Bi-axial bending chart - concrete column

[Pretty Girl]

This is from "Reinforced concrete design to eurocodes" by prab bhat, page 371 and 372.
It has mentioned the it's for My/ (hb^2) = 2.

But I don't know how to reproduce with that ratio kept constant. So, I tried to create it with making the alpha and beta values at a constant ratio of 0.8 (beta = 0.8 alpha). Then I produced a chart.

Since I didn't reproduce the exact chart in the book, now I have another problem. I have got no reference chart to compare my chart with. Can anyone kindly help me find out if my chart is correct for the column dimensions and data I provided.

Are there any free software/ excel sheet to enter the column details mentioned below and compare it with my chart?

I'm concerned that my chart may not be correct as I don't see the part the book's chart have I have shown in the green rectangle below, when I produce my chart. I understand it cannot be the same chart, but if my chart is correct that "nose" like curve should also be in my chart isn't it.

1. Chart from the book






2. The chart I produced

This is a rectangular column, h = 2000 mm, b = 1000 mm. I maintained "beta/ alpha ratio = 0.8".
4 reinforcement bars, 1 bar each corner. Steel percentage 4% (So, 1% bh area for each bar).
40 mm distance from column surface to the centroid of r/f for each bar.
fck = 30 MPa, fcd = 20 MPa, fyk = 500 MPa, fyd = 434.7 MPa.

 

[IDS]

Further to my previous post, I have reviewed the calculation method in my spreadsheet, which is:
For a section with a defined NA angle:
1: Rotate the section about the uncracked centroid, so the NA is horizontal and find the coordinates of all the reinforcement in the new orientation.
2: Find the strain gradient to the point with maximum compressive strain, perpendicular to the NA.
3: Find the strain and stress at each bar, with a stress cut-off of fy/1.15.
4: For bars in compression deduct the concrete stress (f'c/1.5).
5. Calculate the forces and moments about axes through the uncracked centroid, parallel and perpendicular to the NA.
6. Find the magnitude and direction of the resultant moment, which in general will not be perpendicular to the NA.
7. Convert to moments about the original axes.

I have attached a spreadsheet with this calculation (macro-free!) and also a calculation using the un-rotated section, which gives identical results for the resultant magnitude and direction.

 

[Pretty Girl]

Further to my previous post, I have reviewed the calculation method in my spreadsheet, which is:
For a section with a defined NA angle:
1: Rotate the section about the uncracked centroid, so the NA is horizontal and find the coordinates of all the reinforcement in the new orientation.
2: Find the strain gradient to the point with maximum compressive strain, perpendicular to the NA.
3: Find the strain and stress at each bar, with a stress cut-off of fy/1.15.
4: For bars in compression deduct the concrete stress (f'c/1.5).
5. Calculate the forces and moments about axes through the uncracked centroid, parallel and perpendicular to the NA.
6. Find the magnitude and direction of the resultant moment, which in general will not be perpendicular to the NA.
7. Convert to moments about the original axes.

I have attached a spreadsheet with this calculation (macro-free!) and also a calculation using the un-rotated section, which gives identical results for the resultant magnitude and direction.

View attachment 3015View attachment 3016

@IDS
Many thanks for providing this file and for your response.
I'm still going through this. I will have more questions to ask though