Drawing a parallel line to the straight portion of the curve

[svishal03]

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

 

[pbuk]

Fit a straight line to the curve between O and P and measure its slope.

 

[Number Nine]

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.

 

[Integral]

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.

 

[CellCoree]

I would recommend first understanding the concept of the proportional limit and how it relates to the curve being analyzed. The proportional limit is the point at which the material begins to deform permanently (yield) under stress. This is important to determine in material testing as it provides insight into the material's strength and ability to withstand stress before permanent deformation occurs.

To construct a parallel line to the elastic portion of the curve, you will need to determine the slope of the straight portion of the curve. This can be done by selecting two points on the straight portion and using the slope formula (rise/run) to calculate the slope. Once the slope is determined, you can use this value to construct a line parallel to the straight portion of the curve.

In Excel, you can use the "Trendline" function to create a line of best fit for the straight portion of the curve. This line will have the same slope as the straight portion of the curve, and you can extend it to the desired point to create a parallel line. In Matlab, you can use the "polyfit" function to find the slope of the straight portion of the curve and then use the "plot" function to create a parallel line.

It is important to note that the proportional limit is not always a clearly defined point and can vary depending on the material and testing conditions. Therefore, it is crucial to carefully analyze the curve and make sure that the line you construct is parallel to the straight portion of the curve before determining the proportional limit.

In conclusion, constructing a parallel line to the elastic portion of the curve is a crucial step in determining the proportional limit. With the proper understanding of the concept and the use of appropriate tools, such as Excel or Matlab, you can accurately construct this line and determine the proportional limit for your material.