RAMBERG-OSGOOD

[StressMan2506]

Ladies & Gentlemen:

Niu, "Airframe Stress Analysis & Sizing" 2nd edition, p. 62 includes a factor of 3/7 in the second term of the Ramberg-Osgood equation, whereas Bruhn (p. B1.8) does not; which is correct?

Louis

 

[prost]

Is it possible that both are correct? With a little manipulation, you may be able to get one from the other.
My Bruhn, page B1.8 shows
(E*eps)/F70=f/F70+(f/F70)^n (A)
where: eps is strain, f is stress. Rewriting (A) to (A')
eps=f/E+(F70/E)*(f/F70)^n (A')

F70 is written as "F0.7" in my Bruhn--F0.7 is the stress
when the line drawn as f=0.7E*eps intersects the material
curve f vs. eps. F70 is the same value as F0.7, but I
like F70 because it is more convenient form to write. I
don't have the Niu book, but I can guess that the formula
he uses is (the notation may be different from Niu, but
the meanings of the symbols are the same):
eps=f/E+(3/7)*(F70/E)*(f/F70)^n (B)

I think the Bruhn equation is in error. The original
Ramberg Osgood equation was written:
eps=(f/E)+K(f/E)^n (C)

the parameter F70 means the stress 'f' when the stress-
strain curve (C) intersects the line eps=f/(0.7*E), right?
So that we want to solve the following equation:
eps=F70/(0.7*E)=(F70/E)+K(F70/E)^n (D)
Solving (D) for K=(3/7)*(F70/E)^(1-n)=(3/7)*(E/F70)^(n-1)
Plugging in this expression for K into (C):
eps=f/E+(3/7)*(F70/E)*(f/F70)^n (E)--same as (B)

But if we try to find the intersection of (A') and this
F70/(0.7*E) line, then (replacing 'f' with F70):
eps=F70/(0.7*E)=(F70/E)+(F70/E)*(F70/F70)^n

F70/(0.7*E)=(F70/E)+(F70/E)=2*(F70/E)---of course this
is wrong, because 1/0.7 does not equal 2!!!

 

[StressMan2506]

Thanks, Prost. I'll need to study it a bit...

Louis

 

[rb1957]

Prost's post is correct. this can be confirmed by looking at Ramberg and Osgood's paper (NACA TN 902), equation 8

http://naca.larc.nasa.gov/digidoc/report/tn/02/NACA-TN-902.PDF

isn't it amazing what you can find online !

 

[rb1957]

btw, bruhn C2.5 seems to be correct

 

[prost]

StressMan2506
If you cannot understand that jumbled mess I wrote, I will be happy to send you some hand written notes I have on this. You could download the scanned notes from our ftp site, for instance. Or I could email them to you.

 

[StressMan2506]

Hi Prost:

I got hold of NACA Tech. Note 902 (thanks rb1957) and I re-read your reply in conjunction. Yup, I've got it now; Bruhn p. B1.8 is in error and Niu is right.

Louis