Calculating the Modulus of Elasticity

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SUMMARY

The modulus of elasticity can be calculated from the slope of the linear equation derived from stress-strain data. In this discussion, the equation provided is Y = 3E+07x + 2445.3, where the slope (a) is 30 MPa. This indicates that the modulus of elasticity, represented as E, equals 30 MPa. The importance of dimensional analysis and clear definitions of variables is emphasized for accurate calculations.

PREREQUISITES
  • Understanding of stress and strain concepts in mechanics
  • Familiarity with linear equations and their slopes
  • Basic knowledge of dimensional analysis
  • Proficiency in using Excel for data visualization
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  • Study the principles of Young's modulus and its applications in material science
  • Learn about dimensional analysis and its importance in engineering calculations
  • Explore advanced Excel techniques for data analysis and graphing
  • Research common mechanical engineering problems involving stress-strain relationships
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Mechanical engineers, materials scientists, and students studying mechanics who need to understand the calculation of the modulus of elasticity and its implications in engineering applications.

williamx11373
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After making a chart in Excel and obtaining the equation " Y= 3E+07x+2445.3 "

Now i need to calculate the modulus of elasticity. I know that the slope of the equation gives the modulus of elasticity.

but I have no clue how to even begin solving the equation Y= 3E+07x+2445.3I do know E=stress/strain... any hint or advice would help.
(do i just find the slope of elastic portion)? is that the answer?
 
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I am also struggling with a mech problem and it seems there are relatively few mechanical engineers are here. So let's try to help each other. Sorry if I can give you only general advice.
It always helps to write the units with the equations. I could pretend understanding physics a lot of times because I could deduce the rules from the units. Serious scientists also cheat the same way: http://en.wikipedia.org/wiki/Dimensional_analysis
It also helps to state the meaning of the letters used.
For now I will pretend that y is stress, x is strain, and E is not Young modulus, but 3E+07 wants to mean 3*10^7
So we have
y = ax+b
where a=30 MPa
and b=2445.3 (dimensionless)
the stress/strain function is
f(x) = ax + b
it's slope is simply its derivative
f'(x) = a
So the elastic modulus is 30 Mpa
 

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