precision micrometer.


The Attempt at a Solution


Not really sure what this question is asking. Also I'm confused about the equation. Wouldn't the stress xx just cancel out and εxx=1?? I got a bunch of data on the beam from the rosette gauge, but I don't really get this question. Any help on shedding what its asking would be great. thanks.
 
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Greetings xzibition8612! The notation \sigma_{xx}(\epsilon_{xx}) means "find \sigma_{xx} as a function of \epsilon_{xx}". For example, a beam under uniaxial tension might obey \sigma_{xx}(\epsilon_{xx}) = E\epsilon_{xx}, where E is the elastic modulus.
 
alright i figured it out using your formula. So this is my result. Now the question is what kind of material follows this graph? Anyone know or where can i find this info? By the way strain is in micro strain, or 10^-6.

thanks
 

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Given your graph you should be able to find the elastic modulus of the material. Then you may need to consult some tables to see which material has that same elastic modulus.
 

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