Drawing a parallel line to the straight portion of the curve

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SUMMARY

The discussion focuses on determining the proportional limit of a curve using Excel, specifically by constructing a parallel line to the elastic portion of the curve. The proportional limit is identified at point P, where the curve transitions from elastic to plastic behavior. To find this limit, users are advised to fit a straight line between points O and P, calculate its slope, and derive the equation of the line. A linear trend line feature in Excel is recommended for this purpose, allowing users to visualize the equation of the line directly on the graph.

PREREQUISITES
  • Understanding of stress-strain curves and the concept of proportional limit
  • Familiarity with Excel's graphing tools and linear trend line functionality
  • Basic knowledge of slope calculation and linear equations
  • Experience with curve fitting techniques in data analysis
NEXT STEPS
  • Learn how to use Excel's linear trend line feature for curve fitting
  • Explore MATLAB functions for curve fitting and linear regression
  • Study the principles of stress-strain relationships in materials science
  • Investigate methods for determining yield points in engineering materials
USEFUL FOR

Engineers, materials scientists, and data analysts who are involved in stress-strain analysis and need to determine proportional limits in material testing.

svishal03
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I have a curve of this form (as attached) drawn in excel.

Now, the point P upto which the red curve is (almost) a straight line is called the proportional limit.

OK. Now, I need to find the proportional limit as hown by the point p on the curve.

It is given in literature that;

As a convention, to determine the yield point and proportional limit (yield point is the point corresponding to σy on the curve) a straight line is constructed parallel to the elastic portion of the curve (elastic portion means the portion that remains a straight line) corresponding to the value of strain 0.002 as shown in the figure above.

My question is:

How to construct this parallel line to the elastic portion of the curve ?? I need to do it in excel (preferable or even Matlab if you say)- how to do it? That is; how to construct a straight line parallel to the elastic (staright) portion of the red curve above??

Please help
 

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Fit a straight line to the curve between O and P and measure its slope.
 
As MrAnchovy said, you have two points of the curve (O and P), which you can use to calculate the slope. Use the slope to derive the equation of the line.
 
A easy way to do this in Excell is to select a few points on the line and select a linear trend line. Choose to show the equation and you will have your line.
 

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