Figure 4.1.7.6-C NBCC 2020

[EngDM]

Hey all,

Does anyone know of a resource to find out what the equation for the lines in this graph actually are? Jabacus appears to have a way to calculate it, but I can't find any published equation, and the X-axis is non-linear and non-logarithmic. I've tried fitting some points in excel but I can't get an equation that fits perfectly. I would like to know how Jabacus calculates it; are they interpolating and therefor it's not 100% accurate?

Send help I'm going insane.

 

[dik]

My best guess would be to write if-then statements setting forth the limits of the variables... I've never seen a construction of these 'curves'.

-----*****-----
So strange to see the singularity approaching while the entire planet is rapidly turning into a hellscape. -John Coates

-Dik

 

[EngDM]

My best guess would be to write if-then statements setting forth the limits of the variables... I've never seen a construction of these 'curves'.[/code]

Yea this is exactly what I was trying to do, but then I noticed that the axis scale is wack. Like the space between the numbers on the axis shares no relationship. It's not like it always doubles or scales based on the distance between ticks. I plotted based on the value at every X axis, and it's curvy at some points but then flattens and then curves again. It's WACK. I'm trying to make something accurate to not have to whip out a ruler and check it by hand to be precise, but it's like they just threw some numbers on a chart and called it a day.

 

[Celt83]

ASCE 7 has similar charts and I believe it is related to the logarithm of the Area along the sloped regions. You could try using something line WebPlotDigitizer: Link

 

[canwesteng]

Is the X axis not a log scale?

 

[EngDM]

Is the X axis not a log scale?

It looks like it, but it doesn't fit on a log plot correctly.

 

[Celt83]

Believe it's a log scale beyond the shortest constant region:
A rough estimate of the equation for the sloped portion of C is: -5.4 + 3.4 Log A

 

[EngDM]

Believe it's a log scale beyond the shortest constant region:
A rough estimate of the equation for the sloped portion of C is: -5.381 + 3.3583 Log A

I threw it into that webplotdigitizer and calibrated it based off the 1 and 10 coordinates on the X. When I get over to where 50 is supposed to be, it shows as 45, and where 5 is it shows as 4.8.

Not quite log.

Edit: Sloped area is log, area after 10m2 is no longer log.

Edit 2: Just kidding, when plotted it maintains log scale if you look at 1,2,10 positions, but the position for 5 is wrong to be consistently log.

 

[skeletron]

I've always taken it as a log-scale on the x-axis. Are you using log-log interpolation? Or linear interpolation between vertices?
This is a neat exercise. I attempted at one point and then realized how much work it is to do every curve, for every diagram, and it never tempted me to dig back into the spreadsheet again. My preferred method now is to set up all the Figures in a PDF. At a vertical and horizontal baseline, and then adjust manually, eyeball (or scale) the number and print. If I was only designing walls and wall pressures, I would go into more detail. But the amount of precision you may gain probably is only so valuable. I would agree with Dik that the best way to do it is through if-else statements and then log-log interpolation between the known points.

 

[EngDM]

Are you using log-log interpolation? Or linear interpolation between vertices?

Trying to fit an equation for all X in a piecewise manner so no need for interpolation. The equation outlined by Celt works for the most part, but that tick for 5 on the X axis is wrong for it to be strictly log. As minimal of a difference it will make, I will likely use the equation outlined above.

 

[CarlB]

By plotting a few points in Excel, and using Linest feature, I find the horizontal scale is natural log.
For the sloped line I get:
-5.4 + 1.48 x ln(A)

 

[EngDM]

For the sloped line I get:
-5.4 + 1.48 x ln(A

This equation is equal to -5.4 + 3.4 Log(A) if you convert the natural log to log base 10. Neither of these are 100% precise for when x=5.

 

[CarlB]

I checked out the graph scales in CAD to see if it was out of whack.
The tick mark/labels aren't dead on, but pretty close. Sure looks like the y axis is meant to be a log scale, no tick/label is too far off.
The 1-10 scale distance is a little different than the 10-100.
Red lines on image show where precise tic marks would go, holding the 1, 10 & 100.
For the sloped line, the calculation for A=5 gives C=-3.02.
A precise scaling of the graph, using 5 on the x axis, and between -3 & -3.5 on the y gives C=-3.06.
So I'd say the log equation for the line is valid.